Daily Papers

Recently, evolutionary reinforcement learning has obtained much attention in various domains. Maintaining a population of actors, evolutionary reinforcement learning utilises the collected experiences to improve the behaviour policy through efficient exploration. However, the poor scalability of genetic operators limits the efficiency of optimising high-dimensional neural networks. To address this issue, this paper proposes a novel cooperative coevolutionary reinforcement learning (CoERL) algorithm. Inspired by cooperative coevolution, CoERL periodically and adaptively decomposes the policy optimisation problem into multiple subproblems and evolves a population of neural networks for each of the subproblems. Instead of using genetic operators, CoERL directly searches for partial gradients to update the policy. Updating policy with partial gradients maintains consistency between the behaviour spaces of parents and offspring across generations. The experiences collected by the population are then used to improve the entire policy, which enhances the sampling efficiency. Experiments on six benchmark locomotion tasks demonstrate that CoERL outperforms seven state-of-the-art algorithms and baselines. Ablation study verifies the unique contribution of CoERL's core ingredients.

Decision trees are a crucial class of models offering robust predictive performance and inherent interpretability across various domains, including healthcare, finance, and logistics. However, current tree induction methods often face limitations such as suboptimal solutions from greedy methods or prohibitive computational costs and limited applicability of exact optimization approaches. To address these challenges, we propose an evolutionary optimization method for decision tree induction based on genetic programming (GP). Our key innovation is the integration of semantic priors and domain-specific knowledge about the search space into the optimization algorithm. To this end, we introduce LLEGO, a framework that incorporates semantic priors into genetic search operators through the use of Large Language Models (LLMs), thereby enhancing search efficiency and targeting regions of the search space that yield decision trees with superior generalization performance. This is operationalized through novel genetic operators that work with structured natural language prompts, effectively utilizing LLMs as conditional generative models and sources of semantic knowledge. Specifically, we introduce fitness-guided crossover to exploit high-performing regions, and diversity-guided mutation for efficient global exploration of the search space. These operators are controlled by corresponding hyperparameters that enable a more nuanced balance between exploration and exploitation across the search space. Empirically, we demonstrate across various benchmarks that LLEGO evolves superior-performing trees compared to existing tree induction methods, and exhibits significantly more efficient search performance compared to conventional GP approaches.

Agentic AI systems built on large language models (LLMs) offer significant potential for automating complex workflows, from software development to customer support. However, LLM agents often underperform due to suboptimal configurations; poorly tuned prompts, tool descriptions, and parameters that typically require weeks of manual refinement. Existing optimization methods either are too complex for general use or treat components in isolation, missing critical interdependencies. We present ARTEMIS, a no-code evolutionary optimization platform that jointly optimizes agent configurations through semantically-aware genetic operators. Given only a benchmark script and natural language goals, ARTEMIS automatically discovers configurable components, extracts performance signals from execution logs, and evolves configurations without requiring architectural modifications. We evaluate ARTEMIS on four representative agent systems: the ALE Agent for competitive programming on AtCoder Heuristic Contest, achieving a 13.6% improvement in acceptance rate; the Mini-SWE Agent for code optimization on SWE-Perf, with a statistically significant 10.1\% performance gain; and the CrewAI Agent for cost and mathematical reasoning on Math Odyssey, achieving a statistically significant 36.9% reduction in the number of tokens required for evaluation. We also evaluate the MathTales-Teacher Agent powered by a smaller open-source model (Qwen2.5-7B) on GSM8K primary-level mathematics problems, achieving a 22\% accuracy improvement and demonstrating that ARTEMIS can optimize agents based on both commercial and local models.

Building agentic systems that can autonomously self-improve from experience is a longstanding goal of AI. Large language models (LLMs) today primarily self-improve via two mechanisms: self-reflection for context updates, and reinforcement learning (RL) for weight updates. In this work, we propose Evolutionary System Prompt Learning (E-SPL), a method for jointly improving model contexts and model weights. In each RL iteration, E-SPL samples trajectories under multiple system prompts in parallel, then jointly applies RL updates to LLM weights and evolutionary updates to system prompts. System prompts evolve via mutation and crossover, two genetic operators driven by LLM self-reflection; selection is based on relative performance ratings updated across RL iterations. E-SPL encourages a natural division between declarative knowledge encoded in prompts and procedural knowledge encoded in weights, resulting in improved performance across reasoning and agentic tasks. For instance, in an easy-to-hard (AIME rightarrow BeyondAIME) generalization setting, E-SPL improves RL success rate from 38.8% rightarrow 45.1% while also outperforming reflective prompt evolution (40.0%). Overall, our results demonstrate that RL and system prompt evolution are deeply synergistic, and combining the two yields consistent gains in sample efficiency and generalization. Code: https://github.com/LunjunZhang/E-SPL

This paper pursues the insight that large language models (LLMs) trained to generate code can vastly improve the effectiveness of mutation operators applied to programs in genetic programming (GP). Because such LLMs benefit from training data that includes sequential changes and modifications, they can approximate likely changes that humans would make. To highlight the breadth of implications of such evolution through large models (ELM), in the main experiment ELM combined with MAP-Elites generates hundreds of thousands of functional examples of Python programs that output working ambulating robots in the Sodarace domain, which the original LLM had never seen in pre-training. These examples then help to bootstrap training a new conditional language model that can output the right walker for a particular terrain. The ability to bootstrap new models that can output appropriate artifacts for a given context in a domain where zero training data was previously available carries implications for open-endedness, deep learning, and reinforcement learning. These implications are explored here in depth in the hope of inspiring new directions of research now opened up by ELM.

This paper presents a reinforced genetic approach to a defined d-resource system optimization problem. The classical evolution schema was ineffective due to a very strict feasibility function in the studied problem. Hence, the presented strategy has introduced several modifications and adaptations to standard genetic routines, e.g.: a migration operator which is an analogy to the biological random genetic drift.

We present a genetic algorithm framework for automatically discovering deep learning optimization algorithms. Our approach encodes optimizers as genomes that specify combinations of primitive update terms (gradient, momentum, RMS normalization, Adam-style adaptive terms, and sign-based updates) along with hyperparameters and scheduling options. Through evolutionary search over 50 generations with a population of 50 individuals, evaluated across multiple vision tasks, we discover an evolved optimizer that outperforms Adam by 2.6% in aggregate fitness and achieves a 7.7% relative improvement on CIFAR-10. The evolved optimizer combines sign-based gradient terms with adaptive moment estimation, uses lower momentum coefficients than Adam (β_1=0.86, β_2=0.94), and notably disables bias correction while enabling learning rate warmup and cosine decay. Our results demonstrate that evolutionary search can discover competitive optimization algorithms and reveal design principles that differ from hand-crafted optimizers. Code is available at https://github.com/mmarfinetz/evo-optimizer.

A wide range of scientific problems, such as those described by continuous-time dynamical systems and partial differential equations (PDEs), are naturally formulated on function spaces. While function spaces are typically infinite-dimensional, deep learning has predominantly advanced through applications in computer vision and natural language processing that focus on mappings between finite-dimensional spaces. Such fundamental disparities in the nature of the data have limited neural networks from achieving a comparable level of success in scientific applications as seen in other fields. Neural operators are a principled way to generalize neural networks to mappings between function spaces, offering a pathway to replicate deep learning's transformative impact on scientific problems. For instance, neural operators can learn solution operators for entire classes of PDEs, e.g., physical systems with different boundary conditions, coefficient functions, and geometries. A key factor in deep learning's success has been the careful engineering of neural architectures through extensive empirical testing. Translating these neural architectures into neural operators allows operator learning to enjoy these same empirical optimizations. However, prior neural operator architectures have often been introduced as standalone models, not directly derived as extensions of existing neural network architectures. In this paper, we identify and distill the key principles for constructing practical implementations of mappings between infinite-dimensional function spaces. Using these principles, we propose a recipe for converting several popular neural architectures into neural operators with minimal modifications. This paper aims to guide practitioners through this process and details the steps to make neural operators work in practice. Our code can be found at https://github.com/neuraloperator/NNs-to-NOs

Vital to primary visual processing, retinal circuitry shows many similar structures across a very broad array of species, both vertebrate and non-vertebrate, especially functional components such as lateral inhibition. This surprisingly conservative pattern raises a question of how evolution leads to it, and whether there is any alternative that can also prompt helpful preprocessing. Here we design a method using genetic algorithm that, with many degrees of freedom, leads to architectures whose functions are similar to biological retina, as well as effective alternatives that are different in structures and functions. We compare this model to natural evolution and discuss how our framework can come into goal-driven search and sustainable enhancement of neural network models in machine learning.

Gravitational-wave detection strategies are based on a signal analysis technique known as matched filtering. Despite the success of matched filtering, due to its computational cost, there has been recent interest in developing deep convolutional neural networks (CNNs) for signal detection. Designing these networks remains a challenge as most procedures adopt a trial and error strategy to set the hyperparameter values. We propose a new method for hyperparameter optimization based on genetic algorithms (GAs). We compare six different GA variants and explore different choices for the GA-optimized fitness score. We show that the GA can discover high-quality architectures when the initial hyperparameter seed values are far from a good solution as well as refining already good networks. For example, when starting from the architecture proposed by George and Huerta, the network optimized over the 20-dimensional hyperparameter space has 78% fewer trainable parameters while obtaining an 11% increase in accuracy for our test problem. Using genetic algorithm optimization to refine an existing network should be especially useful if the problem context (e.g. statistical properties of the noise, signal model, etc) changes and one needs to rebuild a network. In all of our experiments, we find the GA discovers significantly less complicated networks as compared to the seed network, suggesting it can be used to prune wasteful network structures. While we have restricted our attention to CNN classifiers, our GA hyperparameter optimization strategy can be applied within other machine learning settings.

Agentic Variation Operators (AVO) are a new family of evolutionary variation operators that replace the fixed mutation, crossover, and hand-designed heuristics of classical evolutionary search with autonomous coding agents. Rather than confining a language model to candidate generation within a prescribed pipeline, AVO instantiates variation as a self-directed agent loop that can consult the current lineage, a domain-specific knowledge base, and execution feedback to propose, repair, critique, and verify implementation edits. We evaluate AVO on attention, among the most aggressively optimized kernel targets in AI, on NVIDIA Blackwell (B200) GPUs. Over 7 days of continuous autonomous evolution on multi-head attention, AVO discovers kernels that outperform cuDNN by up to 3.5% and FlashAttention-4 by up to 10.5% across the evaluated configurations. The discovered optimizations transfer readily to grouped-query attention, requiring only 30 minutes of additional autonomous adaptation and yielding gains of up to 7.0% over cuDNN and 9.3% over FlashAttention-4. Together, these results show that agentic variation operators move beyond prior LLM-in-the-loop evolutionary pipelines by elevating the agent from candidate generator to variation operator, and can discover performance-critical micro-architectural optimizations that produce kernels surpassing state-of-the-art expert-engineered attention implementations on today's most advanced GPU hardware.

In this work, we introduce Boolformer, the first Transformer architecture trained to perform end-to-end symbolic regression of Boolean functions. First, we show that it can predict compact formulas for complex functions which were not seen during training, when provided a clean truth table. Then, we demonstrate its ability to find approximate expressions when provided incomplete and noisy observations. We evaluate the Boolformer on a broad set of real-world binary classification datasets, demonstrating its potential as an interpretable alternative to classic machine learning methods. Finally, we apply it to the widespread task of modelling the dynamics of gene regulatory networks. Using a recent benchmark, we show that Boolformer is competitive with state-of-the art genetic algorithms with a speedup of several orders of magnitude. Our code and models are available publicly.

Self-evolution methods enhance code generation through iterative "generate-verify-refine" cycles, yet existing approaches suffer from low exploration efficiency, failing to discover solutions with superior complexity within limited budgets. This inefficiency stems from initialization bias trapping evolution in poor solution regions, uncontrolled stochastic operations lacking feedback guidance, and insufficient experience utilization across tasks. To address these bottlenecks, we propose Controlled Self-Evolution (CSE), which consists of three key components. Diversified Planning Initialization generates structurally distinct algorithmic strategies for broad solution space coverage. Genetic Evolution replaces stochastic operations with feedback-guided mechanisms, enabling targeted mutation and compositional crossover. Hierarchical Evolution Memory captures both successful and failed experiences at inter-task and intra-task levels. Experiments on EffiBench-X demonstrate that CSE consistently outperforms all baselines across various LLM backbones. Furthermore, CSE achieves higher efficiency from early generations and maintains continuous improvement throughout evolution. Our code is publicly available at https://github.com/QuantaAlpha/EvoControl.

Deep artificial neural networks (DNNs) are typically trained via gradient-based learning algorithms, namely backpropagation. Evolution strategies (ES) can rival backprop-based algorithms such as Q-learning and policy gradients on challenging deep reinforcement learning (RL) problems. However, ES can be considered a gradient-based algorithm because it performs stochastic gradient descent via an operation similar to a finite-difference approximation of the gradient. That raises the question of whether non-gradient-based evolutionary algorithms can work at DNN scales. Here we demonstrate they can: we evolve the weights of a DNN with a simple, gradient-free, population-based genetic algorithm (GA) and it performs well on hard deep RL problems, including Atari and humanoid locomotion. The Deep GA successfully evolves networks with over four million free parameters, the largest neural networks ever evolved with a traditional evolutionary algorithm. These results (1) expand our sense of the scale at which GAs can operate, (2) suggest intriguingly that in some cases following the gradient is not the best choice for optimizing performance, and (3) make immediately available the multitude of neuroevolution techniques that improve performance. We demonstrate the latter by showing that combining DNNs with novelty search, which encourages exploration on tasks with deceptive or sparse reward functions, can solve a high-dimensional problem on which reward-maximizing algorithms (e.g.\ DQN, A3C, ES, and the GA) fail. Additionally, the Deep GA is faster than ES, A3C, and DQN (it can train Atari in {raise.17ex\scriptstyle\sim}4 hours on one desktop or {raise.17ex\scriptstyle\sim}1 hour distributed on 720 cores), and enables a state-of-the-art, up to 10,000-fold compact encoding technique.

In this work, we propose a concise neural operator architecture for operator learning. Drawing an analogy with a conventional fully connected neural network, we define the neural operator as follows: the output of the i-th neuron in a nonlinear operator layer is defined by mathcal O_i(u) = sigmaleft( sum_j mathcal W_{ij} u + mathcal B_{ij}right). Here, mathcal W_{ij} denotes the bounded linear operator connecting j-th input neuron to i-th output neuron, and the bias mathcal B_{ij} takes the form of a function rather than a scalar. Given its new universal approximation property, the efficient parameterization of the bounded linear operators between two neurons (Banach spaces) plays a critical role. As a result, we introduce MgNO, utilizing multigrid structures to parameterize these linear operators between neurons. This approach offers both mathematical rigor and practical expressivity. Additionally, MgNO obviates the need for conventional lifting and projecting operators typically required in previous neural operators. Moreover, it seamlessly accommodates diverse boundary conditions. Our empirical observations reveal that MgNO exhibits superior ease of training compared to other CNN-based models, while also displaying a reduced susceptibility to overfitting when contrasted with spectral-type neural operators. We demonstrate the efficiency and accuracy of our method with consistently state-of-the-art performance on different types of partial differential equations (PDEs).

