Oralie Cattan

Christophe Servan

Sophie Rosset

On the Usability of Transformers-based models for a French Question-Answering task

For many tasks, state-of-the-art results have been achieved with Transformer-based architectures, resulting in a paradigmatic shift in practices from the use of task-specific architectures to the fine-tuning of pre-trained language models. The ongoing trend consists in training models with an ever-increasing amount of data and parameters, which requires considerable resources. It leads to a strong search to improve resource efficiency based on algorithmic and hardware improvements evaluated only for English. This raises questions about their usability when applied to small-scale learning problems, for which a limited amount of training data is available, especially for underresourced languages tasks. The lack of appropriately sized corpora is a hindrance to applying data-driven and transfer learning-based approaches with strong instability cases. In this paper, we establish a state-of-the-art of the efforts dedicated to the usability of Transformerbased models and propose to evaluate these improvements on the question-answering performances of French language which have few resources. We address the instability relating to data scarcity by investigating various training strategies with data augmentation, hyperparameters optimization and cross-lingual transfer. We also introduce a new compact model for French FrALBERT which proves to be competitive in low-resource settings.

Introduction

Recent advances in the field of Natural Language Processing (NLP) have been made with the development of transfer learning and the availability of pre-trained language models based on Transformer architectures [START_REF] Vaswani | Attention is all you need[END_REF], such as BERT [START_REF] Devlin | BERT: Pre-training of deep bidirectional transformers for language understanding[END_REF]. As they provide contextualized semantic representation they contribute both to advance the state-of-the-art on several NLP tasks and also to evolve training practices through the use of fine-tuning.

The trend of recent years consists in training large pre-trained language models on ever larger corpora, with an ever-increasing amount of parameters, which requires considerable computational resources that only a few companies and institutions can afford. For example, the base model of BERT with 110 million parameters was pre-trained on 16 gigabytes (GB) of text, while the GPT-3 model [START_REF] Brown | Language models are few-shot learners[END_REF] was pre-trained on 45 terabytes (TB) of text and has 175 billion parameters.

In fact, deploying ever-larger models raises questions and concerns about the increasing magnitude of the temporal, financial, and environmental cost of training and usability [START_REF] Strubell | Energy and policy considerations for deep learning in NLP[END_REF][START_REF] Moosavi | Proceedings of SustaiNLP: Workshop on Simple and Efficient Natural Language Processing[END_REF]. Typically, due to their resource requirements, these models are trained and deployed for industrial operations on remote servers. This leads to a high use of over-the-air communications, which are particularly resourceintensive [START_REF] Gündüz | Machine learning in the air[END_REF]. In particular, some NLP applications (speech recognition, speech to text, etc.) have some known problems related to network latency, transmission path difficulties, or privacy concerns. To reduce the impact of these communications, there is a solution that is to allow these models to run directly on peripheral or mobile devices, that is, in environments with limited resources that require lightweight, responsive models and energy efficiency. Reducing the size of the models is therefore one of the increasingly favoured avenues, especially for the reduction of memory resources and computation time involved in training and use.

To meet these constraints, compact models represent one of the most promising solutions. As far as we know, they have only been evaluated on the comprehension tasks covered by GLUE [START_REF] Wang | GLUE: A multi-task benchmark and analysis platform for natural language understanding[END_REF] and the question-answering task with the SQuAD corpus [START_REF] Rajpurkar | SQuAD: 100,000+ questions for machine comprehension of text[END_REF] with abundant data, in English. The improvements resulting from the algorithmic optimizations of the models, although significant, raise questions about their effectiveness on lower-scale learning problems on poorly endowed languages. The works of [START_REF] Zhang | Revisiting fewsample {bert} fine-tuning[END_REF] and [START_REF] Mosbach | On the stability of fine-tuning {bert}: Misconceptions, explanations, and strong baselines[END_REF] have furthermore shown degraded performance in these conditions. These two reflections are at the origin of a double question which our contribution attempts to answer. On the one hand, what is the behavior of a Transformer-based model in the context of a question-answering task in French, a task that is poorly endowed in this language? On the other hand, what are the impacts of algorithmic improvements of these same models in this context?

To answer these questions, we first establish in section 2 a state-of-the-art that is meant to be broad enough to have a shallow overview depicting the ins and outs and issues around the usability of Transformer-based models whose breadcrumb trail is the issue of resources. Then, we present in the section 3 the recent progress of the questionanswering task, through the use of these latest models. In sections 4 and 5 we introduce our model and present our experiments on the usability of Transformers models in a question-answering task for French, on FQuAD (d'Hoffschmidt et al., 2020) and PIAF [START_REF] Keraron | Project piaf: Building a native french question-answering dataset[END_REF] corpora. We propose to address the instability relating to data scarcity by investigating various training strategies with data augmentation, hyperparameters optimization and cross-lingual transfer. Finally, we present a new compact model for French based on ALBERT [START_REF] Lan | ALBERT: A lite BERT for self-supervised learning of language representations[END_REF] 1 , and compare it to existing monolingual and multilingual models, large and compact, under constrained conditions (notably on learning data).

Usability of Transformers

In this section we present the ins and out of the Transformer models to understand how the approaches meet the need for better usability.

Architecture and pre-trained models

The Transformer architecture [START_REF] Vaswani | Attention is all you need[END_REF] is based on a stack of encoder-decoder blocks, composed at a high level of forward propagation networks and multi-headed self-attention operations.

The self-attention layer is the core element of its architecture that enables its efficiency in modeling the semantic context interdependencies between the units or sub-units of the input sequence.

Transformer-based language models such as BERT [START_REF] Devlin | BERT: Pre-training of deep bidirectional transformers for language understanding[END_REF] are pre-trained on largescale data collections sourced from Wikipedia or Common Crawl (CC) with one or multiple training objectives (masked language modeling, next sentence or sentence order prediction). This pretraining can be followed by supervised fine-tuning according to the tasks, whether generatives (machine translation, abstractive summarization) or discriminatives (classification, question-answering). The ensuing fine-tuning phase allows for better initialization of the models parameters while requiring less task-specific data so as to make the training of subsequent tasks faster.

Recently, [START_REF] Zhang | Revisiting fewsample {bert} fine-tuning[END_REF] and [START_REF] Mosbach | On the stability of fine-tuning {bert}: Misconceptions, explanations, and strong baselines[END_REF] have nevertheless shown that the commonly adopted practices (the number of iterations, the choice of model layers) when fine-tuning Transformers-based langage models are inappropriate under resource constrained conditions and adversely affect the stability of models performances as overfitting, label noise memorization or catastrophic forgetting. Added to this, because the pretraining process is particularly constraining, various works have been oriented towards the research and training of efficient models, both in terms of available capacities and resources and in terms of environmental footprint.

A search for efficiency

Reducing the cost of training Transformers-based models has become an active research area. To this end, methods based on compression techniques or on architecture improvements have been introduced in order to build compact models with comparable performances to large models.

Many works address the issue of model compression with quantization, pruning, knowledge distillation or a combination of these approaches. The idea of quantization [START_REF] Shen | Q-BERT: hessian based ultra low precision quantization of BERT[END_REF] is to take advantage of the use of lower precision bit-width floats to reduce memory usage and increase computational density. Following the same objective, pruning [START_REF] Michel | Are sixteen heads really better than one? In Advances in Neural Information Processing Systems[END_REF] consists in removing parts of a model (weight bindings, attentional heads) with minimal precision losses. Finally, knowledge distillation [START_REF] Sanh | Distilbert, a distilled version of BERT: smaller, faster, cheaper and lighter[END_REF] enables the generation of models that mimic the performance of a large model (or set of models) while having fewer parameters.

Another axis of development concerns the use of neural architecture search [START_REF] Elsken | Neural architecture search: A survey[END_REF] which allows to optimize a model by progressively modifying the design of the network through trial and error, eliminating insignificant operations. To avoid the unnecessary large number of parameters, adapters [START_REF] Houlsby | Parameter-efficient transfer learning for nlp[END_REF] were introduced to allow fine-tuning of the set of parameters specific to the task of interest rather than the entire model.

