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Nadav Cohen

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11 papers

2 author rows

EAAI Journal 2025 Journal Article

Adaptive Kalman-Informed Transformer

Nadav Cohen
Itzik Klein

The extended Kalman filter (EKF) is a widely adopted method for sensor fusion in navigation applications. A crucial aspect of the EKF is the online determination of the process noise covariance matrix reflecting the model uncertainty. While common EKF implementation assumes a constant process noise, in real-world scenarios, the process noise varies, leading to inaccuracies in the estimated state and potentially causing the filter to diverge. Model-based adaptive EKF methods were proposed and demonstrated performance improvements to cope with such situations, highlighting the need for a robust adaptive approach. In this paper, we derive an adaptive Kalman-informed transformer (A-KIT) designed to learn the varying process noise covariance online. Built upon the foundations of the EKF, A-KIT utilizes the well-known capabilities of set transformers, including inherent noise reduction and the ability to capture nonlinear behavior in the data. This approach is suitable for any application involving the EKF. In a case study, we demonstrate the effectiveness of A-KIT in nonlinear fusion between a Doppler velocity log and inertial sensors. This is accomplished using real data recorded from sensors mounted on an autonomous underwater vehicle operating in the Mediterranean Sea. We show that A-KIT outperforms the conventional EKF by more than 49. 5% and model-based adaptive EKF by an average of 35. 4% in terms of position accuracy.

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NeurIPS Conference 2025 Conference Paper

Do Neural Networks Need Gradient Descent to Generalize? A Theoretical Study

‪Yotam Alexander‬‏
Yonatan Slutzky
Yuval Ran-Milo
Nadav Cohen

Conventional wisdom attributes the mysterious generalization abilities of overparameterized neural networks to gradient descent (and its variants). The recent volume hypothesis challenges this view: it posits that these generalization abilities persist even when gradient descent is replaced by Guess & Check (G&C), i. e. , by randomly drawing weight settings until one that fits the training data is found. The validity of the volume hypothesis for wide and deep neural networks remains an open question. In this paper, we theoretically investigate this question for matrix factorization (with linear and non-linear activation): a canonical testbed in neural network theory. We first prove that generalization under G&C deteriorates with increasing width, establishing what is, to our knowledge, the first canonical case where G&C is provably inferior to gradient descent. Conversely, we prove that generalization under G&C improves with increasing depth, revealing a stark contrast between wide and deep networks, which we further validate empirically. These findings suggest that even in simple settings, there may not be a simple answer to the question of whether neural networks need gradient descent to generalize well.

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NeurIPS Conference 2025 Conference Paper

The Implicit Bias of Structured State Space Models Can Be Poisoned With Clean Labels

Yonatan Slutzky
‪Yotam Alexander‬‏
Noam Razin
Nadav Cohen

Neural networks are powered by an implicit bias: a tendency of gradient descent to fit training data in a way that generalizes to unseen data. A recent class of neural network models gaining increasing popularity is structured state space models (SSMs). Prior work argued that the implicit bias of SSMs leads to generalization in a setting where data is generated by a low dimensional teacher. In this paper, we revisit the latter setting, and formally establish a phenomenon entirely undetected by prior work on the implicit bias of SSMs. Namely, we prove that while implicit bias leads to generalization under many choices of training data, there exist special examples whose inclusion in training completely distorts the implicit bias, to a point where generalization fails. This failure occurs despite the special training examples being labeled by the teacher, i. e. , having clean labels! We empirically demonstrate the phenomenon, with SSMs trained independently and as part of non-linear neural networks. In the area of adversarial machine learning, disrupting generalization with cleanly labeled training examples is known as clean-label poisoning. Given the proliferation of SSMs, we believe that delineating their susceptibility to clean-label poisoning, and developing methods for overcoming this susceptibility, are critical research directions to pursue.

