van Vreeswijk Theoretical Neuroscience Seminar

Dense Associative Memories (Dense AMs) are energy-based neural networks that share many desirable features of celebrated Hopfield Networks but have superior information storage capabilities. In contrast to conventional Hopfield Networks, which were popular in the 1980s, DenseAMs have a very large memory storage capacity - possibly exponential in the size of the network. This aspect makes them appealing tools for many problems in AI and neurobiology. In this talk I will describe two theories of how DenseAMs might be built in biological “hardware”. According to the first theory, DenseAMs arise as effective theories after integrating out a large number of neuronal degrees of freedom. According to the second theory, astrocytes, a particular type of glia cells, serve as core computational units enabling large memory storage capabilities. This second theory challenges a common point of view in the neuroscience community that astrocytes play the role of only passive house-keeping support structures in the brain. In contrast, it suggests that astrocytes might be actively involved in brain computation and memory storage and retrieval. This story is an illustration of how computational principles originating in physics may provide insights into novel AI architectures and brain computation. VVTNS New Year Opening Lecture. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2025-01-08. Recording duration: 00:49:16.

Classical views suggest that memories are stored in assemblies of excitatory neurons that become strongly interconnected during learning. However, recent experimental and theoretical results have challenged this view, leading to the hypothesis that memories are encoded in assemblies containing both excitatory (E) and inhibitory (I) neurons. Understanding the effects of these E-I assemblies on memory function is therefore essential. Using a biologically constrained model of an olfactory memory network, I will first describe how introducing E-I assemblies reorganizes odor-evoked activity patterns in neural state space. Indeed, the “geometry” of neural activity provides valuable insights about the computational properties of neural networks. I will then describe the behavior of networks with E-I assemblies upon partial manipulation of inhibitory neurons. Finally, I will discuss recent experimental data supporting predictions of the model. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-12-18. Recording duration: 00:35:13.

Continuous attractors offer a unique class of solutions for storing continuous-valued variables in recurrent system states for indefinitely long time intervals. Unfortunately, continuous attractors suffer from severe structural instability in general---they are destroyed by most infinitesimal changes of the dynamical law that defines them. This fragility limits their utility especially in biological systems as their recurrent dynamics are subject to constant perturbations. We observe that the bifurcations from continuous attractors in theoretical neuroscience models display various structurally stable forms. Although their asymptotic behaviors to maintain memory are categorically distinct, their finite-time behaviors are similar. We build on the persistent manifold theory to explain the commonalities between bifurcations from and approximations of continuous attractors. Fast-slow decomposition analysis uncovers the existence of a persistent slow manifold that survives the seemingly destructive bifurcation, relating the flow within the manifold to the size of the perturbation. Moreover, this allows the bounding of the memory error of these approximations of continuous attractors. Finally, we train recurrent neural networks on analog memory tasks to support the appearance of these systems as solutions and their generalization capabilities. Therefore, we conclude that continuous attractors are functionally robust and remain useful as a universal analogy for understanding analog memory. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-11-27. Recording duration: 00:59:01.

In recent years, my lab and others have demonstrated the value of vector symbolic algebras (VSAs) for capturing a wide variety of neural and behavioural results. In this talk I discuss the surprising and compelling variety of tasks and styles of reasoning that are well-suited to descriptions using a specific VSA. These tasks include path integration, navigation, Bayesian reasoning, sampling, memorization, and logical inference. The resulting spiking neural network models capture various hippocampal cell types (grid, place, border, etc.), behavioural errors, and a variety of observed neural dynamics. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-11-20. Recording duration: 00:47:23.

