Neural network training relies on gradient computation through backpropagation, yet memory requirements for storing layer activations present significant scalability challenges. We present the first adaptation of control-theoretic matrix sketching to neural network layer activations, enabling memory-efficient gradient reconstruction in backpropagation. This work builds on recent matrix sketching frameworks for dynamic optimization problems, where similar state trajectory storage challenges motivate sketching techniques. Our approach sketches layer activations using three complementary sketch matrices maintained through exponential moving averages (EMA) with adaptive rank adjustment, automatically balancing memory efficiency against approximation quality. Empirical evaluation on MNIST, CIFAR-10, and physics-informed neural networks demonstrates a controllable accuracy-memory tradeoff. We demonstrate a gradient monitoring application on MNIST showing how sketched activations enable real-time gradient norm tracking with minimal memory overhead. These results establish that sketched activation storage provides a viable path toward memory-efficient neural network training and analysis.

Summary and Contributions: The authors analyze the effect of gradient quantization for quantized training in a principled fashion, and introduce two methods that reduce the variance of the gradients when doing quantized training. Still I hold that if FQT is compared to QAT, you should quantize the weights and not keep shadow weights. This is what I meant with having the actual weights quantized, and the updates quantized as well. In most FQT applications that are parallelized in compute, you are very often memory movement bound, meaning you're playing a game of reducing memory as much as possible. The gradients are calculated on the fly, used and discarded in the backward pass, the memory overhead of them is small.

Neural networks have demonstrated significant advancements in Neural Machine Translation (NMT) compared to conventional phrase-based approaches. However, Multilingual Neural Machine Translation (MNMT) in extremely low-resource settings remains underexplored. This research investigates how knowledge transfer across languages can enhance MNMT in such scenarios. Using the Tatoeba translation challenge dataset from Helsinki NLP, we perform English-German, English-French, and English-Spanish translations, leveraging minimal parallel data to establish cross-lingual mappings. Unlike conventional methods relying on extensive pre-training for specific language pairs, we pre-train our model on English-English translations, setting English as the source language for all tasks. The model is fine-tuned on target language pairs using joint multi-task and sequential transfer learning strategies. Our work addresses three key questions: (1) How can knowledge transfer across languages improve MNMT in extremely low-resource scenarios? (2) How does pruning neuron knowledge affect model generalization, robustness, and catastrophic forgetting? (3) How can TX-Ray interpret and quantify knowledge transfer in trained models? Evaluation using BLEU-4 scores demonstrates that sequential transfer learning outperforms baselines on a 40k parallel sentence corpus, showcasing its efficacy. However, pruning neuron knowledge degrades performance, increases catastrophic forgetting, and fails to improve robustness or generalization. Our findings provide valuable insights into the potential and limitations of knowledge transfer and pruning in MNMT for extremely low-resource settings.

GNNs are powerful models based on node representation learning that perform particularly well in many machine learning problems related to graphs. The major obstacle to the deployment of GNNs is mostly a problem of societal acceptability and trustworthiness, properties which require making explicit the internal functioning of such models. Here, we propose to mine activation rules in the hidden layers to understand how the GNNs perceive the world. The problem is not to discover activation rules that are individually highly discriminating for an output of the model. Instead, the challenge is to provide a small set of rules that cover all input graphs. To this end, we introduce the subjective activation pattern domain. We define an effective and principled algorithm to enumerate activations rules in each hidden layer. The proposed approach for quantifying the interest of these rules is rooted in information theory and is able to account for background knowledge on the input graph data. The activation rules can then be redescribed thanks to pattern languages involving interpretable features. We show that the activation rules provide insights on the characteristics used by the GNN to classify the graphs. Especially, this allows to identify the hidden features built by the GNN through its different layers. Also, these rules can subsequently be used for explaining GNN decisions. Experiments on both synthetic and real-life datasets show highly competitive performance, with up to 200% improvement in fidelity on explaining graph classification over the SOTA methods.