Neural operators have proven to be a promising approach for modeling spatiotemporal systems in the physical sciences. However, training these models for large systems can be quite challenging as they incur significant computational and memory expense -- these systems are often forced to rely on autoregressive time-stepping of the neural network to predict future temporal states. While this is effective in managing costs, it can lead to uncontrolled error growth over time and eventual instability. We analyze the sources of this autoregressive error growth using prototypical neural operator models for physical systems and explore ways to mitigate it. We introduce architectural and application-specific improvements that allow for careful control of instability-inducing operations within these models without inflating the compute/memory expense. We present results on several scientific systems that include Navier-Stokes fluid flow, rotating shallow water, and a high-resolution global weather forecasting system. We demonstrate that applying our design principles to neural operators leads to significantly lower errors for long-term forecasts as well as longer time horizons without qualitative signs of divergence compared to the original models for these systems. We open-source our https://github.com/mikemccabe210/stabilizing_neural_operators{code} for reproducibility.

Generating molecules, both in a directed and undirected fashion, is a huge part of the drug discovery pipeline. Genetic algorithms (GAs) generate molecules by randomly modifying known molecules. In this paper we show that GAs are very strong algorithms for such tasks, outperforming many complicated machine learning methods: a result which many researchers may find surprising. We therefore propose insisting during peer review that new algorithms must have some clear advantage over GAs, which we call the GA criterion. Ultimately our work suggests that a lot of research in molecule generation should be re-assessed.

We consider controllable DNA sequence design, where sequences are generated by conditioning on specific biological properties. While language models (LMs) such as GPT and BERT have achieved remarkable success in natural language generation, their application to DNA sequence generation remains largely underexplored. In this work, we introduce ATGC-Gen, an Automated Transformer Generator for Controllable Generation, which leverages cross-modal encoding to integrate diverse biological signals. ATGC-Gen is instantiated with both decoder-only and encoder-only transformer architectures, allowing flexible training and generation under either autoregressive or masked recovery objectives. We evaluate ATGC-Gen on representative tasks including promoter and enhancer sequence design, and further introduce a new dataset based on ChIP-Seq experiments for modeling protein binding specificity. Our experiments demonstrate that ATGC-Gen can generate fluent, diverse, and biologically relevant sequences aligned with the desired properties. Compared to prior methods, our model achieves notable improvements in controllability and functional relevance, highlighting the potential of language models in advancing programmable genomic design. The source code is released at (https://github.com/divelab/AIRS/blob/main/OpenBio/ATGC_Gen).

We propose a projection pursuit (PP) algorithm based on Gaussian mixture models (GMMs). The negentropy obtained from a multivariate density estimated by GMMs is adopted as the PP index to be maximised. For a fixed dimension of the projection subspace, the GMM-based density estimation is projected onto that subspace, where an approximation of the negentropy for Gaussian mixtures is computed. Then, Genetic Algorithms (GAs) are used to find the optimal, orthogonal projection basis by maximising the former approximation. We show that this semi-parametric approach to PP is flexible and allows highly informative structures to be detected, by projecting multivariate datasets onto a subspace, where the data can be feasibly visualised. The performance of the proposed approach is shown on both artificial and real datasets.

Symbolic execution is a powerful technique for software testing, but suffers from limitations when encountering external functions, such as native methods or third-party libraries. Existing solutions often require additional context, expensive SMT solvers, or manual intervention to approximate these functions through symbolic stubs. In this work, we propose a novel approach to automatically generate symbolic stubs for external functions during symbolic execution that leverages Genetic Programming. When the symbolic executor encounters an external function, AutoStub generates training data by executing the function on randomly generated inputs and collecting the outputs. Genetic Programming then derives expressions that approximate the behavior of the function, serving as symbolic stubs. These automatically generated stubs allow the symbolic executor to continue the analysis without manual intervention, enabling the exploration of program paths that were previously intractable. We demonstrate that AutoStub can automatically approximate external functions with over 90% accuracy for 55% of the functions evaluated, and can infer language-specific behaviors that reveal edge cases crucial for software testing.

Convolutional Neural Networks (CNN) have gained great success in many artificial intelligence tasks. However, finding a good set of hyperparameters for a CNN remains a challenging task. It usually takes an expert with deep knowledge, and trials and errors. Genetic algorithms have been used in hyperparameter optimizations. However, traditional genetic algorithms with fixed-length chromosomes may not be a good fit for optimizing deep learning hyperparameters, because deep learning models have variable number of hyperparameters depending on the model depth. As the depth increases, the number of hyperparameters grows exponentially, and searching becomes exponentially harder. It is important to have an efficient algorithm that can find a good model in reasonable time. In this article, we propose to use a variable length genetic algorithm (GA) to systematically and automatically tune the hyperparameters of a CNN to improve its performance. Experimental results show that our algorithm can find good CNN hyperparameters efficiently. It is clear from our experiments that if more time is spent on optimizing the hyperparameters, better results could be achieved. Theoretically, if we had unlimited time and CPU power, we could find the optimized hyperparameters and achieve the best results in the future.

The performance of Convolutional Neural Networks (CNNs) highly relies on their architectures. In order to design a CNN with promising performance, extended expertise in both CNNs and the investigated problem is required, which is not necessarily held by every user interested in CNNs or the problem domain. In this paper, we propose to automatically evolve CNN architectures by using a genetic algorithm based on ResNet blocks and DenseNet blocks. The proposed algorithm is completely automatic in designing CNN architectures, particularly, neither pre-processing before it starts nor post-processing on the designed CNN is needed. Furthermore, the proposed algorithm does not require users with domain knowledge on CNNs, the investigated problem or even genetic algorithms. The proposed algorithm is evaluated on CIFAR10 and CIFAR100 against 18 state-of-the-art peer competitors. Experimental results show that it outperforms state-of-the-art CNNs hand-crafted and CNNs designed by automatic peer competitors in terms of the classification accuracy, and achieves the competitive classification accuracy against semi-automatic peer competitors. In addition, the proposed algorithm consumes much less time than most peer competitors in finding the best CNN architectures.

Quality-Diversity algorithms, such as MAP-Elites, are a branch of Evolutionary Computation generating collections of diverse and high-performing solutions, that have been successfully applied to a variety of domains and particularly in evolutionary robotics. However, MAP-Elites performs a divergent search based on random mutations originating from Genetic Algorithms, and thus, is limited to evolving populations of low-dimensional solutions. PGA-MAP-Elites overcomes this limitation by integrating a gradient-based variation operator inspired by Deep Reinforcement Learning which enables the evolution of large neural networks. Although high-performing in many environments, PGA-MAP-Elites fails on several tasks where the convergent search of the gradient-based operator does not direct mutations towards archive-improving solutions. In this work, we present two contributions: (1) we enhance the Policy Gradient variation operator with a descriptor-conditioned critic that improves the archive across the entire descriptor space, (2) we exploit the actor-critic training to learn a descriptor-conditioned policy at no additional cost, distilling the knowledge of the archive into one single versatile policy that can execute the entire range of behaviors contained in the archive. Our algorithm, DCG-MAP-Elites improves the QD score over PGA-MAP-Elites by 82% on average, on a set of challenging locomotion tasks.

In the realm of machine learning, traditional model development and automated approaches like AutoML typically rely on layers of abstraction, such as tree-based or Cartesian genetic programming. Our study introduces "Guided Evolution" (GE), a novel framework that diverges from these methods by utilizing Large Language Models (LLMs) to directly modify code. GE leverages LLMs for a more intelligent, supervised evolutionary process, guiding mutations and crossovers. Our unique "Evolution of Thought" (EoT) technique further enhances GE by enabling LLMs to reflect on and learn from the outcomes of previous mutations. This results in a self-sustaining feedback loop that augments decision-making in model evolution. GE maintains genetic diversity, crucial for evolutionary algorithms, by leveraging LLMs' capability to generate diverse responses from expertly crafted prompts and modulate model temperature. This not only accelerates the evolution process but also injects expert like creativity and insight into the process. Our application of GE in evolving the ExquisiteNetV2 model demonstrates its efficacy: the LLM-driven GE autonomously produced variants with improved accuracy, increasing from 92.52% to 93.34%, without compromising model compactness. This underscores the potential of LLMs to accelerate the traditional model design pipeline, enabling models to autonomously evolve and enhance their own designs.

While Large Language Models (LLMs) have recently shown promise in Automated Heuristic Design (AHD), existing approaches typically formulate AHD around constructive priority rules or parameterized local search guidance, thereby restricting the search space to fixed heuristic forms. Such designs offer limited capacity for structural exploration, making it difficult to escape deep local optima in complex Combinatorial Optimization Problems (COPs). In this work, we propose G-LNS, a generative evolutionary framework that extends LLM-based AHD to the automated design of Large Neighborhood Search (LNS) operators. Unlike prior methods that evolve heuristics in isolation, G-LNS leverages LLMs to co-evolve tightly coupled pairs of destroy and repair operators. A cooperative evaluation mechanism explicitly captures their interaction, enabling the discovery of complementary operator logic that jointly performs effective structural disruption and reconstruction. Extensive experiments on challenging COP benchmarks, such as Traveling Salesman Problems (TSP) and Capacitated Vehicle Routing Problems (CVRP), demonstrate that G-LNS significantly outperforms LLM-based AHD methods as well as strong classical solvers. The discovered heuristics not only achieve near-optimal solutions with reduced computational budgets but also exhibit robust generalization across diverse and unseen instance distributions.

Large Language Models (LLMs) excel at generating synthetic data, but ensuring its quality and diversity remains challenging. We propose Genetic Prompt, a novel framework that combines genetic algorithms with LLMs to augment synthetic data generation. Our approach treats semantic text attributes as gene sequences and leverages the LLM to simulate crossover and mutation operations. This genetic process enhances data quality and diversity by creating novel attribute combinations, yielding synthetic distributions closer to real-world data. To optimize parent selection, we also integrate an active learning scheme that expands the offspring search space. Our experiments on multiple NLP tasks reveal several key findings: Genetic Prompt not only significantly outperforms state-of-the-art baselines but also shows robust performance across various generator model sizes and scales. Moreover, we demonstrate that fusing our synthetic data with the original training set significantly boosts downstream model performance, particularly for class-imbalanced scenarios. Our findings validate that Genetic Prompt is an effective method for producing high-quality synthetic data for a wide range of NLP applications.

Combinatorial and optimization problems are fundamental to many industrial AI applications. Solving large-scale real-world instances of such problems typically requires careful problem formalization, specialized solvers, and expert-designed heuristics. Thus, experts need to specify not only what solutions are, but also how they are derived. By introducing the tool CHECKMATE, we show that algorithm generation via code evolution represents a paradigm shift by eliminating the need to formulate the how. CHECKMATE solely relies on the what. Specifically, a formal specification ensures solutions' correctness and enables systematic performance evaluation of the generated programs, while a natural language description guides the evolutionary process. The effectiveness of our method is demonstrated on selected problems from two industrial domains: configuration and scheduling. In all cases, the evolved algorithms consistently outperform state-of-the-art solvers. This underscores the potential of formal methods in guiding code evolution for automatically solving complex real-world problems.

Large Language Models (LLMs) rely on instruction samples for alignment, but creating these datasets poses challenges, particularly in expert-dependent tasks like coding, which can be cost-prohibitive. One approach to mitigate these challenges is synthesizing data using another LLM. In this paper, we introduce a scalable method for generating synthetic instructions to enhance the code generation capability of LLMs. The proposed algorithm, Genetic-Instruct, mimics evolutionary processes, utilizing self-instruction to create numerous synthetic samples from a limited number of seeds. Genetic-Instruct is designed for efficient scaling of the generation process. Fine-tuning multiple coding LLMs with the synthetic samples demonstrates a significant improvement in their code generation accuracy compared to the baselines.

Symbolic regression (SR) is the problem of learning a symbolic expression from numerical data. Recently, deep neural models trained on procedurally-generated synthetic datasets showed competitive performance compared to more classical Genetic Programming (GP) algorithms. Unlike their GP counterparts, these neural approaches are trained to generate expressions from datasets given as context. This allows them to produce accurate expressions in a single forward pass at test time. However, they usually do not benefit from search abilities, which result in low performance compared to GP on out-of-distribution datasets. In this paper, we propose a novel method which provides the best of both worlds, based on a Monte-Carlo Tree Search procedure using a context-aware neural mutation model, which is initially pre-trained to learn promising mutations, and further refined from successful experiences in an online fashion. The approach demonstrates state-of-the-art performance on the well-known SRBench benchmark.

Recent work such as AlphaEvolve has shown that combining LLM-driven optimization with evolutionary search can effectively improve programs, prompts, and algorithms across domains. In this paradigm, previously evaluated solutions are reused to guide the model toward new candidate solutions. Crucially, the effectiveness of this evolution process depends on the search strategy: how prior solutions are selected and varied to generate new candidates. However, most existing methods rely on fixed search strategies with predefined knobs (e.g., explore-exploit ratios) that remain static throughout execution. While effective in some settings, these approaches often fail to adapt across tasks, or even within the same task as the search space changes over time. We introduce EvoX, an adaptive evolution method that optimizes its own evolution process. EvoX jointly evolves candidate solutions and the search strategies used to generate them, continuously updating how prior solutions are selected and varied based on progress. This enables the system to dynamically shift between different search strategies during the optimization process. Across nearly 200 real-world optimization tasks, EvoX outperforms existing AI-driven evolutionary methods including AlphaEvolve, OpenEvolve, GEPA, and ShinkaEvolve on the majority of tasks.

We investigate the potential of bio-inspired evolutionary algorithms for designing quantum circuits with specific goals, focusing on two particular tasks. The first one is motivated by the ideas of Artificial Life that are used to reproduce stochastic cellular automata with given rules. We test the robustness of quantum implementations of the cellular automata for different numbers of quantum gates The second task deals with the sampling of quantum circuits that generate highly entangled quantum states, which constitute an important resource for quantum computing. In particular, an evolutionary algorithm is employed to optimize circuits with respect to a fitness function defined with the Mayer-Wallach entanglement measure. We demonstrate that, by balancing the mutation rate between exploration and exploitation, we can find entangling quantum circuits for up to five qubits. We also discuss the trade-off between the number of gates in quantum circuits and the computational costs of finding the gate arrangements leading to a strongly entangled state. Our findings provide additional insight into the trade-off between the complexity of a circuit and its performance, which is an important factor in the design of quantum circuits.