Other architectural improvements highlighted with the introduction of the ALBERT model [START_REF] Lan | ALBERT: A lite BERT for self-supervised learning of language representations[END_REF] such as the factorization of the attention matrix or parameter sharing. Indeed, the most time-consuming and memory-intensive operations concerns the forward propagation and attention computation operations. The self-attention layer of BERT pretrained models grows quadratically in respect to the input sequence length. One common approach to this issue consists of approximating the dot-product attention for example by using hashing techniques [START_REF] Kitaev | Reformer: The efficient transformer[END_REF] to accelerate the training and inference phases when long sequence lengths are used. However these solutions have demonstrated they suffer from important computational overheads for tasks with smaller lengths, such as question-answering.

3 The Question-Answering task Question-Answering (QA) based on machine reading comprehension corresponds to the task of extracting an answer given a question and a context document such as from a news or Wikipedia article.

General QA Architecture

Until recently, most of the proposed approaches have relied on an architectural complexification of LSTM-based neural networks and attention mechanism. At a high level, their architectures are all composed of three layers with:

(a) an encoding layer that projects the inputs, as each word within the context, question and answer triples in a latent semantic space;

(b) an interaction layer that models the semantic interdependencies between the embedded inputs through the use of attention mechanisms.

(c) an output layer that extracts the answer to the input question within the related context.

The interaction layer is the core element of the architecture for which several kinds attention mechanisms has been developed to improve the QA matching process such as bi-attention (Seo et al., 2017), co-attention [START_REF] Xiong | Dynamic coattention networks for question answering[END_REF][START_REF] Xiong | DCN+: Mixed objective and deep residual coattention for question answering[END_REF], multi-level inter-attention [START_REF] Huang | Fusionnet: Fusing via fullyaware attention with application to machine comprehension[END_REF] or re-attention [START_REF] Hu | Reinforced mnemonic reader for machine reading comprehension[END_REF], to name just a few.

Recent advances through the availability of Transformer-based pre-trained models and the development of transfer learning methods have enabled to remove the recurrence of previous architectures in order to achieve parallelization efficiencies. This simplified the QA architecture and its training process, replacing the encoding and the interaction layers with attention-based Transformer layers.

Another advantage is that it provides precomputed contextual word representations. QA models based on LSTMs are built on top of static word embeddings models such as GloVe [START_REF] Pennington | Glove: Global vectors for word representation[END_REF]. Even these models have up to 40 times fewer parameters than a BERT-based model, they rely on LSTM-based encoders to produce contextual embeddings which considerably lengthens the time required for training and makes the dependence on supervised data more important.

The standard approach introduced by Devlin et al. ( 2019) we rely on this study, consists in introducing and updating parameter vectors corresponding to the start and end positions of the answer span. Specifically, the start and end position probability distributions are computed by softmax over the dot products between the representation of the tokens and the start and end vectors. In sum, all of the Transformer parameters as well as the two introduced parameter vectors are optimized together.

Despite the fact that there is a number of largescale QA datasets in English, with tens of thousands of annotated training examples, porting a system to a new language with fewer annotated resources (low-resource languages) requires approaches that go far beyond the simple act of retraining the models.

Low-Resourced QA

In recent years, low-resource NLP has drawn an increasing amount of attention with solutions ranging from developing new data collection methodologies either via crowdsourcing or through the use of machine translation (MT), to cross-lingual and transfer learning approaches for which information is shared across languages or tasks.

MT-based data collection

Neural MT as made considerable progress in recent years such as translating large-scale datasets from a high-resourced to under-resourced languages or converserly has become an intuitive way of generating annotated datasets in a cost-effective and rapid manner.

Automatically translating the context, question and answer triples from a high-resource language, such as English (called source domain) to lowresource languages (called target domains) have enabled the evaluation of models for languages with no training data available but also the creation of large-scale MT-based QA corpora for the Italian [START_REF] Croce | Neural learning for question answering in italian[END_REF], Spanish [START_REF] Pio Carrino | Automatic Spanish translation of SQuAD dataset for multi-lingual question answering[END_REF], Arabic [START_REF] Mozannar | Neural Arabic question answering[END_REF] and Korean (Youngmin Kim, 2020) languages.

Another approach consists of translating the QA triples of the target domain into the source domain, so the model trained on the source language can be directly applied on the translated target language testing data. As an exemple, [START_REF] Asai | Multilingual extractive reading comprehension by runtime machine translation[END_REF]'s method consisted of combining the alignment attention scores from a MT model with an English QA model to guide the answer extraction process.

The performance of MT-data approaches depends strongly on the quality of the MT models. Thus, due to the lack of reliable models for some language pairs, approaches that foster the transfer of knowledge from other languages or tasks while requiring less data have been developed.

Pre-training and Transfer approaches

The exploitation of pre-trained models followed by task-specific fine-tuning haved pushed the state-ofthe-art forwards, while requiring much less computational and data resources. The idea behind pre-training is to reuse the weights parameters trained on a set of source tasks and continue to fine-tune them on under-resourced target tasks to achieve knowledge transfer. Dai and [START_REF] Andrew | Semi-supervised sequence learning[END_REF] were the first to propose to pre-train RNNs using auto-encoders and language models as part of their QA encoding layer. [START_REF] Joon | Bidirectional attention flow for machine comprehension[END_REF] and [START_REF] Wiese | Neural domain adaptation for biomedical question answering[END_REF] pre-trained QA models before applying the fine-tuning process between the source and the target domains. Other efforts focused on pretraining Transformer-based models multilingually such as the multilingual version of BERT (called mBERT) [START_REF] Devlin | BERT: Pre-training of deep bidirectional transformers for language understanding[END_REF] or XLM-R [START_REF] Conneau | Unsupervised cross-lingual representation learning at scale[END_REF] to learn cross-lingual representations which are transferable across languages.

Usability concerns

Studies on the usability of Transformer-based models (Section 2) from standard resource efficiency concerns towards a broader set of problems related to their generalizability.

Recently, [START_REF] Pires | How multilingual is multilingual BERT?[END_REF] and [START_REF] Conneau | Unsupervised cross-lingual representation learning at scale[END_REF] have shown that multilingual models underperformed, when applied on poorly endowed languages. Additionally, as mentioned in subsection 2.1, recent works [START_REF] Zhang | Revisiting fewsample {bert} fine-tuning[END_REF][START_REF] Mosbach | On the stability of fine-tuning {bert}: Misconceptions, explanations, and strong baselines[END_REF] have highlighted the limitation of Transformer-based transfer learning with strong instabilities arising from the small-scale learning.

French is a poorly endowed language since we do not have enough annotated data to train a deep learning model on QA tasks. Moreover, unlike the only two large monolingual French models: CamemBERT [START_REF] Martin D'hoffschmidt | FQuAD: French question answering dataset[END_REF] and FlauBERT [START_REF] Le | FlauBERT: Unsupervised language model pre-training for French[END_REF], the English BERT model has become a branching point from which a growing number of large and compact English pre-trained models have emerged. These French monolingual models, although they provide good performances, do not reflect the rapid evolution of the field.

Consequently, in this paper we propose a new compact model FrALBERT for French we present in the following section alongside with the other available pre-trained language models on which we base our experiments.

FrALBERT and Transformer models considered

As mentioned in the previous section there is no compact model for French. We therefore decided to pre-train a new version of ALBERT from scratch we called FrALBERT, thus overcoming some of the discussed limitations.

ALBERT is based on parameter sharing/reduction techniques that allows to reduce the computational complexity and speed up training and inference phases. Compared to previous compact models such as DistilBERT [START_REF] Sanh | Distilbert, a distilled version of BERT: smaller, faster, cheaper and lighter[END_REF], Q-BERT [START_REF] Shen | Q-BERT: hessian based ultra low precision quantization of BERT[END_REF] or TernaryBERT [START_REF] Zhang | Ternary-BERT: Distillation-aware ultra-low bit BERT[END_REF], ALBERT is to the date the smallest pre-trained models with 12 million parameters and <50 megabyte (MB) model size.

FrALBERT Crawl projects such as OSCAR (Ortiz Suárez et al., 2020) or CCNet [START_REF] Wenzek | Ccnet: Extracting high quality monolingual datasets from web crawl data[END_REF] corpora, and because we focus on factual QA, we decide to use only Wikipedia as our primary source of knowledge. We used the same learning configuration as the original model with a batch size of 128 and a initial learning rate set to 3.125 × 10 -4 .