We introduce and detail an atypical neural network architecture, called time elastic neural network (teNN), for multivariate time series classification. The novelty compared to classical neural network architecture is that it explicitly incorporates time warping ability, as well as a new way of considering attention. In addition, this architecture is capable of learning a dropout strategy, thus optimizing its own architecture.Behind the design of this architecture, our overall objective is threefold: firstly, we are aiming at improving the accuracy of instance based classification approaches that shows quite good performances as far as enough training data is available. Secondly we seek to reduce the computational complexity inherent to these methods to improve their scalability. Ideally, we seek to find an acceptable balance between these first two criteria. And finally, we seek to enhance the explainability of the decision provided by this kind of neural architecture.The experiment demonstrates that the stochastic gradient descent implemented to train a teNN is quite effective. To the extent that the selection of some critical meta-parameters is correct, convergence is generally smooth and fast.While maintaining good accuracy, we get a drastic gain in scalability by first reducing the required number of reference time series, i.e. the number of teNN cells required. Secondly, we demonstrate that, during the training process, the teNN succeeds in reducing the number of neurons required within each cell. Finally, we show that the analysis of the activation and attention matrices as well as the reference time series after training provides relevant information to interpret and explain the classification results.The comparative study that we have carried out and which concerns around thirty diverse and multivariate datasets shows that the teNN obtains results comparable to those of the state of the art, in particular similar to those of a network mixing LSTM and CNN architectures for example.

We explore convergence of deep neural networks with the popular ReLU activation function, as the depth of the networks tends to infinity. To this end, we introduce the notion of activation domains and activation matrices of a ReLU network. By replacing applications of the ReLU activation function by multiplications with activation matrices on activation domains, we obtain an explicit expression of the ReLU network. We then identify the convergence of the ReLU networks as convergence of a class of infinite products of matrices. Sufficient and necessary conditions for convergence of these infinite products of matrices are studied. As a result, we establish necessary conditions for ReLU networks to converge that the sequence of weight matrices converges to the identity matrix and the sequence of the bias vectors converges to zero as the depth of ReLU networks increases to infinity. Moreover, we obtain sufficient conditions in terms of the weight matrices and bias vectors at hidden layers for pointwise convergence of deep ReLU networks. These results provide mathematical insights to the design strategy of the well-known deep residual networks in image classification.

We propose a new notion of'non-linearity' of a network layer with respect to an input batch that is based on its proximity to a linear system, which is reflected in the nonnegative rank of the activation matrix. Considering batches of similar samples, we find that high non-linearity in deep layers is indicative of memorization. Furthermore, by applying our approach layer-by-layer, we find that the mechanism for memorization consists of distinct phases. We perform experiments on fully-connected and convolutional neural networks trained on several image and audio datasets. Our results demonstrate that as an indicator for memorization, our technique can be used to perform early stopping. A fundamental challenge in machine learning is balancing the bias-variance tradeoff, where overly simple learning models underfit the data (suboptimal performance on the training data) and overly complex models are expected to overfit or memorize the data (perfect training set performance, but suboptimal test set performance). The latter direction of this tradeoff has come into question with the observation that deep neural networks do not memorize their training data despite having sufficient capacity to do so (Zhang et al., 2016), the explanation of which is a matter of much interest. Due to their convenient gradient properties and excellent performance in practice, rectified-linear units (ReLU) have been widely adopted and are now ubiquitous in the field of deep learning.

A key feature of neural networks, particularly deep convolutional neural networks, is their ability to "learn" useful representations from data. The very last layer of a neural network is then simply a linear model trained on these "learned" representations. Despite their numerous applications in other tasks such as classification, retrieval, clustering etc., a.k.a. transfer learning, not much work has been published that investigates the structure of these representations or whether structure can be imposed on them during the training process. In this paper, we study the dimensionality of the learned representations by models that have proved highly succesful for image classification. We focus on ResNet-18, ResNet-50 and VGG-19 and observe that when trained on CIFAR10 or CIFAR100 datasets, the learned representations exhibit a fairly low rank structure. We propose a modification to the training procedure, which further encourages low rank representations of activations at various stages in the neural network. Empirically, we show that this has implications for compression and robustness to adversarial examples.

We postulate that the nature of information items plays a vital role in the observed spread of these items in a social network. We capture this intuition by proposing a model that assigns to every information item two parameters: endogeneity and exogeneity. The endogeneity of the item quantifies its tendency to spread primarily through the connections between nodes; the exogeneity quantifies its tendency to be acquired by the nodes, independently of the underlying network. We also extend this item-based model to take into account the openness of each node to new information. We quantify openness by introducing the receptivity of a node. Given a social network and data related to the ordering of adoption of information items by nodes, we develop a maximum-likelihood framework for estimating endogeneity, exogeneity and receptivity parameters. We apply our methodology to synthetic and real data and demonstrate its efficacy as a data-analytic tool.