Quentin Ducasse

Pascal Cotret

Loïc Lagadec

Rob Stewart

Benchmarking Quantized Neural Networks on FPGAs with FINN

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Benchmarking Quantized Neural Networks on

FPGAs with FINN Abstract-The ever-growing cost of both training and inference for state-of-the-art neural networks has brought literature to look upon ways to cut off resources used with a minimal impact on accuracy. Using lower precision comes at the cost of negligible loss in accuracy. While training neural networks may require a powerful setup, deploying a network must be possible on lowpower and low-resource hardware architectures. Reconfigurable architectures have proven to be more powerful and flexible than GPUs when looking at a specific application. This article aims to assess the impact of mixed-precision when applied to neural networks deployed on FPGAs. While several frameworks exist that create tools to deploy neural networks using reduced-precision, few of them assess the importance of quantization and the framework quality. It is used on top of FINN and Brevitas, two frameworks from Xilinx labs, to assess the impact of quantization on neural networks using 2 to 8 bit precisions and weights with several parallelization configurations. The benchmark set up in this work is available in a public repository (https://github.com/QDucasse/ nn\ benchmark).

Index Terms-Machine Learning, Neural Networks, Mixed Precision, FPGA

I. INTRODUCTION

Convolutional Neural Networks (CNNs) have gained a rising interest in the field of machine learning. Their deployment to embedded devices is now at the heart of the discussions. Many low-power low-memory IoT devices require to run image classification or voice recognition tasks. Running a CNN inference requires the host device to both hold the network itself and then run the billion of operations an inference implies. Reducing and optimizing this memory and power footprint has been the focus of literature in recent years.

Using a neural network requires a previous phase of Training that should only be done once and can be performed on powerful architectures (clusters of GPUs for example). Then the network goes through a Deployment phase to the target architecture which can be a low-cost device. Moreover, the deployed network should then be able to perform an Inference phase each time a new instance needs to be classified. While Training is only done once, Inference is repeated through the application and should be optimized.

While architecture such as CPUs or GPUs are used to perform the different steps, FPGAs and their natural reducedprecision capabilities seem to perform the best. Mixed-precision (or reduced precision) consists in using numbers representations that require less space to map a number, often at the cost of some precision loss. Going from full 64-bits floating-points to their single-precision (32-bits) or half-precision (16-bits) is a way to reduce the space of numbers in the application. As well as providing an answer to the space issue, there is a tight relation between the numbers representation used and the costs of the operations in terms of memory and power [START_REF] Horowitz | 1.1 computing's energy problem (and what we can do about it)[END_REF], [START_REF] Dally | High-performance hardware for machine learning[END_REF]. Figure 1 shows that increasing precision on the numbers used increases the relative energy cost accordingly. An 8-bit addition costs 0.03 pJ whereas the same addition in 32-bit floating-point costs 0.9 pJ or 30 times more. Fig. 1: Cost of operations in certain representations [START_REF] Horowitz | 1.1 computing's energy problem (and what we can do about it)[END_REF], [START_REF] Dally | High-performance hardware for machine learning[END_REF].

In the field of machine learning, this results in a new type of networks named Quantized Neural Networks (QNNs) [START_REF] Hubara | Quantized neural networks: Training neural networks with low precision weights and activations[END_REF] and their extreme versions, Binarized Neural Networks (BNNs) [START_REF] Courbariaux | Binaryconnect: Training deep neural networks with binary weights during propagations[END_REF], [START_REF] Courbariaux | Binarized neural networks: Training deep neural networks with weights and activations constrained to+ 1 or-1[END_REF] or XNOR-Net [START_REF] Rastegari | Xnor-net: Imagenet classification using binary convolutional neural networks[END_REF]. This type of network is gaining momentum as the overgrowing size of network architectures needs to perform the best on the smallest end architectures. Google Tensorflow Lite (tensorflow.org/lite) can reduce fullprecision networks to 8-bit counterparts. Intel Distiller works as a compression framework over PyTorch [START_REF] Zmora | Neural network distiller: a python package for dnn compression research[END_REF]. Moreover, recent iterations over PyTorch itself to provide the users with means to define QNNs [START_REF] Krishnamoorthi | Quantization in pytorch[END_REF] show the need for quantization, even in industry led neural network frameworks.

Quantization comes as one of the many optimization methods for CNNs. It consists of a type of network compression and uses data type as the main focus for its compression. Other compression methods might involve pure compression through a hash function grouping similar connections and weights [START_REF] Chen | Compressing neural networks with the hashing trick[END_REF] or pruning, where a trade-off objective is set and a pruning routine is used to remove the least important neurons until the objective is met [START_REF] Han | Deep compression: Compressing deep neural networks with pruning, trained quantization and huffman coding[END_REF], [START_REF] Molchanov | Pruning convolutional neural networks for resource efficient inference[END_REF]. Those methods can keep an important accuracy while reducing effectively the network size. Even if recent efforts can be noticed in the literature with a combination of several optimization techniques [START_REF] Paupamah | Quantisation and pruning for neural network compression and regularisation[END_REF], this paper will exclusively focus on quantization.

On the other hand, neural network frameworks are developed focusing on FPGA deployment. Early iterations can be noted [START_REF] Andri | Yodann: An architecture for ultralow power binary-weight cnn acceleration[END_REF], [START_REF] Zhao | F-cnn: An fpga-based framework for training convolutional neural networks[END_REF] but are not actively maintained or open-source, therefore restricting their use. However, FPGAConvNet [START_REF] Venieris | fpgaConvNet: Automated mapping of convolutional neural networks on fpgas[END_REF] provides a way to deploy CNNs on FPGAs. Xilinx FINN [START_REF] Umuroglu | Finn: A framework for fast, scalable binarized neural network inference[END_REF] is another framework to port neural networks on FPGAs and has been extended to QNNs and BNNs [START_REF] Blott | Finn-r: An end-to-end deeplearning framework for fast exploration of quantized neural networks[END_REF], as well as Long-Short Term Memory Neural Networks (LSTM) [START_REF] Rybalkin | Finn-l: Library extensions and design trade-off analysis for variable precision lstm networks on fpgas[END_REF]. The support of the different networks come through Brevitas [START_REF] Pappalardo | Xilinx/brevitas: Cnv test reference vectors r0[END_REF], a quantization-aware trainer facility built as a drop-in replacement of PyTorch and tightly linked to FINN.

