Biology subjects

Sompolinsky, H.

Publications and source records attributed to Sompolinsky, H..

13 recordsLinked to original sources

bioRxiv2026

A complementary learning system for continual episodic memory in large language models

Humans retain memories of individual experiences for a lifetime, an ability attributed to a complementary learning system in which a fast process encodes episodes and a slow process integrates them into semantic knowledge. In classical Hebbian models such as Hopfield networks, memory traces are superposed in shared weights. This makes learning naturally continual but causes strong interference among correlated memories, a failure that reappears as catastrophic forgetting in deep networks. Here we use a large language model as a model system for continual episodic memory, with its pretrained weights supplying the semantic context in which new episodes are embedded. Fast learning is implemented by a hippocampus-like module that assigns each episode to a dedicated, extremely sparse low-rank adapter; competitive gating then selects among these separated traces during recall. Across streams of up to 1,000 factual and autobiographical episodes, each adapter requires only 2-3 parameters per token while preserving excellent recall. An internal retrieval-augmented generation mechanism reconstructs the selected episode in context and supports high-accuracy question answering over stored memories. Finally, slow cortical consolidation is modeled by fine-tuning the base weights through batch replay, enabling reconstruction and direct question answering without episodic adapters. Together, fast storage and slow consolidation implement both components of a complementary learning system within a single language model, yielding a neural-network model that stores, recalls, and consolidates naturalistic episodic memories, thereby capturing key functional features of human memory.

neuroscience↗

bioRxiv2026

Manifold geometry underlies a unified code for category and category-independent features

A central question in neuroscience and machine learning is how a single neural representation can support linear access to multiple kinds of information about the same stimulus. While this ability is widespread in biological and artificial systems, the representational principles that make such joint coding possible remain poorly understood. We address this question for an important class of representations: those jointly encoding discrete stimulus categories and continuous features that vary independently of category. Using the framework of category manifolds (the sets of neural representations elicited by stimuli from the same category) we extend existing theories of manifold classification to the equally essential task of regressing category-independent features, determining which aspects of manifold geometry govern regression performance. This provides a unified framework for understanding how classification- and regression-relevant geometry can be jointly optimized to implement an effective joint code. Applying this framework to convolutional neural networks (CNNs), we find that regression-relevant geometry can be optimized through subtle changes that largely preserve classification-relevant geometry. This explains why common representational-similarity measures previously failed to distinguish joint codes from codes optimized exclusively for classification. Motivated by prior work in visual neuroscience suggesting that macaque inferotemporal cortex may jointly encode object category and category-independent features such as object position and size, we use our framework to identify principled geometric signatures that distinguish joint codes from classification-only codes in CNNs and can be tested in future neural recordings. Finally, we characterize how these signatures are affected by common experimental constraints: limited stimulus categories and neural-population subsampling.

neuroscience↗

bioRxiv2025

Symmetries and continuous attractors in disordered neural circuits

A major challenge in neuroscience is reconciling idealized theoretical models with complex, heterogeneous experimental data. We address this challenge through continuous-attractor networks, which model how neural circuits represent continuous variables such as head direction or spatial location through collective dynamics. Classical continuous-attractor models rely on continuous symmetry in the recurrent weights to generate a manifold of stable states, predicting tuning curves that are identical up to shifts. However, mouse head-direction cells exhibit substantial heterogeneity in their responses, seemingly incompatible with this classical picture. We demonstrate that mammalian circuits could nevertheless rely on the same dynamical mechanisms as classical continuous-attractor models. We construct recurrent neural networks directly from experimental head-direction tuning curves that exhibit quasi-continuous-attractor dynamics, then develop a statistical generative process quantitatively capturing the structure of tuning heterogeneity. This enables large-N analysis, where we show through dynamical mean-field theory that these networks become equivalent to classical ring-attractor models, with Mexican-hat interactions and continuous symmetry that is spontaneously broken, leading to bump states. In the seemingly disordered weights, the continuous symmetry essential to classical models is reflected through eigenvalue degeneracies, positioning spectral structure as a target for detecting continuous-attractor circuits in connectome data. We extend this framework to two-dimensional symmetries, constructing grid-cell models that similarly reduce to classical toroidal attractors. Our work demonstrates that the dynamical mechanisms of classical continuous-attractor models may operate not only in small brains or idealized systems but also in complex mammalian circuits.