The rise of powerful large language models (LLMs) has spurred a new trend in building LLM-based autonomous agents for solving complex tasks, especially multi-agent systems. Despite the remarkable progress, we notice that existing works are heavily dependent on human-designed frameworks, which greatly limits the functional scope and scalability of agent systems. How to automatically extend the specialized agent to multi-agent systems to improve task-solving capability still remains a significant challenge. In this paper, we introduce EvoAgent, a generic method to automatically extend expert agents to multi-agent systems via the evolutionary algorithm, thereby improving the effectiveness of LLM-based agents in solving tasks. Specifically, we consider the existing agent frameworks as the initial individual and then apply a series of evolutionary operators (e.g., mutation, crossover, selection, etc.) to generate multiple agents with diverse agent settings. EvoAgent can be generalized to any LLM-based agent framework, and can automatically extend the existing agent framework to multi-agent systems without any extra human designs. Experimental results across various tasks have shown that EvoAgent can automatically generate multiple expert agents and significantly enhance the task-solving capabilities of LLM-based agents.

We introduce Geometric Neural Operators (GNPs) for accounting for geometric contributions in data-driven deep learning of operators. We show how GNPs can be used (i) to estimate geometric properties, such as the metric and curvatures, (ii) to approximate Partial Differential Equations (PDEs) on manifolds, (iii) learn solution maps for Laplace-Beltrami (LB) operators, and (iv) to solve Bayesian inverse problems for identifying manifold shapes. The methods allow for handling geometries of general shape including point-cloud representations. The developed GNPs provide approaches for incorporating the roles of geometry in data-driven learning of operators.

Fuzz testing, or "fuzzing," refers to a widely deployed class of techniques for testing programs by generating a set of inputs for the express purpose of finding bugs and identifying security flaws. Grey-box fuzzing, the most popular fuzzing strategy, combines light program instrumentation with a data driven process to generate new program inputs. In this work, we present a machine learning approach that builds on AFL, the preeminent grey-box fuzzer, by adaptively learning a probability distribution over its mutation operators on a program-specific basis. These operators, which are selected uniformly at random in AFL and mutational fuzzers in general, dictate how new inputs are generated, a core part of the fuzzer's efficacy. Our main contributions are two-fold: First, we show that a sampling distribution over mutation operators estimated from training programs can significantly improve performance of AFL. Second, we introduce a Thompson Sampling, bandit-based optimization approach that fine-tunes the mutator distribution adaptively, during the course of fuzzing an individual program. A set of experiments across complex programs demonstrates that tuning the mutational operator distribution generates sets of inputs that yield significantly higher code coverage and finds more crashes faster and more reliably than both baseline versions of AFL as well as other AFL-based learning approaches.

In this paper, we construct a mixture of neural operators (MoNOs) between function spaces whose complexity is distributed over a network of expert neural operators (NOs), with each NO satisfying parameter scaling restrictions. Our main result is a distributed universal approximation theorem guaranteeing that any Lipschitz non-linear operator between L^2([0,1]^d) spaces can be approximated uniformly over the Sobolev unit ball therein, to any given varepsilon>0 accuracy, by an MoNO while satisfying the constraint that: each expert NO has a depth, width, and rank of O(varepsilon^{-1}). Naturally, our result implies that the required number of experts must be large, however, each NO is guaranteed to be small enough to be loadable into the active memory of most computers for reasonable accuracies varepsilon. During our analysis, we also obtain new quantitative expression rates for classical NOs approximating uniformly continuous non-linear operators uniformly on compact subsets of L^2([0,1]^d).

LLM-based agents depend on effective tool-use policies to solve complex tasks, yet optimizing these policies remains challenging due to delayed supervision and the difficulty of credit assignment in long-horizon trajectories. Existing optimization approaches tend to be either monolithic, which are prone to entangling behaviors, or single-aspect, which ignore cross-module error propagation. To address these limitations, we propose EvoTool, a self-evolving framework that optimizes a modular tool-use policy via a gradient-free evolutionary paradigm. EvoTool decomposes agent's tool-use policy into four modules, including Planner, Selector, Caller, and Synthesizer, and iteratively improves them in a self-improving loop through three novel mechanisms. Trajectory-Grounded Blame Attribution uses diagnostic traces to localize failures to a specific module. Feedback-Guided Targeted Mutation then edits only that module via natural-language critique. Diversity-Aware Population Selection preserves complementary candidates to ensure solution diversity. Across four benchmarks, EvoTool outperforms strong baselines by over 5 points on both GPT-4.1 and Qwen3-8B, while achieving superior efficiency and transferability. The code will be released once paper is accepted.

We present a novel approach to symbolic regression using vision-capable large language models (LLMs) and the ideas behind Google DeepMind's Funsearch. The LLM is given a plot of a univariate function and tasked with proposing an ansatz for that function. The free parameters of the ansatz are fitted using standard numerical optimisers, and a collection of such ansätze make up the population of a genetic algorithm. Unlike other symbolic regression techniques, our method does not require the specification of a set of functions to be used in regression, but with appropriate prompt engineering, we can arbitrarily condition the generative step. By using Kolmogorov Arnold Networks (KANs), we demonstrate that ``univariate is all you need'' for symbolic regression, and extend this method to multivariate functions by learning the univariate function on each edge of a trained KAN. The combined expression is then simplified by further processing with a language model.

Single-operator learning involves training a deep neural network to learn a specific operator, whereas recent work in multi-operator learning uses an operator embedding structure to train a single neural network on data from multiple operators. Thus, multi-operator learning is capable of predicting a range of operators within one model. In this work, we propose pretraining and fine-tuning strategies for solving PDEs using multi-operator learning. One key aspect is that by increasing the number of families of operators used in pretraining, a PDE foundation model can be fine-tuned to downstream tasks involving new PDEs with a limited number of samples, thus outperforming single operator neural networks. Specifically, a multi-operator learning model pre-trained with data from diverse PDE families can predict unseen operators after fine-tuning with only a limited number of operators from the new family, enabling them to serve as a data-free PDE solver. We also show that the proposed training and fine-tuning method is able to predict new operators in zero-shot prediction without samples. Additionally, we introduce a PDE-agnostic meta-learning algorithm to improve the adaptability of the model to various PDEs by providing a better parameter initialization process. To address the needs of applications with limited computing resources, we explore low-rank adaptation methods that reduce computational costs while enhancing solver accuracy. Lastly, by examining the scaling law with respect to the number of operator families, we establish and highlight its potential for broad adaptation in PDE-solving tasks.

The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets. We propose a generalization of neural networks to learn operators, termed neural operators, that map between infinite dimensional function spaces. We formulate the neural operator as a composition of linear integral operators and nonlinear activation functions. We prove a universal approximation theorem for our proposed neural operator, showing that it can approximate any given nonlinear continuous operator. The proposed neural operators are also discretization-invariant, i.e., they share the same model parameters among different discretization of the underlying function spaces. Furthermore, we introduce four classes of efficient parameterization, viz., graph neural operators, multi-pole graph neural operators, low-rank neural operators, and Fourier neural operators. An important application for neural operators is learning surrogate maps for the solution operators of partial differential equations (PDEs). We consider standard PDEs such as the Burgers, Darcy subsurface flow, and the Navier-Stokes equations, and show that the proposed neural operators have superior performance compared to existing machine learning based methodologies, while being several orders of magnitude faster than conventional PDE solvers.

Symbolic regression is the task of identifying a mathematical expression that best fits a provided dataset of input and output values. Due to the richness of the space of mathematical expressions, symbolic regression is generally a challenging problem. While conventional approaches based on genetic evolution algorithms have been used for decades, deep learning-based methods are relatively new and an active research area. In this work, we present SymbolicGPT, a novel transformer-based language model for symbolic regression. This model exploits the advantages of probabilistic language models like GPT, including strength in performance and flexibility. Through comprehensive experiments, we show that our model performs strongly compared to competing models with respect to the accuracy, running time, and data efficiency.

Interpretability of Deep Learning (DL) is a barrier to trustworthy AI. Despite great efforts made by the Explainable AI (XAI) community, explanations lack robustness -- indistinguishable input perturbations may lead to different XAI results. Thus, it is vital to assess how robust DL interpretability is, given an XAI method. In this paper, we identify several challenges that the state-of-the-art is unable to cope with collectively: i) existing metrics are not comprehensive; ii) XAI techniques are highly heterogeneous; iii) misinterpretations are normally rare events. To tackle these challenges, we introduce two black-box evaluation methods, concerning the worst-case interpretation discrepancy and a probabilistic notion of how robust in general, respectively. Genetic Algorithm (GA) with bespoke fitness function is used to solve constrained optimisation for efficient worst-case evaluation. Subset Simulation (SS), dedicated to estimate rare event probabilities, is used for evaluating overall robustness. Experiments show that the accuracy, sensitivity, and efficiency of our methods outperform the state-of-the-arts. Finally, we demonstrate two applications of our methods: ranking robust XAI methods and selecting training schemes to improve both classification and interpretation robustness.

Neural networks and evolutionary computation have a rich intertwined history. They most commonly appear together when an evolutionary algorithm optimises the parameters and topology of a neural network for reinforcement learning problems, or when a neural network is applied as a surrogate fitness function to aid the evolutionary optimisation of expensive fitness functions. In this paper we take a different approach, asking the question of whether a neural network can be used to provide a mutation distribution for an evolutionary algorithm, and what advantages this approach may offer? Two modern neural network models are investigated, a Denoising Autoencoder modified to produce stochastic outputs and the Neural Autoregressive Distribution Estimator. Results show that the neural network approach to learning genotypes is able to solve many difficult discrete problems, such as MaxSat and HIFF, and regularly outperforms other evolutionary techniques.

Population-based search has recently emerged as a possible alternative to Reinforcement Learning (RL) for black-box neural architecture search (NAS). It performs well in practice even though it is not theoretically well understood. In particular, whereas traditional population-based search methods such as evolutionary algorithms (EAs) draw much power from crossover operations, it is difficult to take advantage of them in NAS. The main obstacle is believed to be the permutation problem: The mapping between genotype and phenotype in traditional graph representations is many-to-one, leading to a disruptive effect of standard crossover. This paper presents the first theoretical analysis of the behaviors of mutation, crossover and RL in black-box NAS, and proposes a new crossover operator based on the shortest edit path (SEP) in graph space. The SEP crossover is shown theoretically to overcome the permutation problem, and as a result, have a better expected improvement compared to mutation, standard crossover and RL. Further, it empirically outperform these other methods on state-of-the-art NAS benchmarks. The SEP crossover therefore allows taking full advantage of population-based search in NAS, and the underlying theory can serve as a foundation for deeper understanding of black-box NAS methods in general.

Human visual perception can easily generalize to out-of-distributed visual data, which is far beyond the capability of modern machine learning models. Domain generalization (DG) aims to close this gap, with existing DG methods mainly focusing on the loss function design. In this paper, we propose to explore an orthogonal direction, i.e., the design of the backbone architecture. It is motivated by an empirical finding that transformer-based models trained with empirical risk minimization (ERM) outperform CNN-based models employing state-of-the-art (SOTA) DG algorithms on multiple DG datasets. We develop a formal framework to characterize a network's robustness to distribution shifts by studying its architecture's alignment with the correlations in the dataset. This analysis guides us to propose a novel DG model built upon vision transformers, namely Generalizable Mixture-of-Experts (GMoE). Extensive experiments on DomainBed demonstrate that GMoE trained with ERM outperforms SOTA DG baselines by a large margin. Moreover, GMoE is complementary to existing DG methods and its performance is substantially improved when trained with DG algorithms.

Generative models in function spaces, situated at the intersection of generative modeling and operator learning, are attracting increasing attention due to their immense potential in diverse scientific and engineering applications. While functional generative models are theoretically domain- and discretization-agnostic, current implementations heavily rely on the Fourier Neural Operator (FNO), limiting their applicability to regular grids and rectangular domains. To overcome these critical limitations, we introduce the Mesh-Informed Neural Operator (MINO). By leveraging graph neural operators and cross-attention mechanisms, MINO offers a principled, domain- and discretization-agnostic backbone for generative modeling in function spaces. This advancement significantly expands the scope of such models to more diverse applications in generative, inverse, and regression tasks. Furthermore, MINO provides a unified perspective on integrating neural operators with general advanced deep learning architectures. Finally, we introduce a suite of standardized evaluation metrics that enable objective comparison of functional generative models, addressing another critical gap in the field.

AI agents are increasingly deployed on complex, domain-specific workflows -- navigating enterprise web applications that require dozens of clicks and form fills, orchestrating multi-step research pipelines that span search, extraction, and synthesis, automating code review across unfamiliar repositories, and handling customer escalations that demand nuanced domain knowledge. Each new task domain requires painstaking, expert-driven harness engineering: designing the prompts, tools, orchestration logic, and evaluation criteria that make a foundation model effective. We present a two-level framework that automates this process. At the first level, the Harness Evolution Loop optimizes a worker agent's harness H for a single task: a Worker Agent W_{H} executes the task, an Evaluator Agent V adversarially diagnoses failures and scores performance, and an Evolution Agent E modifies the harness based on the full history of prior attempts. At the second level, the Meta-Evolution Loop optimizes the evolution protocol Λ= (W_{H}, H^{(0)}, V, E) itself across diverse tasks, learning a protocol Λ^{(text{best)} that enables rapid harness convergence on any new task -- so that adapting an agent to a novel domain requires no human harness engineering at all.} We formalize the correspondence to meta-learning and present both algorithms. The framework shifts manual harness engineering into automated harness engineering, and takes one step further -- automating the design of the automation itself.

Deep Learning (DL) is prevalently used in various industries to improve decision-making and automate processes, driven by the ever-evolving DL libraries and compilers. The correctness of DL systems is crucial for trust in DL applications. As such, the recent wave of research has been studying the automated synthesis of test-cases (i.e., DNN models and their inputs) for fuzzing DL systems. However, existing model generators only subsume a limited number of operators, lacking the ability to pervasively model operator constraints. To address this challenge, we propose NeuRI, a fully automated approach for generating valid and diverse DL models composed of hundreds of types of operators. NeuRI adopts a three-step process: (i) collecting valid and invalid API traces from various sources; (ii) applying inductive program synthesis over the traces to infer the constraints for constructing valid models; and (iii) using hybrid model generation which incorporates both symbolic and concrete operators. Our evaluation shows that NeuRI improves branch coverage of TensorFlow and PyTorch by 24% and 15% over the state-of-the-art model-level fuzzers. NeuRI finds 100 new bugs for PyTorch and TensorFlow in four months, with 81 already fixed or confirmed. Of these, 9 bugs are labelled as high priority or security vulnerability, constituting 10% of all high-priority bugs of the period. Open-source developers regard error-inducing tests reported by us as "high-quality" and "common in practice".

