Topic: Theory

“Brain theory, what is it or what should it be?”

n the neurosciences the need for some 'overarching' theory is sometimes expressed, but it is not always obvious what is meant by this. One can perhaps agree that in modern science observation and experimentation is normally complemented by 'theory', i.e. the development of theoretical concepts that help guiding and evaluating experiments and measurements. A deeper discussion of 'brain theory' will require the clarification of some further distictions, in particular: theory vs. model and brain research (and its theory) vs. neuroscience. Other questions are: Does a theory require mathematics? Or even differential equations? Today it is often taken for granted that the whole universe including everything in it, for example humans, animals, and plants, can be adequately treated by physics and therefore theoretical physics is the overarching theory. Even if this is the case, it has turned out that in some particular parts of physics (the historical example is thermodynamics) it may be useful to simplify the theory by introducing additional theoretical concepts that can in principle be 'reduced' to more complex descriptions on the 'microscopic' level of basic physical particals and forces. In this sense, brain theory may be regarded as part of theoretical neuroscience, which is inside biophysics and therefore inside physics, or theoretical physics. Still, in neuroscience and brain research, additional concepts are typically used to describe results and help guiding experimentation that are 'outside' physics, beginning with neurons and synapses, names of brain parts and areas, up to concepts like 'learning', 'motivation', 'attention'. Certainly, we do not yet have one theory that includes all these concepts. So 'brain theory' is still in a 'pre-newtonian' state. However, it may still be useful to understand in general the relations between a larger theory and its 'parts', or between microscopic and macroscopic theories, or between theories at different 'levels' of description. This is what I plan to do.

Hidden nature of seizures

How seizures emerge from the abnormal dynamics of neural networks within the epileptogenic tissue remains an enigma. Are seizures random events, or do detectable changes in brain dynamics precede them? Are mechanisms of seizure emergence identical at the onset and later stages of epilepsy? Is the risk of seizure occurrence stable, or does it change over time? A myriad of questions about seizure genesis remains to be answered to understand the core principles governing seizure genesis. The last decade has brought unprecedented insights into the complex nature of seizure emergence. It is now believed that seizure onset represents the product of the interactions between the process of a transition to seizure, long-term fluctuations in seizure susceptibility, epileptogenesis, and disease progression. During the lecture, we will review the latest observations about mechanisms of ictogenesis operating at multiple temporal scales. We will show how the latest observations contribute to the formation of a comprehensive theory of seizure genesis, and challenge the traditional perspectives on ictogenesis. Finally, we will discuss how combining conventional approaches with computational modeling, modern techniques of in vivo imaging, and genetic manipulation open prospects for exploration of yet hidden mechanisms of seizure genesis.

Edge Computing using Spiking Neural Networks

Deep learning has made tremendous progress in the last year but it's high computational and memory requirements impose challenges in using deep learning on edge devices. There has been some progress in lowering memory requirements of deep neural networks (for instance, use of half-precision) but there has been minimal effort in developing alternative efficient computational paradigms. Inspired by the brain, Spiking Neural Networks (SNN) provide an energy-efficient alternative to conventional rate-based neural networks. However, SNN architectures that employ the traditional feedforward and feedback pass do not fully exploit the asynchronous event-based processing paradigm of SNNs. In the first part of my talk, I will present my work on predictive coding which offers a fundamentally different approach to developing neural networks that are particularly suitable for event-based processing. In the second part of my talk, I will present our work on development of approaches for SNNs that target specific problems like low response latency and continual learning. References Dora, S., Bohte, S. M., & Pennartz, C. (2021). Deep Gated Hebbian Predictive Coding Accounts for Emergence of Complex Neural Response Properties Along the Visual Cortical Hierarchy. Frontiers in Computational Neuroscience, 65. Saranirad, V., McGinnity, T. M., Dora, S., & Coyle, D. (2021, July). DoB-SNN: A New Neuron Assembly-Inspired Spiking Neural Network for Pattern Classification. In 2021 International Joint Conference on Neural Networks (IJCNN) (pp. 1-6). IEEE. Machingal, P., Thousif, M., Dora, S., Sundaram, S., Meng, Q. (2021). A Cross Entropy Loss for Spiking Neural Networks. Expert Systems with Applications (under review).

