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Researcher profile

Daniel Soudry

Daniel Soudry contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine LearningArtificial IntelligenceComputer VisionEmerging TechnologiesHardware Architecturemath.NANeural and Evolutionary ComputingNumerical Analysis

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Published work

17 published item(s)

preprint2026arXiv

From Continual Learning to SGD and Back: Better Rates for Continual Linear Models

We study the common continual learning setup where an overparameterized model is sequentially fitted to a set of jointly realizable tasks. We analyze forgetting, defined as the loss on previously seen tasks, after $k$ iterations. For continual linear models, we prove that fitting a task is equivalent to a single stochastic gradient descent (SGD) step on a modified objective. We develop novel last-iterate SGD upper bounds in the realizable least squares setup and leverage them to derive new results for continual learning. Focusing on random orderings over $T$ tasks, we establish universal forgetting rates, whereas existing rates depend on problem dimensionality or complexity and become prohibitive in highly overparameterized regimes. In continual regression with replacement, we improve the best existing rate from $O((d-\bar{r})/k)$ to $O(\min(1/\sqrt[4]{k}, \sqrt{(d-\bar{r})}/k, \sqrt{T\bar{r}}/k))$, where $d$ is the dimensionality and $\bar{r}$ the average task rank. Furthermore, we establish the first rate for random task orderings without replacement. The resulting rate $O(\min(1/\sqrt[4]{T},\, (d-\bar{r})/T))$ shows that randomization alone, without task repetition, prevents catastrophic forgetting in sufficiently long task sequences. Finally, we prove a matching $O(1/\sqrt[4]{k})$ forgetting rate for continual linear classification on separable data. Our universal rates extend to broader methods, such as block Kaczmarz and POCS, illuminating their loss convergence under i.i.d. and single-pass orderings.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Normalized Architectures are Natively 4-Bit

Training large language models at 4-bit precision is critical for efficiency. We show that nGPT, an architecture that constrains weights and hidden representations to the unit hypersphere, is inherently more robust to low-precision arithmetic. This removes the need for interventions-such as applying random Hadamard transforms and performing per-tensor scaling calculations-to preserve model quality, and it enables stable end-to-end NVFP4 training. We validate this approach on both a 1.2B dense model and hybrid (Mamba-Transformer) MoE models of up to 3B/30B parameters. We trace this robustness to the dot product: while quantization noise remains largely uncorrelated in both standard and normalized architectures, the signal behaves differently. In nGPT, the hypersphere constraint enhances weak positive correlations among the element-wise products, leading to a constructive accumulation of the signal across the hidden dimension while the noise continues to average out. This yields a higher effective signal-to-noise ratio and a flatter loss landscape, with the effect strengthening as the hidden dimension grows, suggesting increasing advantages at scale. A reference implementation is available at https://github.com/anonymous452026/ngpt-nvfp4

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Retrieval from Within: An Intrinsic Capability of Attention-Based Models

Retrieval-augmented generation (RAG) typically treats retrieval and generation as separate systems. We ask whether an attention-based encoder-decoder can instead retrieve directly from its own internal representations. We introduce INTRA (INTrinsic Retrieval via Attention), a framework where decoder attention queries score pre-encoded evidence chunks that are then directly reused as context for generation. By construction, INTRA unifies retrieval and generation, eliminating the retriever-generator mismatch typical of RAG pipelines. This design also amortizes context encoding by reusing precomputed encoder states across queries. On question-answering benchmarks, INTRA outperforms strong engineered retrieval pipelines on both evidence recall and end-to-end answer quality. Our results demonstrate that attention-based models already possess a retrieval mechanism that can be elicited, rather than added as an external module.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Workspace Optimization: How to Train Your Agent