Large language models (LLMs) have shown impressive promise in code generation, yet their progress remains limited by the shortage of large-scale datasets that are both diverse and well-aligned with human reasoning. Most existing resources pair problems with solutions, but omit the intermediate thought process that guides coding. To close this gap, we present a scalable synthetic data generation pipeline that produces nearly 800k instruction-reasoning-code-test quadruplets. Each sample combines a task, a step-by-step reasoning trace, a working solution, and executable tests, enabling models to learn not just the what but also the how of problem solving. Our pipeline combines four key components: curated contest problems, web-mined content filtered by relevance classifiers, data expansion guided by reasoning patterns, and multi-stage execution-based validation. A genetic mutation algorithm further increases task diversity while maintaining consistency between reasoning traces and code implementations. Our key finding is that fine-tuning LLMs on this dataset yields consistent improvements on coding benchmarks. Beyond raw accuracy, reasoning-aware data can substitute for model scaling, generalize across architectures, and outperform leading open-source alternatives under identical sample budgets. Our work establishes reasoning-centered synthetic data generation as an efficient approach for advancing coding capabilities in LLMs. We publish our dataset and generation pipeline to facilitate further research.

We propose expanding the shared Transformer module to produce and initialize Transformers of varying depths, enabling adaptation to diverse resource constraints. Drawing an analogy to genetic expansibility, we term such module as learngene. To identify the expansion mechanism, we delve into the relationship between the layer's position and its corresponding weight value, and find that linear function appropriately approximates this relationship. Building on this insight, we present Transformer as Linear Expansion of learnGene (TLEG), a novel approach for flexibly producing and initializing Transformers of diverse depths. Specifically, to learn learngene, we firstly construct an auxiliary Transformer linearly expanded from learngene, after which we train it through employing soft distillation. Subsequently, we can produce and initialize Transformers of varying depths via linearly expanding the well-trained learngene, thereby supporting diverse downstream scenarios. Extensive experiments on ImageNet-1K demonstrate that TLEG achieves comparable or better performance in contrast to many individual models trained from scratch, while reducing around 2x training cost. When transferring to several downstream classification datasets, TLEG surpasses existing initialization methods by a large margin (e.g., +6.87% on iNat 2019 and +7.66% on CIFAR-100). Under the situation where we need to produce models of varying depths adapting for different resource constraints, TLEG achieves comparable results while reducing around 19x parameters stored to initialize these models and around 5x pre-training costs, in contrast to the pre-training and fine-tuning approach. When transferring a fixed set of parameters to initialize different models, TLEG presents better flexibility and competitive performance while reducing around 2.9x parameters stored to initialize, compared to the pre-training approach.

Human language is one of the most expressive tools for conveying intent, yet most artificial or biological systems lack mechanisms to interpret or respond meaningfully to it. Bridging this gap could enable more natural forms of control over complex, decentralized systems. In AI and artificial life, recent work explores how language can specify high-level goals, but most systems still depend on engineered rewards, task-specific supervision, or rigid command sets, limiting generalization to novel instructions. Similar constraints apply in synthetic biology and bioengineering, where the locus of control is often genomic rather than environmental perturbation. A key open question is whether artificial or biological collectives can be guided by free-form natural language alone, without task-specific tuning or carefully designed evaluation metrics. We provide one possible answer here by showing, for the first time, that simple agents' collective behavior can be guided by free-form language prompts: one AI model transforms an imperative prompt into an intervention that is applied to simulated cells; a second AI model scores how well the prompt describes the resulting cellular dynamics; and the former AI model is evolved to improve the scores generated by the latter. Unlike previous work, our method does not require engineered fitness functions or domain-specific prompt design. We show that the evolved system generalizes to unseen prompts without retraining. By treating natural language as a control layer, the system suggests a future in which spoken or written prompts could direct computational, robotic, or biological systems to desired behaviors. This work provides a concrete step toward this vision of AI-biology partnerships, in which language replaces mathematical objective functions, fixed rules, and domain-specific programming.

We introduce Topological Neural Operators (TNOs), a principled framework for operator learning on cell complexes that lifts neural operators (NOs) from functions on points and/or edges to topological domains. TNOs represent data as features defined on cells of varying dimension and model their interactions through Discrete Exterior Calculus, enabling explicit cross-dimensional coupling via gradient-, curl-, and divergence-type operators. The key design principle is to decouple where information flows, as governed by fixed topological operators, from how it is transformed (which is learned), yielding models that respect the geometric support of physical quantities and expose conservation and compatibility structure. We further propose Hierarchical TNOs (HTNOs), which incorporate learned coarse complexes to propagate long-range and topology-dependent information. Our framework subsumes existing NOs as a special case, providing a unified perspective on operator learning across discretizations. Across a range of PDE benchmarks, including irregular-geometry flow problems, TNOs and HTNOs improve accuracy; controlled studies further isolate the benefits of native higher-rank and topological structure. Project page: https://circle-group.github.io/research/TNO

Neural architecture search (NAS), the study of automating the discovery of optimal deep neural network architectures for tasks in domains such as computer vision and natural language processing, has seen rapid growth in the machine learning research community. While there have been many recent advancements in NAS, there is still a significant focus on reducing the computational cost incurred when validating discovered architectures by making search more efficient. Evolutionary algorithms, specifically genetic algorithms, have a history of usage in NAS and continue to gain popularity versus other optimization approaches as a highly efficient way to explore the architecture objective space. Most NAS research efforts have centered around computer vision tasks and only recently have other modalities, such as the rapidly growing field of natural language processing, been investigated in depth. In this work, we show how genetic algorithms can be paired with lightly trained objective predictors in an iterative cycle to accelerate multi-objective architectural exploration in a way that works in the modalities of both machine translation and image classification.

This paper introduces PyGAD, an open-source easy-to-use Python library for building the genetic algorithm. PyGAD supports a wide range of parameters to give the user control over everything in its life cycle. This includes, but is not limited to, population, gene value range, gene data type, parent selection, crossover, and mutation. PyGAD is designed as a general-purpose optimization library that allows the user to customize the fitness function. Its usage consists of 3 main steps: build the fitness function, create an instance of the pygad.GA class, and calling the pygad.GA.run() method. The library supports training deep learning models created either with PyGAD itself or with frameworks like Keras and PyTorch. Given its stable state, PyGAD is also in active development to respond to the user's requested features and enhancement received on GitHub https://github.com/ahmedfgad/GeneticAlgorithmPython. PyGAD comes with documentation https://pygad.readthedocs.io for further details and examples.

Search has been proposed as an effective method for self-improving language models and agentic systems, both for post-training sample generation and for inference. However, widely used methods such as best-of-N sampling and tree search face two fundamental limitations: they are guided by sparse verification signals, and they construct candidates primarily through autoregressive expansion, restricting exploration to regions with substantial model probability mass. To address these, we propose Bidirectional Evolutionary Search (BES), a search framework that couples forward candidate evolution with backward goal decomposition. In the forward search, BES augments standard expansion with evolution operators that recombine partial trajectories to generate candidates that are difficult to obtain from a single model rollout. In the backward search, BES recursively decomposes the original task into checkable subgoals, producing dense intermediate feedback that guides forward search. We provide theoretical motivation showing that candidates generated by expansion-only search are confined to a narrow entropy shell while evolutionary operators can escape it, and that backward search can exponentially reduce the number of required samples to find a correct answer. Experiments show that on challenging post-training tasks where mainstream post-training algorithms fail to improve, BES enables consistent gains, and on three open problem solving benchmarks at inference time, BES outperforms existing open-source frameworks in both average and best-case performance. Code and trained models are available at https://github.com/Embodied-Minds-Lab/BES.

A single two-input gate suffices for all of Boolean logic in digital hardware. No comparable primitive has been known for continuous mathematics: computing elementary functions such as sin, cos, sqrt, and log has always required multiple distinct operations. Here I show that a single binary operator, eml(x,y)=exp(x)-ln(y), together with the constant 1, generates the standard repertoire of a scientific calculator. This includes constants such as e, pi, and i; arithmetic operations including addition, subtraction, multiplication, division, and exponentiation as well as the usual transcendental and algebraic functions. For example, exp(x)=eml(x,1), ln(x)=eml(1,eml(eml(1,x),1)), and likewise for all other operations. That such an operator exists was not anticipated; I found it by systematic exhaustive search and established constructively that it suffices for the concrete scientific-calculator basis. In EML (Exp-Minus-Log) form, every such expression becomes a binary tree of identical nodes, yielding a grammar as simple as S -> 1 | eml(S,S). This uniform structure also enables gradient-based symbolic regression: using EML trees as trainable circuits with standard optimizers (Adam), I demonstrate the feasibility of exact recovery of closed-form elementary functions from numerical data at shallow tree depths up to 4. The same architecture can fit arbitrary data, but when the generating law is elementary, it may recover the exact formula.

Efficient operator scheduling is a fundamental challenge in software compilation and hardware synthesis. While recent differentiable approaches have sought to replace traditional ones like exact solvers or heuristics with gradient-based search, they typically rely on categorical distributions that fail to capture the ordinal nature of time and suffer from a parameter space that scales poorly. In this paper, we propose a novel differentiable framework, GauS, that models operator scheduling as a stochastic relaxation using Gaussian distributions, which fully utilize modern parallel computing devices like GPUs. By representing schedules as continuous Gaussian variables, we successfully capture the ordinal nature of time and reduce the optimization space by orders of magnitude. Our method is highly flexible to represent various objectives and constraints, which provides the first differentiable formulation for the complex pipelined scheduling problem. We evaluate our method on a range of benchmarks, demonstrating that Gaus achieves Pareto-optimal results.

We present a novel method for symbolic regression (SR), the task of searching for compact programmatic hypotheses that best explain a dataset. The problem is commonly solved using genetic algorithms; we show that we can enhance such methods by inducing a library of abstract textual concepts. Our algorithm, called LaSR, uses zero-shot queries to a large language model (LLM) to discover and evolve concepts occurring in known high-performing hypotheses. We discover new hypotheses using a mix of standard evolutionary steps and LLM-guided steps (obtained through zero-shot LLM queries) conditioned on discovered concepts. Once discovered, hypotheses are used in a new round of concept abstraction and evolution. We validate LaSR on the Feynman equations, a popular SR benchmark, as well as a set of synthetic tasks. On these benchmarks, LaSR substantially outperforms a variety of state-of-the-art SR approaches based on deep learning and evolutionary algorithms. Moreover, we show that LaSR can be used to discover a novel and powerful scaling law for LLMs.

Optimization can be found in many real-life applications. Designing an effective algorithm for a specific optimization problem typically requires a tedious amount of effort from human experts with domain knowledge and algorithm design skills. In this paper, we propose a novel approach called Algorithm Evolution using Large Language Model (AEL). It utilizes a large language model (LLM) to automatically generate optimization algorithms via an evolutionary framework. AEL does algorithm-level evolution without model training. Human effort and requirements for domain knowledge can be significantly reduced. We take constructive methods for the salesman traveling problem as a test example, we show that the constructive algorithm obtained by AEL outperforms simple hand-crafted and LLM-generated heuristics. Compared with other domain deep learning model-based algorithms, these methods exhibit excellent scalability across different problem sizes. AEL is also very different from previous attempts that utilize LLMs as search operators in algorithms.

We propose a new approach for generative modeling based on training a neural network to be idempotent. An idempotent operator is one that can be applied sequentially without changing the result beyond the initial application, namely f(f(z))=f(z). The proposed model f is trained to map a source distribution (e.g, Gaussian noise) to a target distribution (e.g. realistic images) using the following objectives: (1) Instances from the target distribution should map to themselves, namely f(x)=x. We define the target manifold as the set of all instances that f maps to themselves. (2) Instances that form the source distribution should map onto the defined target manifold. This is achieved by optimizing the idempotence term, f(f(z))=f(z) which encourages the range of f(z) to be on the target manifold. Under ideal assumptions such a process provably converges to the target distribution. This strategy results in a model capable of generating an output in one step, maintaining a consistent latent space, while also allowing sequential applications for refinement. Additionally, we find that by processing inputs from both target and source distributions, the model adeptly projects corrupted or modified data back to the target manifold. This work is a first step towards a ``global projector'' that enables projecting any input into a target data distribution.

Maintaining genetic diversity as a means to avoid premature convergence is critical in Genetic Programming. Several approaches have been proposed to achieve this, with some focusing on the mating phase from coupling dissimilar solutions to some form of self-adaptive selection mechanism. In nature, genetic diversity can be the consequence of many different factors, but when considering reproduction Sexual Selection can have an impact on promoting variety within a species. Specifically, Mate Choice often results in different selective pressures between sexes, which in turn may trigger evolutionary differences among them. Although some mechanisms of Sexual Selection have been applied to Genetic Programming in the past, the literature is scarce when it comes to mate choice. Recently, a way of modelling mating preferences by ideal mate representations was proposed, achieving good results when compared to a standard approach. These mating preferences evolve freely in a self-adaptive fashion, creating an evolutionary driving force of its own alongside fitness pressure. The inner mechanisms of this approach operate from personal choice, as each individual has its own representation of a perfect mate which affects the mate to be selected. In this paper, we compare this method against a random mate choice to assess whether there are advantages in evolving personal preferences. We conducted experiments using three symbolic regression problems and different mutation rates. The results show that self-adaptive mating preferences are able to create a more diverse set of solutions when compared to the traditional approach and a random mate approach (with statistically significant differences) and have a higher success rate in three of the six instances tested.

Machine learning-based supervised classifiers are widely used for security tasks, and their improvement has been largely focused on algorithmic advancements. We argue that data challenges that negatively impact the performance of these classifiers have received limited attention. We address the following research question: Can developments in Generative AI (GenAI) address these data challenges and improve classifier performance? We propose augmenting training datasets with synthetic data generated using GenAI techniques to improve classifier generalization. We evaluate this approach across 7 diverse security tasks using 6 state-of-the-art GenAI methods and introduce a novel GenAI scheme called Nimai that enables highly controlled data synthesis. We find that GenAI techniques can significantly improve the performance of security classifiers, achieving improvements of up to 32.6% even in severely data-constrained settings (only ~180 training samples). Furthermore, we demonstrate that GenAI can facilitate rapid adaptation to concept drift post-deployment, requiring minimal labeling in the adjustment process. Despite successes, our study finds that some GenAI schemes struggle to initialize (train and produce data) on certain security tasks. We also identify characteristics of specific tasks, such as noisy labels, overlapping class distributions, and sparse feature vectors, which hinder performance boost using GenAI. We believe that our study will drive the development of future GenAI tools designed for security tasks.

