Seminars

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.

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.

David Baker presents recent advances in designing proteins for functions that natural evolution has not been required to solve. The approach begins with a desired structure or activity and uses deep learning to propose amino acid sequences expected to realise it. The resulting designs are translated into synthetic genes, produced as proteins and tested experimentally. The lecture connects computational design with laboratory characterisation, explaining how the combination can create new molecular functions relevant to medicine, technology and sustainability. Its focus is the construction and evaluation of proteins from scratch, extending the protein-design research recognised by the 2024 chemistry prize.

Computations in neural circuits are often construed as being implemented through the coordinated dynamics of neurons. In this picture, the role of synaptic connectivity is to sculpt neuronal dynamics to implement computations of interest. Of course, synapses are not static but change on a variety of timescales, including fast timescales comparable to those of neurons. Thus, a more accurate view of computation in neural circuits may involve the coupled dynamics of neurons and synapses. This form of computation is closer to what is implemented by Transformers via an equivalence between ongoing synaptic plasticity and self-attention. I will first describe a nonlinear recurrent neural-network model with ongoing Hebbian dynamics of “fast” synapses atop unstructured “slow” synapses. I will then describe two computations implemented through neuronal-synaptic dynamics, which can be studied in this model using techniques including dynamical mean-field theory and random-matrix theory. First, there exists a novel phase termed “freezable chaos” in which a stable fixed point of neuronal dynamics is continuously destabilized by synaptic dynamics. This allows for the creation of a stable fixed point at any neuronal state visited by the network by halting synaptic plasticity. Second, I will describe an effect termed “persistent oscillations” in which, following stimulation by a periodic signal, a plastic network continues to autonomously reproduce a similar signal for a duration exceeding any intrinsic timescale in the system. Thus, ongoing Hebbian plasticity can provide a dynamic form of working memory, complementing the static form provided by freezable chaos. Ongoing experimental work suggests that this effect is realized in cortical organoids. Overall, this line of work suggests that synapses should be promoted to first-class dynamical degrees of freedom in our conceptual understanding of neural-circuit function. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2026-01-14. Recording duration: 00:43:14.

Modern experimental techniques now reveal the structure and function of neural circuits at unprecedented scale and resolution. How can we use this wealth of data to understand how cells and circuits implement computations underlying behaviour? Achieving this goal requires models that are consistent with biophysical mechanisms and circuit dynamics, yet flexible enough to capture behaviourally relevant computations. We develop simulation-based machine learning methods that address this challenge. I will show how these approaches—in combination with connectomic measurements—make it possible to build large-scale mechanistic models of the fruit fly visual system. Our methods generalize across systems and scales, defining a new way to study biological systems by algorithmically learning interpretable models that reveal how structure and dynamics gives rise to behaviour. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2025-12-17. Recording duration: 00:45:20.

Predictive processing offers a unifying view of neural computation, proposing that brains continuously anticipate sensory input and update internal models based on prediction errors. In this talk, I will present converging evidence for the computational mechanisms underlying this framework across human neuroscience and deep neural networks. I will begin with recent work showing that large-scale distributed prediction-error encoding in the human brain directly predicts how sensory representations reorganize through predictive learning. I will then turn to PredNet, a popular predictive coding inspired deep network that has been widely used to model real-world biological vision systems. Using dynamic stimuli generated with our Spatiotemporal Style Transfer algorithm, we demonstrate that PredNet relies primarily on low-level spatiotemporal structure and remains insensitive to high-level content, revealing limits in its generalization capacity. Finally, I will discuss new recurrent vision models that integrate top-down feedback connections with intrinsic neural variability, uncovering a dual mechanism for robust sensory coding in which neural variability decorrelates unit responses, while top-down feedback stabilizes network dynamics. Together, these results outline how prediction error signaling and top-down feedback pathways shape adaptive sensory processing in biological and artificial systems.

