Seminars

Lenka Zdeborová introduces the Rules-and-Facts model, in which some observations follow a shared rule while others are isolated exceptions requiring memorization. The framework studies when a learner can acquire the rule and retain those exceptions simultaneously. Its results emphasize how capacity is organized and deployed, rather than capacity alone. The talk examines how regularization and the geometry of kernels or learned feature maps can reserve resources for memorization without undermining rule learning. It connects the balance between abstraction and memory to architectural and algorithmic choices, providing a theoretical account of neural networks that both generalize and recall specific facts.

This seminar discusses a proof-of-concept gravitational-waveform model described in arXiv:2511.10522. It augments post-Newtonian equations using physics-informed neural-network methods and universal differential equations. The talk also covers ongoing development of a precessing surrogate model designed to evaluate in less than one millisecond while covering a broader portion of the LVK frequency band.

Understanding how brains learn requires bridging evidence across scales—from behaviour and neural circuits to cells, synapses, and molecules. In our work, we use computational modelling and data analysis to explore how the physical properties of neurons and neural circuits constrain learning. These include limits imposed by brain wiring, energy availability, molecular noise, and the 3D structure of dendritic spines. In this talk I will describe one such project testing if wiring motifs from fly brain connectomes can improve performance of reservoir computers, a type of recurrent neural network. The hope is that these insights into brain learning will lead to improved learning algorithms for artificial systems.

This webinar addressed computational perspectives on how animals and humans make decisions, spanning normative, descriptive, and mechanistic models. Sam Gershman (Harvard) presented a capacity-limited reinforcement learning framework in which policies are compressed under an information bottleneck constraint. This approach predicts pervasive perseveration, stimulus‐independent “default” actions, and trade-offs between complexity and reward. Such policy compression reconciles observed action stochasticity and response time patterns with an optimal balance between learning capacity and performance. Jonathan Pillow (Princeton) discussed flexible descriptive models for tracking time-varying policies in animals. He introduced dynamic Generalized Linear Models (Sidetrack) and hidden Markov models (GLM-HMMs) that capture day-to-day and trial-to-trial fluctuations in choice behavior, including abrupt switches between “engaged” and “disengaged” states. These models provide new insights into how animals’ strategies evolve under learning. Finally, Kenji Doya (OIST) highlighted the importance of unifying reinforcement learning with Bayesian inference, exploring how cortical-basal ganglia networks might implement model-based and model-free strategies. He also described Japan’s Brain/MINDS 2.0 and Digital Brain initiatives, aiming to integrate multimodal data and computational principles into cohesive “digital brains.”

In this talk, I will explore how social affective biases arise even in the absence of motivational factors as an emergent outcome of the basic structure of social learning. In several studies, we found that initial negative interactions with some members of a group can cause subsequent avoidance of the entire group, and that this avoidance perpetuates stereotypes. Additional cognitive modeling discovered that approach and avoidance behavior based on biased beliefs not only influences the evaluative (positive or negative) impressions of group members, but also shapes the depth of the cognitive representations available to learn about individuals. In other words, people have richer cognitive representations of members of groups that are not avoided, akin to individualized vs group level categories. I will end presenting a series of multi-agent reinforcement learning simulations that demonstrate the emergence of these social-structural feedback loops in the development and maintenance of affective biases.

Developing scientifically-grounded theories for representation learning and generalization in artificial deep neural networks remains a grand challenge of fundamental interest to theoretical neuroscience and machine learning. I will discuss our work on one facet of this challenge — namely understanding generalization or “scaling laws” in learned neural networks as a function of basic control variables. I’ll discuss a taxonomy we develop that classifies different regimes of scaling behavior. We identify regimes where generalization exhibits universal scaling behavior and others where it can be traced back to properties of the data and neural architecture. The theoretical analysis is enabled by leveraging exactly solvable models of deep neural networks that arise naturally in the limit of large hidden layers. Along the way, I’ll also discuss our work on these theoretical models, which have been a useful starting point for theoretical descriptions of neural network dynamics. Finally, I’ll discuss our findings connecting generalization in neural networks to properties of the learned data manifold. I’ll close by discussing future directions and new hypotheses that emerge from our findings Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-06-19. Recording duration: 00:46:53.