Gene expression analysis holds the key to many biomedical discoveries, yet extracting insights from raw transcriptomic data remains formidable due to the complexity of multiple large, semi-structured files and the need for extensive domain expertise. Current automation approaches are often limited by either inflexible workflows that break down in edge cases or by fully autonomous agents that lack the necessary precision for rigorous scientific inquiry. GenoMAS charts a different course by presenting a team of LLM-based scientists that integrates the reliability of structured workflows with the adaptability of autonomous agents. GenoMAS orchestrates six specialized LLM agents through typed message-passing protocols, each contributing complementary strengths to a shared analytic canvas. At the heart of GenoMAS lies a guided-planning framework: programming agents unfold high-level task guidelines into Action Units and, at each juncture, elect to advance, revise, bypass, or backtrack, thereby maintaining logical coherence while bending gracefully to the idiosyncrasies of genomic data. On the GenoTEX benchmark, GenoMAS reaches a Composite Similarity Correlation of 89.13% for data preprocessing and an F_1 of 60.48% for gene identification, surpassing the best prior art by 10.61% and 16.85% respectively. Beyond metrics, GenoMAS surfaces biologically plausible gene-phenotype associations corroborated by the literature, all while adjusting for latent confounders. Code is available at https://github.com/Liu-Hy/GenoMAS.

The effort devoted to hand-crafting neural network image classifiers has motivated the use of architecture search to discover them automatically. Although evolutionary algorithms have been repeatedly applied to neural network topologies, the image classifiers thus discovered have remained inferior to human-crafted ones. Here, we evolve an image classifier---AmoebaNet-A---that surpasses hand-designs for the first time. To do this, we modify the tournament selection evolutionary algorithm by introducing an age property to favor the younger genotypes. Matching size, AmoebaNet-A has comparable accuracy to current state-of-the-art ImageNet models discovered with more complex architecture-search methods. Scaled to larger size, AmoebaNet-A sets a new state-of-the-art 83.9% / 96.6% top-5 ImageNet accuracy. In a controlled comparison against a well known reinforcement learning algorithm, we give evidence that evolution can obtain results faster with the same hardware, especially at the earlier stages of the search. This is relevant when fewer compute resources are available. Evolution is, thus, a simple method to effectively discover high-quality architectures.

Neural operator models trained on simulation data often lose accuracy when applied to experimental measurements due to the sim-to-real gap. Standard fine-tuning with limited real data can reduce this gap, but it may also damage the core physics-relevant representations learned during pretraining. Although knowledge-preserving adaptation has been widely investigated in vision or language tasks, it remains unclear whether these methods are suitable for neural operators whose architectures and protected knowledge are fundamentally different. Neural operators need to preserve core-scale physical structures rather than semantic or visual features. We propose PhysGuard, a physics-preserving framework for accurate sim-to-real adaptation of neural operators. Specifically, PhysGuard uses the empirical Fisher Information Matrix computed on simulation data to identify physics-critical parameter directions, then restricts fine-tuning updates to directions that do not interfere with them. A layer-wise Gram-matrix formulation makes this efficient for models with millions of parameters, while an adaptive threshold automatically determines the protected subspace size. A spectral probe experiment shows that the dominant Fisher directions are strongly associated with low-frequency output structures. Experiments on benchmark across four neural operator architectures and different physical systems show that PhysGuard performs strongly on most evaluation metrics compared to baselines. The benefits are most evident under severe domain shift, where it reduces low-frequency error by up to 32\% compared to standard fine-tuning while maintaining adaptability. Our code is available at https://github.com/ZhouChaunge/PhysGuard.

Heuristic design with large language models (LLMs) has emerged as a promising approach for tackling combinatorial optimization problems (COPs). However, existing approaches often rely on manually predefined evolutionary computation (EC) optimizers and single-task training schemes, which may constrain the exploration of diverse heuristic algorithms and hinder the generalization of the resulting heuristics. To address these issues, we propose Meta-Optimization of Heuristics (MoH), a novel framework that operates at the optimizer level, discovering effective optimizers through the principle of meta-learning. Specifically, MoH leverages LLMs to iteratively refine a meta-optimizer that autonomously constructs diverse optimizers through (self-)invocation, thereby eliminating the reliance on a predefined EC optimizer. These constructed optimizers subsequently evolve heuristics for downstream tasks, enabling broader heuristic exploration. Moreover, MoH employs a multi-task training scheme to promote its generalization capability. Experiments on classic COPs demonstrate that MoH constructs an effective and interpretable meta-optimizer, achieving state-of-the-art performance across various downstream tasks, particularly in cross-size settings.

Modern neural networks rely on generic activation functions (ReLU, GELU, SiLU) that ignore the mathematical structure inherent in scientific data. We propose Neuro-Symbolic Activation Discovery, a framework that uses Genetic Programming to extract interpretable mathematical formulas from data and inject them as custom activation functions. Our key contribution is the discovery of a Geometric Transfer phenomenon: activation functions learned from particle physics data successfully generalize to ecological classification, outperforming standard activations (ReLU, GELU, SiLU) in both accuracy and parameter efficiency. On the Forest Cover dataset, our Hybrid Transfer model achieves 82.4% accuracy with only 5,825 parameters, compared to 83.4% accuracy requiring 31,801 parameters for a conventional heavy network -- a 5.5x parameter reduction with only 1% accuracy loss. We introduce a Parameter Efficiency Score (E_{param} = AUC / log_{10}(Params)) and demonstrate that lightweight hybrid architectures consistently achieve 18-21% higher efficiency than over-parameterized baselines. Crucially, we establish boundary conditions: while Physics to Ecology transfer succeeds (both involve continuous Euclidean measurements), Physics to Text transfer fails (discrete word frequencies require different mathematical structures). Our work opens pathways toward domain-specific activation libraries for efficient scientific machine learning.

We present a new implementation of the LLM-driven genetic algorithm {\it funsearch}, whose aim is to generate examples of interest to mathematicians and which has already had some success in problems in extremal combinatorics. Our implementation is designed to be useful in practice for working mathematicians; it does not require expertise in machine learning or access to high-performance computing resources. Applying {\it funsearch} to a new problem involves modifying a small segment of Python code and selecting a large language model (LLM) from one of many third-party providers. We benchmarked our implementation on three different problems, obtaining metrics that may inform applications of {\it funsearch} to new problems. Our results demonstrate that {\it funsearch} successfully learns in a variety of combinatorial and number-theoretic settings, and in some contexts learns principles that generalize beyond the problem originally trained on.

We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to learning the transfer operator or the generator of the system, which in turn can be used for numerous tasks, such as forecasting and interpreting the system dynamics. We show that the search for a good representation can be cast as an optimization problem over neural networks. Our approach is supported by recent results in statistical learning theory, highlighting the role of approximation error and metric distortion in the learning problem. The objective function we propose is associated with projection operators from the representation space to the data space, overcomes metric distortion, and can be empirically estimated from data. In the discrete-time setting, we further derive a relaxed objective function that is differentiable and numerically well-conditioned. We compare our method against state-of-the-art approaches on different datasets, showing better performance across the board.

Comprehending genomic information is essential for biomedical research, yet extracting data from complex distributed databases remains challenging. Large language models (LLMs) offer potential for genomic Question Answering (QA) but face limitations due to restricted access to domain-specific databases. GeneGPT is the current state-of-the-art system that enhances LLMs by utilizing specialized API calls, though it is constrained by rigid API dependencies and limited adaptability. We replicate GeneGPT and propose GenomAgent, a multi-agent framework that efficiently coordinates specialized agents for complex genomics queries. Evaluated on nine tasks from the GeneTuring benchmark, GenomAgent outperforms GeneGPT by 12% on average, and its flexible architecture extends beyond genomics to various scientific domains needing expert knowledge extraction.

To build effective therapeutics, biologists iteratively mutate antibody sequences to improve binding and stability. Proposed mutations can be informed by previous measurements or by learning from large antibody databases to predict only typical antibodies. Unfortunately, the space of typical antibodies is enormous to search, and experiments often fail to find suitable antibodies on a budget. We introduce Clone-informed Bayesian Optimization (CloneBO), a Bayesian optimization procedure that efficiently optimizes antibodies in the lab by teaching a generative model how our immune system optimizes antibodies. Our immune system makes antibodies by iteratively evolving specific portions of their sequences to bind their target strongly and stably, resulting in a set of related, evolving sequences known as a clonal family. We train a large language model, CloneLM, on hundreds of thousands of clonal families and use it to design sequences with mutations that are most likely to optimize an antibody within the human immune system. We propose to guide our designs to fit previous measurements with a twisted sequential Monte Carlo procedure. We show that CloneBO optimizes antibodies substantially more efficiently than previous methods in realistic in silico experiments and designs stronger and more stable binders in in vitro wet lab experiments.

Scientific discovery via symbolic regression is often viewed as statistically and computationally intractable because the hypothesis space of expressions grows combinatorially with depth. This paper revisits the statistical side through the lens of PAC learning, focusing on compositional function trees built from a finite vocabulary of smooth operators (e.g., {+,times,sin,exp} and affine maps). We prove that the relevant generalization quantity, Rademacher complexity, hence the excess risk, does not necessarily blow up exponentially with the number of distinct symbolic structures, but is controlled by (i) the depth d and (ii) the Lipschitz constants of the base operators along the composed computation graph. Concretely, under mild Lipschitz conditions on operators and bounded affine leaves, a finite-union bound over a vocabulary of size K=|H_{base}| together with Maurer-type vector contraction yields R_n(H_{comp}^{d}) leq (Kb2L)^{d-1}R_n(H_{comp}^{1}) with arity bound b; corresponding high-probability risk bounds scale as O(L^{d}/n) when K,b=O(1) and R_n(H_{comp}^{1})=O(n^{-1/2}). We complement the theory with a modular codebase that trains differentiable operator trees (not MLPs) on synthetic "physics-like" targets of controlled depth and shows that the empirical generalization gap correlates positively with the predicted complexity term (L^{d})/n.

Modern machine learning is still largely organized around a single recipe: choose a parameterized model family and optimize its weights. Although highly successful, this paradigm is too narrow for many structured prediction problems, where the main bottleneck is not parameter fitting but discovering what should be computed from the data. Success often depends on identifying the right transformations, statistics, invariances, interaction structures, temporal summaries, gates, or nonlinear compositions, especially when objectives are non-differentiable, evaluation is cross-validation-based, interpretability matters, or continual adaptation is required. We present EvoForest, a hybrid neuro-symbolic system for end-to-end open-ended evolution of computation. Rather than merely generating features, EvoForest jointly evolves reusable computational structure, callable function families, and trainable low-dimensional continuous components inside a shared directed acyclic graph. Intermediate nodes store alternative implementations, callable nodes encode reusable transformation families such as projections, gates, and activations, output nodes define candidate predictive computations, and persistent global parameters can be refined by gradient descent. For each graph configuration, EvoForest evaluates the discovered computation and uses a lightweight Ridge-based readout to score the resulting representation against a non-differentiable cross-validation target. The evaluator also produces structured feedback that guides future LLM-driven mutations. In the 2025 ADIA Lab Structural Break Challenge, EvoForest reached 94.13% ROC-AUC after 600 evolution steps, exceeding the publicly reported winning score of 90.14% under the same evaluation protocol.

This research investigates how Machine Learning (ML) algorithms can assist in workload allocation strategies by detecting tasks with node affinity operators (referred to as constraint operators), which constrain their execution to a limited number of nodes. Using real-world Google Cluster Data (GCD) workload traces and the AGOCS framework, the study extracts node attributes and task constraints, then analyses them to identify suitable node-task pairings. It focuses on tasks that can be executed on either a single node or fewer than a thousand out of 12.5k nodes in the analysed GCD cluster. Task constraint operators are compacted, pre-processed with one-hot encoding, and used as features in a training dataset. Various ML classifiers, including Artificial Neural Networks, K-Nearest Neighbours, Decision Trees, Naive Bayes, Ridge Regression, Adaptive Boosting, and Bagging, are fine-tuned and assessed for accuracy and F1-scores. The final ensemble voting classifier model achieved 98% accuracy and a 1.5-1.8% misclassification rate for tasks with a single suitable node.

Symbolic regression (SR) is a powerful technique for discovering the underlying mathematical expressions from observed data. Inspired by the success of deep learning, recent efforts have focused on two categories for SR methods. One is using a neural network or genetic programming to search the expression tree directly. Although this has shown promising results, the large search space poses difficulties in learning constant factors and processing high-dimensional problems. Another approach is leveraging a transformer-based model training on synthetic data and offers advantages in inference speed. However, this method is limited to fixed small numbers of dimensions and may encounter inference problems when given data is out-of-distribution compared to the synthetic data. In this work, we propose DySymNet, a novel neural-guided Dynamic Symbolic Network for SR. Instead of searching for expressions within a large search space, we explore DySymNet with various structures and optimize them to identify expressions that better-fitting the data. With a topology structure like neural networks, DySymNet not only tackles the challenge of high-dimensional problems but also proves effective in optimizing constants. Based on extensive numerical experiments using low-dimensional public standard benchmarks and the well-known SRBench with more variables, our method achieves state-of-the-art performance in terms of fitting accuracy and robustness to noise.

Is the lottery ticket phenomenon an idiosyncrasy of gradient-based training or does it generalize to evolutionary optimization? In this paper we establish the existence of highly sparse trainable initializations for evolution strategies (ES) and characterize qualitative differences compared to gradient descent (GD)-based sparse training. We introduce a novel signal-to-noise iterative pruning procedure, which incorporates loss curvature information into the network pruning step. This can enable the discovery of even sparser trainable network initializations when using black-box evolution as compared to GD-based optimization. Furthermore, we find that these initializations encode an inductive bias, which transfers across different ES, related tasks and even to GD-based training. Finally, we compare the local optima resulting from the different optimization paradigms and sparsity levels. In contrast to GD, ES explore diverse and flat local optima and do not preserve linear mode connectivity across sparsity levels and independent runs. The results highlight qualitative differences between evolution and gradient-based learning dynamics, which can be uncovered by the study of iterative pruning procedures.

We propose an extension of Thompson sampling to optimization problems over function spaces where the objective is a known functional of an unknown operator's output. We assume that queries to the operator (such as running a high-fidelity simulator or physical experiment) are costly, while functional evaluations on the operator's output are inexpensive. Our algorithm employs a sample-then-optimize approach using neural operator surrogates. This strategy avoids explicit uncertainty quantification by treating trained neural operators as approximate samples from a Gaussian process (GP) posterior. We derive regret bounds and theoretical results connecting neural operators with GPs in infinite-dimensional settings. Experiments benchmark our method against other Bayesian optimization baselines on functional optimization tasks involving partial differential equations of physical systems, demonstrating better sample efficiency and significant performance gains.