Modern agents built on frontier language models often cannot adapt their weights. What, then, remains trainable? We argue it is the agent's \emph{workspace}, the structured external substrate it reads, writes, and tests; we call its evolution workspace optimization. Workspace optimization targets hard multi-turn environments where a frontier model has strong priors but cannot solve the task in a single shot, so the agent must learn through interaction. We propose a principled way to evolve the workspace, mirroring the structure of weight-space training: artifacts in place of parameters, evidence in place of data, counterexamples in place of losses, and textual feedback in place of gradients. We instantiate the idea in DreamTeam, a multi-agent harness for ARC-AGI-3 whose roles build an executable world model, plan, hypothesize, probe, strategize, and route failures. On the current 25-game ARC-AGI-3 public set under the official scoring protocol and averaged over two independent runs, DreamTeam improves the SOTA protocol-matched agent's score from 36% to 38.4%, while using 31% fewer environment actions per game.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

A statistical framework for efficient out of distribution detection in deep neural networks

Background. Commonly, Deep Neural Networks (DNNs) generalize well on samples drawn from a distribution similar to that of the training set. However, DNNs' predictions are brittle and unreliable when the test samples are drawn from a dissimilar distribution. This is a major concern for deployment in real-world applications, where such behavior may come at a considerable cost, such as industrial production lines, autonomous vehicles, or healthcare applications. Contributions. We frame Out Of Distribution (OOD) detection in DNNs as a statistical hypothesis testing problem. Tests generated within our proposed framework combine evidence from the entire network. Unlike previous OOD detection heuristics, this framework returns a $p$-value for each test sample. It is guaranteed to maintain the Type I Error (T1E - incorrectly predicting OOD for an actual in-distribution sample) for test data. Moreover, this allows to combine several detectors while maintaining the T1E. Building on this framework, we suggest a novel OOD procedure based on low-order statistics. Our method achieves comparable or better results than state-of-the-art methods on well-accepted OOD benchmarks, without retraining the network parameters or assuming prior knowledge on the test distribution -- and at a fraction of the computational cost.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

How catastrophic can catastrophic forgetting be in linear regression?

To better understand catastrophic forgetting, we study fitting an overparameterized linear model to a sequence of tasks with different input distributions. We analyze how much the model forgets the true labels of earlier tasks after training on subsequent tasks, obtaining exact expressions and bounds. We establish connections between continual learning in the linear setting and two other research areas: alternating projections and the Kaczmarz method. In specific settings, we highlight differences between forgetting and convergence to the offline solution as studied in those areas. In particular, when T tasks in d dimensions are presented cyclically for k iterations, we prove an upper bound of T^2 * min{1/sqrt(k), d/k} on the forgetting. This stands in contrast to the convergence to the offline solution, which can be arbitrarily slow according to existing alternating projection results. We further show that the T^2 factor can be lifted when tasks are presented in a random ordering.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Stochastic Gradient Descent on Separable Data: Exact Convergence with a Fixed Learning Rate

Stochastic Gradient Descent (SGD) is a central tool in machine learning. We prove that SGD converges to zero loss, even with a fixed (non-vanishing) learning rate - in the special case of homogeneous linear classifiers with smooth monotone loss functions, optimized on linearly separable data. Previous works assumed either a vanishing learning rate, iterate averaging, or loss assumptions that do not hold for monotone loss functions used for classification, such as the logistic loss. We prove our result on a fixed dataset, both for sampling with or without replacement. Furthermore, for logistic loss (and similar exponentially-tailed losses), we prove that with SGD the weight vector converges in direction to the $L_2$ max margin vector as $O(1/\log(t))$ for almost all separable datasets, and the loss converges as $O(1/t)$ - similarly to gradient descent. Lastly, we examine the case of a fixed learning rate proportional to the minibatch size. We prove that in this case, the asymptotic convergence rate of SGD (with replacement) does not depend on the minibatch size in terms of epochs, if the support vectors span the data. These results may suggest an explanation to similar behaviors observed in deep networks, when trained with SGD.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Training of Quantized Deep Neural Networks using a Magnetic Tunnel Junction-Based Synapse

