Computational Neuroscience seminars

Neural representations of time are central to our understanding of the world around us. I review cognitive, neurophysiological and theoretical work that converges on three simple ideas. First, the time of past events is remembered via populations of neurons with a continuum of functional time constants. Second, these time constants evenly tile the log time axis. This results in a neural Weber-Fechner scale for time which can support behavioral Weber-Fechner laws and characteristic behavioral effects in memory experiments. Third, these populations appear as dual pairs---one type of population contains cells that change firing rate monotonically over time and a second type of population that has circumscribed temporal receptive fields. These ideas can be used to build artificial neural networks that have novel properties. Of particular interest, a convolutional neural network built using these principles can generalize to arbitrary rescaling of its inputs. That is, after learning to perform a classification task on a time series presented at one speed, it successfully classifies stimuli presented slowed down or sped up. This result illustrates the point that this confluence of ideas originating in cognitive psychology and measured in the mammalian brain could have wide-reaching impacts on AI research.

It was long hypothesized that natural systems might take advantage of the extended temporal and spatial correlations close to the critical point to improve their computational capabilities. However, on the other side, different distances to criticality were inferred from the recordings of nervous systems. In my talk, I discuss how including additional constraints on the processing time can shift the optimal operating point of the recurrent networks. Moreover, the data from the visual cortex of the monkeys during the attentional task indicate that they flexibly change the closeness to the critical point of the local activity. Overall it suggests that, as we would expect from common sense, the optimal state depends on the task at hand, and the brain adapts to it in a local and fast manner.

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.

In understanding circuit operations, a key issue is the extent to which neuronal spiking reflects local computation or responses to upstream inputs. Because pyramidal cells in CA1 do not have local recurrent projections, it is currently assumed that firing in CA1 is inherited from its inputs – thus, entorhinal inputs provide communication with the rest of the neocortex and the outside world, whereas CA3 inputs provide internal and past memory representations. Several studies have attempted to prove this hypothesis, by lesioning or silencing either area CA3 or the entorhinal cortex and examining the effect of firing on CA1 pyramidal cells. Despite the intense and careful work in this research area, the magnitudes and types of the reported physiological impairments vary widely across experiments. At least part of the existing variability and conflicts is due to the different behavioral paradigms, designs and evaluation methods used by different investigators. Simultaneous manipulations in the same animal or even separate manipulations of the different inputs to the hippocampal circuits in the same experiment are rare. To address these issues, I used optogenetic silencing of unilateral and bilateral mEC, of the local CA1 region, and performed bilateral pharmacogenetic silencing of the entire CA3 region. I combined this with high spatial resolution recording of local field potentials (LFP) in the CA1-dentate axis and simultaneously collected firing pattern data from thousands of single neurons. Each experimental animal had up to two of these manipulations being performed simultaneously. Silencing the medial entorhinal (mEC) largely abolished extracellular theta and gamma currents in CA1, without affecting firing rates. In contrast, CA3 and local CA1 silencing strongly decreased firing of CA1 neurons without affecting theta currents. Each perturbation reconfigured the CA1 spatial map. Yet, the ability of the CA1 circuit to support place field activity persisted, maintaining the same fraction of spatially tuned place fields, and reliable assembly expression as in the intact mouse. Thus, the CA1 network can maintain autonomous computation to support coordinated place cell assemblies without reliance on its inputs, yet these inputs can effectively reconfigure and assist in maintaining stability of the CA1 map.

Excitatory and inhibitory (E & I) inputs to cortical neurons remain balanced across different conditions. The balanced network model provides a self-consistent account of this observation: population rates dynamically adjust to yield a state in which all neurons are active at biological levels, with their E & I inputs tightly balanced. But global tight E/I balance predicts population responses with linear stimulus-dependence and does not account for systematic cortical response nonlinearities such as divisive normalization, a canonical brain computation. However, when necessary connectivity conditions for global balance fail, states arise in which only a localized subset of neurons are active and have balanced inputs. We analytically show that in networks of neurons with different stimulus selectivities, the emergence of such localized balance states robustly leads to normalization, including sublinear integration and winner-take-all behavior. An alternative model that exhibits normalization is the Stabilized Supralinear Network (SSN), which predicts a regime of loose, rather than tight, E/I balance. However, an understanding of the causal relationship between E/I balance and normalization in SSN and conditions under which SSN yields significant sublinear integration are lacking. For weak inputs, SSN integrates inputs supralinearly, while for very strong inputs it approaches a regime of tight balance. We show that when this latter regime is globally balanced, SSN cannot exhibit strong normalization for any input strength; thus, in SSN too, significant normalization requires localized balance. In summary, we causally and quantitatively connect a fundamental feature of cortical dynamics with a canonical brain computation. Time allowing I will also cover our work extending a normative theoretical account of normalization which explains it as an example of efficient coding of natural stimuli. We show that when biological noise is accounted for, this theory makes the same prediction as the SSN: a transition to supralinear integration for weak stimuli.