While other optimization methods exist such as pruning, this paper focuses on the trade-off between accuracy and FPGA resource requirements that the underlying number representation presupposes. The design space explored is the evaluation of QNNs with varying bit-width values for their weights and activations. This design space is important to benchmark as very few initiatives exist to compare frameworks and quantizations between them [START_REF] Blott | Qutibench: Benchmarking neural networks on heterogeneous hardware[END_REF], [START_REF] Blott | Evaluation of optimized cnns on heterogeneous accelerators using a novel benchmarking approach[END_REF].

In this paper, we present the development and setup of an overlay of the Xilinx framework FINN and the Quantized Neural Network (QNN) trainer facility Brevitas to port QNNs on FPGAs. This overlay is then used to assess the impact of quantization on several metrics, both from an accuracy and hardware utilization perspective. The closest related work to our benchmarking detailed in Section III is the work proposed by Bacchus et al. [START_REF] Bacchus | Accuracy, training time and hardware efficiency trade-offs for quantized neural networks on fpgas[END_REF]: this paper proposes a more detailed analysis where several parallelization configurations are explored in order to find the best compromise between quantization parameters and neural networks hardware configurations. Moreover, the framework used by Bacchus et al. has now been archived by the Xilinx team while FINN and Brevitas are in active development.

The rest of the paper is organized as follows. Section II presents the background of the project, the FINN workflow as well as quantization methods through the trainer Brevitas. Section III presents the experimental setup (topology, platform, methodology) as well as the results of the benchmarking. Conclusions are given in Section IV with future works aspirations.

II. BACKGROUND A. FINN Workflow

While several initiatives have been created to port QNNs on FPGAs, few benchmarks are provided between the frameworks or on a common ground. Moreover, few projects can be reused outside of the authors initial work due to the lack of open-source code. A need to benchmark the different FPGA frameworks emerges as there are few comparison between actual FPGA implementations. Only FINN, maintained by Xilinx can be used freely and is in active development. The benchmark will be performed on this particular framework for now. FINN uses the model produced by Brevitas, a quantized neural networks trainer and designer developed by Xilinx as well on top of PyTorch. By first going through Brevitas, the quantized neural network is translated into the intermediate representation, ONNX. The resulting intermediate representation can then be imported by FINN. FINN will perform several transformations and deploy part of the resulting graph on the associated FPGA. To summarize, the workflow is the following: Brevitas for Training, ONNX as the Intermediate Representation and FINN for Network Restructuration, HLS Synthesis and Deployment.

1) Brevitas: Brevitas (xilinx.github.io/brevitas) has been developed with the idea of corresponding to a drop-in replacement of PyTorch. This means that it ensures that PyTorch functionalities will be preserved, even when working with reduced-precision layers. Brevitas implements a set of building blocks to model a reduced precision hardware data-path at training time. While partially biased towards modelling dataflow-style, very low-precision implementations, building blocks can be parametrised and assembled together to target all sorts of reduced precision hardware. Once the neural network is defined and trained, Brevitas provides a way to export it as the intermediate representation. This representation is the focus of the next subsection and will be looked into in more details later on. Brevitas uses specific annotations to define the quantized layers. The intermediate representation, called ONNX does not provide a way to represent layers with precisions under 8 bits: this is why this system of custom annotations has been created. These specific annotations are then be used by FINN to detect the quantization and perform adequate transformations on the layers. An example of the linear layer (FC) and the hyperbolic tangent activation function using PyTorch and Brevitas is shown in Figure 2. This piece of code presents the definition of two sequences of layers as defined in the Sequential class in Pytorch. In addition, Brevitas quantized layers allow the user to choose the bitwidth (iėṗrecision) needed with the additional bit_width argument.

2) ONNX: The Open Neural Network Exchange ONNX (onnx.ai) project provides an open-source format for artificial intelligence and machine learning models. This is done by defining an extensible computation graph model, as well as definitions of operators and data types. ONNX is widely supported in different machine learning frameworks and tools. The main goal behind its design and development was to enable interoperability between different machine learning frameworks to streamline the path between research and production.

3) FINN: FINN workflow (xilinx.github.io/finn) itself is decoupled in several phases. First, Network Preparation where FINN uses different transformations on the ONNX graph to simplify it or make it more convenient for the next steps. Then, IP Generation where the Vivado tool is called to generate a network of High-Level Synthesis (HLS) layers with one Semiconductor Intellectual Property (IP) block per layer and finally stitches all the blocks together. Finally, the network is deployed on an FPGA with a PYNQ shell which is a FPGA utility providing a Python environment on an FPGA. This deployment is made possible by creating a project and driver then transferring it on the board along with the bitfile.

B. Quantization

The idea of quantization is to reduce 32-or 64-bits continuous values to discrete values using a reduced amount of bits. In a neural network, the two types of values that can be quantized are the weights and the activations. Weights are the "shifting" objects in neural networks. While their initial value is either null or randomized, it is then modified by each backpropagation pass of the training phase. Activations on the other side consist of non-linear function outputs that allows simple networks to perform better on non linear data.

The quantization of weights is done using the provided bitwidth to determine a minimum and maximum integer values to perform clamping and scaling to redistribute the floatingpoint values to their nearest rounded k-bit representation. On the other hand, the quantization of activations is done using successive thresholding. For each pair of possible activation, a thresholding value is used in between. When a new value has to be run through the activation, it is simply compared to the thresholds and returns the number of threshold value that the input exceeds. The initial value in the thresholds comes from how the quantized activation is trained in Brevitas. FINN then performs a series of transformation on the trained network representation and among these transformation is a streamline process [START_REF] Umuroglu | Streamlined deployment for quantized neural networks[END_REF]. This process will scale and bias thresholds using scaling factors and results from the Batch Normalization layers and finally will round them up to the nearest number in the given representation.

C. Folding

There is a parallel that needs to be made between the software implementation of a neural network and its hardware counterpart. The software version consists of a succession of layers with a data instance being passed and transformed from a layer to the next. The hardware architecture consists of dataflow with streaming. HLS streams (FIFOs) are used to communicate between layers and each layer is always running, waiting to perform its computation as soon as possible. The number of PE, SIMD and the FIFO depth can be chosen by hand and set in the FINN workflow.

