Seminars

Navid Azizan presents methods that make neural models obey physical, safety and operational constraints at deployment. Hard-constrained neural networks, or HardNets, enforce input-dependent constraints by construction while preserving universal approximation within the feasible function class. Applications include models of chaotic dynamics with bounded trajectories, energy-constrained operator learning, safe reinforcement learning and control with formal guarantees. The talk then turns to enforcing constraints during sampling from pretrained diffusion and flow-matching models. Formulating generation as trajectory optimization allows receding-horizon control to guide outputs toward feasibility without retraining or imposing excessive restrictions on the sampling process. Examples from fluid dynamics, robot planning and control, PDE control and language-guided image editing illustrate how constraints can define admissible behavior while retaining expressive learning and generation.

For decades dynamical systems theory played a pivotal role in theoretical and computational neuroscience, as it links biophysical and biochemical processes to neural computation. In fact, dynamical systems are computationally universal. Rather than hand-crafting computational theories of neural function based on dynamical systems, recent developments in scientific machine learning (ML) and AI suggest that we may be able to infer such dynamical-computational models directly from neurophysiological and behavioral observations. This is called dynamical systems reconstruction (DSR), the learning of generative surrogate models of the underlying dynamics, including its long-term temporal and geometrical properties, from time series data. In my talk I will cover recent ML/AI architectures, training algorithms, and validation procedures for DSR. I will discuss specifically how recent AI architectures for DSR can integrate neuroscience data from multiple modalities (like multiple single-unit recordings and behavioral choices), across diverse time scales, and across many different animals and task designs, into a joint DSR model. This provides first steps toward dynamical systems based AI foundation models for neuroscience. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2025-04-23. Recording duration: 00:53:24.

Recent advances in techniques for monitoring and perturbing neural populations have greatly enhanced our ability to study circuits in the brain. In particular, two-photon holographic optogenetics now enables precise photostimulation of experimenter-specified groups of individual neurons, while simultaneous two-photon calcium imaging enables the measurement of ongoing and induced activity across the neural population. Despite the enormous space of potential photostimulation patterns and the time-consuming nature of photostimulation experiments, very little algorithmic work has been done to determine the most effective photostimulation patterns for identifying the neural population dynamics. Here, I will discuss ongoing development of active learning techniques to efficiently select which neurons to stimulate such that the resulting neural responses will best inform a dynamical model of the neural population activity. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2025-02-05. Recording duration: 00:42:29.

John Hopfield and Geoffrey Hinton explain how ideas from physics helped establish computational models that store patterns and learn from data. Hopfield develops a physical perspective on collective computation, including associative memories in which network dynamics recover stored patterns from incomplete or distorted inputs. Hinton examines Boltzmann machines, connecting probabilistic neural networks and learning to concepts from statistical physics. Together, the lectures link energy landscapes, interacting units and stochastic behaviour with mechanisms for representation and computation. They provide the scientific background to the neural-network contributions recognised by the 2024 physics prize and the conceptual route from models of collective systems to machine learning.

This webinar features presentations from SueYeon Chung (New York University) and Srinivas Turaga (HHMI Janelia Research Campus) on theoretical and computational approaches to sensory cognition. Chung introduced a “neural manifold” framework to capture how high-dimensional neural activity is structured into meaningful manifolds reflecting object representations. She demonstrated that manifold geometry—shaped by radius, dimensionality, and correlations—directly governs a population’s capacity for classifying or separating stimuli under nuisance variations. Applying these ideas as a data analysis tool, she showed how measuring object-manifold geometry can explain transformations along the ventral visual stream and suggested that manifold principles also yield better self-supervised neural network models resembling mammalian visual cortex. Turaga described simulating the entire fruit fly visual pathway using its connectome, modeling 64 key cell types in the optic lobe. His team’s systematic approach—combining sparse connectivity from electron microscopy with simple dynamical parameters—recapitulated known motion-selective responses and produced novel testable predictions. Together, these studies underscore the power of combining connectomic detail, task objectives, and geometric theories to unravel neural computations bridging from stimuli to cognitive functions.

Large-scale recordings of neural activity are providing new opportunities to study network-level dynamics with unprecedented detail. However, the sheer volume of data and its dynamical complexity are major barriers to uncovering and interpreting these dynamics. I will present latent factor analysis via dynamical systems, a sequential autoencoding approach that enables inference of dynamics from neuronal population spiking activity on single trials and millisecond timescales. I will also discuss recent adaptations of the method to uncover dynamics from neural activity recorded via 2P Calcium imaging. Finally, time permitting, I will mention recent efforts to improve the interpretability of deep-learning based dynamical systems models.