Our experiments are also based on the large monolingual French model CamemBERT [START_REF] Martin D'hoffschmidt | FQuAD: French question answering dataset[END_REF] as well as on the two large multilingual models: XLM-R [START_REF] Conneau | Unsupervised cross-lingual representation learning at scale[END_REF] and mBERT [START_REF] Devlin | BERT: Pre-training of deep bidirectional transformers for language understanding[END_REF], both pre-trained from massive corpora dataset in more than 100 languages such as the Common Crawl (CC-100) or Wikipedia (Wiki-100). We also exploit two compact multilingual models with a distilled version of mBERT: distil-mBERT [START_REF] Sanh | Distilbert, a distilled version of BERT: smaller, faster, cheaper and lighter[END_REF] and small-mBERT [START_REF] Abdaoui | Load what you need: Smaller versions of mutililingual BERT[END_REF], a mBERT model whose the original vocabulary has been reduced to two languages (English and French). Table 1 gives a comparison of the models.

Experiments

We propose an assessment of the comparative advantage gains in performance when using different training strategies (data augmentation, hyperparameter search and cross-lingual transfer) over monolingual and multilingual pre-trained models, larges and compacts for a QA task in French under resource constraints.

QA Datasets

We conduct experiments on four QA datasets whose descriptives are presented in Table 2, with:

• SQuAD (v1.1) [START_REF] Rajpurkar | SQuAD: 100,000+ questions for machine comprehension of text[END_REF] ChrF [START_REF] Popović | chrF: character n-gram F-score for automatic MT evaluation[END_REF] a character n-gram precision and recall enhanced with word n-grams. Since answers are largely made up of entities, ChrF score integration is only performed when the answer span is not present in the related context. In order to evaluate the quality of the translation, we manually corrected the translation errors in the output of a subset of the corpus composed of 890 QA pairs and 107 contexts. We obtain a BLEU score [START_REF] Papineni | Bleu: a method for automatic evaluation of machine translation[END_REF] We also explore mixed datasets training strategy with SQuAD-en train + FQuAD train for training models on a concatenation of the training data covering French-English language pairs to test the crosslingual transfer ability of multilingual models.

Evaluation and validation

The performance of QA models are evaluated using the Exact Match (EM) and F1 scores. The EM score is the percentage of system outputs that match exactly with the ground truth answers. The F1 score is a combined measure of precision and recall that is less strict than EM. The evaluation process 3 involves post-processing identical to that presented by d 'Hoffschmidt et al. (2020) and inspired by that proposed for English by [START_REF] Rajpurkar | SQuAD: 100,000+ questions for machine comprehension of text[END_REF], which consists of the removal of punctuation marks and determiners 4 as well as a down-casing of the answers (ground truths and predictions).

To address our considerations related to resource constraints we perform a hyperparameter optimization, that has proven to lead to better solutions in less time. It is based on a population-based learning [START_REF] Jaderberg | Population based training of neural networks[END_REF] in which a population of models and their hyperparameters are jointly optimized. To this end, we build a validation set by randomly extracting 10% of the training data.

2 We share our SQuAD-fr corpus on request and on dataset sharing platforms to support further research in this area. 3 The experiments reported in [START_REF] Martin D'hoffschmidt | FQuAD: French question answering dataset[END_REF]) concern version 1.1 of the FQuAD corpus. Ours are based on the only version available to date (v1.0). Moreover, the test sets are not made public, so we use the development set instead.

4 Determiners are le, la, les, l', du, des, au, aux, un, une.

Results

Table 3 presents the results on the French QA task evaluated on FQuAD dev and PIAF dev . This table shows the scores obtained with Transformer-based models on the baseline training (FQuAD train ), using hyperparameter optimization approach (FQuAD train w/ optim) and with data augmentation approach (FQuAD train + SQuAD-fr train ).

Cross-lingual performances are presented in table 4, on the same French QA tasks FQuAD and PIAF as baseline the English corpus SQuAD-en train , on which we applied hyperparameter optimization (SQuAD-en train w/ optim) and performed data augmentation by adding the French corpus FQuAD to the English QA training corpus (SQuAD-en train + FQuAD train ).

Baseline results

The results obtained from monolingual models with CamemBERT large which has more layers, hidden units and attention heads and Camembert base , both pre-trained with a larger and more diverse amount of data achieve results are better than Camembert base pre-trained on only 4 GB Wikipedia. The highest F1 score is 81.2 on FQuAD dev and 68.1 on PIAF dev . The F1 performances of the FrALBERT base model are close to those of the CamemBERT base model, both pre-trained on the French content of Wikipedia (4GB). Their results turn out to be competitive and of the same order of magnitude as those reported by [START_REF] Lan | ALBERT: A lite BERT for self-supervised learning of language representations[END_REF] on SQuAD-en with 1 point difference on F1 scores when evaluating a BERT base model (90.4 F1) and a compact ALBERT base model (89.3 F1) pre-trained on the same texts (BookCorpus and Wikipedia). Interestingly, these EM scores are higher than those of the CamemBERT base achieving the EM score of 55.1, an increase of 5 points on the FQuAD dev .

hyperparameter results

Automatically tuning the hyperparameter tends to make QA models more accurate with gains in terms of EM scores that are very expressive. Highest F1 / EM scores are 90.2 / 75.5 on FQuAD dev and 71.0 / 44.8 on PIAF dev . Improvement are variable accoring the model considered, especially the French BERT one wich have the highest improvement using this approach (from 6 to 9 F1 points and from 11 to 20 EM points) which is quite imrpessive. FrALBERT stay behind of 5 F1 points of the CamemBERT base trained with the same data (wiki Table 4: Cross-language transfer results obtained with multilingual Transformer models only on the baseline (SQuAD-en train ), using hyperparameter optimization (SQuAD-en train w/ optim) and with data augmentation (SQuAD-en train + FQuAD train ) using F1-measure (F1) and Exact Match (EM), on two French QA tasks (FQuAD dev and PIAF dev ).

4 GB) but regarding the EM scores, FrALBERT is better of 3 points. Surprisingly, multilingual models are close to the French BERT models. The small-mBERT is better than FrALBERT around 2.5 F1 points, while the French one have a better EM score (+2.6 points), while distil-mBERT is lower in both F1 and EM scores.

Data augmentation results

Training strategies based on data augmentation got nearly the best results in both F1 and EM scores except for the CamemBERT large . Apart from CamemBERT base (wiki 4 GB) and FrALBERT base models, results are comparable with an average difference of 1 point regardless of the metric. More generally, the performance gains are up to 11 and 20 of F1 and EM points, respectively, on FQuAD dev and up to 4 points on both metrics on PIAF dev .

Cross-lingual transfer results

The cross-lingual transfer-based approaches using multilingual models outperform the monolingual approaches on FQuAD and PIAF corpora (table 4). Once again the large model XLM-R achieves better results than its base version. XLM-R pretrained with a dual LM objective lens scores better than the mBERT model every time. The highest F1 score is 86.8 on FquAD dev and 70.4 on PIAF dev . There is a significant performance drop between the large multilingual models and their respective compact models. The compact multilingual models based on mBERT substantially underperform, obtaining lower F1 and EM scores than the large models regardless of the training strategy. In the zero-shot configurations where no French data is used for training (SQuAD-en train and SQuAD-en train w/ optim), the models confirm the outstanding crosslingual ability with performances exceeding the performances of the monolingual models with F1 scores with an F1 / EM scores slightly below those obtained on FQuAD train .

General observations

In all configurations, the performance in terms of EM and F1 on PIAF remains significantly lower than that obtained on FQuAD since the PIAF corpus does not include multiple responses as pointed out by d 'Hoffschmidt et al. (2020). Unsurprisingly, PIAF dev offer a more challenging evaluation set, where the answer extraction performance are lower. Indeed, the corpus is more diversified with questions on 191 different Wikipedia articles, whereas on FQuAD dev it only covers 18.