Evolutionary model merging provides a powerful framework for the automated, training-free composition of LLMs through parameter-space search. However, existing methods predominantly rely on stochastic, hand-crafted operators that overlook the underlying performance landscape of the coefficient space. We propose Evolutionary Generative Merging (EvoGM), a framework that transcends manual heuristics by employing learnable generative modeling to optimize merging coefficients. Specifically, EvoGM features a dual-generator architecture with cycle-consistent learning to adaptively sample and refine promising merging candidates. By constructing winner-loser pairs from historical search trajectories, our framework effectively captures high-performance parameter distributions and maximizes data efficiency. This generative process is seamlessly integrated into a multi-round evolutionary pipeline, where elite merged models iteratively serve as new expert foundations. Extensive experiments across diverse benchmarks demonstrate that EvoGM significantly outperforms state-of-the-art baselines, exhibiting robust performance on both seen and unseen tasks. Code and data are available at https://github.com/JiangTao97/evogm.

Solving parametric partial differential equations (PDEs) and associated PDE-based, inverse problems is a central task in engineering and physics, yet existing neural operator methods struggle with high-dimensional, discontinuous inputs and require large amounts of {\em labeled} training data. We propose the Deep Generative Neural Operator (DGNO), a physics-aware framework that addresses these challenges by leveraging a deep, generative, probabilistic model in combination with a set of lower-dimensional, latent variables that simultaneously encode PDE-inputs and PDE-outputs. This formulation can make use of unlabeled data and significantly improves inverse problem-solving, particularly for discontinuous or discrete-valued input functions. DGNO enforces physics constraints without labeled data by incorporating as virtual observables, weak-form residuals based on compactly supported radial basis functions (CSRBFs). These relax regularity constraints and eliminate higher-order derivatives from the objective function. We also introduce MultiONet, a novel neural operator architecture, which is a more expressive generalization of the popular DeepONet that significantly enhances the approximating power of the proposed model. These innovations make DGNO particularly effective for challenging forward and inverse, PDE-based problems, such as those involving multi-phase media. Numerical experiments demonstrate that DGNO achieves higher accuracy across multiple benchmarks while exhibiting robustness to noise and strong generalization to out-of-distribution cases. Its adaptability, and the ability to handle sparse, noisy data while providing probabilistic estimates, make DGNO a powerful tool for scientific and engineering applications.

Neural operators have become increasingly popular in solving partial differential equations (PDEs) due to their superior capability to capture intricate mappings between function spaces over complex domains. However, the data-hungry nature of operator learning inevitably poses a bottleneck for their widespread applications. At the core of the challenge lies the absence of transferability of neural operators to new geometries. To tackle this issue, we propose operator learning with domain decomposition, a local-to-global framework to solve PDEs on arbitrary geometries. Under this framework, we devise an iterative scheme Schwarz Neural Inference (SNI). This scheme allows for partitioning of the problem domain into smaller subdomains, on which local problems can be solved with neural operators, and stitching local solutions to construct a global solution. Additionally, we provide a theoretical analysis of the convergence rate and error bound. We conduct extensive experiments on several representative PDEs with diverse boundary conditions and achieve remarkable geometry generalization compared to alternative methods. These analysis and experiments demonstrate the proposed framework's potential in addressing challenges related to geometry generalization and data efficiency.

Recent advances in LLM-guided evolutionary computation, particularly AlphaEvolve (Novikov et al., 2025; Georgiev et al., 2025), have demonstrated remarkable success in discovering novel mathematical constructions and solving challenging optimization problems. However, the high-level descriptions in published work leave many implementation details unspecified, hindering reproducibility and further research. In this report we present GigaEvo, an extensible open-source framework that enables researchers to study and experiment with hybrid LLM-evolution approaches inspired by AlphaEvolve. Our system provides modular implementations of key components: MAP-Elites quality-diversity algorithms, asynchronous DAG-based evaluation pipelines, LLM-driven mutation operators with insight generation and bidirectional lineage tracking, and flexible multi-island evolutionary strategies. In order to assess reproducibility and validate our implementation we evaluate GigaEvo on challenging problems from the AlphaEvolve paper: Heilbronn triangle placement, circle packing in squares, and high-dimensional kissing numbers. The framework emphasizes modularity, concurrency, and ease of experimentation, enabling rapid prototyping through declarative configuration. We provide detailed descriptions of system architecture, implementation decisions, and experimental methodology to support further research in LLM driven evolutionary methods. The GigaEvo framework and all experimental code are available at https://github.com/AIRI-Institute/gigaevo-core.

A genetic algorithm is suitable for exploring large search spaces as it finds an approximate solution. Because of this advantage, genetic algorithm is effective in exploring vast and unknown space such as molecular search space. Though the algorithm is suitable for searching vast chemical space, it is difficult to optimize pharmacological properties while maintaining molecular substructure. To solve this issue, we introduce a genetic algorithm featuring a constrained molecular inverse design. The proposed algorithm successfully produces valid molecules for crossover and mutation. Furthermore, it optimizes specific properties while adhering to structural constraints using a two-phase optimization. Experiments prove that our algorithm effectively finds molecules that satisfy specific properties while maintaining structural constraints.

In this paper, we propose a generic optimization approach for challenging objective functions that finds applications in various statistical problems. We focus on objective functions with two parameter blocks of one amenable to analytic optimization, and another that is irregular or computationally expensive. To address this setting, we propose the Voronoi-Elitism Genetic Algorithm (VEGA), a derivative-free optimization method that embeds geometric information into genetic search. The proposed algorithm retains elite candidates and constructs Voronoi-based neighborhoods around them, whose crossover and self-adaptive mutation balance exploitation of promising solutions with exploration of under-covered regions. We study the high dimensional behavior of genetic search by analyzing distance concentration, and the effects of population size and shrinking mutation, which shows that the algorithm improves spatial coverage and yields sharper distance bounds under limited computational budgets. Simulation studies are conducted to compare VEGA with two genetic-type algorithms competitors in finite samples. A real data application on Stack Exchange activity data further illustrates its ability to identify stable structural changes, implying the algorithm is computationally flexible for high-dimensional, derivative-free optimization and applicable for various statistical problems.

In recent years, Deep Learning models have shown a great performance in complex optimization problems. They generally require large training datasets, which is a limitation in most practical cases. Transfer learning allows importing the first layers of a pre-trained architecture and connecting them to fully-connected layers to adapt them to a new problem. Consequently, the configuration of the these layers becomes crucial for the performance of the model. Unfortunately, the optimization of these models is usually a computationally demanding task. One strategy to optimize Deep Learning models is the pruning scheme. Pruning methods are focused on reducing the complexity of the network, assuming an expected performance penalty of the model once pruned. However, the pruning could potentially be used to improve the performance, using an optimization algorithm to identify and eventually remove unnecessary connections among neurons. This work proposes EvoPruneDeepTL, an evolutionary pruning model for Transfer Learning based Deep Neural Networks which replaces the last fully-connected layers with sparse layers optimized by a genetic algorithm. Depending on its solution encoding strategy, our proposed model can either perform optimized pruning or feature selection over the densely connected part of the neural network. We carry out different experiments with several datasets to assess the benefits of our proposal. Results show the contribution of EvoPruneDeepTL and feature selection to the overall computational efficiency of the network as a result of the optimization process. In particular, the accuracy is improved, reducing at the same time the number of active neurons in the final layers.

Cis-regulatory elements (CREs), such as promoters and enhancers, are relatively short DNA sequences that directly regulate gene expression. The fitness of CREs, measured by their ability to modulate gene expression, highly depends on the nucleotide sequences, especially specific motifs known as transcription factor binding sites (TFBSs). Designing high-fitness CREs is crucial for therapeutic and bioengineering applications. Current CRE design methods are limited by two major drawbacks: (1) they typically rely on iterative optimization strategies that modify existing sequences and are prone to local optima, and (2) they lack the guidance of biological prior knowledge in sequence optimization. In this paper, we address these limitations by proposing a generative approach that leverages reinforcement learning (RL) to fine-tune a pre-trained autoregressive (AR) model. Our method incorporates data-driven biological priors by deriving computational inference-based rewards that simulate the addition of activator TFBSs and removal of repressor TFBSs, which are then integrated into the RL process. We evaluate our method on promoter design tasks in two yeast media conditions and enhancer design tasks for three human cell types, demonstrating its ability to generate high-fitness CREs while maintaining sequence diversity. The code is available at https://github.com/yangzhao1230/TACO.

Open-ended image generation is no longer a simple prompt-to-image problem. High-quality generation often requires an agent to combine a model's internal generative ability with external resources. As requests become more diverse and demanding, we aim to develop a general image-generation agent that can self-evolve through trajectories and use tools more effectively across varied generation challenges. To this end, we propose GenEvolve, a self-evolving framework based on Tool-Orchestrated Visual Experience Distillation. In GenEvolve, each generation attempt is modeled as a tool-orchestrated trajectory, where the agent gathers evidence, selects references, invokes generation skills, and composes them into a prompt-reference program. Unlike existing agentic generation methods that mainly rely on image-level scalar rewards, GenEvolve compares multiple trajectories for the same request and abstracts best-worst differences into structured visual experience, provided only to a privileged teacher branch. Inspired by on-policy self-distillation, Visual Experience Distillation provides dense token-level supervision, helping the student internalize better search, knowledge activation, reference selection, and prompt construction. We further construct GenEvolve-Data and GenEvolve-Bench. Experiments on public benchmarks and GenEvolve-Bench show substantial gains over strong baselines, achieving state-of-the-art performance among current image-generation frameworks. Our website is as follows: https://ephemeral182.github.io/GenEvolve/

Time domain simulation, i.e., modeling the system's evolution over time, is a crucial tool for studying and enhancing power system stability and dynamic performance. However, these simulations become computationally intractable for renewable-penetrated grids, due to the small simulation time step required to capture renewable energy resources' ultra-fast dynamic phenomena in the range of 1-50 microseconds. This creates a critical need for solutions that are both fast and scalable, posing a major barrier for the stable integration of renewable energy resources and thus climate change mitigation. This paper explores operator learning, a family of machine learning methods that learn mappings between functions, as a surrogate model for these costly simulations. The paper investigates, for the first time, the fundamental concept of simulation time step-invariance, which enables models trained on coarse time steps to generalize to fine-resolution dynamics. Three operator learning methods are benchmarked on a simple test system that, while not incorporating practical complexities of renewable-penetrated grids, serves as a first proof-of-concept to demonstrate the viability of time step-invariance. Models are evaluated on (i) zero-shot super-resolution, where training is performed on a coarse simulation time step and inference is performed at super-resolution, and (ii) generalization between stable and unstable dynamic regimes. This work addresses a key challenge in the integration of renewable energy for the mitigation of climate change by benchmarking operator learning methods to model physical systems.

Transformers, and the attention mechanism in particular, have become ubiquitous in machine learning. Their success in modeling nonlocal, long-range correlations has led to their widespread adoption in natural language processing, computer vision, and time series problems. Neural operators, which map spaces of functions into spaces of functions, are necessarily both nonlinear and nonlocal if they are universal; it is thus natural to ask whether the attention mechanism can be used in the design of neural operators. Motivated by this, we study transformers in the function space setting. We formulate attention as a map between infinite dimensional function spaces and prove that the attention mechanism as implemented in practice is a Monte Carlo or finite difference approximation of this operator. The function space formulation allows for the design of transformer neural operators, a class of architectures designed to learn mappings between function spaces. In this paper, we state and prove the first universal approximation result for transformer neural operators, using only a slight modification of the architecture implemented in practice. The prohibitive cost of applying the attention operator to functions defined on multi-dimensional domains leads to the need for more efficient attention-based architectures. For this reason we also introduce a function space generalization of the patching strategy from computer vision, and introduce a class of associated neural operators. Numerical results, on an array of operator learning problems, demonstrate the promise of our approaches to function space formulations of attention and their use in neural operators.

Neural operators have shown promise in learning solution maps of partial differential equations (PDEs), but they often struggle to generalize when test inputs lie outside the training distribution, such as novel initial conditions, unseen PDE coefficients or unseen physics. Prior works address this limitation with large-scale multiple physics pretraining followed by fine-tuning, but this still requires examples from the new dynamics, falling short of true zero-shot generalization. In this work, we propose a method to enhance generalization at test time, i.e., without modifying pretrained weights. Building on DISCO, which provides a dictionary of neural operators trained across different dynamics, we introduce a neural operator splitting strategy that, at test time, searches over compositions of training operators to approximate unseen dynamics. On challenging out-of-distribution tasks including parameter extrapolation and novel combinations of physics phenomena, our approach achieves state-of-the-art zero-shot generalization results, while being able to recover the underlying PDE parameters. These results underscore test-time computation as a key avenue for building flexible, compositional, and generalizable neural operators.

Large language model (LLM)-based multi-agent systems (MAS) show strong promise for complex reasoning, planning, and tool-augmented tasks, but designing effective MAS architectures remains labor-intensive, brittle, and hard to generalize. Existing automatic MAS generation methods either rely on code generation, which often leads to executability and robustness failures, or impose rigid architectural templates that limit expressiveness and adaptability. We propose Evolutionary Generation of Multi-Agent Systems (EvoMAS), which formulates MAS generation as structured configuration generation. EvoMAS performs evolutionary generation in configuration space. Specifically, EvoMAS selects initial configurations from a pool, applies feedback-conditioned mutation and crossover guided by execution traces, and iteratively refines both the candidate pool and an experience memory. We evaluate EvoMAS on diverse benchmarks, including BBEH, SWE-Bench, and WorkBench, covering reasoning, software engineering, and tool-use tasks. EvoMAS consistently improves task performance over both human-designed MAS and prior automatic MAS generation methods, while producing generated systems with higher executability and runtime robustness. EvoMAS outperforms the agent evolution method EvoAgent by +10.5 points on BBEH reasoning and +7.1 points on WorkBench. With Claude-4.5-Sonnet, EvoMAS also reaches 79.1% on SWE-Bench-Verified, matching the top of the leaderboard.

Recent Meta-learning for Black-Box Optimization (MetaBBO) methods harness neural networks to meta-learn configurations of traditional black-box optimizers. Despite their success, they are inevitably restricted by the limitations of predefined hand-crafted optimizers. In this paper, we present Symbol, a novel framework that promotes the automated discovery of black-box optimizers through symbolic equation learning. Specifically, we propose a Symbolic Equation Generator (SEG) that allows closed-form optimization rules to be dynamically generated for specific tasks and optimization steps. Within Symbol, we then develop three distinct strategies based on reinforcement learning, so as to meta-learn the SEG efficiently. Extensive experiments reveal that the optimizers generated by Symbol not only surpass the state-of-the-art BBO and MetaBBO baselines, but also exhibit exceptional zero-shot generalization abilities across entirely unseen tasks with different problem dimensions, population sizes, and optimization horizons. Furthermore, we conduct in-depth analyses of our Symbol framework and the optimization rules that it generates, underscoring its desirable flexibility and interpretability.