Learning in biological systems takes place in contexts and with dynamics not often accounted for by simple models. I will describe the learning dynamics of two model systems that incorporate either architectural or dynamic constraints from biological observations. In the first case, inspired by the observed mesoscopic structure of the mouse brain as revealed by the Allen Mouse Brain Connectivity Atlas, as well as multiple examples of parallel pathways in mammalian brains, I present a mathematical analysis of learning dynamics in networks that have parallel computational pathways driven by the same cost function. We use the approximation of deep linear networks with large hidden layer sizes to show that, as the depth of the parallel pathways increases, different features of the training set (defined by the singular values of the input-output correlation) will typically concentrate in one of the pathways. This result is derived analytically and demonstrated with numerical simulation with both linear and non-linear networks. Thus, rather than sharing stimulus and task features across multiple pathways, parallel network architectures learn to produce sharply diversified representations with specialized and specific pathways, a mechanism which may hold important consequences for codes in both biological and artificial systems. In the second case, I discuss learning dynamics in a generalization of Hebbian rules and show that these rules allow a neuron to learn tensor decompositions of higher-order input correlations. Unlike the case of the Oja rule and PCA, the resulting learned representation is not unique but selects amongst the tensor eigenvectors according to initial conditions. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-04-10. Recording duration: 00:30:39.

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.

Neural computations are currently conceptualised using two separate approaches: sorting neurons into functional sub-populations or examining distributed collective dynamics. Whether and how these two aspects interact to shape computations is currently unclear. Using a novel approach to extract computational mechanisms from recurrent networks trained on neuroscience tasks, we show that the collective dynamics and sub-population structure play fundamentally complementary roles. Although various tasks can be implemented in networks with fully random population structure, we found that flexible input–output mappings instead require a non-random population structure that can be described in terms of multiple sub-populations. Our analyses revealed that such a sub-population organisation enables flexible computations through a mechanism based on gain-controlled modulations that flexibly shape the collective dynamics.

What is the relationship between task, network architecture, and population activity in nonlinear deep networks? I will describe the Gated Deep Linear Network framework, which schematizes how pathways of information flow impact learning dynamics within an architecture. Because of the gating, these networks can compute nonlinear functions of their input. We derive an exact reduction and, for certain cases, exact solutions to the dynamics of learning. The reduction takes the form of a neural race with an implicit bias towards shared representations, which then govern the model’s ability to systematically generalize, multi-task, and transfer. We show how appropriate network architectures can help factorize and abstract knowledge. Together, these results begin to shed light on the links between architecture, learning dynamics and network performance.

Neural computations are currently investigated using two separate approaches: sorting neurons into functional subpopulations or examining the low-dimensional dynamics of collective activity. Whether and how these two aspects interact to shape computations is currently unclear. Using a novel approach to extract computational mechanisms from networks trained on neuroscience tasks, here we show that the dimensionality of the dynamics and subpopulation structure play fundamentally com- plementary roles. Although various tasks can be implemented by increasing the dimensionality in networks with fully random population structure, flexible input–output mappings instead require a non-random population structure that can be described in terms of multiple subpopulations. Our analyses revealed that such a subpopulation structure enables flexible computations through a mechanism based on gain-controlled modulations that flexibly shape the collective dynamics. Our results lead to task-specific predictions for the structure of neural selectivity, for inactivation experiments and for the implication of different neurons in multi-tasking.

