van Vreeswijk Theoretical Neuroscience Seminar

The factorization of a large matrix into the product of two matrices is an important mathematical problem encountered in many tasks, ranging from dictionary learning to machine learning. Statistical physics can provide on the one hand theoretical limits on the possibility of factorizing matrices in the limit of infinite size, and also practical algorithms. While this program has been successful in the case of finite rank matrices, the regime of extensive rank (scaling linearly with the dimension of the matrix) turns out to be much harder. This talk will describe a new approach to matrix factorization that maps it to neural network models of associative memory: each pattern found in the associative memory corresponds to one factor of the matrix decomposition. A detailed theoretical analysis of this new approach shows that matrix factorization in the extensive rank regime is possible when the rank is below a certain threshold. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-01-03. Recording duration: 00:44:31.

Over the past decade we have demonstrated that the fusion of subject-specific structural information of the human brain with mathematical dynamic models allows building biologically realistic brain network models, which have a predictive value, beyond the explanatory power of each approach independently. The network nodes hold neural population models, which are derived using mean field techniques from statistical physics expressing ensemble activity via collective variables. Our hybrid approach fuses data-driven with forward-modeling-based techniques and has been successfully applied to explain healthy brain function and clinical translation including aging, stroke and epilepsy. Here we illustrate the workflow along the example of epilepsy: we reconstruct personalized connectivity matrices of human epileptic patients using Diffusion Tensor weighted Imaging (DTI). Subsets of brain regions generating seizures in patients with refractory partial epilepsy are referred to as the epileptogenic zone (EZ). During a seizure, paroxysmal activity is not restricted to the EZ, but may recruit other healthy brain regions and propagate activity through large brain networks. The identification of the EZ is crucial for the success of neurosurgery and presents one of the historically difficult questions in clinical neuroscience. The application of latest techniques in Bayesian inference and model inversion, in particular Hamiltonian Monte Carlo, allows the estimation of the EZ, including estimates of confidence and diagnostics of performance of the inference. The example of epilepsy nicely underwrites the predictive value of personalized large-scale brain network models. The workflow of end-to-end modeling is an integral part of the European neuroinformatics platform EBRAINS and enables neuroscientists worldwide to build and estimate personalized virtual brains. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2023-12-06. Recording duration: 00:50:07.

Deep neural network learning dynamics are very complex with large numbers of learnable weights and many sources of disorder. In this talk, I will discuss mean field approaches to analyze the learning dynamics of neural networks in large system size limits when starting from random initial conditions. The result of this analysis is a dynamical mean field theory (DMFT) where all neurons obey independent stochastic single site dynamics. Correlation functions (kernels) and response functions for the features and gradients at each layer can be computed self-consistently from these stochastic processes. Depending on the choice of scaling of the network output, the network can operate in a kernel regime or a feature learning regime in the infinite width limit. I will discuss how this theory can be used to analyze various learning rules for deep architectures (backpropagation, feedback alignment based rules, Hebbian learning etc), where the weight updates do not necessarily correspond to gradient descent on an energy function. I will then present recent extensions of this theory to residual networks at infinite depth and discuss the utility of deriving scaling limits to obtain consistent optimal hyperparameters (such as learning rate) across widths and depths. Feature learning in other types of architectures will be discussed if time permits. Lastly, I will discuss open problems and challenges associated with this theoretical approach to neural network learning dynamics. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2023-11-29. Recording duration: 00:41:18.