We present a feasibility-seeking approach to neural network training. This mathematical optimization framework is distinct from conventional gradient-based loss minimization and uses projection operators and iterative projection algorithms. We reformulate training as a large-scale feasibility problem: finding network parameters and states that satisfy local constraints derived from its elementary operations. Training then involves projecting onto these constraints, a local operation that can be parallelized across the network. We introduce PJAX, a JAX-based software framework that enables this paradigm. PJAX composes projection operators for elementary operations, automatically deriving the solution operators for the feasibility problems (akin to autodiff for derivatives). It inherently supports GPU/TPU acceleration, provides a familiar NumPy-like API, and is extensible. We train diverse architectures (MLPs, CNNs, RNNs) on standard benchmarks using PJAX, demonstrating its functionality and generality. Our results show that this approach is as a compelling alternative to gradient-based training, with clear advantages in parallelism and the ability to handle non-differentiable operations.

We present a tool for exploring the design space of shaders using an interactive evolutionary algorithm integrated with the Unity editor, a well-known commercial tool for video game development. Our framework leverages the underlying graph-based representation of recent shader editors and interactive evolution to allow designers to explore several visual options starting from an existing shader. Our framework encodes the graph representation of a current shader as a chromosome used to seed the evolution of a shader population. It applies graph-based recombination and mutation with a set of heuristics to create feasible shaders. The framework is an extension of the Unity editor; thus, designers with little knowledge of evolutionary computation (and shader programming) can interact with the underlying evolutionary engine using the same visual interface used for working on game scenes.

A variety of infinitely wide neural architectures (e.g., dense NNs, CNNs, and transformers) induce Gaussian process (GP) priors over their outputs. These relationships provide both an accurate characterization of the prior predictive distribution and enable the use of GP machinery to improve the uncertainty quantification of deep neural networks. In this work, we extend this connection to neural operators (NOs), a class of models designed to learn mappings between function spaces. Specifically, we show conditions for when arbitrary-depth NOs with Gaussian-distributed convolution kernels converge to function-valued GPs. Based on this result, we show how to compute the covariance functions of these NO-GPs for two NO parametrizations, including the popular Fourier neural operator (FNO). With this, we compute the posteriors of these GPs in regression scenarios, including PDE solution operators. This work is an important step towards uncovering the inductive biases of current FNO architectures and opens a path to incorporate novel inductive biases for use in kernel-based operator learning methods.

We present Kernel-Smith, a framework for high-performance GPU kernel and operator generation that combines a stable evaluation-driven evolutionary agent with an evolution-oriented post-training recipe. On the agent side, Kernel-Smith maintains a population of executable candidates and iteratively improves them using an archive of top-performing and diverse programs together with structured execution feedback on compilation, correctness, and speedup. To make this search reliable, we build backend-specific evaluation services for Triton on NVIDIA GPUs and Maca on MetaX GPUs. On the training side, we convert long-horizon evolution trajectories into step-centric supervision and reinforcement learning signals by retaining correctness-preserving, high-gain revisions, so that the model is optimized as a strong local improver inside the evolutionary loop rather than as a one-shot generator. Under a unified evolutionary protocol, Kernel-Smith-235B-RL achieves state-of-the-art overall performance on KernelBench with Nvidia Triton backend, attaining the best average speedup ratio and outperforming frontier proprietary models including Gemini-3.0-pro and Claude-4.6-opus. We further validate the framework on the MetaX MACA backend, where our Kernel-Smith-MACA-30B surpasses large-scale counterparts such as DeepSeek-V3.2-think and Qwen3-235B-2507-think, highlighting potential for seamless adaptation across heterogeneous platforms. Beyond benchmark results, the same workflow produces upstream contributions to production systems including SGLang and LMDeploy, demonstrating that LLM-driven kernel optimization can transfer from controlled evaluation to practical deployment.

Building on the probability-domain distillation framework of Sparse-KD, we develop an axiomatic, operator-theoretic framework for multi-teacher ensemble knowledge distillation. Rather than prescribing a specific aggregation formula, we define five core axioms governing valid knowledge aggregation operators, encompassing convexity, positivity, continuity, weight monotonicity, and temperature coherence. We prove the existence and non-uniqueness of operator families satisfying these axioms, establishing that multiple distinct aggregation mechanisms conform to the same foundational principles. Within this framework, we establish operator-agnostic guarantees showing that multi-teacher aggregation reduces both stochastic variance and systematic supervisory bias under heterogeneous teachers, while providing Jensen-type bounds, log-loss guarantees, and safety attenuation properties. For aggregation operators linear in teacher weights, we further establish classical ensemble variance-reduction results under standard independence assumptions, with extensions to correlated-error regimes. The framework provides theoretical grounding for multi-teacher distillation from diverse frontier models while admitting multiple valid implementation strategies.

Training capable Large Language Model (LLM) agents is critically bottlenecked by the high cost and static nature of real-world interaction data. We address this by introducing GenEnv, a framework that establishes a difficulty-aligned co-evolutionary game between an agent and a scalable, generative environment simulator. Unlike traditional methods that evolve models on static datasets, GenEnv instantiates a dataevolving: the simulator acts as a dynamic curriculum policy, continuously generating tasks specifically tailored to the agent's ``zone of proximal development''. This process is guided by a simple but effective α-Curriculum Reward, which aligns task difficulty with the agent's current capabilities. We evaluate GenEnv on five benchmarks, including API-Bank, ALFWorld, BFCL, Bamboogle, and TravelPlanner. Across these tasks, GenEnv improves agent performance by up to +40.3\% over 7B baselines and matches or exceeds the average performance of larger models. Compared to Gemini 2.5 Pro-based offline data augmentation, GenEnv achieves better performance while using 3.3times less data. By shifting from static supervision to adaptive simulation, GenEnv provides a data-efficient pathway for scaling agent capabilities.

We argue that multi-agent test-time evolution is not single-agent evolution replicated N times. A single-agent learner can only evolve its own context and memory. A multi-agent system additionally evolves who collaborates, how they collaborate, and how knowledge flows across the population. These components have no single-agent counterpart and can produce phenomena such as emergent specialization. Yet prior test-time methods either confine experiences to individual agents, forfeiting cross-agent learning, or broadcast symmetrically to all agents, erasing the specialization that makes collaboration valuable. We present EVOCHAMBER, a training-free framework that instantiates test-time evolution at three levels over a coevolving agent pool. At its core is CODREAM (Collaborative Dreaming), a post-task protocol triggered on team failure or disagreement, in which agents collaboratively reflect, distill insights, and route them asymmetrically from strong to weak agents on the failed niche, preserving specialization while filling knowledge gaps. Team-level operators assemble niche-conditioned teams and select collaboration structures online. Population-level lifecycle operators fork, merge, prune, and seed agents under performance pressure. On three heterogeneous task streams with Qwen3-8B, EVOCHAMBER reaches 63.9% on competition math, 75.7% on code, and 87.1% on multi-domain reasoning, outperforming the best baseline by 32% relative on math and confirming asymmetric cross-agent transfer as the primary driver in ablation. Starting from several identically initialized agents, four to five stable niche specialists spontaneously emerge, a structural signature of multi-agent evolution that no single-agent learner can express. See our code at: https://github.com/Mercury7353/EvoChamber

Recent advances in large language models have sparked growing interest in AI agents capable of solving complex, real-world tasks. However, most existing agent systems rely on manually crafted configurations that remain static after deployment, limiting their ability to adapt to dynamic and evolving environments. To this end, recent research has explored agent evolution techniques that aim to automatically enhance agent systems based on interaction data and environmental feedback. This emerging direction lays the foundation for self-evolving AI agents, which bridge the static capabilities of foundation models with the continuous adaptability required by lifelong agentic systems. In this survey, we provide a comprehensive review of existing techniques for self-evolving agentic systems. Specifically, we first introduce a unified conceptual framework that abstracts the feedback loop underlying the design of self-evolving agentic systems. The framework highlights four key components: System Inputs, Agent System, Environment, and Optimisers, serving as a foundation for understanding and comparing different strategies. Based on this framework, we systematically review a wide range of self-evolving techniques that target different components of the agent system. We also investigate domain-specific evolution strategies developed for specialised fields such as biomedicine, programming, and finance, where optimisation objectives are tightly coupled with domain constraints. In addition, we provide a dedicated discussion on the evaluation, safety, and ethical considerations for self-evolving agentic systems, which are critical to ensuring their effectiveness and reliability. This survey aims to provide researchers and practitioners with a systematic understanding of self-evolving AI agents, laying the foundation for the development of more adaptive, autonomous, and lifelong agentic systems.

In this work we build a stack of machine learning models aimed at composing a state-of-the-art credit rating and default prediction system, obtaining excellent out-of-sample performances. Our approach is an excursion through the most recent ML / AI concepts, starting from natural language processes (NLP) applied to economic sectors' (textual) descriptions using embedding and autoencoders (AE), going through the classification of defaultable firms on the base of a wide range of economic features using gradient boosting machines (GBM) and calibrating their probabilities paying due attention to the treatment of unbalanced samples. Finally we assign credit ratings through genetic algorithms (differential evolution, DE). Model interpretability is achieved by implementing recent techniques such as SHAP and LIME, which explain predictions locally in features' space.

Recent advances in scientific machine learning (SciML) have enabled neural operators (NOs) to serve as powerful surrogates for modeling the dynamic evolution of physical systems governed by partial differential equations (PDEs). While existing approaches focus primarily on learning simulations from the target PDE, they often overlook more fundamental physical principles underlying these equations. Inspired by how numerical solvers are compatible with simulations of different settings of PDEs, we propose a multiphysics training framework that jointly learns from both the original PDEs and their simplified basic forms. Our framework enhances data efficiency, reduces predictive errors, and improves out-of-distribution (OOD) generalization, particularly in scenarios involving shifts of physical parameters and synthetic-to-real transfer. Our method is architecture-agnostic and demonstrates consistent improvements in normalized root mean square error (nRMSE) across a wide range of 1D/2D/3D PDE problems. Through extensive experiments, we show that explicit incorporation of fundamental physics knowledge significantly strengthens the generalization ability of neural operators. We will release models and codes at https://sites.google.com/view/sciml-fundemental-pde.

In this work, we introduce CodeEvolve, an open-source evolutionary coding agent that unites Large Language Models (LLMs) with genetic algorithms to solve complex computational problems. Our framework adapts powerful evolutionary concepts to the LLM domain, building upon recent methods for generalized scientific discovery. CodeEvolve employs an island-based genetic algorithm to maintain population diversity and increase throughput, introduces a novel inspiration-based crossover mechanism that leverages the LLMs context window to combine features from successful solutions, and implements meta-prompting strategies for dynamic exploration of the solution space. We conduct a rigorous evaluation of CodeEvolve on a subset of the mathematical benchmarks used to evaluate Google DeepMind's closed-source AlphaEvolve. Our findings show that our method surpasses AlphaEvolve's performance on several challenging problems. To foster collaboration and accelerate progress, we release our complete framework as an open-source repository.

Recent work in probability-domain knowledge distillation has established axiomatic frameworks for temperature scaling, multi-teacher aggregation, and bias-variance trade-offs in single-stage settings. However, the mathematical behavior of recursive or multi-generation distillation remains poorly understood, with prior approaches relying primarily on empirical heuristics. In this work, we introduce an axiomatic and operator-theoretic framework for recursive meta-distillation, formalizing iterative knowledge distillation as a sequence of probability-distribution operators with explicit anchoring to base teachers. We define structural axioms for valid meta-teacher construction and prove the existence of non-trivial operator families satisfying these axioms without specifying particular algorithms or loss functions. Under mild realizability and convexity assumptions, we show that anchored recursive distillation induces contraction in KL divergence, yielding geometric convergence to base teacher distributions and a unique, globally attractive fixed point. The contribution is foundational rather than algorithmic: the framework characterizes when recursive distillation is mathematically well-posed and convergent rather than error-accumulating, independent of model architecture, optimization details, or specific operator instantiations. These results provide a theoretical basis for understanding stability, bias-variance behavior, and failure modes in iterative and multi-teacher distillation under capacity constraints.

Large language model (LLM) agents offer a promising data-driven approach to automating Site Reliability Engineering (SRE), yet their enterprise deployment is constrained by three challenges: restricted access to proprietary data, unsafe action execution under permission-governed environments, and the inability of closed systems to improve from failures. We present AOI (Autonomous Operations Intelligence), a trainable multi-agent framework formulating automated operations as a structured trajectory learning problem under security constraints. Our approach integrates three key components. First, a trainable diagnostic system applies Group Relative Policy Optimization (GRPO) to distill expert-level knowledge into locally deployed open-source models, enabling preference-based learning without exposing sensitive data. Second, a read-write separated execution architecture decomposes operational trajectories into observation, reasoning, and action phases, allowing safe learning while preventing unauthorized state mutation. Third, a Failure Trajectory Closed-Loop Evolver mines unsuccessful trajectories and converts them into corrective supervision signals, enabling continual data augmentation. Evaluated on the AIOpsLab benchmark, our contributions yield cumulative gains. (1) The AOI runtime alone achieves 66.3% best@5 success on all 86 tasks, outperforming the prior state-of-the-art (41.9%) by 24.4 points. (2) Adding Observer GRPO training, a locally deployed 14B model reaches 42.9% avg@1 on 63 held-out tasks with unseen fault types, surpassing Claude Sonnet 4.5. (3) The Evolver converts 37 failed trajectories into diagnostic guidance, improving end-to-end avg@5 by 4.8 points while reducing variance by 35%.

Iterative improvement of model architectures is fundamental to deep learning: Transformers first enabled scaling, and recent advances in model hybridization have pushed the quality-efficiency frontier. However, optimizing architectures remains challenging and expensive. Current automated or manual approaches fall short, largely due to limited progress in the design of search spaces and due to the simplicity of resulting patterns and heuristics. In this work, we propose a new approach for the synthesis of tailored architectures (STAR). Our approach combines a novel search space based on the theory of linear input-varying systems, supporting a hierarchical numerical encoding into architecture genomes. STAR genomes are automatically refined and recombined with gradient-free, evolutionary algorithms to optimize for multiple model quality and efficiency metrics. Using STAR, we optimize large populations of new architectures, leveraging diverse computational units and interconnection patterns, improving over highly-optimized Transformers and striped hybrid models on the frontier of quality, parameter size, and inference cache for autoregressive language modeling.