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NeurIPS Conference 2024 Conference Paper

Provable Benefits of Complex Parameterizations for Structured State Space Models

Yuval Ran-Milo
Eden Lumbroso
Edo Cohen-Karlik
Raja Giryes
Amir Globerson
Nadav Cohen

Structured state space models (SSMs), the core engine behind prominent neural networks such as S4 and Mamba, are linear dynamical systems adhering to a specified structure, most notably diagonal. In contrast to typical neural network modules, whose parameterizations are real, SSMs often use complex parameterizations. Theoretically explaining the benefits of complex parameterizations for SSMs is an open problem. The current paper takes a step towards its resolution, by establishing formal gaps between real and complex diagonal SSMs. Firstly, we prove that while a moderate dimension suffices in order for a complex SSM to express all mappings of a real SSM, a much higher dimension is needed for a real SSM to express mappings of a complex SSM. Secondly, we prove that even if the dimension of a real SSM is high enough to express a given mapping, typically, doing so requires the parameters of the real SSM to hold exponentially large values, which cannot be learned in practice. In contrast, a complex SSM can express any given mapping with moderate parameter values. Experiments corroborate our theory, and suggest a potential extension of the theory that accounts for selectivity, a new architectural feature yielding state of the art performance.

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NeurIPS Conference 2023 Conference Paper

On the Ability of Graph Neural Networks to Model Interactions Between Vertices

Noam Razin
Tom Verbin
Nadav Cohen

Graph neural networks (GNNs) are widely used for modeling complex interactions between entities represented as vertices of a graph. Despite recent efforts to theoretically analyze the expressive power of GNNs, a formal characterization of their ability to model interactions is lacking. The current paper aims to address this gap. Formalizing strength of interactions through an established measure known as separation rank, we quantify the ability of certain GNNs to model interaction between a given subset of vertices and its complement, i. e. between the sides of a given partition of input vertices. Our results reveal that the ability to model interaction is primarily determined by the partition's walk index --- a graph-theoretical characteristic defined by the number of walks originating from the boundary of the partition. Experiments with common GNN architectures corroborate this finding. As a practical application of our theory, we design an edge sparsification algorithm named Walk Index Sparsification (WIS), which preserves the ability of a GNN to model interactions when input edges are removed. WIS is simple, computationally efficient, and in our experiments has markedly outperformed alternative methods in terms of induced prediction accuracy. More broadly, it showcases the potential of improving GNNs by theoretically analyzing the interactions they can model.

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NeurIPS Conference 2023 Conference Paper

What Makes Data Suitable for a Locally Connected Neural Network? A Necessary and Sufficient Condition Based on Quantum Entanglement.

‪Yotam Alexander‬‏
Nimrod De La Vega
Noam Razin
Nadav Cohen

The question of what makes a data distribution suitable for deep learning is a fundamental open problem. Focusing on locally connected neural networks (a prevalent family of architectures that includes convolutional and recurrent neural networks as well as local self-attention models), we address this problem by adopting theoretical tools from quantum physics. Our main theoretical result states that a certain locally connected neural network is capable of accurate prediction over a data distribution if and only if the data distribution admits low quantum entanglement under certain canonical partitions of features. As a practical application of this result, we derive a preprocessing method for enhancing the suitability of a data distribution to locally connected neural networks. Experiments with widespread models over various datasets demonstrate our findings. We hope that our use of quantum entanglement will encourage further adoption of tools from physics for formally reasoning about the relation between deep learning and real-world data.

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EAAI Journal 2022 Journal Article

BeamsNet: A data-driven approach enhancing Doppler velocity log measurements for autonomous underwater vehicle navigation

Nadav Cohen
Itzik Klein

Autonomous underwater vehicles (AUV) perform various applications such as seafloor mapping and underwater structure health monitoring. Commonly, an inertial navigation system aided by a Doppler velocity log (DVL) is used to provide the vehicle’s navigation solution. In such fusion, the DVL provides the velocity vector of the AUV, which determines the navigation solution’s accuracy and helps estimate the navigation states. This paper proposes BeamsNet, an end-to-end deep learning framework to regress the estimated DVL velocity vector that improves the accuracy of the velocity vector estimate, and could replace the model-based approach. Two versions of BeamsNet, differing in their input to the network, are suggested. The first uses the current DVL beam measurements and inertial sensor data, while the other utilizes only DVL data, taking the current and past DVL measurements for the regression process. Both simulation and sea experiments were made to validate the proposed learning approach relative to the model-based approach. Sea experiments were made with the Snapir AUV in the Mediterranean Sea, collecting approximately four and a half hours of DVL and inertial sensor data. Our results show that the proposed approach achieved an improvement of more than 60% in estimating the DVL velocity vector.