Recurrent networks with balanced excitation-inhibition explain a wide range of neurophysiological observations, but can only implement a limited set of transformations on their input. On the other hand networks of firing-rate units with low-rank connectivity have universal computational capabilities, but do not work with spikes or generate noise self-consistently. Although empirical approaches to merge these two computational frameworks have been constructed, there is no established theory describing their unification. Here we develop such a theory. We study analytically and numerically networks with connectivity comprising random “strong”, and low-rank “weak” components. When the low-rank connectivity is slow, a well-defined notion of instantaneous firing rate emerges which implies universal computation as previously shown. However, the fact that such time-varying rates are the result of E-I balance has important implications. We show that internally or externally generated fluctuations along particular latent modes tend to break the E-I balance. Its maintenance is obtained through the emergence of a spontaneous coupling between the mean and the variance of the membrane potential and the norm of the latent state driving these modes. This leads to several predictions, the most counterintuitive of which is that coherent global fluctuations in subthreshold membrane potential (Vm) should coexist with desynchronized activity at constant firing rates when the dynamics of these modes is excited. To test our theory, we show that the coupling between the average Vm and the latent state adds new non-linear dimensions to the low-dimensional manifold of the network, which lead to a frequency doubling when the input to the network is periodic, a prediction that is borne out in population recordings from mouse V1. Our results unify two prevalent frameworks for cortical computation and clarify the relationship between computation, dynamics and geometry in circuits of spiking neurons. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2025-11-26. Recording duration: 00:39:26.

Minimising cortical prediction errors is thought to be a key computation underlying perception, action, and learning. Yet, how the cortex represents and uses uncertainty in this process remains unclear. In the first part of this talk, I will present a normative framework showing how uncertainty can modulate prediction error activity to yield uncertainty-modulated prediction errors (UPEs), hypothesised to be represented by layer 2/3 pyramidal neurons. We propose that these UPEs are computed through inhibitory mechanisms involving SST and PV interneurons. A circuit model demonstrates how cortical cell types can locally compute means, variances, and UPEs, leading to adaptive learning rates. In the second part, I will discuss how uncertainty modulation could be controlled by higher-level representations. We formally derived neural dynamics that minimise prediction errors under the assumption that cortical areas must not only predict the activity in other areas and sensory streams but also jointly project their inverse expected uncertainty about their predictions, which we call “confidence”. This yields a confidence-weighted integration of bottom-up and top-down signals, consistent with Bayesian principles, and predicts the existence of second-order errors that compare confidence with performance. We predict that these second-order errors propagate alongside classical prediction errors through the cortical hierarchy, and simulations demonstrate that this mechanism enables nonlinear classification within a single cortical area. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2025-11-12. Recording duration: 00:29:21.

Assessing how brain activity generalizes across individuals is a central challenge in experimental neuroscience. Traditional task- or stimulus-driven approaches align data through trial averaging and anatomical registration, but these methods fail for spontaneous activity, where no shared temporal reference exists. In this talk, I will introduce a statistical framework, called latent-aligned Restricted Boltzmann Machines, to build a common representational space from whole-brain recordings of spontaneous activity in multiple zebrafish larvae. This shared latent space, composed of spatially localized co-activation motifs or cell assemblies, allows bidirectional mapping of brain states: activity patterns from one fish can be encoded and decoded into another. The translated activity patterns retain their original spatial structure and show high plausibility within the recipient brain. We further use this shared space to segment spontaneous activity into discrete brain states and we quantify their Markovian transition statistics. Remarkably, these state-to-state dynamics are stereotyped across individuals, suggesting that spontaneous activity reflects intrinsic computational priors of neural processing. Together, these results demonstrate how probabilistic generative modeling can bridge individual variability and reveal conserved organizational principles of vertebrate brains. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2025-11-05. Recording duration: 00:36:37.

This talk aims to answer these questions along four dimensions. First is history. RL was the basis of AI long before the term AI was introduced in 1956. The first machine learning (ML) systems were based on RL even before digital computers existed. Despite notable early successes of ML based on RL, RL essentially disappeared from ML until relatively recently. A second reason for renewed interest in RL is the clarification of some misunderstandings that have been prevalent in the ML community. A third, and most important, reason for this resurgence is that new, or rediscovered, algorithms and connections to well developed mathematical and engineering methods have been worked out. Finally, a fourth reason for the renewed interest in RL is its strong links to animal reward systems, in particular, to the role that dopamine plays in motivation and learning. VVTNS Sixth Season Opening Lecture. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2025-10-29. Recording duration: 00:55:21.