In offline multi-objective optimization (MOO), we leverage an offline dataset of designs and their associated labels to simultaneously minimize multiple objectives. This setting more closely mirrors complex real-world problems compared to single-objective optimization. Recent works mainly employ evolutionary algorithms and Bayesian optimization, with limited attention given to the generative modeling capabilities inherent in such data. In this study, we explore generative modeling in offline MOO through flow matching, noted for its effectiveness and efficiency. We introduce ParetoFlow, specifically designed to guide flow sampling to approximate the Pareto front. Traditional predictor (classifier) guidance is inadequate for this purpose because it models only a single objective. In response, we propose a multi-objective predictor guidance module that assigns each sample a weight vector, representing a weighted distribution across multiple objective predictions. A local filtering scheme is introduced to address non-convex Pareto fronts. These weights uniformly cover the entire objective space, effectively directing sample generation towards the Pareto front. Since distributions with similar weights tend to generate similar samples, we introduce a neighboring evolution module to foster knowledge sharing among neighboring distributions. This module generates offspring from these distributions, and selects the most promising one for the next iteration. Our method achieves state-of-the-art performance across various tasks.

The core challenge of high-dimensional and expensive black-box optimization (BBO) is how to obtain better performance faster with little function evaluation cost. The essence of the problem is how to design an efficient optimization strategy tailored to the target task. This paper designs a powerful optimization framework to automatically learn the optimization strategies from the target or cheap surrogate task without human intervention. However, current methods are weak for this due to poor representation of optimization strategy. To achieve this, 1) drawing on the mechanism of genetic algorithm, we propose a deep neural network framework called B2Opt, which has a stronger representation of optimization strategies based on survival of the fittest; 2) B2Opt can utilize the cheap surrogate functions of the target task to guide the design of the efficient optimization strategies. Compared to the state-of-the-art BBO baselines, B2Opt can achieve multiple orders of magnitude performance improvement with less function evaluation cost. We validate our proposal on high-dimensional synthetic functions and two real-world applications. We also find that deep B2Opt performs better than shallow ones.

Learning partial differential equations' (PDEs) solution operators is an essential problem in machine learning. However, there are several challenges for learning operators in practical applications like the irregular mesh, multiple input functions, and complexity of the PDEs' solution. To address these challenges, we propose a general neural operator transformer (GNOT), a scalable and effective transformer-based framework for learning operators. By designing a novel heterogeneous normalized attention layer, our model is highly flexible to handle multiple input functions and irregular meshes. Besides, we introduce a geometric gating mechanism which could be viewed as a soft domain decomposition to solve the multi-scale problems. The large model capacity of the transformer architecture grants our model the possibility to scale to large datasets and practical problems. We conduct extensive experiments on multiple challenging datasets from different domains and achieve a remarkable improvement compared with alternative methods. Our code and data are publicly available at https://github.com/thu-ml/GNOT.

The evolution of generative artificial intelligence (GenAI) constitutes a turning point in reshaping the future of technology in different aspects. Wireless networks in particular, with the blooming of self-evolving networks, represent a rich field for exploiting GenAI and reaping several benefits that can fundamentally change the way how wireless networks are designed and operated nowadays. To be specific, large language models (LLMs), a subfield of GenAI, are envisioned to open up a new era of autonomous wireless networks, in which a multimodal large model trained over various Telecom data, can be fine-tuned to perform several downstream tasks, eliminating the need for dedicated AI models for each task and paving the way for the realization of artificial general intelligence (AGI)-empowered wireless networks. In this article, we aim to unfold the opportunities that can be reaped from integrating LLMs into the Telecom domain. In particular, we aim to put a forward-looking vision on a new realm of possibilities and applications of LLMs in future wireless networks, defining directions for designing, training, testing, and deploying Telecom LLMs, and reveal insights on the associated theoretical and practical challenges.

Large Language Models (LLMs) have shown remarkable performance in automated code generation. However, existing approaches often rely heavily on pre-defined test cases, which become impractical in scenarios where such cases are unavailable. While prior works explore filtering techniques between programs and test cases, they overlook the refinement of test cases. To address this limitation, we introduce CoCoEvo, a novel LLM-based co-evolution framework that simultaneously evolves programs and test cases. CoCoEvo eliminates the dependency on pre-defined test cases by generating both programs and test cases directly from natural language problem descriptions and function headers. The framework employs specialized evolutionary operators, including LLM-based crossover and mutation operators for program evolution, along with a test case generation operator for test case evolution. Additionally, we propose optimization strategies such as a crossover rate scheduler to balance exploration and convergence, and a multi-objective optimization method for test case selection. Experimental results on multiple state-of-the-art LLMs demonstrate that CoCoEvo surpasses existing methods, achieving state-of-the-art performance in automated code generation and testing. These results underscore the potential of co-evolutionary techniques in advancing the field of automated programming.

In this work, we propose marginalized operators, a new class of off-policy evaluation operators for reinforcement learning. Marginalized operators strictly generalize generic multi-step operators, such as Retrace, as special cases. Marginalized operators also suggest a form of sample-based estimates with potential variance reduction, compared to sample-based estimates of the original multi-step operators. We show that the estimates for marginalized operators can be computed in a scalable way, which also generalizes prior results on marginalized importance sampling as special cases. Finally, we empirically demonstrate that marginalized operators provide performance gains to off-policy evaluation and downstream policy optimization algorithms.

Pre-trained language models like ChatGPT have significantly improved code generation. As these models scale up, there is an increasing need for the output to handle more intricate tasks. Moreover, in bioinformatics, generating functional programs poses additional notable challenges due to the amount of domain knowledge, the need for complicated data operations, and intricate functional dependencies between the operations. Here, we present BioCoder, a benchmark developed to evaluate existing pre-trained models in generating bioinformatics code. In relation to function-code generation, BioCoder covers potential package dependencies, class declarations, and global variables. It incorporates 1026 functions and 1243 methods in Python and Java from GitHub and 253 examples from the Rosalind Project. BioCoder incorporates a fuzz-testing framework for evaluation, and we have applied it to evaluate many models including InCoder, CodeGen, CodeGen2, SantaCoder, StarCoder, StarCoder+, InstructCodeT5+, and ChatGPT. Our detailed analysis of these models emphasizes the importance of domain knowledge, pragmatic code generation, and contextual understanding. Our dataset, benchmark, Docker images, and scripts required for testing are all available at https://github.com/gersteinlab/biocoder.

Conventional agent systems often struggle in open-ended environments where task distributions continuously drift and external supervision is scarce. Their reliance on static toolsets or offline training lags behind these dynamics, leaving the system's capability boundaries rigid and unknown. To address this, we propose the In-Situ Self-Evolving paradigm. This approach treats sequential task interactions as a continuous stream of experience, enabling the system to distill short-term execution feedback into long-term, reusable capabilities without access to ground-truth labels. Within this framework, we identify tool evolution as the critical pathway for capability expansion, which provides verifiable, binary feedback signals. Within this framework, we develop Yunjue Agent, a system that iteratively synthesizes, optimizes, and reuses tools to navigate emerging challenges. To optimize evolutionary efficiency, we further introduce a Parallel Batch Evolution strategy. Empirical evaluations across five diverse benchmarks under a zero-start setting demonstrate significant performance gains over proprietary baselines. Additionally, complementary warm-start evaluations confirm that the accumulated general knowledge can be seamlessly transferred to novel domains. Finally, we propose a novel metric to monitor evolution convergence, serving as a function analogous to training loss in conventional optimization. We open-source our codebase, system traces, and evolved tools to facilitate future research in resilient, self-evolving intelligence.

Recent image generation models have shown strong capabilities in generating high-fidelity and photorealistic images. However, they are fundamentally constrained by frozen internal knowledge, thus often failing on real-world scenarios that are knowledge-intensive or require up-to-date information. In this paper, we present Gen-Searcher, as the first attempt to train a search-augmented image generation agent, which performs multi-hop reasoning and search to collect the textual knowledge and reference images needed for grounded generation. To achieve this, we construct a tailored data pipeline and curate two high-quality datasets, Gen-Searcher-SFT-10k and Gen-Searcher-RL-6k, containing diverse search-intensive prompts and corresponding ground-truth synthesis images. We further introduce KnowGen, a comprehensive benchmark that explicitly requires search-grounded external knowledge for image generation and evaluates models from multiple dimensions. Based on these resources, we train Gen-Searcher with SFT followed by agentic reinforcement learning with dual reward feedback, which combines text-based and image-based rewards to provide more stable and informative learning signals for GRPO training. Experiments show that Gen-Searcher brings substantial gains, improving Qwen-Image by around 16 points on KnowGen and 15 points on WISE. We hope this work can serve as an open foundation for search agents in image generation, and we fully open-source our data, models, and code.

We explore efficient neural architecture search methods and show that a simple yet powerful evolutionary algorithm can discover new architectures with excellent performance. Our approach combines a novel hierarchical genetic representation scheme that imitates the modularized design pattern commonly adopted by human experts, and an expressive search space that supports complex topologies. Our algorithm efficiently discovers architectures that outperform a large number of manually designed models for image classification, obtaining top-1 error of 3.6% on CIFAR-10 and 20.3% when transferred to ImageNet, which is competitive with the best existing neural architecture search approaches. We also present results using random search, achieving 0.3% less top-1 accuracy on CIFAR-10 and 0.1% less on ImageNet whilst reducing the search time from 36 hours down to 1 hour.

Data Darwinism (Part I) established a ten-level hierarchy for data processing, showing that stronger processing can unlock greater data value. However, that work relied on manually designed strategies for a single category. Modern pretraining corpora comprise hundreds of heterogeneous categories spanning domains and content types, each demanding specialized treatment. At this scale, manual strategy design becomes prohibitive. This raises a key question: can strategies evolve in an automated way? We introduce DataEvolve, a framework that enables strategies to evolve through iterative optimization rather than manual design. For each data category, DataEvolve operates in a closed evolutionary loop: it identifies quality issues, generates candidate strategies, executes them on sampled data, evaluates results, and refines approaches across generations. The process accumulates knowledge through an experience pool of discovered issues and a strategy pool tracking performance across iterations. Applied to 8 categories spanning 672B tokens from Nemotron-CC, DataEvolve produces Darwin-CC, a 504B-token dataset with strategies evolved through 30 iterations per category. Training 3B models on 500B tokens, Darwin-CC outperforms raw data (+3.96 points) and achieves a 44.13 average score across 18 benchmarks, surpassing DCLM, Ultra-FineWeb, and FineWeb-Edu, with strong gains on knowledge-intensive tasks such as MMLU. Analysis shows evolved strategies converge on cleaning-focused approaches: targeted noise removal and format normalization with domain-aware preservation, echoing the L4 (Generative Refinement) principles from Part I. Ablation studies confirm iterative evolution is essential: optimized strategies outperform suboptimal ones by 2.93 points, establishing evolutionary strategy design as feasible and necessary for pretraining-scale data curation.

kooplearn is a machine-learning library that implements linear, kernel, and deep-learning estimators of dynamical operators and their spectral decompositions. kooplearn can model both discrete-time evolution operators (Koopman/Transfer) and continuous-time infinitesimal generators. By learning these operators, users can analyze dynamical systems via spectral methods, derive data-driven reduced-order models, and forecast future states and observables. kooplearn's interface is compliant with the scikit-learn API, facilitating its integration into existing machine learning and data science workflows. Additionally, kooplearn includes curated benchmark datasets to support experimentation, reproducibility, and the fair comparison of learning algorithms. The software is available at https://github.com/Machine-Learning-Dynamical-Systems/kooplearn.

Predicting high-dimensional transcriptional responses to genetic perturbations is challenging due to severe experimental noise and sparse gene-level effects. Existing methods often suffer from mean collapse, where high correlation is achieved by predicting global average expression rather than perturbation-specific responses, leading to many false positives and limited biological interpretability. Recent approaches incorporate biological knowledge graphs into perturbation models, but these graphs are typically treated as dense and static, which can propagate noise and obscure true perturbation signals. We propose AdaPert, a perturbation-conditioned framework that addresses mean collapse by explicitly modeling sparsity and biological structure. AdaPert learns perturbation-specific subgraphs from biological knowledge graphs and applies adaptive learning to separate true signals from noise. Across multiple genetic perturbation benchmarks, AdaPert consistently outperforms existing baselines and achieves substantial improvements on DEG-aware evaluation metrics, indicating more accurate recovery of perturbation-specific transcriptional changes.

Retrieval-augmented generation (RAG) systems enhance large language models by incorporating external knowledge, addressing issues like outdated internal knowledge and hallucination. However, their reliance on external knowledge bases makes them vulnerable to corpus poisoning attacks, where adversarial passages can be injected to manipulate retrieval results. Existing methods for crafting such passages, such as random token replacement or training inversion models, are often slow and computationally expensive, requiring either access to retriever's gradients or large computational resources. To address these limitations, we propose Dynamic Importance-Guided Genetic Algorithm (DIGA), an efficient black-box method that leverages two key properties of retrievers: insensitivity to token order and bias towards influential tokens. By focusing on these characteristics, DIGA dynamically adjusts its genetic operations to generate effective adversarial passages with significantly reduced time and memory usage. Our experimental evaluation shows that DIGA achieves superior efficiency and scalability compared to existing methods, while maintaining comparable or better attack success rates across multiple datasets.

The paradigm of automated program generation is shifting from one-shot generation to inference-time search, where Large Language Models (LLMs) function as semantic mutation operators within evolutionary loops. While effective, these systems are currently governed by static schedules that fail to account for the non-stationary dynamics of the search process. This rigidity results in substantial computational waste, as resources are indiscriminately allocated to stagnating populations while promising frontiers remain under-exploited. We introduce AdaEvolve, a framework that reformulates LLM-driven evolution as a hierarchical adaptive optimization problem. AdaEvolve uses an "accumulated improvement signal" to unify decisions across three levels: Local Adaptation, which dynamically modulates the exploration intensity within a population of solution candidates; Global Adaptation, which routes the global resource budget via bandit-based scheduling across different solution candidate populations; and Meta-Guidance which generates novel solution tactics based on the previously generated solutions and their corresponding improvements when the progress stalls. We demonstrate that AdaEvolve consistently outperforms the open-sourced baselines across 185 different open-ended optimization problems including combinatorial, systems optimization and algorithm design problems.

Deep Neural Networks (DNNs) are generated by sequentially performing linear and non-linear processes. Using a combination of linear and non-linear procedures is critical for generating a sufficiently deep feature space. The majority of non-linear operators are derivations of activation functions or pooling functions. Mathematical morphology is a branch of mathematics that provides non-linear operators for a variety of image processing problems. We investigate the utility of integrating these operations in an end-to-end deep learning framework in this paper. DNNs are designed to acquire a realistic representation for a particular job. Morphological operators give topological descriptors that convey salient information about the shapes of objects depicted in images. We propose a method based on meta-learning to incorporate morphological operators into DNNs. The learned architecture demonstrates how our novel morphological operations significantly increase DNN performance on various tasks, including picture classification and edge detection.