Defining specific folding factors allows the user to obtain the most out of its FPGA considering the incoming network architecture and quantization. While, in this paper, those factors have remained constant for comparison purposes, they should be tuned according to the desired performance. This sizing will soon be automated inside of FINN. This will be done by running a simulation of the Register Transfer Level and determining the maximal occupancy of FIFOs.

The folding and parallelization will occur for specific layers such as the Fully-Connected ones. The two controllable degrees of parallelism are the Multiply Accumulate (MACs) inside a single product through the Single Instruction Multiple Data (SIMD) and the inner products in parallel through the Physical Element (PE). The software representation of this parallelism can be seen on Figure 3 where the two levels can be used to process the pixels of an image in parallel in an FC layer. Its direct counterpart is presented on Figure 4 where the different SIMD lanes and PEs translate the parallelism. Fig. 3: Folding factors in an FC layer [START_REF] Gambardella | Finn deep dive: Hw scheduling and folding[END_REF].

Fig. 4: Folding in Hardware [START_REF] Gambardella | Finn deep dive: Hw scheduling and folding[END_REF].

III. EXPERIMENTS

A. Benchmark Implementation and hardware target

In order to design a benchmark of the framework and to assess the impact of quantization, there is a need for another layer on top of Brevitas that should be able to train, evaluate and export neural networks. While Xilinx developers provide several examples to train and export neural networks, they do not respect a common API nor the same structure rules. They are bundled in separate projects with instructions on how to run the training again but no insight is provided on what hardcoded values mean on several quantized layers.

The different objectives of the benchmark are to Present a common API to train neural networks, quantized or not; be able to Resume the training at any point; Log the different parts of the training, Define well-known neural networks and their quantized counterparts; Set an easy access to well-known datasets; Provide a common API to evaluate neural networks; be able to Export the trained neural network to ONNX.

The hardware platform used in this work is the Pynq-Z1 board including a Zynq Z-7020 device: it includes 13,300 slices, 106,400 flip-flops and 630KB Block RAMs. The enviroment development used Vivado 2019.2, ONNX 1.5.0, Brevitas and FINN as previously described.

B. Experiments Methodology 1) Topology and Dataset:

The machine learning image recognition field features a wide variety of benchmarks consisting of famous datasets against which specific network architectures are run. Most famous ones are MNIST, CIFAR-10 and Imagenet. The number of networks and their variations is thriving as well, each year presenting new networks, outperforming the predecessors. Striving for simplicity, the choice of the network architecture is conducted towards a variation of a Multilayer Perceptron (MLP) network with three Fully-Connected (FC) layers and HardTanh activations. The dataset on which this network performs is Fashion-MNIST [START_REF] Xiao | Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms[END_REF] dataset with images resized to 32 × 32 pixels. This dataset is an extension of MNIST [START_REF] Lecun | MNIST handwritten digit database[END_REF] and makes it harder for simpler architecture to classify instances while keeping the same datatype. The network is Multi-Layer Perceptron using Dropout, Fully-Connected (FC) and Batch Normalization layers. The activation used is Hard Hyperbolic Tangent and is used before the Dropout layers.

2) Parameters and Hyper-parameters: Training of the different networks is conducted with the parameters and hyperparameters shown in Table I Along with those parameters, the bit-widths of weights and activations are chosen from 2 to 8 bits. Inputs layers are always quantized to 8 bits: using higher inputs precisions over the other quantizations will improve the end accuracy at very little cost. The deployment step is performed through the different FINN transformations. While the training is performed with differentiated bit-widths for weights and activations, only the models with no differences between the weights and activations are conducted through the deployment step. While Bacchus et al. [START_REF] Bacchus | Accuracy, training time and hardware efficiency trade-offs for quantized neural networks on fpgas[END_REF] differentiate the bit-widths in the deployment step, this functionality is only very recently supported in FINN.

While all networks with the different bit-width combinations (2 to 8 bits) have been trained, only a subset has been deployed. Only networks with identical bit-width for activations and weights have been run through the transformation and deployment process. Out of the 7 networks (2-to 8-bit activations and weights), only the 8-bit version was not deployed due to its size. It is important to note that the exact same folding technique has been applied to all the different networks for comparison purposes. The same comparison could be conducted using the soon-available automated folding feature from FINN.

C. Results

1) Accuracy over Time: Using the configuration presented above, all the networks are trained. Every each holds a different combination of bit-widths for weights and activations. Those bitwidths range from 2 to 8 and the network using 2-bit activations and 5-bit weights will be called A2W5 for the rest of the paper. Figures 5a and5b presents the evolution of the error rate of each network against the number of epochs used in the training. The bit-widths of activations and weights are differentiated in order to assess their impact separately. The more training the network gets, the more precise it becomes. The difference becomes less and less important over time and finally reaches 88%, a state-of-the-art result for this type of network. The 49 different implementations present a tendency for the weight bit-width to dictate the performance while the activation bit-width presents no consistent variations. Figures 6a and6b presents separately the variations in performance for several weights and activations bit-widths. For clarity purposes, only two sets of networks are presented, after 40 epochs of training and after 100 epochs of training. They highlight two important results. First, the weight bit-width seems to be much more impactful on the overall performance than the activation bit-width. Next, the training time can make lower-bits implementations meet the performance of higher-bits implementations. In the example, the 64 implementations are presented after 40 and 100 epochs. The 2-bit representation obtains the same error rate after 100 epochs than the 8-bit representation after 40 epochs.

2) Hardware Resource Utilization: Once trained, networks with the same bit-widths for activations and weights are deployed to the PYNQ board. This deployment is done using the same folding factors for comparison purposes and results in a synthesis and implementation for each network. While the implementation is not possible for the A8W8 network, its synthesis report still allows us to look at the potential hardware utilization. The two main areas that an application uses on an FPGA are classified under logic and memory.

Regarding logic, the number of LUTs and FFs is compared over all the implementations. The comparison is made in Figure 7a. The hardware utilization on the logic side is intuitive: the higher the bit-width, the higher the number of LUTs and FFs required. The growth in hardware requirements is linear up until 6 bits where higher representations require even more resources.