How the brain stores a sequence in memory remains largely unknown. We investigated the neural code underlying sequence working memory using two-photon calcium imaging to record thousands of neurons in the prefrontal cortex of macaque monkeys memorizing and then reproducing a sequence of locations after a delay. We discovered a regular geometrical organization: The high-dimensional neural state space during the delay could be decomposed into a sum of low-dimensional subspaces, each storing the spatial location at a given ordinal rank, which could be generalized to novel sequences and explain monkey behavior. The rank subspaces were distributed across large overlapping neural groups, and the integration of ordinal and spatial information occurred at the collective level rather than within single neurons. Thus, a simple representational geometry underlies sequence working memory.

Ali Weber (University of Washington, USA) uses the the hawkmoth as a model system, to investigate how information from a small number of mechanoreceptors on the wings are used in flight control. She employs a combination of experimental and computational techniques to study how these sensors respond during flight and how one might optimally array a set of these sensors to best provide feedback during flight.

Resonance is defined as a maximal amplification of the response of a system to periodic inputs in a limited, intermediate input frequency band. Resonance may serve to optimize inter-neuronal communication, and has been observed at multiple levels of neuronal organization including membrane potential fluctuations, single neuron spiking, postsynaptic potentials, and neuronal networks. However, it is unknown how resonance observed at one level of neuronal organization (e.g., network) depends on the properties of the constituting building blocks, and whether, and if yes how, it affects the resonant and oscillatory properties upstream. One difficulty is the absence of a conceptual framework that facilitates the interrogation of resonant neuronal circuits and organizes the mechanistic investigation of network resonance in terms of the circuit components, across levels of organization. We address these issues by discussing a number of representative case studies. The dynamic mechanisms responsible for the generation of resonance involve disparate processes, including negative feedback effects, history-dependence, spiking discretization combined with subthreshold passive dynamics, combinations of these, and resonance inheritance from lower levels of organization. The band-pass filters associated with the observed resonances are generated by primarily nonlinear interactions of low- and high-pass filters. We identify these filters (and interactions) and we argue that these are the constitutive building blocks of a resonance framework. Finally, we discuss alternative frameworks and we show that different types of models (e.g., spiking neural networks and rate models) can show the same type of resonance by qualitative different mechanisms.

Research in our lab focuses on the circuit mechanisms underlying sensory computation. We use the mouse retina as a model system because it allows us to stimulate the circuit precisely with its natural input, patterns of light, and record its natural output, the spike trains of retinal ganglion cells. We harness the power of genetic manipulations and detailed information about cell types to uncover new circuits and discover their role in visual processing. Our methods include electrophysiology, computational modeling, and circuit tracing using a variety of imaging techniques.

To localize ourselves in an environment for spatial navigation, we rely on vision and self-motion inputs, which only provide noisy and partial information. It is unknown how the resulting uncertainty affects navigation behavior and neural representations. Here we show that spatial uncertainty underlies key effects of environmental geometry on navigation behavior and grid field deformations. We develop an ideal observer model, which continually updates probabilistic beliefs about its allocentric location by optimally combining noisy egocentric visual and self-motion inputs via Bayesian filtering. This model directly yields predictions for navigation behavior and also predicts neural responses under population coding of location uncertainty. We simulate this model numerically under manipulations of a major source of uncertainty, environmental geometry, and support our simulations by analytic derivations for its most salient qualitative features. We show that our model correctly predicts a wide range of experimentally observed effects of the environmental geometry and its change on homing response distribution and grid field deformation. Thus, our model provides a unifying, normative account for the dependence of homing behavior and grid fields on environmental geometry, and identifies the unavoidable uncertainty in navigation as a key factor underlying these diverse phenomena.

Solving complex planning problems efficiently and flexibly requires reusing expensive previous computations. The brain can do this, but how? I present a new theory that addresses this question and connects planning to hitherto distinct areas within cognitive neuroscience, such as entorhinal representation of cognitive maps and cognitive control.