neuroscience↗

bioRxiv2022

Associative memory of structured knowledge

A long standing challenge in biological and artificial intelligence is to understand how new knowledge can be constructed from known building blocks in a way that is amenable for computation by neuronal circuits. Here we focus on the task of storage and recall of structured knowledge in long-term memory. Specifically, we ask how recurrent neuronal networks can store and retrieve multiple knowledge structures. We model each structure as a set of binary relations between events and attributes (attributes may represent e.g., temporal order, spatial location, role in semantic structure), and map each structure to a distributed neuronal activity pattern using a vector symbolic architecture (VSA) scheme. We then use associative memory plasticity rules to store the binarized patterns as fixed points in a recurrent network. By a combination of signal-to-noise analysis and numerical simulations, we demonstrate that our model allows for efficient storage of these knowledge structures, such that the memorized structures as well as their individual building blocks (e.g., events and attributes) can be subsequently retrieved from partial retrieving cues. We show that long-term memory of structured knowledge relies on a new principle of computation beyond the memory basins. Finally, we show that our model can be extended to store sequences of memories as single attractors.

neuroscience↗

bioRxiv2021

A Minimum Perturbation Theory of Deep Perceptual Learning

Perceptual learning (PL) involves long-lasting improvement in perceptual tasks following extensive training and is accompanied by modified neuronal responses in sensory cortical areas in the brain. Understanding the dynamics of PL and the resultant synaptic changes is important for causally connecting PL to the observed neural plasticity. This is theoretically challenging because learning-related changes are distributed across many stages of the sensory hierarchy. In this work, we modeled the sensory hierarchy as a deep nonlinear neural network and studied PL of fine discrimination, a common and well-studied paradigm of PL. Using tools from statistical physics, we developed a mean-field theory of the network in the limit of large number of neurons and large number of examples. Our theory suggests that, in this "thermodynamic" limit, the input-output function of the network can be exactly mapped to that of a deep linear network, allowing us to characterize the space of solutions for the task. Surprisingly, we found that modifications of synaptic weights in lower levels of the hierarchy are both sufficient and necessary for PL. To address the degeneracy of the space of solutions, we postulate that PL dynamics are constrained by a normative "minimum perturbation" (MP) principle, which favors weight matrices with minimal changes relative to their pre-learning values. Interestingly, MP plasticity induces changes to weights and neural representations in all layers of the network, except for the readout weight vector. In addition, such plasticity can be learned simply through slow learning. We further elucidate the properties of MP changes and compare them against experimental findings. Overall, our statistical mechanics theory of PL provides mechanistic and normative understanding of several important empirical findings of PL.

neuroscience↗

bioRxiv2021

Stochastic Consolidation of Lifelong Memory

Humans have the remarkable ability to continually store new memories, while maintaining old memories for a lifetime. How the brain avoids catastrophic forgetting of memories due to interference between encoded memories is an open problem in computational neuroscience. Here we present a model for continual learning in a recurrent neural network combining Hebbian learning, synaptic decay and a novel memory consolidation mechanism. Memories undergo stochastic rehearsals with rates proportional to the memorys basin of attraction, causing self-amplified consolidation, giving rise to memory lifetimes that extend much longer than synaptic decay time, and capacity proportional to a power of the number of neurons. Perturbations to the circuit model cause temporally-graded retrograde and anterograde deficits, mimicking observed memory impairments following neurological trauma.

neuroscience↗

bioRxiv2021

The Geometry of Concept Learning

Understanding the neural basis of the remarkable human cognitive capacity to learn novel concepts from just one or a few sensory experiences constitutes a fundamental problem. We propose a simple, biologically plausible, mathematically tractable, and computationally powerful neural mechanism for few-shot learning of naturalistic concepts. We posit that the concepts that can be learnt from few examples are defined by tightly circumscribed manifolds in the neural firing rate space of higher order sensory areas. We further posit that a single plastic downstream readout neuron learns to discriminate new concepts based on few examples using a simple plasticity rule. We demonstrate the computational power of our proposal by showing it can achieve high few-shot learning accuracy on natural visual concepts using both macaque inferotemporal cortex representations and deep neural network models of these representations, and can even learn novel visual concepts specified only through linguistic descriptors. Moreover, we develop a mathematical theory of few-shot learning that links neurophysiology to behavior by delineating several fundamental and measurable geometric properties of high-dimensional neural representations that can accurately predict the few-shot learning performance of naturalistic concepts across all our numerical simulations. We discuss testable predictions of our theory for psychophysics and neurophysiological experiments.