Regarding memory requirements, the amount of BRAM used is compared in Figure 7b. The memory utilization shows an important use of RAMB18 when the representation exceeds 7 bits. This is due to the way FINN represents activations: as presented in Section II-B, each pair of potential output from the quantized activation is separated by a threshold value. This means that for k-bit activations, FINN needs 2 k -1 threshold values and therefore that the storage for threshold values grows exponentially when the activation bit-width grows. This thresholding method is more detailed by Umuroglu et al. in [START_REF] Umuroglu | Streamlined deployment for quantized neural networks[END_REF] along with the streamlining process to reduce layer operations.

3) Throughput: FINN provides a default API to perform a remote throughput test in the network once the network is deployed. This test is run with a batch size of 10,000 instances in order to measure both the throughput and DRAM In bandwidth. The ability of a network to quickly process an input directly comes from the parallelization factors set in each of the layers. As presented earlier in Section II-C, PE and SIMD can be chosen to determine the "folding" of each layer. In Table II Note that out of all the implementations, A4W4 using parallelization factors of 16/16 could not be deployed on the target board as the design was too large to fit in the Pynq-Z1, this is represented as Not Applicable (N/A). Among the different configurations (A2W2, A3W3, A4W4), no significant difference can be highlighted. The variation of PE/SIMD is the only reason for throughput variation, weights and activation bit-widths do not have an impact on those results.

To assess the impact of PE and SIMD variations, we have taken the A3W3 configuration and created 9 variations with different combinations of PE and SIMD instances. The results can be seen in The throughput logic is tightly linked to the parallelization factors since the higher they are, the higher the throughput and DRAM bandwidth will be. A3W3 still comes out as a good compromise since it allows parallelization factors up to 16 for both PE and SIMD simultaneously and therefore gets the highest output possible with a correct accuracy as stated earlier.

D. Discussion

These experiments confirm observations made by Bacchus et al. [START_REF] Bacchus | Accuracy, training time and hardware efficiency trade-offs for quantized neural networks on fpgas[END_REF] that no important improvement is made in accuracy using beyond 3-bit representations. The eventual difference in accuracy can be covered up with enough training. The experiments highlight that:

• Accuracy is linked to the weight bit-width: the higher the weight precision, the higher the overall accuracy. • Activation bit-width has less importance on the overall accuracy. • Hardware utilization grows exponentially due to the successive thresholding method used for activation quantization.

• Training can cover up accuracy gaps between more and less precise representations. For example, the 2-bit weights implementations trained on Fashion-MNIST reach the same accuracy after 100 epochs than their 8-bit counterparts after 40 epochs. • Throughput and DRAM bandwidth are tied to the parallelization factors, the higher the PE and SIMD, the higher the throughput and bandwidth. An important note is that the Folding Factors used have remained the same for all the deployed implementations. While this was done for comparison purposes, it might not show the best version of lower bit-width representations. Those representation often use a small part of the target board and most of them (especially the 2-and 3-bit representations) could be better parallelized. Overall, the lowest representation implementations outperform most of their 7-or 8-bit counterparts in terms of hardware utilization, throughput and can reach a tie in accuracy given enough training.

IV. CONCLUSION CNNs are getting more and more complex in terms of architecture and costly in terms of training, inference and deployment. Interest on compression techniques has grown up in the past years. Porting ever-growing network architectures on low-power low-memory hardware architectures is still of key interest. While several methods to both and separately quantize and deploy neural networks on specific hardware architectures, very few benchmarks have been led to compare the different quantization and deployment benchmarks among them [START_REF] Blott | Qutibench: Benchmarking neural networks on heterogeneous hardware[END_REF], [START_REF] Blott | Evaluation of optimized cnns on heterogeneous accelerators using a novel benchmarking approach[END_REF].

This paper presents an open-source (github.com/QDucasse/ nn benchmark) and extensible trainer, built over FINN [START_REF] Umuroglu | Finn: A framework for fast, scalable binarized neural network inference[END_REF], [START_REF] Blott | Finn-r: An end-to-end deeplearning framework for fast exploration of quantized neural networks[END_REF] and Brevitas, to train QNNs on any dataset. This tool is used to assess the impact of quantization on 49 implementations of an MLP network trained on both MNIST and Fashion-MNIST. While only a subset of those implementations has been deployed on an FPGA board, results still show that enough training on a lower-precision network will make it comparable to its 8-bits counterpart while keeping hardware utilization low and throughput high. A3W3 seems to be the best compromise between the different representations.

Future works may come from several steps out of the experiments. First, using well-known network architectures is extremely important as they have been thoroughly studied and benchmarked. The same goes for the datasets and requires no effort from the Brevitas development team as it is already available in PyTorch. While any network can be trained on any dataset for now, the issue comes from the latter parts of the workflow. FINN does not cover all the layer configurations for now and additional benchmarks will need to be conducted to cover the new architectures and their coupled datasets. On the other hand, comparison with classic quantization and compression frameworks (i.e. that do not require to be deployed on an FPGA board) would be interesting. Working with Intel Distiller [START_REF] Zmora | Neural network distiller: a python package for dnn compression research[END_REF] for example or the newly added quantization packages in PyTorch or TensorFlow could help broaden the comparison.

Fig. 2 :

 2 Fig. 2: Layers comparison between PyTorch and Brevitas.

  (a) MNIST dataset. (b) Fashion-MNIST dataset.

Fig. 5 :

 5 Fig. 5: Networks error rate over time.

  (a) MNIST dataset. (b) Fashion-MNIST dataset.

Fig. 6 :

 6 Fig. 6: Weights and activations impact.

Fig. 7 :

 7 Fig. 7: Hardware resources.

  .

	Name	Chosen Value	Motivation
	Network	Multilayer	Simplest network
	Architecture	Perceptron (MLP)	architecture
	Dataset	MNIST [26] Fashion-MNIST [25]	Simplest dataset Harder iteration
	Epochs	100	[22], [27]
	Momentum	0.9	[22], [27]
	Learning Rate (LR)	0.01	[22], [27]
	Scheduler	Multi-step LR × 0.1 at epochs 90 and 95	[27]
	Batch Size	100 instances per batch	Common choice for MLP/MNIST
	Loss Function	Cross Entropy	Common choice for MLP/MNIST
	Optimizer	ADAM	[28]

TABLE I :

 I Parameters and Hyper-parameters tuning.

