Seminars

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.

Sharan Banagiri uses gravitational-wave observations to investigate how stellar-mass binary black holes form. The first part of the fourth LIGO–Virgo–KAGRA observing run more than doubled the number of detections, revealing new population features and clarifying earlier ones. The talk surveys notable and puzzling subpopulations, relates them to formation channels, and connects the evidence with transient phenomena and compact-object astrophysics. As the sample grows, these identifiable subpopulations can support a broader physical account of binary black-hole formation.

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.

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.

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.

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.

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.

Traditionally, touch is associated with exteroception and is rarely considered a relevant sensory cue for controlling movements in space, unlike vision. We developed a technique to isolate and measure tactile involvement in controlling sliding finger movements over a surface. Young adults traced a 2D shape with their index finger under direct or mirror-reversed visual feedback to create a conflict between visual and somatosensory inputs. In this context, increased reliance on somatosensory input compromises movement accuracy. Based on the hypothesis that tactile cues contribute to guiding hand movements when in contact with a surface, we predicted poorer performance when the participants traced with their bare finger compared to when their tactile sensation was dampened by a smooth, rigid finger splint. The results supported this prediction. EEG source analyses revealed smaller current in the source-localized somatosensory cortex during sensory conflict when the finger directly touched the surface. This finding supports the hypothesis that, in response to mirror-reversed visual feedback, the central nervous system selectively gated task-irrelevant somatosensory inputs, thereby mitigating, though not entirely resolving, the visuo-somatosensory conflict. Together, our results emphasize touch’s involvement in movement control over a surface, challenging the notion that vision predominantly governs goal-directed hand or finger movements.

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.

The Nature versus Nurture debate has generally been considered from the lens of genome versus experience dichotomy and has dominated our thinking about behavioral individuality and personality traits. In contrast, the role of nonheritable noise during brain development in behavioral variation is understudied. Using the Drosophila melanogaster visual system, I will discuss our efforts to dissect how individuality in circuit wiring emerges during development, and how that helps generate individual behavioral variation.

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.

Accurate perception of the environment is a constructive process that requires integration of external bottom-up sensory signals with internally-generated top-down information reflecting past experiences and current aims. Decades of work have elucidated how sensory neocortex processes physical stimulus features. In contrast, examining how memory-related-top-down information is encoded and integrated with bottom-up signals has long been challenging. Here, I will discuss our recent work pinpointing the outermost layer 1 of neocortex as a central hotspot for processing of experience-dependent top-down information threat during perception, one of the most fundamentally important forms of sensation.

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.

Functional connectomics reveals general wiring rule in mouse visual cortex