Credit Assignment in Neural Networks through Deep Feedback Control

The success of deep learning sparked interest in whether the brain learns by using similar techniques for assigning credit to each synaptic weight for its contribution to the network output. However, the majority of current attempts at biologically-plausible learning methods are either non-local in time, require highly specific connectivity motives, or have no clear link to any known mathematical optimization method. Here, we introduce Deep Feedback Control (DFC), a new learning method that uses a feedback controller to drive a deep neural network to match a desired output target and whose control signal can be used for credit assignment. The resulting learning rule is fully local in space and time and approximates Gauss-Newton optimization for a wide range of feedback connectivity patterns. To further underline its biological plausibility, we relate DFC to a multi-compartment model of cortical pyramidal neurons with a local voltage-dependent synaptic plasticity rule, consistent with recent theories of dendritic processing. By combining dynamical system theory with mathematical optimization theory, we provide a strong theoretical foundation for DFC that we corroborate with detailed results on toy experiments and standard computer-vision benchmarks.

Novel Object Detection and Multiplexed Motion Representation in Retinal Bipolar Cells

Detection of motion is essential for survival, but how the visual system processes moving stimuli is not fully understood. Here, based on a detailed analysis of glutamate release from bipolar cells, we outline the rules that govern the representation of object motion in the early processing stages. Our main findings are as follows: (1) Motion processing begins already at the first retinal synapse. (2) The shape and the amplitude of motion responses cannot be reliably predicted from bipolar cell responses to stationary objects. (3) Enhanced representation of novel objects - particularly in bipolar cells with transient dynamics. (4) Response amplitude in bipolar cells matches visual salience reported in humans: suddenly appearing objects > novel motion > existing motion. These findings can be explained by antagonistic interactions in the center-surround receptive field, demonstrate that despite their simple operational concepts, classical center-surround receptive fields enable sophisticated visual computations.

Navigation Turing Test: Toward Human-like RL

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Abstraction and Inference in the Prefrontal Hippocampal Circuitry

The cellular representations and computations that allow rodents to navigate in space have been described with beautiful precision. In this talk, I will show that some of these same computations can be found in humans doing tasks that appear very different from spatial navigation. I will describe some theory that allows us to think about spatial and non-spatial problems in the same framework, and I will try to use this theory to give a new perspective on the beautiful spatial computations that inspired it. The overall goal of this work is to find a framework where we can talk about complicated non-spatial inference problems with the same precision that is only currently available in space.

An inference perspective on meta-learning

While meta-learning algorithms are often viewed as algorithms that learn to learn, an alternative viewpoint frames meta-learning as inferring a hidden task variable from experience consisting of observations and rewards. From this perspective, learning to learn is learning to infer. This viewpoint can be useful in solving problems in meta-RL, which I’ll demonstrate through two examples: (1) enabling off-policy meta-learning, and (2) performing efficient meta-RL from image observations. I’ll also discuss how this perspective leads to an algorithm for few-shot image segmentation.

Cones with character: An in vivo circuit implementation of efficient coding

In this talk I will summarize some of our recent unpublished work on spectral coding in the larval zebrafish retina. Combining 2p imaging, hyperspectral stimulation, computational modeling and connectomics, we take a renewed look at the spectral tuning of cone photoreceptors in the live eye. We find that already cones optimally rotate natural colour space in a PCA-like fashion to disambiguate greyscale from "colour" information. We then follow this signal through the retinal layers and ultimately into the brain to explore the major spectral computations performed by the visual system at its consecutive stages. We find that by and large, zebrafish colour vision can be broken into three major spectral zones: long wavelength grey-scale-like vision, short-wavelength prey capture circuits, and spectrally diverse mid-wavelength circuits which possibly support the bulk of "true colour vision" in this tetrachromate vertebrate.

Physics in Life and Medicine

An Algorithmic Barrier to Neural Circuit Understanding

Neuroscience is witnessing extraordinary progress in experimental techniques, especially at the neural circuit level. These advances are largely aimed at enabling us to understand precisely how neural circuit computations mechanistically cause behavior. Establishing this type of causal understanding will require multiple perturbational (e.g optogenetic) experiments. It has been unclear exactly how many such experiments are needed and how this number scales with the size of the nervous system in question. Here, using techniques from Theoretical Computer Science, we prove that establishing the most extensive notions of understanding need exponentially-many experiments in the number of neurons, in many cases, unless a widely-posited hypothesis about computation is false (i.e. unless P = NP). Furthermore, using data and estimates, we demonstrate that the feasible experimental regime is typically one where the number of experiments performable scales sub-linearly in the number of neurons in the nervous system. This remarkable gulf between the worst-case and the feasible suggests an algorithmic barrier to such an understanding. Determining which notions of understanding are algorithmically tractable to establish in what contexts, thus, becomes an important new direction for investigation. TL; DR: Non-existence of tractable algorithms for neural circuit interrogation could pose a barrier to comprehensively understanding how neural circuits cause behavior. Preprint: https://biorxiv.org/content/10.1101/639724v1/…

