Seminars

Luca Mrini presents work in progress on quantising singular configuration spaces using the non-smooth calculus of metric-measure spaces. The framework generalises smooth quantum mechanics through Hilbert spaces, position and momentum operators, Hamiltonians, unitary dynamics, and observable algebras. A method for bounding mass gaps after symplectic reduction uses the curvature of the unreduced configuration space. Examples include the harmonic oscillator constrained to zero angular momentum, lattice Yang–Mills theory, and fractional-dimensional Laakso spaces. The talk closes with prospective applications to the Yang–Mills mass-gap problem and quantum gravity.

Isaac Newton Institute seminar in the 'Mathematics of many-body entanglement' (MMB) programme: Ignacio Cirac of the Max-Planck-Institut für Quantenoptik speaks on the preparation of tensor network states.

Michelle M. Li examines how computational analyses can preserve the biological context of a proposed treatment, including cell type, disease state, genetic background and patient characteristics. She introduces Medea, an AI system that combines biological software, predictive models and literature retrieval while checking intermediate steps and reconciling evidence. The seminar presents evaluations involving cell-specific target selection, cancer-cell synthetic lethality and immunotherapy response. A separate yeast experiment tests predictions against previously unpublished measurements of gene-pair interactions under DNA-damaging treatments. The research addresses whether an agent can transfer useful evidence between contexts while recognizing when that transfer is unsupported. Reported comparisons cover predictive performance, computational failures and the ability to abstain. This recording retains the original seminar date.

Convergence Seminar by Alexis Battle, PhD (Wu and Zhang Professor of Biomedical Engineering and Computer Science, Johns Hopkins University), on computational and machine-learning approaches for analyzing how genetic variation impacts gene regulation and disease, including noncoding sequences and rare variants.

Jiaqi Zhang examines how computational models can learn the effects of genetic interventions from single-cell experiments. Such experiments reveal causal relationships, but their high-dimensional measurements are costly to collect and difficult to interpret. The seminar connects identifiable causal representations with a predictive method for previously unseen perturbations. The approach incorporates prior biological knowledge and changes in data distributions to estimate responses at individual-cell resolution. It also uses predictions to guide subsequent experiments. An application identifies and experimentally validates previously unknown T-cell regulators with potential relevance to cancer immunotherapy. The recording follows the original July seminar; the series lists Zhang at MIT, while the recording biography describes her incoming Columbia appointment.

Benoit Assi examines limits on reliable theoretical predictions for present and future particle colliders. Low-order simulations of QCD radiation carry large uncertainties, hadronization is commonly modeled rather than derived, and effective theories contain more operators than measurements can constrain. Information theory and machine learning can incorporate improved calculations into simulations, quantify uncertainty, choose informative observables and advance hadronization theory. Geometry of effective-theory field space combines infinite operator families into finite physical quantities, while information measures identify the combinations experiments can resolve. The talk develops these complementary approaches to extracting the available information from LHC and future-collider data.

Large recurrent networks are important models in several fields, including neuroscience, machine learning, physics, and applied mathematics. Yet their dynamics are difficult to study directly, because high-dimensional nonlinear systems can exhibit rich behavior that is hard to summarize in terms of individual trajectories. In this talk, I will discuss an approach that seeks to understand such dynamics through the structure of the network’s equilibria. I will focus on a random balanced network of threshold-linear units that undergoes a transition from a single stable equilibrium to extensive chaos as the disorder strength crosses a critical value. Using a combination of Kac–Rice theory, replica calculations, numerical root-finding, and dynamical mean-field theory, we show that the chaotic regime contains an exponentially large number of equilibria. These equilibria are all saddles, but with only a fractionally small number of unstable directions. Surprisingly, despite the completely random connectivity, the equilibria are not scattered randomly through phase space. Instead, they are strongly correlated and confined to a comparatively small region. The chaotic attractor lies within this same region, suggesting a direct geometric link between the organization of unstable equilibria and the collective structure of the dynamics. This picture helps explain why networks with extensive chaos can nevertheless display dynamics dominated by a relatively small number of collective modes. More broadly, the results suggest that the geometry of equilibria provides a useful complementary perspective to dynamical mean-field theory for understanding high-dimensional neural dynamics. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2026-05-27. Recording duration: 00:46:40.

