Dynamical Systems seminars

The description of neural computations currently relies on two competing views: (i) a classical single-cell view that aims to relate the activity of individual neurons to sensory or behavioural variables, and organize them into functional classes; (ii) a more recent population view that instead characterises computations in terms of collective neural trajectories, and focuses on the dimensionality of these trajectories as animals perform tasks. How the two key concepts of functional cell classes and low-dimensional trajectories interact to shape neural computations is however at present not understood. Here I will address this question by combining machine-learning tools for training recurrent neural networks with reverse-engineering and theoretical analyses of network dynamics.

Cognitive tasks typically require the integration of working memory, contextual processing, and planning to be carried out in close coordination. However, these computations are typically studied within neuroscience as independent modular processes in the brain. In this talk I will present an alternative view, that neural representations of mappings between expected stimuli and contingent goal actions can unify working memory and planning computations. We term these stored maps contingency representations. We developed a "conditional delayed logic" task capable of disambiguating the types of representations used during performance of delay tasks. Human behaviour in this task is consistent with the contingency representation, and not with traditional sensory models of working memory. In task-optimized artificial recurrent neural network models, we investigated the representational geometry and dynamical circuit mechanisms supporting contingency-based computation, and show how contingency representation explains salient observations of neuronal tuning properties in prefrontal cortex. Finally, our theory generates novel and falsifiable predictions for single-unit and population neural recordings.

Sensory cortices display a suite of ubiquitous dynamical features, such as ongoing noise variability, transient overshoots, and oscillations, that have so far escaped a common, principled theoretical account. We developed a unifying model for these phenomena by training a recurrent excitatory-inhibitory neural circuit model of a visual cortical hypercolumn to perform sampling-based probabilistic inference. The optimized network displayed several key biological properties, including divisive normalization, as well as stimulus-modulated noise variability, inhibition-dominated transients at stimulus onset, and strong gamma oscillations. These dynamical features had distinct functional roles in speeding up inferences and made predictions that we confirmed in novel analyses of awake monkey recordings. Our results suggest that the basic motifs of cortical dynamics emerge as a consequence of the efficient implementation of the same computational function — fast sampling-based inference — and predict further properties of these motifs that can be tested in future experiments

Firing-rate (FR) or neural-mass models are widely used for studying computations performed by neural populations. Despite their success, classical firing-rate models do not capture spike timing effects on the microscopic level such as spike synchronization and are difficult to link to spiking data in experimental recordings. For large neuronal populations, the gap between the spiking neuron dynamics on the microscopic level and coarse-grained FR models on the population level can be bridged by mean-field theory formally valid for infinitely many neurons. It remains however challenging to extend the resulting mean-field models to finite-size populations with biologically realistic neuron numbers per cell type (mesoscopic scale). In this talk, I present a mathematical framework for mesoscopic populations of generalized integrate-and-fire neuron models that accounts for fluctuations caused by the finite number of neurons. To this end, I will introduce the refractory density method for quasi-renewal processes and show how this method can be generalized to finite-size populations. To demonstrate the flexibility of this approach, I will show how synaptic short-term plasticity can be incorporated in the mesoscopic mean-field framework. On the other hand, the framework permits a systematic reduction to low-dimensional FR equations using the eigenfunction method. Our modeling framework enables a re-examination of classical FR models in computational neuroscience under biophysically more realistic conditions.

Animals perform learned actions with remarkable consistency for years after acquiring a skill. What is the neural correlate of this stability? We explore this question from the perspective of neural populations. Recent work suggests that the building blocks of neural function may be the activation of population-wide activity patterns: neural modes that capture the dominant co-variation patterns of population activity and define a task specific low dimensional neural manifold. The time-dependent activation of the neural modes results in latent dynamics. We hypothesize that the latent dynamics associated with the consistent execution of a behaviour need to remain stable, and use an alignment method to establish this stability. Once identified, stable latent dynamics allow for the prediction of various behavioural features via fixed decoder models. We conclude that latent cortical dynamics within the task manifold are the fundamental and stable building blocks underlying consistent behaviour.