Self-organisation in interneuron circuits

Inhibitory interneurons come in different classes and form intricate circuits. While our knowledge of these circuits has advanced substantially over the last decades, it is not fully understood how the structure of these circuits relates to their function. I will present some of our recent attempts to “understand” the structure of interneuron circuits by means of computational modeling. Surprisingly (at least for us), we found that prominent features of inhibitory circuitry can be accounted for by an optimisation for excitation-inhibition (E/I) balance. In particular, we find that such an optimisation generates networks that resemble mouse V1 in terms of the structure of synaptic efficacies between principal cells and parvalbumin-positive interneurons. Moreover, an optimisation for E/I balance across neuronal compartments promotes a functional diversification of interneurons into two classes that resemble parvalbumin and somatostatin-positive interneurons. Time permitting, I may briefly touch on recent work in which we link E/I balance to prediction error coding in V1.

Local and global organization of synaptic inputs on cortical dendrites

Synaptic inputs on cortical dendrites are organized with remarkable subcellular precision at the micron level. This organization emerges during early postnatal development through patterned spontaneous activity and manifests both locally where synapses with similar functional properties are clustered, and globally along the axis from dendrite to soma. Recent experiments reveal species-specific differences in the local and global synaptic organization in mouse, ferret and macaque visual cortex. I will present a computational framework that implements functional and structural plasticity from spontaneous activity patterns to generate these different types of organization across species and scales. Within this framework, a single anatomical factor - the size of the visual cortex and the resulting magnification of visual space - can explain the observed differences. This allows us to make predictions about the organization of synapses also in other species and indicates that the proximal-distal axis of a dendrite might be central in endowing a neuron with powerful computational capabilities.

Theory of gating in recurrent neural networks

Recurrent neural networks (RNNs) are powerful dynamical models, widely used in machine learning (ML) for processing sequential data, and also in neuroscience, to understand the emergent properties of networks of real neurons. Prior theoretical work in understanding the properties of RNNs has focused on models with additive interactions. However, real neurons can have gating i.e. multiplicative interactions, and gating is also a central feature of the best performing RNNs in machine learning. Here, we develop a dynamical mean-field theory (DMFT) to study the consequences of gating in RNNs. We use random matrix theory to show how gating robustly produces marginal stability and line attractors – important mechanisms for biologically-relevant computations requiring long memory. The long-time behavior of the gated network is studied using its Lyapunov spectrum, and the DMFT is used to provide a novel analytical expression for the maximum Lyapunov exponent demonstrating its close relation to relaxation-time of the dynamics. Gating is also shown to give rise to a novel, discontinuous transition to chaos, where the proliferation of critical points (topological complexity) is decoupled from the appearance of chaotic dynamics (dynamical complexity), contrary to a seminal result for additive RNNs. Critical surfaces and regions of marginal stability in the parameter space are indicated in phase diagrams, thus providing a map for principled parameter choices for ML practitioners. Finally, we develop a field-theory for gradients that arise in training, by incorporating the adjoint sensitivity framework from control theory in the DMFT. This paves the way for the use of powerful field-theoretic techniques to study training/gradients in large RNNs.

What can we further learn from the brain for artificial intelligence?

Deep learning is a prime example of how brain-inspired computing can benefit development of artificial intelligence. But what else can we learn from the brain for bringing AI and robotics to the next level? Energy efficiency and data efficiency are the major features of the brain and human cognition that today’s deep learning has yet to deliver. The brain can be seen as a multi-agent system of heterogeneous learners using different representations and algorithms. The flexible use of reactive, model-free control and model-based “mental simulation” appears to be the basis for computational and data efficiency of the brain. How the brain efficiently acquires and flexibly combines prediction and control modules is a major open problem in neuroscience and its solution should help developments of more flexible and autonomous AI and robotics.