neuroscience↗

bioRxiv2020

The spectrum of covariance matrices of randomly connected recurrent neuronal networks

A key question in theoretical neuroscience is the relation between the connectivity structure and the collective dynamics of a network of neurons. Here we study the connectivity-dynamics relation as reflected in the distribution of eigenvalues of the covariance matrix of the dynamic fluctuations of the neuronal activities, which is closely related to the networks Principal Component Analysis (PCA) and the associated effective dimensionality. We consider the spontaneous fluctuations around a steady state in a randomly connected recurrent network of stochastic neurons. An exact analytical expression for the covariance eigenvalue distribution in the large-network limit can be obtained using results from random matrices. The distribution has a finitely supported smooth bulk spectrum and exhibits an approximate power-law tail for coupling matrices near the critical edge. We generalize the results to include connectivity motifs and discuss extensions to Excitatory-Inhibitory networks. The theoretical results are compared with those from finite-size networks and and the effects of temporal and spatial sampling are studied. Preliminary application to whole-brain imaging data is presented. Using simple connectivity models, our work provides theoretical predictions for the covariance spectrum, a fundamental property of recurrent neuronal dynamics, that can be compared with experimental data.

neuroscience↗

bioRxiv2020

Object manifold geometry across the mouse cortical visual hierarchy

Despite variations in appearance, we recognize objects robustly. Neuronal populations responding to objects presented under varying transformations form object manifolds, and hierarchically organized visual areas are hypothesized to untangle pixel intensities into linearly decodable object representations. However, the associated changes in the geometry of the object manifolds along the cortex remain unknown. Using home cage training, we showed that mice are capable of invariant object recognition. We recorded the responses of thousands of neurons to measure the information about object identity across the visual cortex and found that the lateral areas LM, LI, and AL carry more linearly decodable object information compared to other visual areas. We applied the theory of linear separability of manifolds and found that the increase in classification capacity is associated with a decrease in the dimension and radius of the object manifold, identifying the key features in the geometry of the population neural code that are associated with invariant object coding.

neuroscience↗

bioRxiv2019

Separability and Geometry of Object Manifolds in Deep Neural Networks

Stimuli are represented in the brain by the collective population responses of sensory neurons, and an object presented under varying conditions gives rise to a collection of neural population responses called an object manifold. Changes in the object representation along a hierarchical sensory system are associated with changes in the geometry of those manifolds, and recent theoretical progress connects this geometry with classification capacity, a quantitative measure of the ability to support object classification. Deep neural networks trained on object classification tasks are a natural testbed for the applicability of this relation. We show how classification capacity improves along the hierarchies of deep neural networks with different architectures. We demonstrate that changes in the geometry of the associated object manifolds underlie this improved capacity, and shed light on the functional roles different levels in the hierarchy play to achieve it, through orchestrated reduction of manifolds radius, dimensionality and inter-manifold correlations.