Learning in biological systems takes place in contexts and with dynamics not often accounted for by simple models. I will describe the learning dynamics of two model systems that incorporate either architectural or dynamic constraints from biological observations. In the first case, inspired by the observed mesoscopic structure of the mouse brain as revealed by the Allen Mouse Brain Connectivity Atlas, as well as multiple examples of parallel pathways in mammalian brains, I present a mathematical analysis of learning dynamics in networks that have parallel computational pathways driven by the same cost function. We use the approximation of deep linear networks with large hidden layer sizes to show that, as the depth of the parallel pathways increases, different features of the training set (defined by the singular values of the input-output correlation) will typically concentrate in one of the pathways. This result is derived analytically and demonstrated with numerical simulation with both linear and non-linear networks. Thus, rather than sharing stimulus and task features across multiple pathways, parallel network architectures learn to produce sharply diversified representations with specialized and specific pathways, a mechanism which may hold important consequences for codes in both biological and artificial systems. In the second case, I discuss learning dynamics in a generalization of Hebbian rules and show that these rules allow a neuron to learn tensor decompositions of higher-order input correlations. Unlike the case of the Oja rule and PCA, the resulting learned representation is not unique but selects amongst the tensor eigenvectors according to initial conditions. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-04-10. Recording duration: 00:30:39.

Changes in ocular hemodynamics may be indicative of pathological conditions in the eye (e.g. glaucoma, age-related macular degeneration), but also elsewhere in the body (e.g. systemic hypertension, diabetes, neurodegenerative disorders). Thanks to its transparent fluids and structures that allow the light to go through, the eye offers a unique window on the circulation from large to small vessels, and from arteries to veins. Deciphering the causes that lead to changes in ocular hemodynamics in a specific individual could help prevent vision loss as well as aid in the diagnosis and management of diseases beyond the eye. In this talk, we will discuss how mathematical and computational modelling can help in this regard. We will focus on two main factors, namely blood pressure (BP), which drives the blood flow through the vessels, and intraocular pressure (IOP), which compresses the vessels and may impede the flow. Mechanism-driven models translates fundamental principles of physics and physiology into computable equations that allow for identification of cause-to-effect relationships among interplaying factors (e.g. BP, IOP, blood flow). While invaluable for causality, mechanism-driven models are often based on simplifying assumptions to make them tractable for analysis and simulation; however, this often brings into question their relevance beyond theoretical explorations. Data-driven models offer a natural remedy to address these short-comings. Data-driven methods may be supervised (based on labelled training data) or unsupervised (clustering and other data analytics) and they include models based on statistics, machine learning, deep learning and neural networks. Data-driven models naturally thrive on large datasets, making them scalable to a plethora of applications. While invaluable for scalability, data-driven models are often perceived as black- boxes, as their outcomes are difficult to explain in terms of fundamental principles of physics and physiology and this limits the delivery of actionable insights. The combination of mechanism-driven and data-driven models allows us to harness the advantages of both, as mechanism-driven models excel at interpretability but suffer from a lack of scalability, while data-driven models are excellent at scale but suffer in terms of generalizability and insights for hypothesis generation. This combined, integrative approach represents the pillar of the interdisciplinary approach to data science that will be discussed in this talk, with application to ocular hemodynamics and specific examples in glaucoma research.

Humans and animals are not always rational. They not only rationally exploit rewards but also explore an environment owing to their curiosity. However, the mechanism of such curiosity-driven irrational behavior is largely unknown. Here, we developed a decision-making model for a two-choice task based on the free energy principle, which is a theory integrating recognition and action selection. The model describes irrational behaviors depending on the curiosity level. We also proposed a machine learning method to decode temporal curiosity from behavioral data. By applying it to rat behavioral data, we found that the rat had negative curiosity, reflecting conservative selection sticking to more certain options and that the level of curiosity was upregulated by the expected future information obtained from an uncertain environment. Our decoding approach can be a fundamental tool for identifying the neural basis for reward–curiosity conflicts. Furthermore, it could be effective in diagnosing mental disorders.