Quantized neural networks (QNNs) are being actively researched as a solution for the computational complexity and memory intensity of deep neural networks. This has sparked efforts to develop algorithms that support both inference and training with quantized weight and activation values, without sacrificing accuracy. A recent example is the GXNOR framework for stochastic training of ternary (TNN) and binary (BNN) neural networks. In this paper, we show how magnetic tunnel junction (MTJ) devices can be used to support QNN training. We introduce a novel hardware synapse circuit that uses the MTJ stochastic behavior to support the quantize update. The proposed circuit enables processing near memory (PNM) of QNN training, which subsequently reduces data movement. We simulated MTJ-based stochastic training of a TNN over the MNIST, SVHN, and CIFAR10 datasets and achieved an accuracy of 98.61%, 93.99% and 82.71%, respectively (less than 1% degradation compared to the GXNOR algorithm). We evaluated the synapse array performance potential and showed that the proposed synapse circuit can train ternary networks in situ, with 18.3TOPs/W for feedforward and 3TOPs/W for weight update.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

On the Implicit Bias of Initialization Shape: Beyond Infinitesimal Mirror Descent

Recent work has highlighted the role of initialization scale in determining the structure of the solutions that gradient methods converge to. In particular, it was shown that large initialization leads to the neural tangent kernel regime solution, whereas small initialization leads to so called "rich regimes". However, the initialization structure is richer than the overall scale alone and involves relative magnitudes of different weights and layers in the network. Here we show that these relative scales, which we refer to as initialization shape, play an important role in determining the learned model. We develop a novel technique for deriving the inductive bias of gradient-flow and use it to obtain closed-form implicit regularizers for multiple cases of interest.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

At Stability's Edge: How to Adjust Hyperparameters to Preserve Minima Selection in Asynchronous Training of Neural Networks?

Background: Recent developments have made it possible to accelerate neural networks training significantly using large batch sizes and data parallelism. Training in an asynchronous fashion, where delay occurs, can make training even more scalable. However, asynchronous training has its pitfalls, mainly a degradation in generalization, even after convergence of the algorithm. This gap remains not well understood, as theoretical analysis so far mainly focused on the convergence rate of asynchronous methods. Contributions: We examine asynchronous training from the perspective of dynamical stability. We find that the degree of delay interacts with the learning rate, to change the set of minima accessible by an asynchronous stochastic gradient descent algorithm. We derive closed-form rules on how the learning rate could be changed, while keeping the accessible set the same. Specifically, for high delay values, we find that the learning rate should be kept inversely proportional to the delay. We then extend this analysis to include momentum. We find momentum should be either turned off, or modified to improve training stability. We provide empirical experiments to validate our theoretical findings.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Beyond Signal Propagation: Is Feature Diversity Necessary in Deep Neural Network Initialization?

Deep neural networks are typically initialized with random weights, with variances chosen to facilitate signal propagation and stable gradients. It is also believed that diversity of features is an important property of these initializations. We construct a deep convolutional network with identical features by initializing almost all the weights to $0$. The architecture also enables perfect signal propagation and stable gradients, and achieves high accuracy on standard benchmarks. This indicates that random, diverse initializations are \textit{not} necessary for training neural networks. An essential element in training this network is a mechanism of symmetry breaking; we study this phenomenon and find that standard GPU operations, which are non-deterministic, can serve as a sufficient source of symmetry breaking to enable training.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Characterizing Implicit Bias in Terms of Optimization Geometry

We study the implicit bias of generic optimization methods, such as mirror descent, natural gradient descent, and steepest descent with respect to different potentials and norms, when optimizing underdetermined linear regression or separable linear classification problems. We explore the question of whether the specific global minimum (among the many possible global minima) reached by an algorithm can be characterized in terms of the potential or norm of the optimization geometry, and independently of hyperparameter choices such as step-size and momentum.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Implicit Bias in Deep Linear Classification: Initialization Scale vs Training Accuracy