The internal and external world is thought to be represented by distributed patterns of cortical activity. The emergence of these cortical representations over the course of development remains an unresolved question. In this talk, I share results from a series of recent studies combining theory and experiments in the cortex of the ferret, a species with a well-defined columnar organization and modular network of orientation-selective responses in visual cortex. I show that prior to the onset of structured sensory experience, endogenous mechanisms set up a highly organized cortical network structure that is evident in modular patterns of spontaneous activity characterized by strong, clustered local and long-range correlations. This correlation structure is remarkably consistent across both sensory and association areas in the early neocortex, suggesting that diverse cortical representations initially develop according to similar principles. Next, I explore a classical candidate mechanism for producing modular activity – local excitation and lateral inhibition. I present the first empirical test of this mechanism through direct optogenetic cortical activation and discuss a plausible circuit implementation. Then, focusing on the visual cortex, I demonstrate that these endogenously structured networks enable orientation-selective responses immediately after eye opening. However, these initial responses are highly variable, lacking the reliability and low-dimensional structure observed in the mature cortex. Reliable responses are achieved after an experience-dependent co-reorganization of stimulus- evoked and spontaneous activity following eye opening. Based on these observations, I propose the hypothesis that the alignment between feedforward inputs and the recurrent network plays a crucial role in transforming the initially variable responses into mature and reliable representations. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2023-11-22. Recording duration: 00:56:31.

Humans and animals learn and plan with flexibility and efficiency well beyond that of modern Machine Learning methods. This is hypothesized to owe in part to the ability of animals to build structured representations of their environments, and modulate these representations to rapidly adapt to new settings. In the first part of this talk, I will discuss theoretical work describing how learned representations in hippocampus enable rapid adaptation to new goals by learning predictive representations. I will also cover work extending this account, in which we show how the predictive model can be adapted to the probabilistic setting to describe a broader array of generalization results in humans and animals, and how entorhinal representations can be modulated to support sample generation optimized for different behavioral states. I will also talk about work applying this perspective to the deep RL setting, where we can study the effect of predictive learning on representations that form in a deep neural network and how these results compare to neural data. In the second part of the talk, I will overview some of the ways in which we have combined many of the same mathematical concepts with state-of-the-art deep learning methods to improve efficiency and performance in machine learning applications like physical simulation, relational reasoning, and design. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2023-11-01. Recording duration: 00:50:44.

We continuously detect sensory data, like sights and sounds, and use this information to guide our behaviour. However, rather than relying on single sensory channels, which are noisy and can be ambiguous alone, we merge information across our senses and leverage this combined signal. In biological networks, this process (multisensory integration) is implemented by multimodal neurons which are often thought to receive the information accumulated by unimodal areas, and to fuse this across channels; an algorithm we term accumulate-then-fuse. However, it remains an open question how well this theory generalises beyond the classical tasks used to test multimodal integration. Here, we explore this by developing novel multimodal tasks and deploying probabilistic, artificial and spiking neural network models. Using these models we demonstrate that multimodal units are not necessary for accuracy or balancing speed/accuracy in classical multimodal tasks, but are critical in a novel set of tasks in which we comodulate signals across channels. We show that these comodulation tasks require multimodal units to implement an alternative fuse-then-accumulate algorithm, which excels in naturalistic settings and is optimal for a wide class of multimodal problems. Finally, we link our findings to experimental results at multiple levels; from single neurons to behaviour. Ultimately, our work suggests that multimodal neurons may fuse-then-accumulate evidence across channels, and provides novel tasks and models for exploring this in biological systems. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2023-10-25. Recording duration: 00:30:13.

To understand subjective evaluation of an option, various disciplines have quantified the interaction between reward and effort during decision making, producing an estimate of economic utility, namely the subject ‘goodness’ of an option. However, those same variables that affect the utility of an option also influence the vigor (speed) of movements to acquire it. To better understand this, we have developed a mathematical framework demonstrating how utility can influence not only the choice of what to do, but also the speed of the movement follows. I will present results demonstrating that expectation of reward increases speed of saccadic eye and reaching movements, whereas expectation of effort expenditure decreases this speed. Intriguingly, when deliberating between two visual options, saccade vigor to each option increases differentially, encoding their relative value. These results and others imply that vigor may serve as a new, real-time metric with which to quantify subjective utility, and that the control of movements may be an implicit reflection of the brain’s economic evaluation of the expected outcome. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2023-10-18. Recording duration: 00:45:32.