Talk & Tutorial

Animals exhibit remarkable learning capabilities with little direct supervision. Likewise, self-supervised learning is an emergent paradigm in artificial intelligence, closing the performance gap to supervised learning. In the context of biology, self-supervised learning corresponds to a setting where one sense or specific stimulus may serve as a supervisory signal for another. After learning, the latter can be used to predict the former. On the implementation level, it has been demonstrated that such predictive learning can occur at the single neuron level, in compartmentalized neurons that separate and associate information from different streams. We demonstrate the power such self-supervised learning over unsupervised (Hebb-like) learning rules, which depend heavily on stimulus statistics, in two examples: First, in the context of animal navigation where predictive learning can associate internal self-motion information always available to the animal with external visual landmark information, leading to accurate path-integration in the dark. We focus on the well-characterized fly head direction system and show that our setting learns a connectivity strikingly similar to the one reported in experiments. The mature network is a quasi-continuous attractor and reproduces key experiments in which optogenetic stimulation controls the internal representation of heading, and where the network remaps to integrate with different gains. Second, we show that incorporating global gating by reward prediction errors allows the same setting to learn conditioning at the neuronal level with mixed selectivity. At its core, conditioning entails associating a neural activity pattern induced by an unconditioned stimulus (US) with the pattern arising in response to a conditioned stimulus (CS). Solving the generic problem of pattern-to-pattern associations naturally leads to emergent cognitive phenomena like blocking, overshadowing, saliency effects, extinction, interstimulus interval effects etc. Surprisingly, we find that the same network offers a reductionist mechanism for causal inference by resolving the post hoc, ergo propter hoc fallacy.

Flexible computation is a hallmark of intelligent behavior. Yet, little is known about how neural networks contextually reconfigure for different computations. Humans are able to perform a new task without extensive training, presumably through the composition of elementary processes that were previously learned. Cognitive scientists have long hypothesized the possibility of a compositional neural code, where complex neural computations are made up of constituent components; however, the neural substrate underlying this structure remains elusive in biological and artificial neural networks. Here we identified an algorithmic neural substrate for compositional computation through the study of multitasking artificial recurrent neural networks. Dynamical systems analyses of networks revealed learned computational strategies that mirrored the modular subtask structure of the task-set used for training. Dynamical motifs such as attractors, decision boundaries and rotations were reused across different task computations. For example, tasks that required memory of a continuous circular variable repurposed the same ring attractor. We show that dynamical motifs are implemented by clusters of units and are reused across different contexts, allowing for flexibility and generalization of previously learned computation. Lesioning these clusters resulted in modular effects on network performance: a lesion that destroyed one dynamical motif only minimally perturbed the structure of other dynamical motifs. Finally, modular dynamical motifs could be reconfigured for fast transfer learning. After slow initial learning of dynamical motifs, a subsequent faster stage of learning reconfigured motifs to perform novel tasks. This work contributes to a more fundamental understanding of compositional computation underlying flexible general intelligence in neural systems. We present a conceptual framework that establishes dynamical motifs as a fundamental unit of computation, intermediate between the neuron and the network. As more whole brain imaging studies record neural activity from multiple specialized systems simultaneously, the framework of dynamical motifs will guide questions about specialization and generalization across brain regions.

Spiking recurrent neural networks (RNNs) are a promising tool for solving a wide variety of complex cognitive and motor tasks, due to their rich temporal dynamics and sparse processing. However training spiking RNNs on dedicated neuromorphic hardware is still an open challenge. This is due mainly to the lack of local, hardware-friendly learning mechanisms that can solve the temporal credit assignment problem and ensure stable network dynamics, even when the weight resolution is limited. These challenges are further accentuated, if one resorts to using memristive devices for in-memory computing to resolve the von-Neumann bottleneck problem, at the expense of a substantial increase in variability in both the computation and the working memory of the spiking RNNs. In this talk, I will present our recent work where we introduced a PyTorch simulation framework of memristive crossbar arrays that enables accurate investigation of such challenges. I will show that recently proposed e-prop learning rule can be used to train spiking RNNs whose weights are emulated in the presented simulation framework. Although e-prop locally approximates the ideal synaptic updates, it is difficult to implement the updates on the memristive substrate due to substantial device non-idealities. I will mention several widely adapted weight update schemes that primarily aim to cope with these device non-idealities and demonstrate that accumulating gradients can enable online and efficient training of spiking RNN on memristive substrates.

The free-energy principle and active inference have received a significant attention in the fields of neuroscience and machine learning. However, it remains to be established whether active inference is an apt explanation for any given neural network that actively exchanges with its environment. To address this issue, we show that a class of canonical neural networks of rate coding models implicitly performs variational Bayesian inference under a well-known form of partially observed Markov decision process model (Isomura, Shimazaki, Friston, Commun Biol, 2022). Based on the proposed theory, we demonstrate that canonical neural networks—featuring delayed modulation of Hebbian plasticity—can perform planning and adaptive behavioural control in the Bayes optimal manner, through postdiction of their previous decisions. This scheme enables us to estimate implicit priors under which the agent’s neural network operates and identify a specific form of the generative model. The proposed equivalence is crucial for rendering brain activity explainable to better understand basic neuropsychology and psychiatric disorders. Moreover, this notion can dramatically reduce the complexity of designing self-learning neuromorphic hardware to perform various types of tasks.