According results, we can confirm that data aug-mentation is the better way to improve results, even if data comes from another language. We observe from multilingual results that combining training data gives better results with similar performance whether data are translated or not.

Analysis

In this section, we conduct an analysis of our results to understand what remains as challenges for state-of-the-art models, with a focus on the usability concerns of Transformers under resource constraints.

The success of supervised methods depends heavily on the availability of large-scale training data. Pre-training large models on massive corpora using unsupervised language modeling and finetuning the model with pre-trained weights requires less task-specific data. Our experimental results are in line with this, since we obtain satisfactory results with transfer learning when large and high quality annotated data are not available. The highest F1 score is 81.2 on FQuAD dev and 68.1 on PIAF dev . Nevertheless, the performance of the models can benefit from several training strategies.

Effect of MT-data augmentation

The lack of human-annotated datasets for languages other than English can be overcome by enriching our training data with the translated version of SQuAD-en train . Regardless of the pre-trained model used, their performance are competitive on FQuAD dev and PIAF dev , close to human performance.

Effect of hyperparameter tuning A generally unstated assumption is that pre-trained linguistic models are under-optimized and that practices commonly adopted for the fine-tuning stage can be detrimental to performance [START_REF] Zhang | Revisiting fewsample {bert} fine-tuning[END_REF][START_REF] Mosbach | On the stability of fine-tuning {bert}: Misconceptions, explanations, and strong baselines[END_REF]. This is quite apparent in all settings, with better gains through hyperparameter optimization stages. Fine-tuning CamemBERT large on the French dataset yields 90.2 / 75.5 F1 / EM on the FQuAD dev set. By means of comparison, CamemBERT large scores were 81.2 / 55.9 F1 / EM on the same set with no hyperparameter tuning.

Crosslingual QA Pre-training language models on the concatenation of multiple languages has proven to be a competitive approach for crosslingual language modeling. If monolingual models often perform better than multilingual models, we observe that, for comparable model sizes this is not the case in our task where the performance gap is smaller. This gap is further reduced when the strategies are combined. Scores of fine tuned XLM-R base is 82.1 / 66.8 on FQuAD dev and 65.0 / 39.6 on PIAF dev .

The zero-shot experiments show that multilingual models can reach strong performances on the task in French when the model has not encountered data of the French language. For example, the XLM-R base model fine-tuned solely on SQuADen train reaches a performance on FQuaD just a few points below the performance obtained when finetuning is performed on FQuAD train .

Finally, our results suggest that data-driven augmentation, either by translating datasets from high resource languages or by concatenating the available corpora are a particularly appropriate strategy to exploit the potential of cross-lingual transferability of models and data for improving model performances.

Improvements over a small scale dataset With resource-limited training data we obtain an average F1 score of 74.2 on FQuAD dev and 61.7 on PIAF dev when we fine-tuned FrALBERT -higher performance than any of the compact multilingual models, but slightly below the performance of the large monolingual models. We believe that the lower performance of small multilingual models is not due to their lower number of parameters, but to the usability of these models which is dependent on the reduction technique used. This can be seen very clearly since the performance of the FrALBERT model is close to that of the large models.

Here again, these performances can be boosted via the use of translated data or hyperparameter search which allows us to bring the maximum performances obtained with FrALBERT base and CamemBERT base pre-trained on 4 GB Wikipedia closer in a consistent way. Their scores remain slightly below those obtained with models pretrained on more data suggesting limitations related to the corpus domain of the language model. Computational costs Compact models provide alternatives to high-energy consumption models by showing comparable performance while reducing their size and computational complexity. Decreasing the environmental impact of NLP model training, as a research topic, is very recent [START_REF] Moosavi | Proceedings of SustaiNLP: Workshop on Simple and Efficient Natural Language Processing[END_REF]. We decided to monitor our experiments conducted on one NVIDIA V100 GPU with 16GB of memory using Table 5: Comparison of models by computational costs on FQuAD train experiment-impact-tracker [START_REF] Henderson | Towards the systematic reporting of the energy and carbon footprints of machine learning[END_REF]. Table 5 shows the energy consumption in kilowatt-hour (kWh), the emission intensity in grams of carbon dioxide (g CO 2 ), and the duration in seconds (s) for a fine tuning session of 10 epochs with a batch size of 4 on FQuAD train . The footprint of the large versions of XLM-R large and CamemBERT large models is 3 times more than their base versions. Their training time is also significantly longer, over 5 hours. Finally, in terms of watt usage, carbon emissions and training time, FrALBERT is two times less the distilled version of BERT.

Conclusion and outlook

Recently, important progress has been made in neural language modeling using Transformer networks. Its popularity now well established lies in its effectiveness in modeling long-term dependencies. In this study, we have shown that a number of significant shortcomings of usability have recently been pointed out and that some solutions have been drawn up with compact models. We have also overviewed how the use of Transformer-based pretrained language models have sparked a paradigmatic shift in question-answering training practices from task-specific architectures to the use of transfer learning through fine-tuning.

Comparing performances on a French questionanswering task using large and compact models provides insight into the usability of these models for under-resourced languages. As others, we argued that large and compact models cannot be used with limited data. Our experimental results suggest that training strategy such as hyperparameter tuning or data augmentation can help to alleviate the data-gathering burden, with performances close to those of a high-resourced language such as English.

Finally, we present a new compact model for French FrALBERT (12M parameters), which proves to be as competitive as the large monolin-gual model CamemBERT (110M parameters) pretrained on the same amount of text. In term of computational cost, we shown this compact model is twice less greedy than the BERT base models. We also release a high-quality translated version of the SQuAD corpus in French consisting of around 90K+ QA pairs.

In a future work, we aim to continue this study from a meta-learning perspective with a modelagnostic approach generalizable to low-resource languages. We also plan to extend our model to other languages and to evaluate it on other NLP tasks such as named entity recognition or natural language understanding.

Table 1 :

 1 is pre-trained on the French version of the Wikipedia encyclopedia of 04/05/2021, i.e. 4 GB of text and 17 million (M) sentences. Beyond concerns about the rights to use data from Common Characteristics of the pre-trained models used in the proposed small-scale QA framework.

	model	pre-training data	vocab. size # param. model size
	CamemBERTbase French OSCAR (138 GB of text)	32005	110 M	445 MB
	CamemBERTlarge French CCNet (135 GB of text)	32005	335 M	1.35 GB
	CamemBERTbase French Wikipedia (4 GB of text)	32005	110 M	445 MB
	FrALBERTbase	French Wikipedia (4 GB of text)	32005	12 M	50 MB
	XLM-Rbase	CC-100 (2.5 TB of text)	250002	278 M	1.12 GB
	XLM-Rlarge	CC-100 (2.5 TB of text)	250002	559 M	1.24 GB
	mBERTbase	Wiki-100	119547	177 M	714 MB
	small-mBERTbase Wiki-100	33407	111 M	447 MB
	distil-mBERTbase Wiki-100	119547	134 M	542 MB

Table 2 :

 2

	(we

Descriptives of SQuAD-en, FQuAD and PIAF datasets.

  of 68.89 and 72.38 for questions and contexts respectively. SQuADfr train serves as a means of data augmentation on FQuAD and PIAF benchmarks, with 90K+ translated QA training pairs 2 .

Available at HuggingFace's model hub page.

Acknowledgments

This work has been partially funded by the French National Research Agency (ANR) through the project TextToKids (AAPG2019).


Sumit Mehan

Laure Herrmann

Jean-Paul Chapel

Jacques Jestin

Jean-Francois Berret

Fabrice Cousin

The desalting/salting pathway: a route to form metastable aggregates with tuneable morphologies and lifetimes

We investigate the formation/re-dissociation mechanisms of hybrid complexes made from negatively charged PAA2k coated γ-Fe2O3 nanoparticles (NP) and positively charged polycations (PDADMAC) in aqueous solution in the regime of very high ionic strength (I). When the building blocks are mixed at large ionic strength (1M NH4Cl), the electrostatic interaction is screened and complexation does not occur. If the ionic strength is then lowered down to a targeted ionic strength Itarget, there is a critical threshold Ic = 0.62 M at which complexation occurs, that is independent on the charge ratio Z and the pathway used to reduce salinity (drop-by-drop mixing or fast mixing). If salt is added back up to 1M, the transition is not reversible and persistent out-of-equilibrium aggregates are formed. The lifetimes of such aggregates depends on Itarget: the closer Itarget to Ic is, the more difficult it is to dissolve the aggregates. Such peculiar behavior is driven by the inner structure of the complexes that are formed after desalting. When Itarget is far below Ic, strong electrostatic interactions induce the formation of dense, compact and frozen aggregates. Such aggregates can only poorly reorganize further on with time, which makes their dissolution upon resalting almost reversible. Conversely, when Itarget is close to Ic more open aggregates are formed due to weaker electrostatic interactions upon desalting. System can thus rearrange with time to lower its free energy and reach more stable out-of-equilibrium states which are very difficult to dissociate back upon resalting, even at very high ionic strength.