  , configurations A2W2, A3W3 and A4W4 are used with numbers of PE and SIMD both set to either 2, 8 and 16.

	Configuration	PE/SIMD	Throughput [img/s]	DRAM In Bandwidth [Mb/s]
		2/2	6,100	6.24
	A2W2	8/8	96,5334	98.85
		16/16	373,112	382.06
		2/2	6,099	6.24
	A3W3	8/8	96,533	98.85
		16/16	372,877	381.82
		2/2	6,099	6.24
	A4W4	8/8	96,512	98.82
		16/16	N/A	N/A

TABLE II :

 II Throughput and DRAM In bandwidths with varying PE/SIMD.

Table

  III and highlight an important fact: no clear separation can be made between the impact of the PE and SIMD values (e.g. the results of the combinations 2/8 and 8/2 or 2/16 and 16/2 are extremely similar).

	SIMD	PE	2	8	16
	2		6,098	24,343	48,545
	8		24,347	96,533	190,869
	16		48,569	190,935	372,877

TABLE III :

 III Throughput with varying PE/SIMD in the A3W3 configuration.

V. ACKNOWLEDGMENTS This project has been supported by the French Directorate General od Armaments (DGA), the European Regional Development Fund (ERDF) of the European Union, the Brittany Region (France), the Departmental Council of Finistere and Brest Metropole as part of the Cyber-SSI project within the framework of the Brittany 2015-2020 State-Region Contract (CPER).


Mégane Muschi

Anusha Lalitha

Saad Sene

Damien Aureau

Mathieu Frégnaux

Imène Esteve

Lucie Rivier

Naseem Ramsahye

Sabine Devautour-Vinot

Clémence Sicard

Formation of a Single-Crystal Aluminum-Based MOF Nanowire with Graphene Oxide Nanoscrolls as Structure-Directing Agents

Keywords: metal-organic frameworks, graphene oxide, nanowire, self-assembly, template

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Formation of Single Crystal Aluminum-based MOF Nanowire with Graphene Oxide Nanoscrolls as Structure-Directing Agents

Mégane Muschi, [a] Anusha Lalitha, [b] Saad Sene, [a] Damien Aureau, [c] Mathieu Fregnaux, [c] Imène Esteve [d] Lucie Rivier, [c] Naseem Ramsahye, [b] Sabine Devautour-Vinot, [b] Clémence Sicard, [c] Nicolas Menguy, [d] Christian Serre, [a] Guillaume Maurin,* [b] Nathalie Steunou. * [c] [a] In memory of Prof. François Couty Abstract: Here we propose an innovative strategy to synthesize single-crystal nanowires (NWs) of the Al 3+ dicarboxylate MIL-69(Al) MOF by using graphene oxide nanoscrolls as structure directing agents. MIL-69(Al) NWs with an average diameter of 70 ± 20 nm and lengths up to 2 m were found to preferentially grow along the [001] crystallographic direction. Advanced characterization tools (electron diffraction, TEM, STEM-HAADF, SEM, XPS) and molecular modelling revealed the mechanism of formation of MIL-69(Al) NWs involving size-confinement and templating effects. The formation of MIL-69(Al) seeds and the self-scroll of GO sheets followed by the anisotropic growth of MIL-69(Al) crystals are mediated by specific GO sheets/MOF interactions. This study delivers an unprecedented approach to control the design of 1D MOF nanostructures and superstructures.

MOFs have attracted a tremendous interest over the last decades in material science since this family of porous solids offers a unique opportunity to design a wide range of architectures with modulated porosities and chemical functionality. 1,2 These materials constructed through the assembly of metal ions and organic polydentate ligands present crystalline hybrid porous structures 3,4 of interest for a wide range of applications including gas storage/separation, catalysis, sensing, electronics, biomedicine etc. 1 To date, most of the works on MOFs have been devoted to the discovery of novel structures, properties testing and composites processing. [1][2][3][4][5][6][7][8][9][10][11] The control over the crystal size, morphology, and multi-scale porosity of MOFs as well as the shape of their crystal aggregates have been much less explored. Indeed, this was rarely achieved by using polymers, proteins, or metal oxides as additives. [12][13][14][15][16] In particular, low-symmetry nano-crystals (NCs), which exhibit high energy facets are of interest in the fields of catalysis, sensing and electronics. 17,18 However, only very few one-dimensional (1D) anisotropic MOF nanostructures has been discovered so far since MOF nanoparticles (NPs) are mostly obtained as polycrystalline powders or spherical NCs. [19][20][21][22][23][24] The rare existing 1D MOF architectures in the forms of nanowires (NW), nanotubes and nanorods were synthesized through a bottom-up solution route or hydrothermal process eventually templated by polymer or inorganic 1D nanostructures. [19][20][21][22][23][24] Note that the nucleation and growth processes of 1D MOFs are far to be understood similarly to a wide range of anisotropic oxides and metal nanostructures. 17,25,26,27 Furthermore, MOFs still present other shortcomings, which restrict their applications to a great extent. Above all, most MOFs are inherently electrically non-conductive and numerous MOFs are not robust against water/vapour or high temperature. To circumvent these drawbacks, MOF/graphene oxide (GO)-based materials [5][6][7][8][9][10][11] have attracted widespread attention in recent years since they can present an improved stability, enhanced electrical conductivity and processability as a result of a synergistic effect of the two components. These composites have been explored in various applications including sensors, supercapacitors, batteries, gas storage, and catalysis. [5][6][7][8][9][10][11] However, the development of such MOF/GO composites suffers from a disordered spatial arrangement of GO sheets and MOF particles as well as a strong aggregation of MOFs NPs. Therefore, the engineering of MOF/GO composite with hierarchical architectures, such as core-shell structure and layer-by-layer, would be most desirable to further optimize the performance of such systems.