While anatomical connectivity changes slowly through synaptic learning, the functional connectivity of neurons changes rapidly with ongoing activity of neurons and their functional interactions. Functional networks of neurons and neural populations reflect how their interactions change with behaviors, stimulus types, and internal states. Therefore, the information propagation across a network can be analyzed through the varying topological properties of the functional networks. Our study investigates the functional networks of the visual cortex at both the single-cell and population levels. Our analyses of functional connectivity of single neurons, constructed from spiking activity in neural populations of the visual cortex, reveal local and global network structures shaped by stimulus complexity. In addition, we propose a new method for inferring functional interactions between neural populations that preserves biologically constrained anatomical connectivity and signs. Applying our method to 2-photon data from the mouse visual cortex, we uncover functional interactions between cell types and cortical layers, suggesting distinct pathways for processing expected and unexpected visual information. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-11-06. Recording duration: 00:49:10.

A fundamental problem in neuroscience is understanding how the properties of individual neurons and synapses contribute to neuronal circuit dynamics and behavior. In recent years we have done both computational and experimental studies that demonstrate that the same physiological output can arise from multiple, degenerate solutions, and that individual animals with similar behavior can nonetheless have quite different sets of underlying circuit parameters. Most recently, we have been studying the resilience of individual animals to perturbations such as temperature and high potassium concentrations. This has revealed that extreme environmental experiences can produce long-term changes in circuit performance that can be hidden, or “cryptic” unless the animals are again challenged or perturbed. Our present experimental and computational work is designed to understand differential resilience in natural, wild-caught animals in response to climate change, and shows long-lasting influences of the animals’ temperature history. VVTNS Fourth Season Closing Lecture. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-06-26. Recording duration: 00:49:33.

Developing scientifically-grounded theories for representation learning and generalization in artificial deep neural networks remains a grand challenge of fundamental interest to theoretical neuroscience and machine learning. I will discuss our work on one facet of this challenge — namely understanding generalization or “scaling laws” in learned neural networks as a function of basic control variables. I’ll discuss a taxonomy we develop that classifies different regimes of scaling behavior. We identify regimes where generalization exhibits universal scaling behavior and others where it can be traced back to properties of the data and neural architecture. The theoretical analysis is enabled by leveraging exactly solvable models of deep neural networks that arise naturally in the limit of large hidden layers. Along the way, I’ll also discuss our work on these theoretical models, which have been a useful starting point for theoretical descriptions of neural network dynamics. Finally, I’ll discuss our findings connecting generalization in neural networks to properties of the learned data manifold. I’ll close by discussing future directions and new hypotheses that emerge from our findings Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-06-19. Recording duration: 00:46:53.

Biological systems must selectively encode partial information about the environment, as dictated by the capacity constraints at work in all living organisms. For example, we cannot see every feature of the light field that reaches our eyes; temporal resolution is limited by transmission noise and delays, and spatial resolution is limited by the finite number of photoreceptors and output cells in the retina. Classical efficient coding theory describes how sensory systems can maximize information transmission given such capacity constraints, but it treats all input features equally. Not all inputs are, however, of equal value to the organism. Our work quantifies whether and how the brain selectively encodes stimulus features, specifically predictive features, that are most useful for fast and effective movements. We have shown that efficient predictive computation starts at the earliest stages of the visual system in the retina. We borrow techniques from machine learning, statistical physics, and information theory to assess how we get terrific, predictive vision from these imperfect (lagged and noisy) component parts. In broader terms, we aim to build a more complete theory of efficient encoding in the brain, and along the way have found some intriguing connections between approaches to coarse graining in biology, machine learning, and physics. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-06-05. Recording duration: 00:41:40.

Theoretical neuroscience aims to understand the relationship between neuron dynamics and connectivity in recurrent circuits. This has been intensively studied at the local level, where dynamics is described by pairwise correlations. Recent advances in simultaneous recordings of many neurons have allowed researchers to address the question at the global level, such as for the dimensionality of population dynamics. Our work contributes to this effort by analyzing the impact of connectivity statistics, including certain motifs, on the bulk and outlier covariance eigenvalues. By considering linearized dynamics around a steady state, we obtained analytically the covariance spectrum which exhibits a signature long tail robust to model variants and matches zebrafish calcium imaging data. This provides a local circuit mechanism for shaping the geometry of population dynamics and a quantitative benchmark for interpreting data. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-05-22. Recording duration: 00:53:15.