Much as Santiago Ramón y Cajal is the godfather of neuronal computation, which occurs among neurons that communicate predominantly via threshold logic, Camillo Golgi is the inadvertent godfather of neurovascular signaling, in which the endothelial cells that form the lumen of blood vessels communicate via electrodiffusion as well as threshold logic. I will address questions that define spatiotemporal patterns of constriction and dilation that develop across the network of cortical vasculature: First - is there a common topology and geometry of brain vasculature (our work)? Second - what mechanisms govern neuron-to-vessel and vessel-to-vessel signaling (work of Mark Nelson at U Vermont)? Last - what is the nature of competition among arteriole smooth muscle oscillators and the underlying neuronal drive (our work)? This answers to these questions bear on fundamental aspects of brain science as well as practical issues, including the relation of fMRI signals to neuronal activity and the impact of vascular dysfunction on cognition. Challenges and opportunities for experimentalists and theorists alike will be discussed. The organizer explicitly announced an exceptional 11:15 am ET start. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2023-10-11. Recording duration: 00:56:46.

The traditional view of a neuron as a feature detector or an efficient encoder has difficulties in explaining the function of motor neurons and experimentally observed variable and context-dependent response properties of neurons. We put forward an alternative perspective, modeling each neuron as a feedback controller within a closed loop that includes other neurons and the external environment. Based on the recently developed Direct Data-Driven Control (DD-DC) approach, we propose a biologically plausible controller which implicitly identifies the dynamics of the rest of the loop, infers its latent state and optimizes control. The DD-DC model of a neuron accounts for multiple neurophysiological observations, including the switch from potentiation to depression in Spike-Timing-Dependent Plasticity (STDP) and its asymmetry; temporally extended feedforward and feedback neuronal filters and their adaptation to input statistics; imprecision of the neuronal spike-generation mechanism under constant input; as well as the prevalence of variability and/or noise in brain operation. The DD-DC neuron offers an alternative to the feedforward, instantaneously responding McCulloch-Pitts-Rosenblatt unit as a primitive for constructing biologically-inspired neural networks. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2023-06-28. Recording duration: 00:52:20.

One of the fundamental functions of the brain is to flexibly plan and control movement production at different timescales in order to efficiently shape structured behaviors. I will present research investigating how these complex computations are performed in the mammalian brain, with an emphasis on autonomous motor control. Specifically, I will focus on the mechanisms supporting efficient interfacing between 'higher-level' planning commands and 'lower-level' motor cortical dynamics that ultimately drive muscles. I will take advantage of the fact that the anatomy of the circuits underlying motor control is well known. It notably involves the primary motor cortex, a recurrent network that generates learned commands to drive muscles while interacting through loops with thalamic neurons that lack recurrent excitation. Using an analytically tractable model that incorporates these architectural constraints, I will explain how this motor circuit can implement a form of efficient modularity by combining (i) plastic thalamocortical loops that are movement-specific and (ii) shared hardwired circuits. I will show that this modular architecture can balance two different objectives: first, supporting the flexible recombination of an extensible library of re-usable motor primitives; and second, promoting the efficient use of neural resources by taking advantage of shared connections between modules. I will finally show that these insights are relevant for designing artificial neural networks able to flexibly and robustly compose hierarchical analog behaviors from a library of motor primitives. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2023-01-11. Recording duration: 00:49:52.

Carl van Vreeswijk (1962-2022) Carl van Vreeswijk passed away on the 13th of April, 2022, in Paris, as he was getting ready to go to the lab for the WWTNS of the week. Carl was an exceptionally gifted theoretical neuroscientist. With his deep understanding of theoretical tools, his curiosity and collaborations with experimentalists, he introduced and developed many pioneering concepts and techniques which have shaped our current understanding of recurrent neuronal networks and cortical dynamics. Beyond his prolific scientific wisdom and creativity, Carl was an inspiration to many, a generous and beloved friend and collaborator, and an extraordinarily caring mentor. He was keen on teaching. He spent ample time bringing his exceptional knowledge to many young researchers over many summer schools, workshops, and conferences. The World Wide Theoretical Neuroscience Seminar (WWTNS) series, that Carl and I founded (November 2020) as a space where theoreticians can present their work in-depth, including equations and mathematical tools will be renamed the "van Vreeswijk Theoretical Neuroscience Seminar" (VVTNS) series to honour his memory. David Hansel The provider supplies a memorial description; a complete speaker roster is not published. Carl van Vreeswijk is the person commemorated, not a listed speaker. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2022-04-27. Recording duration: 00:35:48.