When interacting with complex environments, humans can rapidly adapt their behavior to changes in task or context. To facilitate this adaptation, we often spend substantial periods of time contemplating possible futures before acting. For such planning to be rational, the benefits of planning to future behavior must at least compensate for the time spent thinking. Here we capture these features of human behavior by developing a neural network model where not only actions, but also planning, are controlled by prefrontal cortex. This model consists of a meta-reinforcement learning agent augmented with the ability to plan by sampling imagined action sequences drawn from its own policy, which we refer to as 'rollouts'. Our results demonstrate that this agent learns to plan when planning is beneficial, explaining the empirical variability in human thinking times. Additionally, the patterns of policy rollouts employed by the artificial agent closely resemble patterns of rodent hippocampal replays recently recorded in a spatial navigation task, in terms of both their spatial statistics and their relationship to subsequent behavior. Our work provides a new theory of how the brain could implement planning through prefrontal-hippocampal interactions, where hippocampal replays are triggered by - and in turn adaptively affect - prefrontal dynamics.

What is the relationship between task, network architecture, and population activity in nonlinear deep networks? I will describe the Gated Deep Linear Network framework, which schematizes how pathways of information flow impact learning dynamics within an architecture. Because of the gating, these networks can compute nonlinear functions of their input. We derive an exact reduction and, for certain cases, exact solutions to the dynamics of learning. The reduction takes the form of a neural race with an implicit bias towards shared representations, which then govern the model’s ability to systematically generalize, multi-task, and transfer. We show how appropriate network architectures can help factorize and abstract knowledge. Together, these results begin to shed light on the links between architecture, learning dynamics and network performance.

Humans and animals learn and plan with flexibility and efficiency well beyond that of modern Machine Learning methods. This is hypothesized to owe in part to the ability of animals to build structured representations of their environments, and modulate these representations to rapidly adapt to new settings. In the first part of this talk, I will discuss theoretical work describing how learned representations in hippocampus enable rapid adaptation to new goals by learning predictive representations, while entorhinal cortex compresses these predictive representations with spectral methods that support smooth generalization among related states. I will also cover recent work extending this account, in which we show how the predictive model can be adapted to the probabilistic setting to describe a broader array of generalization results in humans and animals, and how entorhinal representations can be modulated to support sample generation optimized for different behavioral states. In the second part of the talk, I will overview some of the ways in which we have combined many of the same mathematical concepts with state-of-the-art deep learning methods to improve efficiency and performance in machine learning applications like physical simulation, relational reasoning, and design.

The affinity between statistical physics and machine learning has a long history. I will describe the main lines of this long-lasting friendship in the context of current theoretical challenges and open questions about deep learning. Theoretical physics often proceeds in terms of solvable synthetic models, I will describe the related line of work on solvable models of simple feed-forward neural networks. I will highlight a path forward to capture the subtle interplay between the structure of the data, the architecture of the network, and the optimization algorithms commonly used for learning.

Understanding Human ability to learn novel concepts from just a few sensory experiences is a fundamental problem in cognitive neuroscience. I will describe a recent work with Ben Sorcher and Surya Ganguli (PNAS, October 2022) in which we propose a simple, biologically plausible, and mathematically tractable neural mechanism for few-shot learning of naturalistic concepts. We posit that the concepts that can be learned from few examples are defined by tightly circumscribed manifolds in the neural firing-rate space of higher-order sensory areas. Discrimination between novel concepts is performed by downstream neurons implementing ‘prototype’ decision rule, in which a test example is classified according to the nearest prototype constructed from the few training examples. We show that prototype few-shot learning achieves high few-shot learning accuracy on natural visual concepts using both macaque inferotemporal cortex representations and deep neural network (DNN) models of these representations. We develop a mathematical theory that links few-shot learning to the geometric properties of the neural concept manifolds and demonstrate its agreement with our numerical simulations across different DNNs as well as different layers. Intriguingly, we observe striking mismatches between the geometry of manifolds in intermediate stages of the primate visual pathway and in trained DNNs. Finally, we show that linguistic descriptors of visual concepts can be used to discriminate images belonging to novel concepts, without any prior visual experience of these concepts (a task known as ‘zero-shot’ learning), indicated a remarkable alignment of manifold representations of concepts in visual and language modalities. I will discuss ongoing effort to extend this work to other high level cognitive tasks.