Introduction

Non-equilibrium assemblies show various interesting and timedependent properties that are not accessible to systems at equilibrium, the most prominent examples being living systems. 1,2,3 The possibility to realize controlled time dependent features provide these systems both complexity and potential for applications in designing new materials with dedicated properties. 4,5,6,7 These systems are either dissipative assemblies that require constant supply of energy 8 or pathway dependent kinetically trapped assemblies. The latter are molecular assemblies that have reached free energy local minima when exploring phase space along a given pathway, but are still away from the true minimum (equilibrium structure). 4,9,2 Depending on the energy landscape, a large number of local minima's are potentially accessible, and consequently different macromolecular assemblies with various morphologies and properties may be obtained from the same chemistry and predefined building blocks with the same final solution conditions. 10,11 If a specific property of the system that corresponds to a local minima is targeted, the pathway has to be chosen properly to reach such minima. 4,12,13,14 Usually the molecular assemblies are kinetically trapped when strong noncovalent interactions drive the assembly process into the kinetically trapped metastable states far from the true minimum of the free energy. 6,4,15,16,17,18,19 Complexes of oppositely charged polyelectrolytes (PECs) are one of the interesting examples of kinetically controlled assemblies in solution 20,21,22 but also at interfaces. [START_REF] Giermanska | Colloids Surfaces A Physicochem[END_REF] The complexes of oppositely charged synthetic polyelectrolytes, which are excellent model to depict biopolymers systems, show diverse phase behaviour depending on the charge ratio of oppositely charged polyelectrolytes, molecular weight and mixing pathway. 24,16,25,26,27,28,29,30 In such system, there exists a critical threshold ionic strength Ic above which electrostatic attractions between species of opposite charges are so screened that complexation no longer operates. 24,31,32,33,34 The presence of such threshold enables to drive the complexation of these structures using a desalting pathway. Starting from a mixture of oppositely charged polyelectroytes in a highly salted ''dormant'' solution where the building-blocks are not interacting anymore, it is then possible to trigger complexation by lowering the ionic strength below Ic, i.e. the electrostatic interaction can be switched on and off by tuning the ionic strength.

Such desalting route strategy is not limited to PECs and can be used with complexes of inorganic charged nanoparticles (NPs) and polyelectroytes of opposite charges to design different functional materials. 34,35,36,37,18 Ic depends on several parameters (polyelectroyte length 38 , particle size 39,40 , polyelectroyte stiffness 41 , or volume ratio of charged species due to ion-pairing [START_REF] Demirelli | Colloids Surfaces A Physicochem[END_REF] ) and is usually larger than 0.1M. This route has for example already been used to form stable spherical large complexes of magnetic nanoparticles of maghemite γ-Fe2O3 coated with negatively charged PAA2k polyelectrolyte (polyacrylic acid) and positively charged PDADMAC (poly(diallyldimethylammonium chloride)) polyelectrolytes by crossing Ic by dialysis. 35,36 Such complexes are further resistant to dilution. When the dialysis is performed in the presence of a magnetic field to cross the desalting transition, nano-rods are obtained instead of spheres due to magnetic dipolar interactions between magnetic NPs in the system. The thickness and length of these magnetic nano-rods can be modified by tuning the formulation conditions. These magnetic nano-rods are superparamagnetic, biocompatible and can be functionalized with nano-dots for fluorescent properties, providing them a huge potential in biomedical applications. Remarkably, they keep their anisotropic shape out of magnetic field and do not reorganize themselves into spherical objects, suggesting that they are frozen structures. The desalting pathway can be used as well between oppositely charged NPs (CeO2) in solution and at interfaces. [START_REF] Sekar | Colloids Surfaces A Physicochem[END_REF] In the present work, we study the impact of desalting/resalting pathway on mixtures of oppositely charged nanoparticles and polymers. Shortly, the idea is to monitor the evolution of the structure of the system along the formulation pathway : (a) start from a "dormant" solution made from a building-block mixture at a very high ionic strength far above Ic; (b) cross the transition by desalting down to a targeted ionic strength Itarget < Ic; (c) let the system evolve at Itarget for a given time, (d) and cross back the transition by resalting back up to the nominal ionic strength. Owing to the potential for applications of the PDADMAC/PAA@γ-Fe2O3 system, we have chosen to investigate the very same experimental system. Moreover, as it has been shown in literature that different mixing pathways (e.g. fast versus drop by drop mixing) may lead to different quenched morphologies, we will assess if the mixing pathway does influence the final morphology of the quenched complexes. We address the following questions: (i) Does Ic depends on Z (charge ratio between oppositely charged species) and/or on the formulation pathway ? (ii) Is the desalting transition perfectly reversible ? (iii) Can this system be utilized to form frozen assemblies ? (iv) What is the internal structure of frozen assemblies?

Materials and Methods

Materials

The sodium salt of poly(acrylic acid) (MW = 2100 g/mol) with Batch No. 420344 and poly(diallyldimethylammonium chloride) (PDADMAC) (MW < 100,000 g/mol) with Batch No. 522376 were purchased from Aldrich. The iron oxide nanoparticles (γ-Fe2O3) were synthesized by Massart method 44 by alkaline coprecipitation of iron(II) and iron(III) salts. At the end of synthesis, the nanoparticles were positively charged which ensures colloidal stability at low pH (~2) (>1 year) due to a combination of electrostatic and short range hydration repulsions and their counterions were HNO3 -. The nanoparticles were then coated with small poly(acrylic acid) (PAA) chains using precipitation-redispersion protocol. 45,46 Since the pKa of PAA chains is around 4.7, coated γ-Fe2O3 nanoparticles, hereafter named PAA@γ-Fe2O3, are negatively charged at neutral and high pH, and are thus stabilized by electro-steric interactions and have stability for years around neutral pH. The characterization, coating properties and stabilization of these particles are described in previous publications. 46 In particular, the charge on nanoparticles have been measured by titration measurements. The size distribution of the bare γ-Fe2O3 nanoparticles follow a lognormal distribution with a mean diameter Rmean = 4.7nm (R0 = 4.5 nm and  = 0.2), as determined by SAXS. The nanoparticles are organized in solution as small branched clusters of ~ 4 NPs, modelled by the form factor of a pearl neckless (see Figure S1 in supplementary information). 47

Sample preparation

The charge ratio Z of PDADMAC to nanoparticles is calculated as described in reference 46 from the charges of nanoparticles (titration measurements) and the MW and charges of the PDADMAC chains.

Preparation of initial stock solution and mixing protocol.

A stock solution of 0.05 v/v% γ-Fe2O3 at 1 M NH4Cl and pH 8 is prepared from a stock solution of γ-Fe2O3 nanoparticles at 1.15 wt% γ-Fe2O3 by dilution using deionized milli-Q water. A stock solution of PDADMAC at 1 M NH4Cl and pH 8 was prepared separately and its concentration was varied in order to reach the targeted Z after mixing. The ionic strength and pH of solutions were set to 1 M NH4Cl and pH 8 using 4M NH4Cl, NH4OH and HCl solutions. The NH4Cl salt was chosen to allow comparison with complexation processes of very close systems already probed in literature (pure PAA2K/PDADMAC or PAA@CeO2 NPs/PDADMAC) [START_REF] Giermanska | Colloids Surfaces A Physicochem[END_REF]46 . pH 8 was chosen in order to ensure that PAA chains are fully charged. The equal volumes of 2Z-PDADMAC + 1 M NH4Cl and 0.05 v/v% γ-Fe2O3 + 1 M NH4Cl solutions were then mixed together to form the non-reactive clear solution, i.e. the so-called "dormant" solution of 0.025 v/v% γ-Fe2O3/Z-PDADMAC + 1 M NH4Cl.