We provide a detailed asymptotic study of gradient flow trajectories and their implicit optimization bias when minimizing the exponential loss over "diagonal linear networks". This is the simplest model displaying a transition between "kernel" and non-kernel ("rich" or "active") regimes. We show how the transition is controlled by the relationship between the initialization scale and how accurately we minimize the training loss. Our results indicate that some limit behaviors of gradient descent only kick in at ridiculous training accuracies (well beyond $10^{-100}$). Moreover, the implicit bias at reasonable initialization scales and training accuracies is more complex and not captured by these limits.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Is Feature Diversity Necessary in Neural Network Initialization?

Standard practice in training neural networks involves initializing the weights in an independent fashion. The results of recent work suggest that feature "diversity" at initialization plays an important role in training the network. However, other initialization schemes with reduced feature diversity have also been shown to be viable. In this work, we conduct a series of experiments aimed at elucidating the importance of feature diversity at initialization. We show that a complete lack of diversity is harmful to training, but its effects can be counteracted by a relatively small addition of noise - even the noise in standard non-deterministic GPU computations is sufficient. Furthermore, we construct a deep convolutional network with identical features at initialization and almost all of the weights initialized at 0 that can be trained to reach accuracy matching its standard-initialized counterpart.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Kernel and Rich Regimes in Overparametrized Models

A recent line of work studies overparametrized neural networks in the "kernel regime," i.e. when the network behaves during training as a kernelized linear predictor, and thus training with gradient descent has the effect of finding the minimum RKHS norm solution. This stands in contrast to other studies which demonstrate how gradient descent on overparametrized multilayer networks can induce rich implicit biases that are not RKHS norms. Building on an observation by Chizat and Bach, we show how the scale of the initialization controls the transition between the "kernel" (aka lazy) and "rich" (aka active) regimes and affects generalization properties in multilayer homogeneous models. We also highlight an interesting role for the width of a model in the case that the predictor is not identically zero at initialization. We provide a complete and detailed analysis for a family of simple depth-$D$ models that already exhibit an interesting and meaningful transition between the kernel and rich regimes, and we also demonstrate this transition empirically for more complex matrix factorization models and multilayer non-linear networks.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Kernel and Rich Regimes in Overparametrized Models

A recent line of work studies overparametrized neural networks in the "kernel regime," i.e. when the network behaves during training as a kernelized linear predictor, and thus training with gradient descent has the effect of finding the minimum RKHS norm solution. This stands in contrast to other studies which demonstrate how gradient descent on overparametrized multilayer networks can induce rich implicit biases that are not RKHS norms. Building on an observation by Chizat and Bach, we show how the scale of the initialization controls the transition between the "kernel" (aka lazy) and "rich" (aka active) regimes and affects generalization properties in multilayer homogeneous models. We provide a complete and detailed analysis for a simple two-layer model that already exhibits an interesting and meaningful transition between the kernel and rich regimes, and we demonstrate the transition for more complex matrix factorization models and multilayer non-linear networks.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

The Knowledge Within: Methods for Data-Free Model Compression

Recently, an extensive amount of research has been focused on compressing and accelerating Deep Neural Networks (DNN). So far, high compression rate algorithms require part of the training dataset for a low precision calibration, or a fine-tuning process. However, this requirement is unacceptable when the data is unavailable or contains sensitive information, as in medical and biometric use-cases. We present three methods for generating synthetic samples from trained models. Then, we demonstrate how these samples can be used to calibrate and fine-tune quantized models without using any real data in the process. Our best performing method has a negligible accuracy degradation compared to the original training set. This method, which leverages intrinsic batch normalization layers' statistics of the trained model, can be used to evaluate data similarity. Our approach opens a path towards genuine data-free model compression, alleviating the need for training data during model deployment.

0 citations0 reviewsNo code linkedOpen access