Networks of interconnected neurons display diverse patterns of activity. Relating these patterns to the structure of the network is a central goal of theoretical neuroscience. Classic neural field and rate models have been powerful tools for this purpose due to their analytical tractability. Here, we show that the recently-developed combinatorial threshold-linear network (CTLN) model is a mean-field theory for excitatory-inhibitory Hawkes networks, with clustered connectivity, in an inhibition-stabilized regime. This mapping allows us to leverage powerful analytical results for CTLN networks to predict diverse macroscopic dynamics of clustered Hawkes networks, including metastability between various macroscopic fixed points, limit cycles, and chaotic attractors. We will then examine an extension of this approach to models with nonlinear dendritic dynamics, focusing on dendritic calcium spikes.We uncover a marked point process mean-field theory for these n etworks and use this to examine how somatic vs dendritic-targeting connectivity shapes the mean-field equilibrium phase diagram. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2026-05-13. Recording duration: 00:54:14.

How does a cat gracefully walk and suddenly freeze when spotting a mouse? In this talk, we look at how networks in the spinal cord generate movement. In particular, we address the fundamental yet poorly understood question of motor control: How can rhythmic movements, such as walking, be generated and stopped at any point in the cycle while posture is preserved? Since conventional models of spinal motor function rely on alternation between flexor and extensor modules, which are limited to just two phases, this question exposes the essential shortcoming of the conventional understanding: How can a system with only two phases generate and stop walking in any phase? To address this question and better understand the generation and stopping of motor activity, we use Neuropixels probes in the rat spinal cord during voluntary, freely moving locomotion. We utilize optogenetic activation of a brainstem nucleus to induce stopping. During locomotion, neuronal manifold activity exhibits robust rotational patterns that are topologically invariant with respect to speed (Linden 2022). Furthermore, this trajectory converges on a stable point-attractor precisely at the moment of arrest, and it persists until the movement is resumed. Through computational modeling, we propose that the walk-to-stop represents a bifurcation from a limit cycle to a fixed point attractor. We also propose a structural network mechanism for its physical implementation (Komi 2026). The structural mechanism entails a longitudinal projectome with a skewed Mexican hat topology, i.e., primarily local recurrent excitation and longer-range inhibition. Such a network can generate motor patterns via traveling waves, with frequency and amplitude controlled independently, and rhythm induced without requiring cellular pacemaker mechanisms. Together, our experimental observations support a new theory for the mechanism behind the generation of movement by networks in the spinal cord. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2026-03-25. Recording duration: 00:37:44.

Useful internal representations should explain the patterns of regularities and dependencies among observations. Probabilistic graphical models promise a principled way to uncover latent factors as such, but they are hard to scale to handle high-dimensional sensory observations and complicated dependencies structures. Neural-networks, on the other hand, excel at approximating complicated high-dimensional functions, but their internal representations do not easily lend themselves to a probabilistic interpretation. Despite some successes, a general unified approach is still missing for integrating the two approaches. I will describe a novel approach towards merging adaptive neural-network components into a probabilistic framework, based on three core ideas. The first is to train a set of networks to collectively perform inference, leveraging the ability of pattern-recognition methods to amortise complicated transformations. The second is to constrain the way in which the outputs of these networks are interpreted, transformed, and combined together. These constraints, together with the learning objective itself, are derived directly from probabilistic considerations encoded in a graphical model. Finally, the third core idea is that of recognition-parametrisation, allowing the inference ("recognition") procedure to directly define the model itself, without requiring an explicit "generative" decoder. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2026-03-04. Recording duration: 00:48:26.

Much is known about the neural representations of current environmental location and direction within the hippocampal formation, but use of such a “cognitive map” requires the online representation of desired locations and how to get there, and the neural basis for this function has been more elusive. I will discuss how “theta sweeps” of place and grid cell firing encode the current location (at early phases of each theta cycle) while, at later phases, sampling around the forward direction during exploration and indicating the direction to desired locations during goal-directed navigation. I will show how a relatively simple attractor model captures these results, but requires inputs signalling movement-direction and goal-direction.I will discuss why it is useful to consider the hippocampus as a generative model (in which head-direction, rather than movement-direction, is required, to translate egocentric sensory inputs to allocentric latent representations and back again) in explaining its roles in both spatial cognition and memory consolidation. “Replay sequences” are thought to support offline consolidation, and likely resemble theta sweeps more than behavioural experience. I will finish (given time) by considering how human memory consolidation can be seen as extraction of latent variables from replay via self-supervised learning, and how this perspective explains aspects of human memory such as gist-based distortions, imagination and planning. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2026-02-25. Recording duration: 00:46:52.

Although stress can be considered as an ongoing process that helps an organism to cope with present and future challenges, when it is too intense or uncontrollable, it can lead to adverse consequences for physical and mental health. Social stress specifically, is a highly prevalent traumatic experience, present in multiple contexts, such as war, bullying and interpersonal violence, and it has been linked with increased risk for major depression and anxiety disorders. Nevertheless, not all individuals exposed to strong stressful events develop psychopathology, with the mechanisms of resilience and vulnerability being still under investigation. During this talk, I will identify key gaps in our knowledge about stress vulnerability and I will present our recent data from our contextual fear learning protocol based on social defeat stress in mice.