Understanding the causal connectivity within a network is crucial for unraveling its functional dynamics. However，the inferred causal connections are fundamentally influenced by the choice of causality measure employed, which may not always align with the actual structural connectivity of the network. The relationship between causal and structural connectivity, especially how different causality measures affect the inferred causal links, requires further exploration. In this talk, we examine nonlinear networks characterized by pulse signal outputs, such as spiking neural networks, using four prevalent causality measures: time-delayed correlation coefficient, time-delayed mutual information, Granger causality, and transfer entropy. We provide a theoretical analysis of the interconnections among these measures when applied to pulse signals. Utilizing both a simulated Hodgkin–Huxley network and an empirical mouse brain network as case studies, we validate the quantitative relationships between these causality measures. Our results show a strong correspondence between the causal connectivity derived from any of these measures and the actual structural connectivity, thereby establishing a direct linkage between them. We highlight that structural connectivity in networks with output pulse signals can be reconstructed on a pairwise basis, without needing global information from all network nodes, effectively avoiding the curse of dimensionality. Our approach offers a robust and practical methodology for reconstructing networks based on pulse outputs. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-05-08. Recording duration: 00:45:20.

Persistent, stimulus-dependent neuronal activity has been observed in numerous brain areas during tasks that require the temporary maintenance of information. Several competing hypotheses for the neuronal mechanisms underlying persistent activity have been proposed. We have employed data-driven models in conjunction with optogenetic disruptions of neural circuits within memory-guided motor tasks. Our findings revealed a mechanism governed by dynamic attractors, pivotal in sustaining neuronal activity. This mechanism, shaped by time-varying inputs reflecting temporal predictions, is instrumental in regulating the impact of sensory information on the premotor cortex, thereby preserving memory traces from distracting stimuli. We then asked how persistent activity driven by attractor dynamics emerges during motor learning. It has been proposed that activity-dependent synaptic plasticity underpins motor learning, as it can reconfigure network architectures to produce the appropriate neural dynamics for specific behaviors. To verify this hypothesis, we investigated how the mouse premotor cortex acquires specific neural dynamics that govern the planning of movement at different stages of motor learning. We developed network models that replicated the effects of acute manipulations of synaptic plasticity. The models, which display attractor dynamics, also explain flexible behavior after learning has ended. By leveraging the model's predictions, we can formulate testable hypotheses regarding the distinct mechanisms governing movement planning at various stages of the learning process. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-05-01. Recording duration: 00:39:52.

Neural computation is inextricably bound to decisions that must be made under time pressure and uncertainty. At the level of neural circuits, single neurons need to decide whether to spike. On longer timescales, the component circuitry needs to decide whether to reconfigure to store memories and adapt to novel situations. In this talk I will focus on two fun ideas in each of these contexts by showing how nonlinearities in neural components naturally form excitable switches that enable reliable decisions to be made in fluctuating environments. I will also issue propaganda that the kind of high level, cognitive faculties that we normally associate with decision making apply equally well and are understudied at the level of neural and synaptic populations. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-04-17. Recording duration: 00:41:08.

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.

In this talk, I will explain a theory of connectome-constrained neural networks in which a “student” networks is trained to reproduce the activity of a ground-truth “teacher”, representing a neural system for which a connectome is available. Unlike standard paradigms with unconstrained connectivity, here both networks have the same connectivity but they have different biophysical parameters, reflecting uncertainty in neuronal and synaptic properties. We find that the connectome is often insufficient to constrain the dynamics of networks that perform a specific task, illustrating the difficulty of inferring function from connectivity alone. However, recordings from a small subset of neurons can remove this degeneracy, producing dynamics in the student that agree with the teacher. Our theory can prioritize which neurons to record from to most efficiently unmeasured network activity. The analysis shows that the solution spaces of connectome-constrained and unconstrained models are qualitatively different, and provides a framework to determine when such models yield consistent dynamics. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-04-03. Recording duration: 00:42:28.