Theoretical and computational models of neural systems have been traditionally focused on small neural circuits, given the lack of reliable data on large-scale brain structures. The situation has started to change in recent years, with novel recording technologies and large organized efforts to describe the brain at a larger scale. In this talk, Professor Mejias from the University of Amsterdam will review his recent work on developing anatomically constrained computational models of large-scale cortical networks of monkeys, and how this approach can help to answer important questions in large-scale neuroscience. He will focus on three main aspects: (i) the emergence of functional interactions in different frequency regimes, (ii) the role of balance for efficient large-scale communication, and (iii) new paradigms of brain function, such as working memory, in large-scale networks.

Bursts in gamma and other frequency ranges are thought to contribute to the efficiency of working memory or communication tasks. Abnormalities in bursts have also been associated with motor and psychiatric disorders. The determinants of burst generation are not known, specifically how single cell and connectivity parameters influence burst statistics and the corresponding brain states. We first present a generic mathematical model for burst generation in an excitatory-inhibitory (EI) network with self-couplings. The resulting equations for the stochastic phase and envelope of the rhythm’s fluctuations are shown to depend on only two meta-parameters that combine all the network parameters. They allow us to identify different regimes of amplitude excursions, and to highlight the supportive role that network finite-size effects and noisy inputs to the EI network can have. We discuss how burst attributes, such as their durations and peak frequency content, depend on the network parameters. In practice, the problem above follows the a priori challenge of fitting such E-I spiking networks to single neuron or population data. Thus, the second part of the talk will discuss a novel method to fit mesoscale dynamics using single neuron data along with a low-dimensional, and hence statistically tractable, single neuron model. The mesoscopic representation is obtained by approximating a population of neurons as multiple homogeneous ‘pools’ of neurons, and modelling the dynamics of the aggregate population activity within each pool. We derive the likelihood of both single-neuron and connectivity parameters given this activity, which can then be used to either optimize parameters by gradient ascent on the log-likelihood, or to perform Bayesian inference using Markov Chain Monte Carlo (MCMC) sampling. We illustrate this approach using an E-I network of generalized integrate-and-fire neurons for which mesoscopic dynamics have been previously derived. We show that both single-neuron and connectivity parameters can be adequately recovered from simulated data.

During periods of persistent and inescapable stress, animals can switch from active to passive coping strategies to manage effort-expenditure. Such normally adaptive behavioural state transitions can become maladaptive in disorders such as depression. We developed a new class of multi-region recurrent neural network (RNN) models to infer brain-wide interactions driving such maladaptive behaviour. The models were trained to match experimental data across two levels simultaneously: brain-wide neural dynamics from 10-40,000 neurons and the realtime behaviour of the fish. Analysis of the trained RNN models revealed a specific change in inter-area connectivity between the habenula (Hb) and raphe nucleus during the transition into passivity. We then characterized the multi-region neural dynamics underlying this transition. Using the interaction weights derived from the RNN models, we calculated the input currents from different brain regions to each Hb neuron. We then computed neural manifolds spanning these input currents across all Hb neurons to define subspaces within the Hb activity that captured communication with each other brain region independently. At the onset of stress, there was an immediate response within the Hb/raphe subspace alone. However, RNN models identified no early or fast-timescale change in the strengths of interactions between these regions. As the animal lapsed into passivity, the responses within the Hb/raphe subspace decreased, accompanied by a concomitant change in the interactions between the raphe and Hb inferred from the RNN weights. This innovative combination of network modeling and neural dynamics analysis points to dual mechanisms with distinct timescales driving the behavioural state transition: early response to stress is mediated by reshaping the neural dynamics within a preserved network architecture, while long-term state changes correspond to altered connectivity between neural ensembles in distinct brain regions.

Synaptic plasticity is believed to be a key physiological mechanism for learning. It is well-established that it depends on pre and postsynaptic activity. However, models that rely solely on pre and postsynaptic activity for synaptic changes have, to date, not been able to account for learning complex tasks that demand hierarchical networks. Here, we show that if synaptic plasticity is regulated by high-frequency bursts of spikes, then neurons higher in the hierarchy can coordinate the plasticity of lower-level connections. Using simulations and mathematical analyses, we demonstrate that, when paired with short-term synaptic dynamics, regenerative activity in the apical dendrites, and synaptic plasticity in feedback pathways, a burst-dependent learning rule can solve challenging tasks that require deep network architectures. Our results demonstrate that well-known properties of dendrites, synapses, and synaptic plasticity are sufficient to enable sophisticated learning in hierarchical circuits.