Desalting transition pathway protocols. Three different charge ratios Z of respectively 0.004, 0.2 and 1 were investigated in the study. Two pathways were assessed to lower the ionic strength of the dormant solution at a given Z, hereafter named respectively the quenching and the drop-by-drop mixing pathway.

For the quenching pathway, the stock dormant solution (0.025 v/v% γ-Fe2O3/Z-PDADMAC at 1 M NH4Cl) was diluted 10 times in one shot using a syringe or a pipette to correspond to the final targeted ionic strength Itarget in the range (0.1-1 M NH4Cl). Samples were shaken gently by hand to ensure homogenization.

For the drop-by-drop mixing pathway, the stock dormant solution (0.025 v/v% γ-Fe2O3/Z-PDADMAC at 1 M NH4Cl) was diluted 10 times drop by drop using a syringe filled with milli-Q water. After each drop, the solution was stirred to achieve a proper mixing. Typically, 100 drops were added sequentially to reach the targeted ionic strength. Drops were added every 3 seconds to achieve a characteristic time around 5 minutes for the whole process.

Resalting pathway protocols. The resalting pathway consists in diluting a desalted sample with a very concentrated solution of NH4Cl to increase back the overall ionic strength to its initial value of 1 M NH4Cl. It has been performed on samples that have been desalted by either the quenching or the drop-by-drop pathway after a specified time. For DLS measurements, the resalting was performed 1h or 30h after desalting. For the SAXS measurements, the resalting was performed 10 days after desalting. In practice, 75 v/v% of the desalting solution (0.0025 v/v% γ-Fe2O3/Z-PDADMAC at x M NH4Cl, where x < 1) is diluted with 25v/v% of corresponding solution at high ionic strength (y M NH4Cl, where y ≤ 4) to set the NH4Cl concentration back to 1 M NH4Cl. This thus reduces the overall concentration of nanoparticles. In order to recover the nominal concentration of nanoparticle for the DLS measurements, we took benefit from the fact that the nanoparticles aggregate and settle at the bottom with time after desalting (see results part). That results in a two-phase system with solid precipitates and a supernatant solution almost free of nanoparticles. We removed 25v/v% of the supernatant from the desalted solution, and added a similar volume of high concentration y M NH4Cl solution to increase the ionic strength to 1 M NH4Cl. For the SAXS measurements, a rather high concentration of nanoparticles was mandatory to obtain a good signal-to-noise ratio, which prompted us to modify the protocol. 5 ml of desalting solution of 0.0025 v/v% γ-Fe2O3/Z-PDADMAC at x M NH4Cl was prepared and was kept during 10 days for ageing. This time was sufficient for the nanoparticles to sediment. 4.5 ml of supernatant was then removed from this desalting solution to increase its concentration of nanoparticles by approximately 10 times. The 0.5 ml resultant solution was then gently shaken to make it homogeneous. Then, 0.125 ml of the solution was removed and an equivalent volume at y M NH4Cl was added to set the final concentration to 1 M NH4Cl.

Small-angle X-ray scattering

Small-angle X-ray scattering experiments were carried out with an Xeuss 2.0 instrument from Xenocs (Grenoble, France). It uses a micro-focused sealed tube Cu K-alpha source with a wavelength of 1.54 Å. The experiments were performed with collimated beam size of 0.5 x 0.6 mm. The sample to detector distance was set to 2.5 m to achieve a Q range from 0.045 nm - 1 to 0.25 nm -1 . The solutions were poured (0.025 v/v% γ-Fe2O3/Z-PDADMAC) inside 1.5 mm glass capillaries. The measurements were performed for 30 minutes to achieve a good statistics on the whole Q range. The respective scattering from capillaries, solvent and dark count were subtracted using standard protocols. The data were normalized to absolute units in cm -1 . For the samples showing a macroscopic phase separation (sedimentation), we checked that the structure of the complexes was similar all along the capillary, except for the concentration factor. In order to optimize statistics, scattering curves were then taken at the bottom of the capillary where the complexes concentration was the highest. The respective electronic scattering densities of the components are respectively ρe(γ-Fe2O3) = 39.42 10 10 cm -2 , ρe(PDADMAC) = 9.95 10 10 cm -2 , ρe(PAA) = 9.89 10 10 cm -2 , and ρe(H2O) = 9.46 10 10 cm -2 . Since the scattering of a given object within the solution is proportional to (ρe(object)-ρe(solvent)) 2 , the scattering of the coated nanoparticles in water is completely dominated by the γ-Fe2O3 core due to contrast reasons ( (ρe(γ-Fe2O3)-ρe(H2O)) 2 /(ρe(PDADMAC)-ρe(H2O)) 2 ~ 4000 and (ρe(γ-Fe2O3)-ρe(H2O))2/(ρe(PAA)-ρe(H2O)) 2 ~ 5000).

Dynamic light scattering

Dynamic light scattering (DLS) experiments were carried out using a Zetasizer Nano ZS instrument from Malvern. The instrument uses monochromatic light with a 633 nm wavelength provided by a He-Ne laser at a fixed angle of 173°. The concentration of the nanoparticles (0.0025 v/v% γ-Fe2O3/Z-PDADMAC) was dilute to avoid any concentration effects (interparticle interactions) and determine the true self-diffusion coefficient/hydrodynamic size. Zav is the Intensity weighted harmonic mean size using cumulant analysis. In Figure 1 State diagram of the PAA@γ-Fe2O3 nanoparticles/PDADMAC system, Zav is an average of three measurements of two minutes each. When the hydrodynamic sizes were above a micron (in aggregated systems) and in turn affected by gravity (sedimentation effects), no attempts are made to accurately predict the size distributions.

Optical microscopy:

Optical microscopy was used with respective magnification lenses of 10X, 20X, 60X. The samples were deposited on a transparent glass slide, which was furthermore sealed to reduce the evaporation.

Results and discussion

Probing the desalting/resalting transition by light scattering: highlighting the formation of persistent aggregates

We firstly established the state diagram of the system and determined the critical ionic strength Ic by combining visual observation and DLS. The dormant stock solution of 0.025 v/v% γ-Fe2O3 + Z-PDADMAC + 1 M NH4Cl was diluted by a factor 10 to lower the salinity down to the targeted ionic strength Itarget. Two dilution pathways were used, respectively fast (or quenching) and drop-by-drop mixing where water is progressively added to the dormant solution (see Material and methods). For both desalting pathways, different charge ratios (Z = 0.04, 0.2, 1) were explored over targeted ionic strength Itarget ranging from I = 0.1 to 1 M NH4Cl. It immediately appears that: (i) there exist two clear-cut regimes depending on Itarget with a critical threshold Ic located at ~ 0.62 M; (ii) the state diagram does not depend on the pathway, since samples appear similar for a given set of conditions (Z, I) whether desalting is achieved by quenching or drop-by-drop mixing. For Itarget ≥ Ic, samples appear clear and limpid with an orange colour due to the presence of γ-Fe2O3 maghemite nanoparticles and their aspect does not evolve with time. Complexation does not occur, as shown by DLS (Figure 1.a). Indeed, the hydrodynamic size does not evolve with a value of 32 nm similar to the individual PAA@γ-Fe2O3 nanoparticles.