On the purpose and origin of spontaneous neural activity

Spontaneous firing, observed in many neurons, is often attributed to ion channel or network level noise. Cortical cells during slow wave sleep exhibit transitions between so called Up and Down states. In this sleep state, with limited sensory stimuli, neurons fire in the Up state. Spontaneous firing is also observed in slices of cholinergic interneurons, cerebellar Purkinje cells and even brainstem inspiratory neurons. In such in vitro preparations, where the functional relevance is long lost, neurons continue to display a rich repertoire of firing properties. It is perplexing that these neurons, instead of saving their energy during information downtime and functional irrelevance, are eager to fire. We propose that spontaneous firing is not a chance event but instead, a vital activity for the well-being of a neuron. We postulate that neurons, in anticipation of synaptic inputs, keep their ATP levels at maximum. As recovery from inputs requires most of the energy resources, neurons are ATP surplus and ADP scarce during synaptic quiescence. With ADP as the rate-limiting step, ATP production stalls in the mitochondria when ADP is low. This leads to toxic Reactive Oxygen Species (ROS) formation, which are known to disrupt many cellular processes. We hypothesize that spontaneous firing occurs at these conditions - as a release valve to spend energy and to restore ATP production, shielding the neuron against ROS. By linking a mitochondrial metabolism model to a conductance-based neuron model, we show that spontaneous firing depends on baseline ATP usage and on ATP-cost-per-spike. From our model, emerges a mitochondrial mediated homeostatic mechanism that provides a recipe for different firing patterns. Our findings, though mostly affecting intracellular dynamics, may have large knock-on effects on the nature of neural coding. Hitherto it has been thought that the neural code is optimised for energy minimisation, but this may be true only when neurons do not experience synaptic quiescence.

Distributed replay in the human brain, and how to find it

I will present work on a novel fMRI analysis method that allows us to investigate sequential reactivation in the hippocampus. Our method focuses on analysing the time courses of probabilistic multivariate classifiers and allows us to infer the presence and frequency of fast sequential reactivation events. Using a paradigm in which we controlled the speed of sequential visually elicited activations, we validated the method in visual cortex for event sequences with only 32 ms between items. We show that detectability remains possible if low signal-to-noise ratio and when sequence events occur at unknown times. In a preliminary analysis, we show that even the exposure to our visual paradigm elicits reactivations in visual cortex at rest following the task. I then present work in which we tested how representations influence replay by asking whether transitions between task-state representations are reactivated at rest during hippocampal replay events. Participants learned to make decisions about ambiguous stimuli that depended on past events and attentionally filtered stimulus processing. FMRI signals during rest periods following this task indicated sequential reactivation of task states. These results indicate that adaptive task state representations are computed and replayed at different cortical sites. In combination with other methods, fMRI may allow us to unravel this coordinated nature of replay.

Towards hybrid models of retinal circuits - integrating biophysical realism, anatomical constraints and predictive performance

Visual processing in the retina has been studied in great detail at all levels such that a comprehensive picture of the retina's cell types and the many neural circuits they form is emerging. However, the currently best performing models of retinal function are black-box CNN models which are agnostic to such biological knowledge. Here, I present two of our recent attempts to develop computational models of processing in the inner retina, which both respect biophysical and anatomical constraints yet provide accurate predictions of retinal activity

Multi-resolution Multi-task Gaussian Processes: London air pollution

Poor air quality in cities is a significant threat to health and life expectancy, with over 80% of people living in urban areas exposed to air quality levels that exceed World Health Organisation limits. In this session, I present a multi-resolution multi-task framework that handles evidence integration under varying spatio-temporal sampling resolution and noise levels. We have developed both shallow Gaussian Process (GP) mixture models and deep GP constructions that naturally handle this evidence integration, as well as biases in the mean. These models underpin our work at the Alan Turing Institute towards providing spatio-temporal forecasts of air pollution across London. We demonstrate the effectiveness of our framework on both synthetic examples and applications on London air quality. For further information go to: https://www.turing.ac.uk/research/research-projects/london-air-quality. Collaborators: Oliver Hamelijnck, Theodoros Damoulas, Kangrui Wang and Mark Girolami.

Learning from the infant’s point of view

Learning depends on both the learning mechanism and the regularities in the training material, yet most research on human and machine learning focus on the discovering the mechanisms that underlie powerful learning. I will present evidence from our research focusing on the statistical structure of infant visual learning environments. The findings suggest that the statistical structure of those learning environments are not like those used in laboratory experiments on visual learning, in machine learning, or in our adult assumptions about how teach visual categories. The data derive from our use of head cameras and head-mounted eye trackers capturing FOV experiences in the home as well as in simulated home environments in the laboratory. The participants range from 1 month of age to 24 months. The observed statistical structure offers new insights into the developmental foundations of visual object recognition and suggest a computational rethinking of the problem of visual category formation. The observed environmental statistics also have direct implications for understanding the development of cortical visual systems.