The connectivity structure of many biological systems, including neural circuits, is highly non-uniform. Recent technologies allow detailed mapping of these irregularities, but our understanding of their effect on the overall circuit dynamics is still lacking. By developing complex system analytical tools that perform reduction of the network, I determine the impact of connectivity features on network dynamics. I will demonstrate the use of these tools on neural assemblies (clusters), a ubiquitous non-uniform structure in our brains. I will show how neural assemblies of different sizes naturally generate multiple timescales of activity spanning several orders of magnitude. I will demonstrate how the analytical theory we develop for rate networks, supported by spiking network simulations, reveals the dependency between neural timescales and assembly sizes and how new recordings of spontaneous activity from a million neurons support this analysis. I will also show how our model can naturally explain the particular long-tailed timescale distribution observed in the awake primate cortex. In olfactory cortex, neural assemblies represent odor stimuli. Previously, I showed how the diffuse recurrent excitation among these assemblies allows the conversion of time-encoded inputs from the bulb to spacial neural assembly representations in olfactory cortex. Here, I will show how changes in the dynamical properties of these assemblies alter both their timing response and properties of the time-encoded inputs via feedback. This demonstrates the role of neural assemblies in time-sensitive modulation needed for cognitive tasks, such as attention. Our results offer a biologically plausible mechanism of assemblies in network connectivity for explaining multiple puzzling dynamical phenomena: The ability of neural circuits to transform external simultaneous temporal fluctuations into spatial representations and alter them; and the ability of neuronal circuits to generate simultaneous temporal fluctuations across a large range of timescales; Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-03-20. Recording duration: 00:41:28.

In theoretical neuroscience, the brain is usually described as an information processing system that encodes and manipulates representations of knowledge to produce plans of action. This view leads to a decomposition of brain functions into putative processes such as object recognition, working memory, decision-making, action planning, etc., inspiring the search for the neural correlates of these processes. However, neurophysiological data do not support many of the predictions of these classic subdivisions. Instead, there is divergence and broad distribution of functions that should be unified, mixed representations combining functions that should be distinct, and a general incompatibility with the conceptual subdivisions posited by theories of information processing. In this talk, I will explore the possibility of resynthesizing a different set of functional subdivisions, guided by the growing body of data on the evolutionary process that produced the human brain. I will summarize, in chronological order, a proposed sequence of innovations that appeared in nervous systems along the lineage that leads from the earliest multicellular animals to humans. Along the way, functional subdivisions and elaborations will be introduced in parallel with the neural specializations that made them possible, gradually building up an alternative conceptual taxonomy of brain functions. These functions emphasize mechanisms for real-time interaction with the world, rather than for building explicit knowledge of the world, and the relevant representations emphasize pragmatic outcomes rather than decoding accuracy, mixing variables in the way seen in real neural data. I suggest that this alternative taxonomy may better delineate the real functional pieces into which the brain is organized, and can offer a more natural mapping between behavior and neural mechanisms. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-03-13. Recording duration: 00:52:50.

Performing learned behaviors requires animals to produce precisely timed motor sequences. The underlying neuronal circuits must convert incoming spike trains into precisely timed firing to indicate the onset of crucial sensory cues or to carry out well-coordinated muscle movements. Birdsong is a remarkable example of a complex, learned and precisely timed natural behavior which is controlled by a brainstem-thalamocortical feedback loop. Projection neurons within the zebra finch cortical nucleus HVC (used as a proper name), produce precisely timed, highly reliable and ultra-sparse neural sequences that are thought to underlie song dynamics. However, the origin of short timescale dynamics of the song is debated. One model posits that these dynamics reside in HVC and are mediated through a synaptic chain mechanism. Alternatively, the upstream motor thalamic nucleus Uveaformis (Uva), could drive HVC bursts as part of a brainstem-thalamocortical distributed network. Using focal temperature manipulation we found that the song dynamics reside chiefly in HVC. We then characterized the activity of thalamic nucleus Uva, which provides input to HVC. We developed a lightweight (~1 g) microdrive for juxtacellular recordings and with it performed the very first extracellular single unit recordings in Uva during song. Recordings revealed HVC-projecting Uva neurons contain timing information during the song, but compared to HVC neurons, fire densely in time and are much less reliable. Computational models of Uva-driven HVC neurons estimated that a high degree of synaptic convergence is needed from Uva to HVC to overcome the inconsistency of Uva firing patterns. However, axon terminals of single Uva neurons exhibit low convergence within HVC such that each HVC neuron receives input from 2-7 Uva neurons. These results suggest that thalamus maintains sequential cortical activity during song but does not provide unambiguous timing information. Our observations are consistent with a model in which the brainstem-thalamocortical feedback loop acts at the syllable timescale (~100 ms) and does not support a model in which the brainstem-thalamocortical feedback loop acts at fast timescale (~10 ms) to generate sequences within cortex. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-02-14. Recording duration: 00:39:45.