The cerebellum resembles a feedforward, three-layer network of neurons in which the “hidden layer” consists of Purkinje cells (P-cells) and the output layer consists of deep cerebellar nucleus (DCN) neurons. In this analogy, the output of each DCN neuron is a prediction that is compared with the actual observation, resulting in an error signal that originates in the inferior olive. Efficient learning requires that the error signal reach the DCN neurons, as well as the P-cells that project onto them. However, this basic rule of learning is violated in the cerebellum: the olivary projections to the DCN are weak, particularly in adulthood. Instead, an extraordinarily strong signal is sent from the olive to the P-cells, producing complex spikes. Curiously, P-cells are grouped into small populations that converge onto single DCN neurons. Why are the P-cells organized in this way, and what is the membership criterion of each population? Here, I apply elementary mathematics from machine learning and consider the fact that P-cells that form a population exhibit a special property: they can synchronize their complex spikes, which in turn suppress activity of DCN neuron they project to. Thus complex spikes cannot only act as a teaching signal for a P-cell, but through complex spike synchrony, a P-cell population may act as a surrogate teacher for the DCN neuron that produced the erroneous output. It appears that grouping of P-cells into small populations that share a preference for error satisfies a critical requirement of efficient learning: providing error information to the output layer neuron (DCN) that was responsible for the error, as well as the hidden layer neurons (P-cells) that contributed to it. This population coding may account for several remarkable features of behavior during learning, including multiple timescales, protection from erasure, and spontaneous recovery of memory.

Modeling brain mechanisms is often confined to a given scale, such as single-cell models, network models or whole-brain models, and it is often difficult to relate these models. Here, we show an approach to build models across scales, starting from the level of circuits to the whole brain. The key is the design of accurate population models derived from biophysical models of networks of excitatory and inhibitory neurons, using mean-field techniques. Such population models can be later integrated as units in large-scale networks defining entire brain areas or the whole brain. We illustrate this approach by the simulation of asynchronous and slow-wave states, from circuits to the whole brain. At the mesoscale (millimeters), these models account for travelling activity waves in cortex, and at the macroscale (centimeters), the models reproduce the synchrony of slow waves and their responsiveness to external stimuli. This approach can also be used to evaluate the impact of sub-cellular parameters, such as receptor types or membrane conductances, on the emergent behavior at the whole-brain level. This is illustrated with simulations of the effect of anesthetics. The program codes are open source and run in open-access platforms (such as EBRAINS).

Discovering dynamical patterns from high fidelity timeseries is typically a challenging task. In this talk, the timeseries data consist of neural recordings taken from the auditory cortex of human subjects who listened to sequences of repeated triplets of tones and reported their perception by pressing a button. Subjects reported spontaneous alternations between two auditory perceptual states (1-stream and 2-streams). We discuss a data-driven method, which leverages time-delayed coordinates, diffusion maps, and dynamic mode decomposition, to identify neural features that correlated with subject-reported switching between perceptual states.

A key insight from the foraging literature is the importance of assessing the overall environmental quality — via global reward rate or similar measures, which capture the opportunity cost of time and can guide behavioral allocation toward relatively richer options. Meanwhile, the majority of research in decision neuroscience and computational psychiatry has focused instead on how choices are guided by much more local, event-locked evaluations: of individual situations, actions, or outcomes. I review a combination of research and theoretical speculation from my lab and others that emphasizes the role of foraging's average rewards and opportunity costs in a much larger range of decision problems, including risk, time discounting, vigor, cognitive control, and deliberation. The broad range of behaviors affected by this type of evaluation gives a new theoretical perspective on the effects of stress and autonomic mobilization, and on mood and the broad range of symptoms associated with mood disorders.

A central goal of vision science is to understand the principles underlying the perception and neural coding of the complex visual environment of our everyday experience. In the visual cortex, foundational work with artificial stimuli, and more recent work combining natural images and deep convolutional neural networks, have revealed much about the tuning of cortical neurons to specific image features. However, a major limitation of this existing work is its focus on single-neuron response strength to isolated images. First, during natural vision, the inputs to cortical neurons are not isolated but rather embedded in a rich spatial and temporal context. Second, the full structure of population activity—including the substantial trial-to-trial variability that is shared among neurons—determines encoded information and, ultimately, perception. In the first part of this talk, I will argue for a normative approach to study encoding of natural images in primary visual cortex (V1), which combines a detailed understanding of the sensory inputs with a theory of how those inputs should be represented. Specifically, we hypothesize that V1 response structure serves to approximate a probabilistic representation optimized to the statistics of natural visual inputs, and that contextual modulation is an integral aspect of achieving this goal. I will present a concrete computational framework that instantiates this hypothesis, and data recorded using multielectrode arrays in macaque V1 to test its predictions. In the second part, I will discuss how we are leveraging this framework to develop deep probabilistic algorithms for natural image and video segmentation.