Mathematical Modeling seminars

In the brain, while early sensory areas encode and process external inputs rapidly, higher-association areas are endowed with slow dynamics to benefit information accumulation over time. This property raises the question of why diverse timescales are well localized rather than being mixed up across the cortex, despite high connection density and an abundance of feedback loops that support reliable signal propagation. In this talk, we will address this question by analyzing a large-scale network model of the primate cortex, and we identify a novel dynamical regime termed "interference-free propagation". In this regime, the mean components of the synaptic currents to each downstream area are imbalanced to ensure signals to propagate reliably, while the temporally fluctuating components of the synaptic inputs governed by upstream areas' timescales are largely canceled out, leading to the localization of its own timescale in each downstream area. Our result provides new insights into the operational regime of the cortex, leading to the coexistence of hierarchical timescale localization and reliable signal propagation. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2025-02-26. Recording duration: 00:48:02.

Brain Emulation Challenge workshop will tackle cutting-edge topics such as ground-truthing for validation, leveraging artificial datasets generated from virtual brain tissue, and the transformative potential of virtual brain platforms, such as applied to the forthcoming Brain Emulation Challenge.

Brain Emulation Challenge workshop will tackle cutting-edge topics such as ground-truthing for validation, leveraging artificial datasets generated from virtual brain tissue, and the transformative potential of virtual brain platforms, such as applied to the forthcoming Brain Emulation Challenge.

Brain Emulation Challenge workshop will tackle cutting-edge topics such as ground-truthing for validation, leveraging artificial datasets generated from virtual brain tissue, and the transformative potential of virtual brain platforms, such as applied to the forthcoming Brain Emulation Challenge.

The centre of memory is the medial temporal lobe (MTL) and especially the hippocampus. In our research, a more flexible brain-inspired computational microcircuit of the CA1 region of the mammalian hippocampus was upgraded and used to examine how information retrieval could be affected under different conditions. Six models (1-6) were created by modulating different excitatory and inhibitory pathways. The results showed that the increase in the strength of the feedforward excitation was the most effective way to recall memories. In other words, that allows the system to access stored memories more accurately.

Networks of excitatory and inhibitory (EI) neurons form a canonical circuit in the brain. Classical theoretical analyses of dynamics in EI networks have revealed key principles such as EI balance or paradoxical responses to external inputs. These seminal results assume that synaptic strengths depend on the type of neurons they connect but are otherwise statistically independent. However, recent synaptic physiology datasets have uncovered connectivity patterns that deviate significantly from independent connection models. Simultaneously, studies of task-trained recurrent networks have emphasized the role of connectivity structure in implementing neural computations. Despite these findings, integrating detailed connectivity structures into mean-field theories of EI networks remains a substantial challenge. In this talk, I will outline a theoretical approach to understanding dynamics in structured EI networks by employing a low-rank approximation based on an analytical computation of the dominant eigenvalues of the full connectivity matrix. I will illustrate this approach by investigating the effects of pair-wise connectivity motifs on linear dynamics in EI networks. Specifically, I will present recent results demonstrating that an over-representation of chain motifs induces a strong positive eigenvalue in inhibition-dominated networks, generating a potential instability that challenges classical EI balance criteria. Furthermore, by examining the effects of external input, we found that chain motifs can, on their own, induce paradoxical responses, wherein an increased input to inhibitory neurons leads to a counterintuitive decrease in their activity through recurrent feedback mechanisms. Altogether, our theoretical approach opens new avenues for relating recorded connectivity structures with dynamics and computations in biological networks. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2025-01-22. Recording duration: 00:47:27.

The dynamics of learning in natural and artificial environments is a problem of great interest to both neuroscientists and artificial intelligence experts. However, standard analyses of animal training data either treat behavior as fixed, or track only coarse performance statistics (e.g., accuracy and bias), providing limited insight into the dynamic evolution of behavioral strategies over the course of learning. To overcome these limitations, we propose a dynamic psychophysical model that efficiently tracks trial-to-trial changes in behavior over the course of training. In this talk, I will describe recent work based on a dynamic logistic regression model that captures the time-varying dependencies of behavior on stimuli and other task covariates, which we applied to mouse training data from the International Brain Lab (IBL). Secondly, I will discuss efforts to infer animal learning rules from time-varying behavior in order to characterize how they adjust their policy in response to reward. Finally, I will describe recent work on adaptive optimal training, which combines ideas from reinforcement learning and adaptive experimental design to formulate methods for inferring animal learning rules from behavior, and using these rules to speed up animal training. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2025-01-15. Recording duration: 00:49:39.

Social experiences can have lasting changes on behavior and affective state. In particular, repeated wins and losses during fighting can facilitate and suppress future aggressive behavior, leading to persistent high aggression or low aggression states. We use a combination of techniques for multi-region neural recording, perturbation, behavioral analysis, and modeling to understand how nodes in the brain’s subcortical “social decision-making network” encode and transform aggressive motivation into action, and how these circuits change following social experience.