Learning Theory for Continual and Meta-Learning

High-dimensional geometry of visual cortex

Interpreting high-dimensional datasets requires new computational and analytical methods. We developed such methods to extract and analyze neural activity from 20,000 neurons recorded simultaneously in awake, behaving mice. The neural activity was not low-dimensional as commonly thought, but instead was high-dimensional and obeyed a power-law scaling across its eigenvalues. We developed a theory that proposes that neural responses to external stimuli maximize information capacity while maintaining a smooth neural code. We then observed power-law eigenvalue scaling in many real-world datasets, and therefore developed a nonlinear manifold embedding algorithm called Rastermap that can capture such high-dimensional structure.

Understanding machine learning via exactly solvable statistical physics models

The affinity between statistical physics and machine learning has long history, this is reflected even in the machine learning terminology that is in part adopted from physics. I will describe the main lines of this long-lasting friendship in the context of current theoretical challenges and open questions about deep learning. Theoretical physics often proceeds in terms of solvable synthetic models, I will describe the related line of work on solvable models of simple feed-forward neural networks. I will highlight a path forward to capture the subtle interplay between the structure of the data, the architecture of the network, and the learning algorithm.

Disentangling the roles of dimensionality and cell categories in neural computations

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.

Neural circuit redundancy, stability, and variability in developmental brain disorders

Despite the consistency of symptoms at the cognitive level, we now know that brain disorders like Autism and Schizophrenia can each arise from mutations in >100 different genes. Presumably there is a convergence of “symptoms” at the level of neural circuits in diagnosed individuals. In this talk I will argue that redundancy in neural circuit parameters implies that we should take a circuit-function rather that circuit-component approach to understanding these disorders. Then I will present our recent empirical work testing a circuit-function theory for Autism: the idea that neural circuits show excess trial-to-trial variability in response to sensory stimuli, and instability in the representations across a timescale of days. For this we analysed in vivo neural population activity data recorded from somatosensory cortex of mouse models of Fragile-X syndrome, a disorder related to autism. Work with Beatriz Mizusaki (Univ of Bristol), Nazim Kourdougli, Anand Suresh, and Carlos Portera-Cailliau (Univ of California, Los Angeles).

Human reconstruction of local image structure from natural scenes

Retinal projections often poorly represent the structure of the physical world: well-defined boundaries within the eye may correspond to irrelevant features of the physical world, while critical features of the physical world may be nearly invisible at the retinal projection. Visual cortex is equipped with specialized mechanisms for sorting these two types of features according to their utility in interpreting the scene, however we know little or nothing about their perceptual computations. I will present novel paradigms for the characterization of these processes in human vision, alongside examples of how the associated empirical results can be combined with targeted models to shape our understanding of the underlying perceptual mechanisms. Although the emerging view is far from complete, it challenges compartmentalized notions of bottom-up/top-down object segmentation, and suggests instead that these two modes are best viewed as an integrated perceptual mechanism.

Deep learning for model-based RL

Model-based approaches to control and decision making have long held the promise of being more powerful and data efficient than model-free counterparts. However, success with model-based methods has been limited to those cases where a perfect model can be queried. The game of Go was mastered by AlphaGo using a combination of neural networks and the MCTS planning algorithm. But planning required a perfect representation of the game rules. I will describe new algorithms that instead leverage deep neural networks to learn models of the environment which are then used to plan, and update policy and value functions. These new algorithms offer hints about how brains might approach planning and acting in complex environments.

The geometry of abstraction in artificial and biological neural networks

The curse of dimensionality plagues models of reinforcement learning and decision-making. The process of abstraction solves this by constructing abstract variables describing features shared by different specific instances, reducing dimensionality and enabling generalization in novel situations. We characterized neural representations in monkeys performing a task where a hidden variable described the temporal statistics of stimulus-response-outcome mappings. Abstraction was defined operationally using the generalization performance of neural decoders across task conditions not used for training. This type of generalization requires a particular geometric format of neural representations. Neural ensembles in dorsolateral pre-frontal cortex, anterior cingulate cortex and hippocampus, and in simulated neural networks, simultaneously represented multiple hidden and explicit variables in a format reflecting abstraction. Task events engaging cognitive operations modulated this format. These findings elucidate how the brain and artificial systems represent abstract variables, variables critical for generalization that in turn confers cognitive flexibility.