In this context herein, we report the synthesis of single-crystal Al 3+ dicarboxylate MOF (i.e. MIL-69(Al) MIL, Material of Institut Lavoisier) NW by using graphene oxide (GO) nanoscrolls as structure-directing agents. GO nanoscrolls are 1D carbon materials formed by rolling GO sheets from one side or from the corner into Archimedean-type spirals. 28 They present open structures at both ends and interlayer galleries that can be easily intercalated. Recently, the assembly of GO sheets with preformed oxide or metal NPs led to the formation of GO nanoscrolls decorated by NPs. 28,29,30,31 Inspired by these findings, here we have exploited the potential rolling of GO to control the As a proof of concept, the microporous Al 2,6 naphtalene dicarboxylate (2,6 ndc) based MOF, denoted MIL-69(Al) was considered as a typical example. 32 This network which is structurally analogue to the terephtalate-based MIL-53, is built up from the connection of infinite chains of corner-sharing octahedral AlO4(OH)2 units with 2,6 ndc ligand. Its hydrated form presents one-dimensional narrow rhombic channels with a window size around 2.7 x 13.6 Å (see scheme 1). 33,34 The synthesis of MIL-69(Al) NWs was conducted in-situ with a mixture of MOF precursors e.g. Al 3+ salts, NaOH and 2,6 ndc and GO as a co-reactant in DMF/H2O solution heated under reflux. Note that the same reactants without GO led to MIL-69(Al) NPs (see SI for details). 35 TEM images reveal that the pure MIL-69(Al) NPs are polydisperse in size and morphology with diameters ranging from 20 to 90 nm (Figures 1(a) andS1).

Varying the GO content and the heating time led to different nanostructured composites. These materials are denoted MIL-69/GO-X-Y with X and Y corresponding to the initial Al/GO weight ratio (calculated from the amount of Al(NO3)3.9H2O precursor) and the reflux time respectively. The powder X-ray diffraction (PXRD) pattern of MIL-69/GO-X-24 composites displays the characteristic Bragg peaks of MIL-69(Al) in its narrow pore form, however they are much sharper and intense for X=4.5 & 9 than for X= 18 and MIL-69(Al) NPs (see Figure S2). In comparison to micrometer scale MIL-69(Al) particles, h00 reflections are much more intense in the PXRD pattern of MIL-69/GO-X-24, suggesting a preferential orientation of such crystals with a possible shape anisotropy. MIL-69(Al) NWs were typically obtained for X= 4.5 and after a reflux of 24 hours. As shown by N2 porosimetry (Figure S3), MIL-69/GO-4.5-24 presents a hierarchical porous structure that consists in an ordered array of micropores inherent of the MOF framework and mesoporous inter-particle voids. Such mesoporous voids may result from the packing of MIL-69(Al)/GO NWs or formed at the MOF/GO interfaces as previously shown for numerous MOFs based composites. 7,14 TGA, FT-IR, Raman and XPS spectroscopies (see SI for details), revealed that this composite results from the assembling of GO and MIL-69(Al) with a GO content of 30 wt% (Figures S4-S8). Both TEM Bright field (TEM-BF) and Scanning TEM using the High Angle Annular Dark Field mode (STEM-HAADF) images evidenced that MIL-69/GO-4.5-24 is composed of inter-grown MIL-69(Al) NWs and GO sheets (Figure 1b-e). MIL-69(Al) NWs present an average diameter of 70 ± 20 nm, lengths up to 2 µm and aspect ratio up to 20, as evaluated from 50 NWs randomly selected from TEM images (Figures S9-S11). Note that the morphology of MIL-69(Al) NWs is completely different than nano-or micrometer sized MIL-69(Al) particles (see Figure S1). Selected area electron diffraction (SAED) analyses were performed at low voltage (60 kV) in order to reduce the irradiation damage on a series of isolated NWs, showing the presence of single crystalline MIL-69(Al) NWs. (Figures 1f, S9-S10). To fully demonstrate that each MIL-69(A) NW does not consist of an assembly of smaller single-crystalline particles, three SAEDs were acquired along the long axis for each NW (Figure S10). These corresponding SAED patterns clearly show that each NW corresponds to a single crystal of MIL-69(Al). From the SAED indexation, it can be inferred that each NW grows along the [001] direction which is parallel to the chain axis of the corner-sharing Al 3+ octahedra in the structure of MIL-69(Al) (Figures S9-S10). 32 MIL-69/GO composites were also prepared with a higher Al content. MIL-69/GO-9-24 consists of bundles of MIL-69(Al) 1D tubular nanostructures interwoven with GO sheets as shown by STEM-HAADF (Figures 2 andS12). TEM and SAED experiments evidenced analogous single crystal NWs than those of MIL-69/GO-4.5-24 with a [001] growth direction. Remarkably, STEM-HAADF and SEM images show that MIL-69/GO-9-24 contains a high amount of GO nanoscrolls with a diameter ranging between 70 and 100 nm (Figures 2 andS12). Note that the diameter of GO nanoscrolls is close to that of MIL-69(Al) NW suggesting a templating effect of GO. Their archimedean-type nanoscrolls morphology is reminiscent to that previously reported for maghemite/graphene composites. 28 Upon increasing X to 18, both TEM and STEM-HAADF images revealed the co-existence of GO sheets and bundles of 1D GO nanoscrolls. (Figure S13) with only MIL-69(Al) as NPs. This observation emphasizes that Al/GO content needs to be critically controlled to ensure the formation of MIL-69(Al) NWs. A series of samples was collected at different stages of the reflux and further characterized by TEM, STEM-HAADF and PXRD (Figure 3 & Figures S14-S15) in order to follow the GOassisted formation of MIL-69(Al) NWs. At this stage, MIL-69/GO-9 was considered as a model system to emphasize the interplay between the formation of GO nanoscrolls and of MIL-69(Al) NWs. After a reflux of 2 hours, the sample consists of individual GO sheets and aggregates of a few 100 nm in size (Figures 3 andS14). These aggregates result from the assembly of GO sheets and MIL-69(Al) nanoparticles as shown by PXRD and FT-IR (Figure S15). The progressive crystallization and growth of MIL-69(Al) NWs starts to be observed after a reflux of 4 hours. As shown by high resolution TEM, MIL-69(Al) NWs with a diameter of 10 nm can be observed growing along the [001] direction (Figure S14 B). For a reflux of 12 hours, bundles of almost parallel GO nanoscrolls and MIL-69(Al) NWs emerge from the aggregates (Figures 3e andS14). This suggests that these aggregates act as anchors for the initial formation of MIL-69(Al) seeds, followed by their further outward growth, gradually forming the 1D GO nanoscrolls and MIL-69(Al) NWs.