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NeurIPS Conference 2021 Conference Paper

Continuous vs. Discrete Optimization of Deep Neural Networks

Omer Elkabetz
Nadav Cohen

Existing analyses of optimization in deep learning are either continuous, focusing on (variants of) gradient flow, or discrete, directly treating (variants of) gradient descent. Gradient flow is amenable to theoretical analysis, but is stylized and disregards computational efficiency. The extent to which it represents gradient descent is an open question in the theory of deep learning. The current paper studies this question. Viewing gradient descent as an approximate numerical solution to the initial value problem of gradient flow, we find that the degree of approximation depends on the curvature around the gradient flow trajectory. We then show that over deep neural networks with homogeneous activations, gradient flow trajectories enjoy favorable curvature, suggesting they are well approximated by gradient descent. This finding allows us to translate an analysis of gradient flow over deep linear neural networks into a guarantee that gradient descent efficiently converges to global minimum almost surely under random initialization. Experiments suggest that over simple deep neural networks, gradient descent with conventional step size is indeed close to gradient flow. We hypothesize that the theory of gradient flows will unravel mysteries behind deep learning.

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NeurIPS Conference 2020 Conference Paper

Implicit Regularization in Deep Learning May Not Be Explainable by Norms

Noam Razin
Nadav Cohen

Mathematically characterizing the implicit regularization induced by gradient-based optimization is a longstanding pursuit in the theory of deep learning. A widespread hope is that a characterization based on minimization of norms may apply, and a standard test-bed for studying this prospect is matrix factorization (matrix completion via linear neural networks). It is an open question whether norms can explain the implicit regularization in matrix factorization. The current paper resolves this open question in the negative, by proving that there exist natural matrix factorization problems on which the implicit regularization drives all norms (and quasi-norms) towards infinity. Our results suggest that, rather than perceiving the implicit regularization via norms, a potentially more useful interpretation is minimization of rank. We demonstrate empirically that this interpretation extends to a certain class of non-linear neural networks, and hypothesize that it may be key to explaining generalization in deep learning.

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NeurIPS Conference 2019 Conference Paper

Implicit Regularization in Deep Matrix Factorization

Sanjeev Arora
Nadav Cohen
Wei Hu
Yuping Luo

Efforts to understand the generalization mystery in deep learning have led to the belief that gradient-based optimization induces a form of implicit regularization, a bias towards models of low "complexity. " We study the implicit regularization of gradient descent over deep linear neural networks for matrix completion and sensing, a model referred to as deep matrix factorization. Our first finding, supported by theory and experiments, is that adding depth to a matrix factorization enhances an implicit tendency towards low-rank solutions, oftentimes leading to more accurate recovery. Secondly, we present theoretical and empirical arguments questioning a nascent view by which implicit regularization in matrix factorization can be captured using simple mathematical norms. Our results point to the possibility that the language of standard regularizers may not be rich enough to fully encompass the implicit regularization brought forth by gradient-based optimization.

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ICML Conference 2018 Conference Paper

On the Optimization of Deep Networks: Implicit Acceleration by Overparameterization

Sanjeev Arora
Nadav Cohen
Elad Hazan

Conventional wisdom in deep learning states that increasing depth improves expressiveness but complicates optimization. This paper suggests that, sometimes, increasing depth can speed up optimization. The effect of depth on optimization is decoupled from expressiveness by focusing on settings where additional layers amount to overparameterization – linear neural networks, a well-studied model. Theoretical analysis, as well as experiments, show that here depth acts as a preconditioner which may accelerate convergence. Even on simple convex problems such as linear regression with $\ell_p$ loss, $p>2$, gradient descent can benefit from transitioning to a non-convex overparameterized objective, more than it would from some common acceleration schemes. We also prove that it is mathematically impossible to obtain the acceleration effect of overparametrization via gradients of any regularizer.

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