neuroscience↗

bioRxiv2018

Coherent chaos in a recurrent neural network with structured connectivity

We present a simple model for coherent, spatially correlated chaos in a recurrent neural network. Networks of randomly connected neurons exhibit chaotic fluctuations and have been studied as a model for capturing the temporal variability of cortical activity. The dynamics generated by such networks, however, are spatially uncorrelated and do not generate coherent fluctuations, which are commonly observed across spatial scales of the neocortex. In our model we introduce a structured component of connectivity, in addition to random connections, which effectively embeds a feedforward structure via unidirectional coupling between a pair of orthogonal modes. Local fluctuations driven by the random connectivity are summed by an output mode and drive coherent activity along an input mode. The orthogonality between input and output mode preserves chaotic fluctuations even as coherence develops. In the regime of weak structured connectivity we apply a perturbative approach to solve the dynamic mean-field equations, showing that in this regime coherent fluctuations are driven passively by the chaos of local residual fluctuations. Strikingly, the chaotic dynamics are not subdued even by very strong structured connectivity if we add a row balance constraint on the random connectivity. In this regime the system displays longer time-scales and switching-like activity reminiscent of \"Up-Down\" states observed in cortical circuits. The level of coherence grows with increasing strength of structured connectivity until the dynamics are almost entirely constrained to a single spatial mode. We describe how in this regime the model achieves intermittent self-tuned criticality in which the coherent component of the dynamics self-adjusts to yield periods of slow chaos. Furthermore, we show how the dynamics depend qualitatively on the particular realization of the connectivity matrix: a complex leading eigenvalue can yield coherent oscillatory chaos while a real leading eigenvalue can yield chaos with broken symmetry. We examine the effects of network-size scaling and show that these results are not finite-size effects. Finally, we show that in the regime of weak structured connectivity, coherent chaos emerges also for a generalized structured connectivity with multiple input-output modes.\n\nAuthor SummaryNeural activity observed in the neocortex is temporally variable, displaying irregular temporal fluctuations at every accessible level of measurement. Furthermore, these temporal fluctuations are often found to be spatially correlated whether at the scale of local measurements such as membrane potentials and spikes, or global measurements such as EEG and fMRI. A thriving field of study has developed models of recurrent networks which intrinsically generate irregular temporal variability, the paradigmatic example being networks of randomly connected rate neurons which exhibit chaotic dynamics. These models have been examined analytically and numerically in great detail, yet until now the intrinsic variability generated by these networks have been spatially uncorrelated, yielding no large-scale coherent fluctuations. Here we present a simple model of a recurrent network of firing-rate neurons that intrinsically generates spatially correlated activity yielding coherent fluctuations across the entire network. The model incorporates random connections and adds a structured component of connectivity that sums network activity over a spatial \"output\" mode and projects it back to the network along an orthogonal \"input\" mode. We show that this form of structured connectivity is a general mechanism for producing coherent chaos.

neuroscience↗

bioRxiv2018

Brainwide organization of neuronal activity and convergent sensorimotor transformations in larval zebrafish

Simultaneous recordings of large populations of neurons in behaving animals allow detailed observation of high-dimensional, complex brain activity. However, experimental design and analysis approaches have not sufficiently evolved to fully realize the potential of these methods. We recorded whole-brain neuronal activity for larval zebrafish presented with a battery of visual stimuli while recording fictive motor output. These data were used to develop analysis methods including regression techniques that leverage trial-to-trial variations and unsupervised clustering techniques that organize neurons into functional groups. We used these methods to obtain brain-wide maps of concerted activity, which revealed both known and heretofore uncharacterized brain nuclei. We also identified neurons tuned to each stimulus type and motor output, and revealed nuclei in the anterior hindbrain that respond to multiple stimuli that elicit the same behavior. However, these convergent sensorimotor representations were only weakly correlated to instantaneous motor behavior, suggesting that they inform, but do not directly generate, behavioral output. These findings motivate a novel model of sensorimotor transformation spanning distinct behavioral contexts, within which these hindbrain convergence neurons likely constitute a key step.

neuroscience↗

bioRxiv2017

Optimal Sensory Coding By Populations Of ON And OFF Neurons

In many sensory systems the neural signal is coded by the coordinated response of heterogeneous populations of neurons. What computational benefit does this diversity confer on information processing? We derive an efficient coding framework assuming that neurons have evolved to communicate signals optimally given natural stimulus statistics and metabolic constraints. Incorporating nonlinearities and realistic noise, we study optimal population coding of the same sensory variable using two measures: maximizing the mutual information between stimuli and responses, and minimizing the error incurred by the optimal linear decoder of responses. Our theory is applied to a commonly observed splitting of sensory neurons into ON and OFF that signal stimulus increases or decreases, and to populations of monotonically increasing responses of the same type, ON. Depending on the optimality measure, we make different predictions about how to optimally split a population into ON and OFF, and how to allocate the firing thresholds of individual neurons given realistic stimulus distributions and noise, which accord with certain biases observed experimentally.

neuroscience↗