An atomistic model of the interface formed between the GO sheet and the MIL-69(Al) surface was constructed and further analyzed by applying our recently developed computational strategy. 36,37 A GO model integrating both basal functions, i.e., epoxy and hydroxyl groups and edged carboxylic acid groups, was brought into contact with two distinct 3D MIL-69(Al) slab models that represent its crystallographic (010) and (001) surfaces and the resulting composites were geometry optimized by Molecular Dynamics (MD) simulations (see SI for details). The plot of the normalized atomic density along the z axis for the optimized MIL-69(010)/GO (Figure 4a) and MIL-69(001)/GO models (Figure S21a) respectively emphasizes the formation of an interfacial zone denoted A with a z-length of 4.5 Å where the GO terminations penetrate the pore pocket of the MIL-69(Al) surfaces. This observation confirms the good affinity observed experimentally between the two components. The radial distribution functions (RDFs) plotted for diverse MOF/GO pairs evidenced (Figure 4b and Figure S23a) that the MOF/GO interactions imply the OH groups present along the chain of MIL-69(Al) and the functional groups of GO. The most prominent interaction between the edged carboxylic acid functions and the OH groups of MIL-69(Al) (Figure 4c) leads to a significant twisting of the GO-layer in direct contact with the MOF as also suggested by the analysis of the dihedral angle distribution plotted for GO (Figure S22). Such predicted high degree of distortion for the first GO layers is expected to act as a driving force for the scrolling of GO evidenced experimentally. Interestingly, the intensity of the RDF peaks for all MOF/GO pairs is four times higher for MIL-69(010)/GO (Figure 4b) than for MIL-69(001)/GO (Figure S23a). This reveals that GO more strongly interacts with MIL-69(010) than MIL-69(001). We further disclosed that GO arranges at the MIL-69(Al) (010) surface in such a way to establish -- like-stacking interactions where the naphthalene linker lies parallel to the aromatic ring of GO (Figure 4d). Besides reinforcing the affinity between the two components, such π-π like-stacking interactions may limit the relative crystal growth of the MIL-69(010) surface. This prediction is fully consistent with the experimental observation of an anisotropic growth of MIL-69(Al) NW along the [001] direction. The key role of the -- stacking interactions through the naphthalene ring of MIL-69(Al) in the formation of NWs is also supported experimentally with the absence of NWs when we considered the in situ formation of the isostructural MIL-53(Al)-NH2 in the presence of GO (see Figures S24 for more details).

The combination of ex situ experiments and molecular modelling not only revealed the GO-assisted formation of MIL-69(Al) NWs but also grasped a series of evidences that led us to propose the mechanism of formation summarized in Scheme 1. This is a stepwise mesoscale mechanism that involves a mutual recognition between GO and MIL-69(Al): GO directs the formation of the MOF while conversely, the MOF surface may drive the structuring of GO. The first step implies a coordination of Al 3+ cations to both the basal plane hydroxyl groups and edged carboxylate functions of GO which is favoured by the attractive electrostatic interactions between the negatively charged GO sheets (i.e., negative zeta potential of GO in aqueous solution) and Al 3+ cations. This most probably initiates the assembly of GO sheets and the nucleation of MIL-69(Al) NPs (Scheme 1a), as previously mentioned for the MOF-253/GO composite. 38 Indeed for the three MIL-69/GO-X-24 composites, the surface of GO sheets is coated by MIL-69(Al) NPs with a diameter up to 50 nm as revealed by combining STEM-HAADF and STEM-XEDS elemental mapping (Figures 2a andS12). Moreover, MIL-69(Al) nanorods up to 100 nm in length were also observed at the surface of GO for X=4.5 (Figure S11b). Molecular modelling supports an anisotropic growth of MIL-69(Al) nanostructures along the [001] direction (Scheme1a). The following step is the rolling up of GO sheets into nanoscrolls (Scheme 1b) that is favoured by relative strong interactions between GO sheets and MIL-69(Al) surfaces. In particular, MIL-69(Al) NPs located at the edges of the bended part of GO sheets may be attracted by the inner part of GO. Moreover, the spontaneous scrolling of GO sheets can occur in the presence of DMF due to the inhomogeneous distribution of hydrophilic groups (hydroxy, epoxide and carboxylic acid) of GO and surface tension, as previously shown. 39 Finally, the growth of MIL-69(Al) NWs most probably occurs in the inner part of the GO nanoscrolls (Scheme 1c) based on the electrical data recorded on the composites (see Figure S25). Indeed, despite the introduction of insulating MIL-69(Al), the semi-conducting behavior of GO is maintained for MIL69/GO-X-24. In contrast, an insulating behaviour was observed by mixing preformed MIL-69(Al) NPs with GO. These results show that the homogeneous distribution of the MOF inside the GO nanoscrolls in MIL69/GO-X-24 does not disrupt the carrier traveling through the extended conjugated network in the GO sheets and sheet-to-sheet junctions. Since the internal surface of GO nanoscrolls is decorated by numerous spatially close MIL-69(Al) nanorods and NPs, their growth and assembly are thus constrained in a confined space that may drive the crystalline growth orientation in a direction parallel to the NW axis. This mechanism can involve redissolution-crystallization steps due to the highly reversible nature of coordination bonds of the MOF network. The crystal coarsening can be thus driven by the Ostwald ripening process while the ʺoriented attachmentʺ mechanism previously reported for the anisotropic growth of inorganic nanocrystals or biomineralization systems can also play a significant role. This ʺoriented attachmentʺ mechanism involves spontaneous selforganization of primary adjacent particles by sharing a common crystallographic orientation, followed by their fusion into singlecrystalline particles. 40 As a consequence, the growth of MIL-69(Al) nanorods may proceed from the GO surface inward, forming bundles of primary smaller aligned NWs (Figure 3e and scheme 1c) growing along the [001] direction, as shown in high resolution TEM images of Figure S14B. The lateral aggregation and crystallite fusion of these smaller NWs through ʺoriented attachmentʺ mechanism can lead to one single-crystalline NW (Scheme 1d) as previously reported for anisotropic metal or oxide nanostructures. 40,41 This last crystallization step could be explained by the spatial proximity of the primary NWs. Their constrained growth may proceed through coordination reactions with unreacted MOF precursors or grain boundary consumption at the interfaces as previously reported for MOF-74-II tubular superstructures. 42 In summary, GO nanoscrolls were demonstrated to act as structure-directing agents to form 1D MOF NWs. The interplay between multimodal characterization techniques and molecular modelling unravels their mechanism of formation. The selfscrolling of GO sheets and the subsequent anisotropic growth of MIL-69(Al) NWs in the inner cavity of GO nanoscrolls are driven by the covalent bonding between MIL-69(Al) NPs and the hydroxyl and carboxylic acid functions of GO that restrict the crystal growth on certain facets. This leads to the formation of hierarchical porous MOF/GO composites with a core-shell microstructure allowing homogeneous and high dispersion of MIL-69(Al) NWs in the GO matrix. Considering the chemical tunability of MOFs and the possible functionalization of GO, this strategy opens up a new avenue for fabricating hierarchical and nanostructured MOF-GO composites that might be optimal systems for different applications including separation, energy storage and sensing. 43 As illustrated in the case of MIL-69(Al)/GO composites, the design of core-shell MOF-GO nanostructures appears as a valuable approach to integrate MOFs into GO without any agglomeration of MOFs NPs or restacked GO layers while imparting electron transport properties. Typically, such composites combining a hierarchical porous structure in synergy with electrical conductivity might facilitate the current and electrolyte transport efficiency. This will be exploited in future work for possible applications in the field of batteries, supercapacitors and electrochemical sensors.