To act effectively and flexibly in an imperfectly predictable environment with only incomplete and unreliable sensory information, animals must learn to form and compute with internal representations that reflect their necessarily uncertain beliefs about the state of the world. The optimal approach to handling uncertainty is rooted in Bayesian probability, and indeed humans and other animals often approach Bayes optimality with a degree of robustness and flexibility that continues to evade artificial systems. However, the question of how neural circuits organise to achieve this performance remains one of the fundamental mysteries of neuroscience. I will discuss a series of models built around the idea that distributional information is naturally encoded in a distributed fashion by neural population firing rates that converge on the mean values of non-linear functions of state. We will see that such representations emerge naturally in task-optimised systems, and also provide a simple and effective substrate for unsupervised learning. Finally, I will sketch ongoing work that links the emergence of such representations to the architecture of recurrent neural circuits. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2021-07-07. Recording duration: 00:52:28.

Waves and patterns in the brain are well known to subserve natural computation. Much attention in the theoretical neuroscience community has been devoted to analysing networks of relatively simple spiking neurons (IF type) or firing rate models (Wilson-Cowan type) and to great effect! Indeed, the understanding of how spatio-temporal patterns of neural activity may arise in the cortex has advanced significantly with the development and analysis of such models. To replicate this success for sub-cortical tissues requires an extension to include relevant ionic currents that can further shape firing response. Here I will advocate for two complementary approaches: i) that augments the approach for IF networks to include piecewise linear caricatures of gating dynamics for nonlinear ionic current models, ii) firing rate reductions for systems where the nonlinear ionic currents are slow. By way of illustration, I will show how to construct spatially periodic waves and patterns in i) a simple spiking tissue model of medial enthorinal cortex (with an I_h current), ii) a firing rate model of thalamus (with an I_T current). The biological commonality between these two models is that both express local 'rebound' currents that can usefully shape global tissue response. The mathematical commonality is the use of tools from non-smooth dynamical systems theory to make analytical progress in determining patterns and their stability. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2021-06-30. Recording duration: 00:40:23.

Threshold-linear networks (TLNs) are popular firing rate models of recurrent networks. They have been used to model associative memory, decision-making, and position coding in cortical and hippocampal networks. Unlike rate models with other choices of nonlinearity, TLNs are piecewise linear, making them more amenable to mathematical analysis. In this talk I will present ten theorems about TLNs from the past five years. Many of these theorems connect the fixed points of a network to the structure of an underlying connectivity graph. These results have enabled us to develop graph rules to predict both static and dynamic attractors from network motifs. The theorems will be complemented with examples that illustrate how the mathematical results can be used to analyze and design recurrent networks that support a rich variety of computations and dynamics. Examples include internally-generated sequences, neural integrators, and central pattern generator circuits. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2021-06-23. Recording duration: 00:53:51.