Conversely, as soon as the critical ionic strength Ic is crossed, complexes are formed whose size grows exponentially with time, as shown by the kinetic evolution of the hydrodynamic radius determined by time resolved DLS measurements (see figure 2.a). Such evolution does not depend on Itarget. The initial stage complexation kinetics was quite fast with a hydrodynamic radius already 10 times larger than individual PAA@γ-Fe2O3 nanoparticles after just 1 minute, whatever Itarget. Once the complexes reached a sufficiently large size prone to gravity forces, they started to sediment. Visually, macroscopic samples looked homogeneous up to 30 minutes and progressively started sedimenting afterwards. The characteristic sedimentation time may slightly vary from one sample to another with typical values ranging from 1h to 5h. After 24h, the sedimentation process is over with samples presenting a two-phase system with a clear supernatant and a solid-like precipitate at the bottom of the vial. We characterized then such steady state to establish the state diagram of the system presented in Figure 1. The samples were slightly shaken by hand to get a homogeneous solution just before starting DLS measurements, which enables proper measurements since the measurement time is shorter than the characteristic sedimentation time. The transition threshold is very sharp with onset located at Itarget = 0.62 M, an ionic strength for which the electrostatic interaction is highly screened since the corresponding Debye length is ~ 0.4 nm. For 0.58 M ≥ Itarget > 0.62 M, the hydrodynamic radius of the complexes sharply increased when decreasing Itarget and reached typical values larger than a few hundreds of nm for Itarget < 0.58 M. The value of Ic is neither influenced by Z (see Figure 1.b) nor by the formulation pathway as both fast mixing and drop by drop mixing give identical results. Such Ic is much larger than those measured in the case of the pure PAA-PDADMAC polyelectrolyte system with the same respective chains Mw and located at 0.3M. [START_REF] Giermanska | Colloids Surfaces A Physicochem[END_REF] The difference arises from the fact that free PAA chains have to pay greater entropic penalty to form a complex with PDADMAC, whereas PAA chains coated on γ-Fe2O3 nanoparticles have already lost most of their conformational entropy when adsorbed onto the nanoparticles and can thus easily form complexes with PDADMAC chains upon desalting. Such Ic is however very close to those obtained on the same system when the desalting transition was crossed by dialysis (Ic = 0.54 M). 36

Ionic Strength after desalting (x M) Ionic Strength after desalting (x M)

In order to assess if the transition is driven by either a liquidsolid (precipitation) or a liquid-liquid transition, i.e. a complex coacervation, we imaged the aggregates by optical microscopy. Images were taken 3 days after mixing (figure 2.b). They appeared as dense polymorph precipitates and not at all to spherical objects with an overall size that slightly increased from a few tens of m at Itarget = 0.1M up to a few hundreds of m at Itarget = 0.5M. This suggests at first sight that the system undergoes precipitation rather than complex coacervation. Interesting results were obtained when crossing back the transition by resalting the system to the nominal 1 M ionic strength (Figure 3). The behaviour of the system was indeed dependent on the "quenching time" defined as the time elapsed between the desalting and resalting steps, or in other words the resting time at Itarget. For short quenching times (from a few minutes up to ~1 hour), the complexes re-dissociate upon salt addition as shown by time-resolved DLS experiments (Figure 3.a), which suggests that the desalting transition is reversible. However, when the quenching time was much longer (~days), persistent aggregates were still visible (Figure 3.b). There is thus in the system an ageing time during which aggregates tend to reorganise toward more stable states after quenching. Moreover, Itarget strongly influenced the stability of such permanent aggregates. Indeed, Figure 3.b presents the kinetic evolution of the size after resalting for different Itarget:

the closer Itarget to Ic is, the more difficult it is to dissolve the aggregates. Moreover, for a given Itarget, the overall size of the aggregates increases with the quenching time (figure 3.c). This result is at first sight rather counterintuitive, as one would expect that the reversibility of the transition would be easier when electrostatic interactions are highly screened close to the threshold. Actually, it comes from the way Itarget tunes the internal morphologies of the complexes, as will be shown further down with the help of SAXS experiments.

Interestingly, at very long quenching times (3 months), the dissolution rate for Itarget = 0.5 was slow enough to enable a visualization of the complexes immediately after resalting by optical microscopy (figure 3.d). Contrary to what was observed just after quenching, some aggregates appeared spherical, which suggests that they form a dense liquid phase. It is then likely that the system undergoes complex coacervation rather than precipitation upon quenching in the vicinity of Ic well in line with a weaker electrostatic interaction strength. Coacervates are usually very viscous 48,49 and it takes them a very long time to reach a spherical droplet shape, a process that is made possible by the reorganizations that occur upon ageing. The behaviour of the system recalls thus those already observed in oppositely charged polyelectrolyte complexes where precipitation occurs far from Ic and coacervation close to Ic 50 . Probing the structure of aggregates by SAXS: Itarget tunes their inner structure and in turn their ability to re-dissociate DLS time-resolved results suggested that depending on Itarget, the inner morphology of the complexes presented some differences. This prompted us to determine their inner structure at the SAXS scale. Since both Z and the formulation pathway have only a very weak influence on the complexes formation (Figure 1), we decided to focus only on the quenching pathway at Z=0.2. In the SAXS experiments, only the γ-Fe2O3 core nanoparticle contributes to the scattering due to contrast reasons (see materials and methods). The scattering intensity writes then:

𝐼(𝑞)(𝑐𝑚 -1 ) = ∆𝜌 2 𝑃(𝑞)𝑆(𝑞) (1)
where  is the volume fraction of γ-Fe2O3 nanoparticles,  the difference of electronic scattering length density between γ-Fe2O3 nanoparticles and water, P(q) and S(q) the form and the structure factor of γ-Fe2O3 nanoparticles respectively. SAXS experiments were performed 24h after quenching. When the dispersion have phase-separated below Ic, the dense phase present at the bottom of the vial was studied. Figure 4.a shows a series of SAXS curves measured for various Itarget ranging from 0.1 M to 0.65M together with the form factor of individual γ-Fe2O3 nanoparticles. At 0.65M, the SAXS spectra superimpose with the nanoparticles form factor because complexation has not yet occurred. For all others Itarget, the scattering is strongly modified and present two main features : (i) at low q, it decays like q -4 (Porod law) in line with the formation of large and dense complexes (seen by DLS); (ii) at intermediate q, there is a strong correlation peak at ~ 0.6 nm -1 that corresponds to the mean distance between nanoparticles within the aggregates. The intensity and q-position of such peak q * strongly depend on Itarget, as highlighted in Figure 4.b that presents the structure factor of the nanoparticles within aggregates.

Two regimes can be identified. When Itarget is in the vicinity of Ic (Itarget > 0.48), the inner structure of the aggregates strongly changes upon a slight variation of Itarget. The correlation peak is initially very broad at 0.6 M just below Ic. As one moves away from the transition by decreasing Itarget , q * is shifted towards larger q (from 0.54 nm -1 at 0.6M up to 0.615 nm -1 at 0.48 M, which corresponds to a decrease of ~ 15% of the mean distance between nanoparticles) while its height S(q * ) increases (see Figure S2 in supplementary information). It suggests that the complexes contain a certain amount of water at 0.6 M and become progressively denser and more compact and then less solvated when moving away for the transition. In order to account quantitatively for such change of compactness in this regime of Itarget, we have used a Percus-Yevick structure factor 51 in order to obtain the total inner volume fraction of objects of nanoparticles and PDADMAC within the aggregates ΦPAA@γ- When Itarget is far from Ic (Itarget ≤ 0.48), q * stays constant at 0.615 nm -1 (10.2 nm in direct space) showing that compactness has reached a maximal value. The correlation peak broadens and its height S(q * ) slightly decreases when Itarget decreases, showing that the system is less organized (see Figure 4.b.). This is probably due to a system that freezes during complexation with a magnitude increasing inversely with Itarget in line with a stronger electrostatic interaction. It turns out that nanoparticles have more freedom to move and reorganise within the complexes in the first regime (Itarget > 0.48) since their compactness is still far from its maximal value. It does not however hamper the integrity of such aggregates, which remain persistent with time. The final aggregates morphology is thus tuneable with a very slight modification of the ionic strength Itarget. DLS data (Figure 2.a) have shown that these complexes are formed within short time scales (less than 1h, mostly few minutes or less). In order to assess if their inner structure does evolve on a much longer time scale, we have performed SAXS experiments from 24h to 30 days after quenching for different ionic strengths. We have found that the complex inner structure does not evolve with time as SAXS curves were similar up to 1 month after quenching (see figure S3 in Supplementary information that compares data for several Itarget ranging from 0.1 M to 0.56 M).