This webinar brings together three leaders in theoretical and computational neuroscience—Larry Abbott, Haim Sompolinsky, and Terry Sejnowski—to discuss how neural circuits generate fundamental aspects of the mind. Abbott illustrates mechanisms in electric fish that differentiate self-generated electric signals from external sensory cues, showing how predictive plasticity and two-stage signal cancellation mediate a sense of self. Sompolinsky explores attractor networks, revealing how discrete and continuous attractors can stabilize activity patterns, enable working memory, and incorporate chaotic dynamics underlying spontaneous behaviors. He further highlights the concept of object manifolds in high-level sensory representations and raises open questions on integrating connectomics with theoretical frameworks. Sejnowski bridges these motifs with modern artificial intelligence, demonstrating how large-scale neural networks capture language structures through distributed representations that parallel biological coding. Together, their presentations emphasize the synergy between empirical data, computational modeling, and connectomics in explaining the neural basis of cognition—offering insights into perception, memory, language, and the emergence of mind-like processes.

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.”

This webinar on learning and memory features three experts—Nicolas Brunel, Ashok Litwin-Kumar, and Julijana Gjorgieva—who present theoretical and computational approaches to understanding how neural circuits acquire and store information across different scales. Brunel discusses calcium-based plasticity and how standard “Hebbian-like” plasticity rules inferred from in vitro or in vivo datasets constrain synaptic dynamics, aligning with classical observations (e.g., STDP) and explaining how synaptic connectivity shapes memory. Litwin-Kumar explores insights from the fruit fly connectome, emphasizing how the mushroom body—a key site for associative learning—implements a high-dimensional, random representation of sensory features. Convergent dopaminergic inputs gate plasticity, reflecting a high-dimensional “critic” that refines behavior. Feedback loops within the mushroom body further reveal sophisticated interactions between learning signals and action selection. Gjorgieva examines how activity-dependent plasticity rules shape circuitry from the subcellular (e.g., synaptic clustering on dendrites) to the cortical network level. She demonstrates how spontaneous activity during development, Hebbian competition, and inhibitory-excitatory balance collectively establish connectivity motifs responsible for key computations such as response normalization.

Continuous attractors offer a unique class of solutions for storing continuous-valued variables in recurrent system states for indefinitely long time intervals. Unfortunately, continuous attractors suffer from severe structural instability in general---they are destroyed by most infinitesimal changes of the dynamical law that defines them. This fragility limits their utility especially in biological systems as their recurrent dynamics are subject to constant perturbations. We observe that the bifurcations from continuous attractors in theoretical neuroscience models display various structurally stable forms. Although their asymptotic behaviors to maintain memory are categorically distinct, their finite-time behaviors are similar. We build on the persistent manifold theory to explain the commonalities between bifurcations from and approximations of continuous attractors. Fast-slow decomposition analysis uncovers the existence of a persistent slow manifold that survives the seemingly destructive bifurcation, relating the flow within the manifold to the size of the perturbation. Moreover, this allows the bounding of the memory error of these approximations of continuous attractors. Finally, we train recurrent neural networks on analog memory tasks to support the appearance of these systems as solutions and their generalization capabilities. Therefore, we conclude that continuous attractors are functionally robust and remain useful as a universal analogy for understanding analog memory. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-11-27. Recording duration: 00:59:01.

In recent years, my lab and others have demonstrated the value of vector symbolic algebras (VSAs) for capturing a wide variety of neural and behavioural results. In this talk I discuss the surprising and compelling variety of tasks and styles of reasoning that are well-suited to descriptions using a specific VSA. These tasks include path integration, navigation, Bayesian reasoning, sampling, memorization, and logical inference. The resulting spiking neural network models capture various hippocampal cell types (grid, place, border, etc.), behavioural errors, and a variety of observed neural dynamics. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-11-20. Recording duration: 00:47:23.

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.

Theoretical neuroscience aims to understand the relationship between neuron dynamics and connectivity in recurrent circuits. This has been intensively studied at the local level, where dynamics is described by pairwise correlations. Recent advances in simultaneous recordings of many neurons have allowed researchers to address the question at the global level, such as for the dimensionality of population dynamics. Our work contributes to this effort by analyzing the impact of connectivity statistics, including certain motifs, on the bulk and outlier covariance eigenvalues. By considering linearized dynamics around a steady state, we obtained analytically the covariance spectrum which exhibits a signature long tail robust to model variants and matches zebrafish calcium imaging data. This provides a local circuit mechanism for shaping the geometry of population dynamics and a quantitative benchmark for interpreting data. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-05-22. Recording duration: 00:53:15.

Through recent advances in microscopy, we now have an unprecedented view of the brain and body of the fruit fly Drosophila melanogaster. We now know the connectivity at single neuron resolution across the whole brain. How do we translate these new measurements into a deeper understanding of how the brain processes sensory information and produces behavior? I will describe two computational efforts to model the brain and the body of the fruit fly. First, I will describe a new modeling method which makes highly accurate predictions of neural activity in the fly visual system as measured in the living brain, using only measurements of its connectivity from a dead brain [1], joint work with Jakob Macke. Second, I will describe a whole body physics simulation of the fruit fly which can accurately reproduce its locomotion behaviors, both flight and walking [2], joint work with Google DeepMind.