1. Can we reconstruct images that a person saw, directly from their fMRI brain recordings? 2. Can we reconstruct the training data that a deep-network trained on, directly from the parameters of the network? The answer to both of these intriguing questions is “Yes!” In this talk I will present some of our work in both domains. I will then show how combining the power of Brains and Machines can lead to significant breakthroughs in both areas, and potentially bridge the gap between Minds and Machines. Finally, I will show how combining the power of Multiple Brains (with NO shared data) may lead to new breakthrough discoveries in Brain-Science, and allow mapping of information between different brains. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2026-02-18. Recording duration: 00:50:24.

In sensory systems, stimuli are represented through the diverse firing responses and receptive fields of neurons. These features emerge from the interaction between excitatory (E) and inhibitory (I) neuron populations within the network. Changes in sensory inputs alter this balance, leading to shifts in firing patterns and the input-output properties of individual neurons and the network. While these phenomena have been studied extensively with experiments and theory, the underlying principles for combining E and I inputs are still unclear. Here, the rules for probabilistically combining E and I inputs are derived that describe how neurons in a feedforward inhibitory circuit respond to stimuli. This simple model is broadly applicable, capturing a wide range of response features that would otherwise require multiple separate models and offers insights into the cellular and network mechanisms influencing the input-output properties of neurons, gain modulation, and the emergence of diverse temporal firing patterns. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2026-02-11. Recording duration: 00:48:34.

Current machine learning systems consume vastly more energy than biological brains. Neuromorphic systems aim to overcome this difference by mimicking the brain’s information coding via discrete voltage spikes. However, it remains unclear how both artificial and natural networks of spiking neurons can learn energy-efficient information processing strategies. Here we propose Predictive Coding Light (PCL), a recurrent hierarchical spiking neural network for unsupervised representation learning. In contrast to previous predictive coding approaches, PCL does not transmit prediction errors to higher processing stages. Instead, it suppresses the most predictable spikes and transmits a compressed representation of the input. Using only biologically plausible spike-timing based learning rules, PCL reproduces a wealth of findings on information processing in visual cortex and permits strong performance in downstream classification tasks. Overall, PCL offers a new approach to predictive coding and its implementation in natural and artificial spiking neural networks

Robert Gower introduces Polar Express for the polar decomposition and matrix sign function, motivated by Muon neural-network training. Using only matrix-matrix products makes the method suited to high-throughput GPUs. Each iteration adapts its polynomial update through minimax optimization, building on Chen and Chow and Nakatsukasa and Freund. Worst-case error minimization gives rapid initial and asymptotic convergence. The talk addresses finite-precision implementation in bfloat16 and reports improved validation loss when training GPT-2 on one billion FineWeb tokens across several learning rates.

Chris Musco studies how to approximate an unknown matrix by a structured one using a limited, adaptively chosen sequence of matrix-vector products. This models operator learning in scientific machine learning as well as computational algorithms. Randomized SVD provides strong guarantees for low-rank targets; analogous results for sparse and hierarchical structures are less developed. The talk presents progress on efficient algorithms for these classes and a broader complexity theory. Joint work with Noah Amsel, Pratyush Avi, Tyler Chen, Prathamesh Dharangutte, Chinmay Hegde, Feyza Duman Keles, Diana Halikias, Cameron Musco, and David Persson.

Lior Horesh presents tensor-tensor algebra designed to retain key properties of matrix algebra while representing multidimensional correlations. An Eckart–Young-like tensor representation theorem underpins computationally feasible, provably optimal decompositions. Matrix-mimetic operations allow existing computational workflows to be adapted to tensors. Examples include tensorized neural-network structures and tensor graph convolutional networks for time-evolving graphs. The discussion concludes with tensor group symmetries and extensions to equivariant learning.

Many animals rely on persistent internal representations of continuous angular variables for working memory, motor control, and navigation. Theories have proposed that such representations are maintained by a class of recurrently connected networks called ring attractor networks. These networks rely on large numbers of neurons to maintain continuous and stable representations and to accurately integrate incoming signals. The head direction system of the fruit fly, however, seems to achieve these properties with a remarkably small network. These findings challenge our understanding of ring attractors and their putative implementation in neural circuits. In this talk, I will show analytically how small networks can overcome the constraints of their size to generate a ring attractor and are hence capable of stably maintaining an internal representation of a continuous, periodic variable. Further, I will show how ring attractors emerge in small threshold linear networks through the coordination of a discrete set of line attractors. More broadly, this work informs our understanding of the functional capabilities of small, discrete systems. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2026-02-04. Recording duration: 00:44:59.