The kinetics of dissolution of complexes after resalting(crossing back the threshold to 1M NH4Cl) was probed for 3representative Itarget (0.1 M, 0.3 M and 0.5 M, Figure 5.a to Figure 5.c). The quenching time was set to 10 days, a much larger time that the characteristic time used for DLS observations. The measurements were performed just after the resalting step. For Itarget = 0.1 M, dissolution is almost immediate as the SAXS curve superimposes well with the form factor after 45 minutes only with no observed evolution afterwards. Only a slight aggregation is present in the system, as shown by a very small increase of the scattering intensity at the lowest q. For Itarget = 0.3 M, where the system is slightly less frozen, the behaviour is very close to those at 0.1 M, even though some aggregates still persist and do not disassociate with time, in accordance with DLS results. On the contrary, for Itarget = 0.5 M, when the complexes contain more water, the morphology of the complexes evolves progressively over hours with aggregates still present after 1 day. The dissolution of the structures with a quenching time of 10 days is thus very slow. The way the correlation peak evolves upon dissolution at Itarget = 0.5 M is also informative: it broadens with dissolution time but its q-position does not change. This shows that the internal morphology of the aggregates remains the same after resalting, the broadening arising from the decrease of the overall size of the aggregates with time. This means that the dissolution mechanisms is probably driven by a progressive release of the nanoparticles from the outer surface of aggregates.

Such kinetic SAXS experiments demonstrate that the inner structure of the complexes drives their ability to reorganize toward more stable states. Indeed, for strong electrostatic interactions, frozen aggregates are formed. The freezing process has thus trapped the system in a long-lived configuration as far from its minimal free energy as Itarget is low.

The system cannot then reorganize, evolve or age after quenching while it can recover easily its initial state upon desalting, which makes the transition almost reversible. At 0.1 M, dissolution is fully reversible while a very limited amount of aggregates persists at 0.3M. It is likely that the system has reached a more stable configuration at 0.3M than at 0.1M. On the contrary, for weak electrostatic interactions, when Itarget is close to Ic, the compactness of the aggregates is not maximal. Reorganizations can then occur with time and may follow entropy driven rearrangements toward kinetically trapped metastable assemblies, which have a lower free energy than the states formed just after quenching. Aggregates reach then a configuration where they are more stable and therefore very difficult to dissolve, which increases consecutively their lifetime after desalting. Permanent metastable aggregates can thus be obtained upon resalting if the time elapsed after the initial desalting is long enough. Figure 6 presents a schematic overview of the evolution of the system.

Conclusion

In summary we have shown that, the desalting/resalting pathway enable to form aggregates with different dissolution rates: they dissolve fast upon resalting at low ionic strength (Itarget = 0.1 M) far below Ic, whereas they are more stable and dissolve very slowly at higher ionic strength (Itarget = 0.5 M) close to Ic. While such results may appear counterintuitive at first sight (stronger electrostatic interactions lead to less stable aggregates), they can be rationalized by the way the freezing of the system upon quenching restrict any further entropy driven rearrangements within complexes. The re-dissolution of complexes upon resalting is indeed driven by the internal morphology of complexes which is set by Itarget. Internal rearrangements within the aggregates are the largest in the vicinity of Ic when the volume fraction of nanoparticles within the aggregates is the lowest (Figure 4.c). Within this limited range of Itarget (0.5M to 0.6 M NH4Cl), the reorganization rate within the aggregates is sufficiently large to enable the formation of very stable aggregates resistant to dissolution. The desalting/resalting pathway is then ideal to form metastable states with various morphologies, sizes, dissolution rates and lifetimes. In particular, it can be used advantageously (i) when stabilization of specific nanoparticle co-assemblies is required in conditions where they are not spontaneously associated at equilibrium at very high ionic strength; (ii) or to slowly deliver drugs or precursors in chemical reactions.

  a. Laboratoire Léon Brillouin, Université Paris-Saclay, CEA Saclay, 91191 Gif sur Yvette Cedex, France. Email : fabrice.cousin@cea.fr b. Université de Paris, CNRS, Matière et systèmes complexes, 75013 Paris, France. c. Centre de Recherche Paul Pascal (CRPP), UMR CNRS 5031, Université ́ de Bordeaux, 33600 Pessac, France.

Figure 1

 1 Figure 1 State diagram of the PAA@γ-Fe2O3 nanoparticles/PDADMAC system upon desalting when starting from an ionic strength of 1M NH4Cl for 2 desalting pathways and various Z: (a) Quenching pathway. Evolution of hydrodynamic radius of size complexes, as measured by DLS, versus ionic strength Itarget; Pictures illustrate the macroscopic aspect of samples below Ic (left) and upon the threshold Ic (right). (b) Drop by drop pathway. Evolution of hydrodynamic radius of size complexes, as measured by DLS, versus ionic stren gth Itarget; Pictures illustrate the macroscopic aspect of samples below Ic (left) and upon the threshold Ic (right).

Figure 2 .

 2 Figure 2. Evolution of the aggregates morphology after desalting in the case of the fast mixing pathway at Z = 0.2 for various Itarget: (a) kinetic evolution of the size by DLS; the dotted line recalls the hydrodynamic radius of single PAA@γ-Fe2O3 nanoparticles. (b) Optical images of the aggregates are obtained after quenching time of 72h.

Figure 3 .

 3 Figure 3. Evolution of the aggregates morphology after resalting along the desalting/resalting pathway in the case of the fast mixing pathway at Z = 0.2 for various Itarget. (a) and (b): kinetic evolution of their average size by DLS, respectively when the salting step has been achieved 1h after initial desalting (a) or 30 h after initial desalting (b); the dotted line recalls the hydrodynamic radius of single PAA@γ-Fe2O3 nanoparticles. (c) Evolution of the average size as function of quenching time for Itarget = 0.5M. (d) Optical images of the aggregates obtained immediately after resalting after an elapsed quenching time of 3 months for Itarget = 0.5M.

Fe2O3/

  PDADMAC. Such structure factor describes hard-spheres systems and usually reproduces well the scattering features of the inner structure of dense aggregates of spheres with only two parameters: the hard sphere radius RHS and volume fraction.

Figure 4 .

 4 c shows the results obtained from the fits of the PY structure factors for a constant RHS of 5.6±0.1nm. The parameters of the fits are given in supplementary information. RHS is slightly larger than the individual γ-Fe2O3 nanoparticles (4.7nm) because it takes into account the overall size of the nanoparticles made of a γ-Fe2O3 core, a functional adsorbed PAA layer and the PDADMAC chains. PAA@γ-Fe2O3/PDADMAC decreases continuously from 0.33 at 0.5 M down to 0.19 at 0.62 M.

Figure 4

 4 Figure 4 SAXS scattering curves of the PAA@γ-Fe2O3 nanoparticles/PDADMAC system upon desalting from 1M NH4Cl by quenching at Z = 0.2. (a) SAXS data in log-log scale at different ionic strengths compared with the form factor of pure PAA@γ-Fe2O3 nanoparticles (purple). The scattering of pure PAA@γ-Fe2O3 nanoparticles is in absolute scale. As the nanoparticle concentration may change from one sample to another in presence of salt due to sedimentation, all curves have been scaled on the form factor at large q. They were thene shifted from one to another by a factor 3.33 for clarity; (b) Structure factor of complexes for Itarget ≤ 0.6 M , as obtained by dividing the scattering intensity by the form factor of individual PAA@γ-Fe2O3 nanoparticles. All curves are separated one from each other by 0.2 for clarity. The continuous black lines are fits by a Percus-Yevick structure factor. The error bars are smaller than the symbols. (c) Evolution of the compactness of aggregates as function of Itarget in the vicinity of Ic.

Figure 5 .

 5 Figure 5. Kinetic evolution of the inner morphology of the complexes by SAXS after salting back (dequenching) 10 days after quenching along the desalting/salting pathway in the case of the quenching mixing pathway at Z = 0.2 for various Itarget. (a) Itarget = 0.1 M; (b) Itarget = 0.3 M; (c) Itarget = 0.5 M. SAXS curves are compared to the form factor of individual PAA@γ-Fe2O3 nanoparticles (brown curve).

Acknowledgements

This research was supported by Agence Nationale de la Recherche (PANORAMA project, ANR-13-BS08-0015).

Conflicts of interest

There are no conflicts to declare.

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