Physiological experiments have highlighted how the dendrites of biological neurons can nonlinearly process distributed synaptic inputs. However, it is unclear how qualitative aspects of a dendritic tree, such as its branched morphology, its repetition of presynaptic inputs, voltage-gated ion channels, electrical properties and complex synapses, determine neural computation beyond this apparent nonlinearity. While it has been speculated that the dendritic tree of a neuron can be seen as a multi-layer neural network and it has been shown that such an architecture could be computationally strong, we do not know if that computational strength is preserved under these qualitative biological constraints. Here we simulate multi-layer neural network models of dendritic computation with and without these constraints. We find that dendritic model performance on interesting machine learning tasks is not hurt by most of these constraints and may synergistically benefit from all of them combined. Our results suggest that single real dendritic trees may be able to learn a surprisingly broad range of tasks through the emergent capabilities afforded by their properties.

A central problem in biological learning is how information about the outcome of a decision or behavior can be used to reliably guide learning across distributed neural circuits while obeying biological constraints. This “credit assignment” problem is commonly solved in artificial neural networks through supervised gradient descent and the backpropagation algorithm. In contrast, biological learning is typically modelled using unsupervised Hebbian learning rules. While these rules only use local information to update synaptic weights, and are sometimes combined with weight constraints to reflect a diversity of excitatory (only positive weights) and inhibitory (only negative weights) cell types, they do not prescribe a clear mechanism for how to coordinate learning across multiple layers and propagate error information accurately across the network. In recent years, several groups have drawn inspiration from the known dendritic non-linearities of pyramidal neurons to propose new learning rules and network architectures that enable biologically plausible multi-layer learning by processing error information in segregated dendrites. Meanwhile, recent experimental results from the hippocampus have revealed a new form of plasticity—Behavioral Timescale Synaptic Plasticity (BTSP)—in which large dendritic depolarizations rapidly reshape synaptic weights and stimulus selectivity with as little as a single stimulus presentation (“one-shot learning”). Here we explore the implications of this new learning rule through a biologically plausible implementation in a rate neuron network. We demonstrate that regulation of dendritic spiking and BTSP by top-down feedback signals can effectively coordinate plasticity across multiple network layers in a simple pattern recognition task. By analyzing hidden feature representations and weight trajectories during learning, we show the differences between networks trained with standard backpropagation, Hebbian learning rules, and BTSP.

The ability to record large neural populations—hundreds to thousands of cells simultaneously—is a defining feature of modern systems neuroscience. Aside from improved experimental efficiency, what do these technologies fundamentally buy us? I'll argue that they provide an exciting opportunity to move beyond studying the "average" neural response. That is, by providing dense neural circuit measurements in individual subjects and moments in time, these recordings enable us to track changes across repeated behavioral trials and across experimental subjects. These two forms of variability are still poorly understood, despite their obvious importance to understanding the fidelity and flexibility of neural computations. Scientific progress on these points has been impeded by the fact that individual neurons are very noisy and unreliable. My group is investigating a number of customized statistical models to overcome this challenge. I will mention several of these models but focus particularly on a new framework for quantifying across-subject similarity in stochastic trial-by-trial neural responses. By applying this method to noisy representations in deep artificial networks and in mouse visual cortex, we reveal that the geometry of neural noise correlations is a meaningful feature of variation, which is neglected by current methods (e.g. representational similarity analysis).

Neural computations are currently investigated using two separate approaches: sorting neurons into functional subpopulations or examining the low-dimensional dynamics of collective activity. Whether and how these two aspects interact to shape computations is currently unclear. Using a novel approach to extract computational mechanisms from networks trained on neuroscience tasks, here we show that the dimensionality of the dynamics and subpopulation structure play fundamentally com- plementary roles. Although various tasks can be implemented by increasing the dimensionality in networks with fully random population structure, flexible input–output mappings instead require a non-random population structure that can be described in terms of multiple subpopulations. Our analyses revealed that such a subpopulation structure enables flexible computations through a mechanism based on gain-controlled modulations that flexibly shape the collective dynamics. Our results lead to task-specific predictions for the structure of neural selectivity, for inactivation experiments and for the implication of different neurons in multi-tasking.

Artificial neural networks can be useful for studying brain functions. In cognitive neuroscience, recurrent neural networks are often used to model cognitive functions. I will first offer my opinion on what is missing in the classical use of recurrent neural networks. Then I will discuss two lines of ongoing efforts in our group to move beyond the classical recurrent neural networks by studying multi-system neural networks (the talk will focus on two-system networks). These are networks that combine modules for several neural systems, such as vision, audition, prefrontal, hippocampal systems. I will showcase how multi-system networks can potentially be constrained by experimental data in fundamental ways and at scale.