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.

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.

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.

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.

Different brain cell types exhibit distinct metabolic signatures that link energy economy to cellular function. Astrocytes and neurons, for instance, diverge dramatically in their reliance on glycolysis versus oxidative phosphorylation, underscoring that metabolic fuel efficiency is not uniform across cell types. A key factor shaping this divergence is the structural organization of the mitochondrial respiratory chain into supercomplexes. Specifically, complexes I (CI) and III (CIII) form a CI–CIII supercomplex, but the degree of this assembly varies by cell type. In neurons, CI is predominantly integrated into supercomplexes, resulting in highly efficient mitochondrial respiration and minimal reactive oxygen species (ROS) generation. Conversely, in astrocytes, a larger fraction of CI remains unassembled, freely existing apart from CIII, leading to reduced respiratory efficiency and elevated mitochondrial ROS production. Despite this apparent inefficiency, astrocytes boast a highly adaptable metabolism capable of responding to diverse stressors. Their looser CI–CIII organization allows for flexible ROS signaling, which activates antioxidant programs via transcription factors like Nrf2. This modular architecture enables astrocytes not only to balance energy production but also to support neuronal health and influence complex organismal behaviors.

Cellular crosstalk is an essential process during brain development and is influenced by numerous factors, including cell morphology, adhesion, the local extracellular matrix and secreted vesicles. Inspired by mutations associated with neurodevelopmental disorders, we focus on understanding the role of extracellular mechanisms essential for the proper development of the human brain. Therefore, we combine 2D and 3D in vitro human models to better understand the molecular and cellular mechanisms involved in progenitor proliferation and fate, migration and maturation of excitatory and inhibitory neurons during human brain development and tackle the causes of neurodevelopmental disorders.

Distinct synaptic plasticity rules operate across dendritic compartments in vivo during learning

Nervous system function relies on the polarized architecture of neurons, established by directional transport of pre- and postsynaptic cargoes. While delivery of postsynaptic components depends on the secretory pathway, the identity of the membrane compartment(s) that supply presynaptic active zone (AZ) and synaptic vesicle (SV) proteins is largely unknown. I will discuss our recent advances in our understanding of how key components of the presynaptic machinery for neurotransmitter release are transported and assembled focussing on our studies in genome-engineered human induced pluripotent stem cell-derived neurons. Specifically, I will focus on the composition and cell biological identity of the axonal transport vesicles that shuttle key components of neurotransmission to nascent synapses and on machinery for axonal transport and its control by signaling lipids. Our studies identify a crucial mechanism mediating the delivery of SV and active zone proteins to developing synapses and reveal connections to neurological disorders. In the second part of my talk, I will discuss how exocytosis and endocytosis are coupled to maintain presynaptic membrane homeostasis. I will present unpublished data regarding the role of membrane tension in the coupling of exocytosis and endocytosis at synapses. We have identified an endocytic BAR domain protein that is capable of sensing alterations in membrane tension caused by the exocytotic fusion of SVs to initiate compensatory endocytosis to restore plasma membrane area. Interference with this mechanism results in defects in the coupling of presynaptic exocytosis and SV recycling at human synapses.

Applications are invited for our third edition of Systems Vision Science (SVS) summer school since 2023, designed for everyone interested in gaining a systems level understanding of biological vision. We plan a coherent, graduate-level, syllabus on the integration of experimental data with theory and models, featuring lectures, guided exercises and discussion sessions. The summer school will end with a Systems Vision Science symposium on frontier topics on August 20-22, with additional invited and contributed presentations and posters. Call for contributions and participations to the symposium will be sent out spring of 2025. All summer school participants are invited to attend, and welcome to submit contributions to the symposium.

Applications are invited for our third edition of Systems Vision Science (SVS) summer school since 2023, designed for everyone interested in gaining a systems level understanding of biological vision. We plan a coherent, graduate-level, syllabus on the integration of experimental data with theory and models, featuring lectures, guided exercises and discussion sessions. The summer school will end with a Systems Vision Science symposium on frontier topics on August 20-22, with additional invited and contributed presentations and posters. Call for contributions and participations to the symposium will be sent out spring of 2025. All summer school participants are invited to attend, and welcome to submit contributions to the symposium.

Applications are invited for our third edition of Systems Vision Science (SVS) summer school since 2023, designed for everyone interested in gaining a systems level understanding of biological vision. We plan a coherent, graduate-level, syllabus on the integration of experimental data with theory and models, featuring lectures, guided exercises and discussion sessions. The summer school will end with a Systems Vision Science symposium on frontier topics on August 20-22, with additional invited and contributed presentations and posters. Call for contributions and participations to the symposium will be sent out spring of 2025. All summer school participants are invited to attend, and welcome to submit contributions to the symposium.