Animals and humans rapidly adapt their behavior to dynamic environmental changes, such as predator threats or fluctuating food resources, often without immediate rewards. Existing literature posits that animals rely on internal representations of the environment, termed “beliefs”, for their decision policy. However, previous work ties belief updates to external reward signals, which does not explain adaptation in scenarios where trial-and-error approaches are inefficient or potentially perilous. In this work, we propose that the brain utilize dynamic representations that continuously infer the state of the environment, allowing it to update behavior rapidly. I will present a Bayesian theory for state inference in a partially observed Markov Decision Process with multiple interacting latent variables. Optimal behavior requires knowledge of hidden interactions between latent states. I will show that recurrent neural networks trained through reinforcement solve the task by learning the hidden interaction between latent states, and their activity encodes the dynamics of the optimal Bayesian estimators. The behavior of rodents trained on an identical task aligns with our theoretical model and neural network simulations, suggesting that the brain utilizes dynamic internal state representation and inference. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-01-31. Recording duration: 00:51:21.

Learning induces changes in neural activity over slow timescales. These changes can be summarized by restructuring neural population data into a three-dimensional array or tensor, of size neurons by time points by trials. Classic dimensionality reduction methods often assume that neural representations are constrained to a fixed low-dimensional latent subspace. Consequently, this view does not capture how the latent subspace could evolve over learning, nor how high-dimensional neural activity could emerge over learning. Furthermore, the link between these empirically-observed changes in neural activity as a result of learning and circuit-level changes in recurrent dynamics is unclear. In this talk I will discuss our recent efforts towards developing dimensionality reduction and data-driven modeling methods based on tensors in order to identify how neural representations change over learning. First we introduce a new tensor decomposition, sliceTCA, which is able to disentangle latent variables of multiple covariability classes that are often mixed in neural population data. We demonstrate in three datasets that sliceTCA is able to capture more behaviorally-relevant information in neural data than previous methods. Second, to probe for how circuit-level changes in neural dynamics implement the observed changes in neural activity, we develop a data-driven RNN-based framework in which the recurrent connectivity is constrained to be low tensor rank. We demonstrate that such low tensor rank RNNs (ltrRNNs) are able to capture changes in neural geometry and dynamics in motor cortical data from a motor adaptation task. Together, both sliceTCA and ltrRNN demonstrate the utility of interpretable, tensor-based methods for discovery of learning-induced changes in neural representations directly from data. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-01-24. Recording duration: 00:45:54.

As we interact with the world around us, we experience a constant stream of sensory inputs, and must generate a constant stream of behavioral actions. What makes brains more than simple input-output machines is their capacity to integrate sensory inputs with an animal’s own internal motivational state to produce behavior that is flexible and adaptive. Working with neural recordings from subcortical structures involved in regulation of survival behaviors, we show how the dynamical properties of neural populations give rise to motivational states that change animal behavior on a timescale of minutes. We also show how neuromodulation can alter these dynamics to change behavior on timescales of hours to days. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-01-17. Recording duration: 00:42:58.