Many engineered and biological systems must trade off performance and energy use, and the brain is no exception. While there are theories on how activity levels are controlled in biological networks through feedback control (homeostasis), it is not clear what the effects on population coding are, and therefore how performance and energy can be traded off. In this talk we will consider this tradeoff in auto-encoding networks, in which there is a clear definition of performance (the coding loss). We first show how SNNs follow a characteristic trade-off curve between activity levels and coding loss, but that standard networks need to be retrained to achieve different tradeoff points. We next formalize this tradeoff with a joint loss function incorporating coding loss (performance) and activity loss (energy use). From this loss we derive a class of spiking networks which coordinates its spiking to minimize both the activity and coding losses -- and as a result can dynamically adjust its coding precision and energy use. The network utilizes several known activity control mechanisms for this --- threshold adaptation and feedback inhibition --- and elucidates their potential function within neural circuits. Using geometric intuition, we demonstrate how these mechanisms regulate coding precision, and thereby performance. Lastly, we consider how these insights could be transferred to trained SNNs. Overall, this work addresses a key energy-coding trade-off which is often overlooked in network studies, expands on our understanding of homeostasis in biological SNNs, as well as provides a clear framework for considering performance and energy use in artificial SNNs.

Reservoir computing is a promising framework to study cortical computation, as it is based on continuous, online processing and the requirements and operating principles are compatible with cortical circuit dynamics. However, the framework has issues that limit its scope as a generic model for cortical processing. The most obvious of these is that, in traditional models, learning is restricted to the output projections and takes place in a fully supervised manner. If such an output layer is interpreted at face value as downstream computation, this is biologically questionable. If it is interpreted merely as a demonstration that the network can accurately represent the information, this immediately raises the question of what would be biologically plausible mechanisms for transmitting the information represented by a reservoir and incorporating it in downstream computations. Another major issue is that we have as yet only modest insight into how the structural and dynamical features of a network influence its computational capacity, which is necessary not only for gaining an understanding of those features in biological brains, but also for exploiting reservoir computing as a neuromorphic application. In this talk, I will first demonstrate a method for quantifying the representational capacity of reservoirs without training them on tasks. Based on this technique, which allows systematic comparison of systems, I then present our recent work towards understanding the roles of heterogeneity and connectivity patterns in enhancing both the computational properties of a network and its ability to reliably transmit to downstream networks. Finally, I will give a brief taster of our current efforts to apply the reservoir computing framework to magnetic systems as an approach to neuromorphic computing.

Biological brains possess an exceptional ability to infer relevant behavioral responses to a wide range of stimuli from only a few examples. This capacity to generalize beyond the training set has been proven particularly challenging to realize in artificial systems. How neural processes enable this capacity to extrapolate to novel stimuli is a fundamental open question. A prominent but underexplored hypothesis suggests that generalization is facilitated by a low-dimensional organization of collective neural activity, yet evidence for the underlying neural mechanisms remains wanting. Combining network modeling, theory and neural data analysis, we tested this hypothesis in the framework of flexible timing tasks, which rely on the interplay between inputs and recurrent dynamics. We first trained recurrent neural networks on a set of timing tasks while minimizing the dimensionality of neural activity by imposing low-rank constraints on the connectivity, and compared the performance and generalization capabilities with networks trained without any constraint. We then examined the trained networks, characterized the dynamical mechanisms underlying the computations, and verified their predictions in neural recordings. Our key finding is that low-dimensional dynamics strongly increases the ability to extrapolate to inputs outside of the range used in training. Critically, this capacity to generalize relies on controlling the low-dimensional dynamics by a parametric contextual input. We found that this parametric control of extrapolation was based on a mechanism where tonic inputs modulate the dynamics along non-linear manifolds in activity space while preserving their geometry. Comparisons with neural recordings in the dorsomedial frontal cortex of macaque monkeys performing flexible timing tasks confirmed the geometric and dynamical signatures of this mechanism. Altogether, our results tie together a number of previous experimental findings and suggest that the low-dimensional organization of neural dynamics plays a central role in generalizable behaviors.