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Jonathan Kadmon

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4 papers

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NeurIPS Conference 2025 Conference Paper

Curl Descent : Non-Gradient Learning Dynamics with Sign-Diverse Plasticity

Hugo Ninou
Jonathan Kadmon
N Alex Cayco Gajic

Gradient-based algorithms are a cornerstone of artificial neural network training, yet it remains unclear whether biological neural networks use similar gradient-based strategies during learning. Experiments often discover a diversity of synaptic plasticity rules, but whether these amount to an approximation to gradient descent is unclear. Here we investigate a previously overlooked possibility: that learning dynamics may include fundamentally non-gradient "curl"-like components while still being able to effectively optimize a loss function. Curl terms naturally emerge in networks with excitatory-inhibitory connectivity or Hebbian/anti-Hebbian plasticity, resulting in learning dynamics that cannot be framed as gradient descent on any objective. To investigate the impact of these curl terms, we analyze feedforward networks within an analytically tractable student-teacher framework, systematically introducing non-gradient dynamics through rule-flipped neurons. Small curl terms preserve the stability of the original solution manifold, resulting in learning dynamics similar to gradient descent. Beyond a critical value, strong curl terms destabilize the solution manifold. Depending on the network architecture, this loss of stability can lead to chaotic learning dynamics that destroy performance. In other cases, the curl terms can counterintuitively speed up learning compared to gradient descent by allowing the weight dynamics to escape saddles by temporarily ascending the loss. Our results identify specific architectures capable of supporting robust learning via diverse learning rules, providing an important counterpoint to normative theories of gradient-based learning in neural networks.

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NeurIPS Conference 2020 Conference Paper

Predictive coding in balanced neural networks with noise, chaos and delays

Jonathan Kadmon
Jonathan Timcheck
Surya Ganguli

Biological neural networks face a formidable task: performing reliable computations in the face of intrinsic stochasticity in individual neurons, imprecisely specified synaptic connectivity, and nonnegligible delays in synaptic transmission. A common approach to combatting such biological heterogeneity involves averaging over large redundant networks of N neurons resulting in coding errors that decrease classically as the square root of N. Recent work demonstrated a novel mechanism whereby recurrent spiking networks could efficiently encode dynamic stimuli achieving a superclassical scaling in which coding errors decrease as 1/N. This specific mechanism involved two key ideas: predictive coding, and a tight balance, or cancellation between strong feedforward inputs and strong recurrent feedback. However, the theoretical principles governing the efficacy of balanced predictive coding and its robustness to noise, synaptic weight heterogeneity and communication delays remain poorly understood. To discover such principles, we introduce an analytically tractable model of balanced predictive coding, in which the degree of balance and the degree of weight disorder can be dissociated unlike in previous balanced network models, and we develop a mean-field theory of coding accuracy. Overall, our work provides and solves a general theoretical framework for dissecting the differential contributions neural noise, synaptic disorder, chaos, synaptic delays, and balance to the fidelity of predictive neural codes, reveals the fundamental role that balance plays in achieving superclassical scaling, and unifies previously disparate models in theoretical neuroscience.

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NeurIPS Conference 2018 Conference Paper

Statistical mechanics of low-rank tensor decomposition

Jonathan Kadmon
Surya Ganguli

Often, large, high dimensional datasets collected across multiple modalities can be organized as a higher order tensor. Low-rank tensor decomposition then arises as a powerful and widely used tool to discover simple low dimensional structures underlying such data. However, we currently lack a theoretical understanding of the algorithmic behavior of low-rank tensor decompositions. We derive Bayesian approximate message passing (AMP) algorithms for recovering arbitrarily shaped low-rank tensors buried within noise, and we employ dynamic mean field theory to precisely characterize their performance. Our theory reveals the existence of phase transitions between easy, hard and impossible inference regimes, and displays an excellent match with simulations. Moreover, it reveals several qualitative surprises compared to the behavior of symmetric, cubic tensor decomposition. Finally, we compare our AMP algorithm to the most commonly used algorithm, alternating least squares (ALS), and demonstrate that AMP significantly outperforms ALS in the presence of noise.

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NeurIPS Conference 2016 Conference Paper

Optimal Architectures in a Solvable Model of Deep Networks

Jonathan Kadmon
Haim Sompolinsky

Deep neural networks have received a considerable attention due to the success of their training for real world machine learning applications. They are also of great interest to the understanding of sensory processing in cortical sensory hierarchies. The purpose of this work is to advance our theoretical understanding of the computational benefits of these architectures. Using a simple model of clustered noisy inputs and a simple learning rule, we provide analytically derived recursion relations describing the propagation of the signals along the deep network. By analysis of these equations, and defining performance measures, we show that these model networks have optimal depths. We further explore the dependence of the optimal architecture on the system parameters.

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