(1) We (Grace Lindsay) used convolutional neural nets to model attention, by scaling the input/output function of neurons in an imagenet-trained network according to their selectivity for the feature or object category being attended. While this was effective in improving performance on difficult tasks, it was far less effective in earlier than in later layers. This indicated that neurons selective for a feature in earlier layers did not necessarily drive neurons selective for that feature in later layers. In contrast, applying attention according to the gradient for improving task performance worked well in early as well as late layers. This raises the question whether biological attentional modulation might reflect task requirements and not only the features of the stimuli to be attended. We suggest a simple experiment to answer this question, which we hope to convince an appropriate lab to carry out. (2) In E/I networks, a "paradoxical" response to stimulation has been shown: If the excitatory neurons would be unstable by themselves, but are stabilized by feedback inhibition (an "inhibition-stabilized network", or ISN), then, in response to addition of excitatory input to inhibitory neurons, their steady-state firing rates paradoxically decrease. In circuits with multiple inhibitory cell types, this has been generalized: in an ISN, if there is an added stimulus only to inhibitory cells, there will be a paradoxical change in the net inhibition received by excitatory cells -- e.g., if excitatory firing rates increase, so too will the net inhibition they receive. This does not imply that the firing rates of any particular inhibitory cell type will change paradoxically. Here we (Agostina Palmigiano along with Francesco Fumarola, and experimental work of Dan Mossing in the Adesnik lab) generalize the conditions for a paradoxical firing rate response, including in responses to partial as well as full perturbation of the neurons of a given cell type. We work in the context of the circuit with three inhibitory cell types (PV, SOM, VIP) in mouse V1. We show that, if a given cell type shows a paradoxical response to its own full stimulation, then the circuit without that cell type is unstable. This and experimental results to date, as well as our models fitted to data, suggest that PV but not SOM interneurons stabilize the circuit of layer 2/3 of mouse V1, at least for smaller visual stimulus sizes. For partial perturbations of a fraction f of a cell type that responds paradoxically to a full perturbation, there is a "fractional paradoxical effect": the proportion of all the cells of that type, stimulated and unstimulated, that respond opposite to the stimulation (i.e. negative response to excitation), changes non-monotonically, approaching 1 for f→0, decreasing with increasing f, and then increasing again to again approach 1 as f→1. I'll explain the origins of this behavior.3) We (Mario Dipoppa, in collaboration with the experimental work of Andy Keller and Morgane Roth from the Scanziani lab) have studied the E-PV-SOM-VIP circuit underlying contextual modulation in layer 2/3 of mouse V1. Experiments showed that E, PV, and VIP are suppressed by a surround stimuus that has the same orientation as, but not by one orthogonal to, the center stimulus. SOM neurons show the opposite behavior, being suppressed by an orthogonal but much less by a parallel surround. A combination of theory and optogenetic experiments show that the disinhibitory circuit -- VIP inhibits SOM, which inhibits E -- modulate responses between the two conditions. However, it does so, as part of the recurrent circuit, primarily by changing the recurrent excitation E cells receive, rather than by directly changing the inhibition received, in a manner reminiscent of the paradoxical response. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2021-06-09. Recording duration: 00:51:59.

The ability to simultaneously record the activity from tens to thousands to tens of thousands of neurons has allowed us to analyze the computational role of population activity as opposed to single neuron activity. Recent work on a variety of cortical areas suggests that neural function may be built on the activation of population-wide activity patterns, the neural modes, rather than on the independent modulation of individual neural activity. These neural modes, the dominant covariation patterns within the neural population, define a low dimensional neural manifold that captures most of the variance in the recorded neural activity. We refer to the time-dependent activation of the neural modes as their latent dynamics, and argue that latent cortical dynamics within the manifold are the fundamental and stable building blocks of neural population activity. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2021-03-17. Recording duration: 00:47:16.

Classic studies show that in many species – from leech and cricket to primate – responses of neural populations can be quite successfully read out using a measure neural population activity termed the population vector. However, despite its successes, detailed analyses have shown that the standard population vector discards substantial amounts of information contained in the responses of a neural population, and so is unlikely to accurately describe how signal communication between parts of the nervous system. I will describe recent theoretical results showing how to modify the population vector expression in order to read out neural responses without information loss, ideally. These results make it possible to quantify the contribution of weakly tuned neurons to perception. I will also discuss numerical methods that can be used to minimize information loss when reading out responses of large neural populations. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2021-03-03. Recording duration: 00:45:35.

Learning a new skill requires assimilating into our brain the regularities of the external world and how our body interacts with them as we engage in this skill. Trained Recurrent Neural Networks (TRNNs) are increasingly used as models of neural circuits of animals that were trained in laboratory setups, but the learning process itself has received less attention. Furthermore, most use of TRNNs is of a heuristic, rather than theory-based, nature, leaving many open questions: Which tasks yield to this approach and why? How do initial network architecture and learning rules bias the resultant network? In this talk, I will argue that studying the learning process of TRNNs can both advance our understanding of TRNNs and set up possible comparisons to the biological process of learning. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2021-01-06. Recording duration: 00:42:41.