Single-crystal nanowires (NWs) of the Al 3+ dicarboxylate MIL-69(Al) MOF were synthesized by using graphene oxide nanoscrolls as structure directing agents. The interplay between multimodal characterization techniques and molecular modelling unravels their mechanism of formation involving size-confinement and specific interactions.

Single-crystal nanowires (NWs) of the Al 3+ dicarboxylate MIL-69(Al) MOF

Authors should provide a short Table of Contents graphical abstract and accompanying text on the last page of the manuscript with 1) a text of up to 50 words (ca. 450 characters), 2) an image (5.5×5.0 cm (h×w) or 11×2.5 cm (h×w), font size: 6-7 point), and 3) a maximum of five alphabetized keywords in American English. At least two of the keywords should be taken from the "Keyword Catalogue" (see Section 3.6). The graphical abstract should stimulate curiosity. Repetition or paraphrasing of the title and experimental details should be avoided.

Scheme 1 .

 1 Scheme 1. Mechanistic scheme summarizing the main stages of the MIL-69(Al) NWs formation.

  Muschi, Dr S. Sene, Dr C. Serre, Pr N. Steunou Institut des Matériaux Poreux de Paris, UMR 8004 CNRS-ENS-ESPCI, PSL research university, Paris, France. E-mail: nathalie.steunou@uvsq.fr [b] A. Lalitha, Dr N. Ramsahye, Dr S. Devautour-Vinot, Pr G. Maurin Institut Charles Gerhardt Montpellier, UMR 5253 CNRS, Université de Montpellier, Montpellier, France. E-mail : Guillaume.Maurin@univ-montp2.fr [c] Dr D. Aureau, Dr M. Fregnaux, Dr L. Rivier, Dr C. Sicard, Pr N. Steunou Institut Lavoisier de Versailles, UMR CNRS 8180, Université de Versailles St Quentin en Yvelines, Université Paris Saclay, Versailles, France. [d] Dr I. Esteve, Pr N. Menguy Sorbonne Université, UMR CNRS 7590, MNHN, IRD, Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, IMPMC, 75005 Paris, France.Supporting information for this article is given via a link at the end of the document. of single-crystal MOF NWs. The growth of these MOFs NWs were further scrutinized by combining multimodal ex situ advanced characterization techniques (electron diffraction, TEM, STEM-HAADF, SEM, XPS) and molecular modelling, thereby allowing us to propose a mechanism of formation as illustrated in scheme 1. To the best of our knowledge, this is the first study reporting the possible synthesis of single-crystal MOF NW directed by GO nanscrolls.

Figure 1 . 11 Figure 2 .

 1112 Figure 1. (a) TEM-BF image of MIL-69 NPs; (b, e) TEM-BF, (c,d) STEM-HAADF images of MIL-69/GO-4.5-24 (f) SAED of the area highlighted by the red circle in (e).The SAED indexation is given with respect to the MIL-69(Al) structure. 32 The stereographic projection (g) -related to the crystallographic orientation deduced from (f) indicates unambiguously that the crystal growth proceeds along the [001] direction (see SI for details)

Figure 3 .

 3 Figure 3. TEM images of MIL-69/GO-9-Y prepared with different duration Y of the reflux namely a) 1 h b) 2 h c) 4 h d) 8 h e) 12 h f) 24 h.

Figure 4 .

 4 Figure 4. MIL-69(Al)(010)/GO model a) Representation of the normalized atomic density showing the interfacial region denoted A. (b) Radial Distribution Functions calculated between HOH of MIL-69(Al) and the different O atoms of the functional groups of GO (c) Illustrative snapshot showing the main interactions between the edge carboxylic acid groups of GO and HOH of MIL-69(Al). (d) Snapshot showing preferential π-π like interactions at the MIL-69(Al)(010)/GO interface. Color schemes are GO layers: C-black; O-red, Hwhite; MIL-69(010): C-gray, Al-pink, O-red and H-white.

Dr

  Mégane Muschi, Anusha Lalitha, Dr Saad Sene, Dr Damien Aureau, Dr Mathieu Fregnaux, Dr Imène Esteve Dr Lucie Rivier, Dr Naseem Ramsahye, Dr Sabine Devautour-Vinot, Dr Clémence Sicard, Prof. Nicolas Menguy, Dr Christian Serre, Prof. Guillaume Maurin,* Prof. Nathalie Steunou. * Page No. -Page No.

Acknowledgements

The authors would like to acknowledge the European Community Horizon 2020 Program (H2020/2014-2020) for funding the research presented in this article under Grant Agreement No. 727619 (project Gramofon). The authors would like to acknowledge B. Alonso, A. Ortega from Graphenea S. A. (www.graphenea.com) for providing the graphene oxide sample. N. Heymans and G. De Weireld (University of Mons) are acknowledged for useful discussions. NM is grateful to Dr Jean-Michel Guigner (IMPMC) for JEOL LaB6 TEM settings at 60 kV. NS would like to thank Dr Effrosyni Gkaniatsou for SEM measurements on MIL-69(Al) microparticles.