Cortical-like dynamics in recurrent circuits optimized for sampling-based probabilistic inference

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

Mean-field models for finite-size populations of spiking neurons

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.

Multilevel Causal Modeling

Complex systems can be modeled at various levels of granularity, e.g., we can model a person at the cognitive level, on the neuronal level, or down to the biochemical level. When multiple models represent the same system at different scales, we would like to be able to reason about the causal effects of interventions on each level in such a way that the models remain consistent across levels. In the first part of this talk, I consider which conditions must be fulfilled for two structural equation models (SEMs) to stand in such a causally consistent relation. In the second part of the talk, I present recent work on learning causally consistent SEMs across multiple levels, distinguishing between bottom-up (micro- to macro-level) and top-down (macro- to micro-level) approaches.

Spanning the arc between optimality theories and data

Ideas about optimization are at the core of how we approach biological complexity. Quantitative predictions about biological systems have been successfully derived from first principles in the context of efficient coding, metabolic and transport networks, evolution, reinforcement learning, and decision making, by postulating that a system has evolved to optimize some utility function under biophysical constraints. Yet as normative theories become increasingly high-dimensional and optimal solutions stop being unique, it gets progressively hard to judge whether theoretical predictions are consistent with, or "close to", data. I will illustrate these issues using efficient coding applied to simple neuronal models as well as to a complex and realistic biochemical reaction network. As a solution, we developed a statistical framework which smoothly interpolates between ab initio optimality predictions and Bayesian parameter inference from data, while also permitting statistically rigorous tests of optimality hypotheses.

The butterfly strikes back: neurons doing 'network' computation

We live in the age of the network: Internet social neural ecosystems. This has become one of the main metaphors for how we think about complex systems. This view also dominates the account of brain function. The role of neuronsdescribed by Cajal as the "butterflies of the soul" has become diminished to leaky integrate-and-fire point objects in many models of neural network computation. It is perhaps not surprising that networkexplanations of neural phenomena use neurons as elementary particles andascribe all their wonderful capabilities to their interactions in a network. In the network view the Connectome defines the brain and the butterflies have no role. In this talk I'd like to reclaim some key computations from the networkand return them to their rightful place at the cellular and subcellular level. I'll start with a provocative look at potential computational capacity ofdifferent kinds of brain computation: network vs. subcellular. I'll then consider different levels of pattern and sequence computationwith a glimpse of the efficiency of the subcellular solutions. Finally I propose that there is a suggestive mapping between entire nodesof deep networks to individual neurons. This in my view is how we can walk around with 1.3 litres and 20 watts of installed computational capacity still doing far more than giant AI server farms.

Causality for Neuroscience

Circuit and synaptic mechanisms of plasticity in neural ensembles

Inhibitory microcircuits play an important role regulating cortical responses to sensory stimuli. Interneurons that inhibit dendritic or somatic integration are gatekeepers for neural activity, synaptic plasticity and the formation of sensory representations. We have been investigating the synaptic plasticity mechanisms underlying the formation of ensembles in olfactory and orbitofrontal cortex. We have been focusing on the roles of three inhibitory neuron classes in gating excitatory synaptic plasticity in olfactory cortex- somatostatin (SST-INs), parvalbumin (PV-INs), and vasoactive intestinal polypeptide (VIP-INs) interneurons. Further, we are investigating the rules for inhibitory plasticity and a potential role in stabilizing ensembles in associative cortices. I will present new findings to support distinct roles for different interneuron classes in the gating and stabilization of ensemble representations of olfactory responses.

Flexible motor sequencing through thalamic control of cortical dynamics

The mechanisms by which neural circuits generate an extensible library of motor motifs and flexibly string them into arbitrary sequences are unclear. We developed a model in which inhibitory basal ganglia output neurons project to thalamic units that are themselves bidirectionally connected to a recurrent cortical network. During movement sequences, electrophysiological recordings of basal ganglia output neurons show sustained activity patterns that switch at the boundaries between motifs. Thus, we model these inhibitory patterns as silencing some thalamic neurons while leaving others disinhibited and free to interact with cortex during specific motifs. We show that a small number of disinhibited thalamic neurons can control cortical dynamics to generate specific motor output in a noise robust way. If the thalamic units associated with each motif are segregated, many motor outputs can be learned without interference and then combined in arbitrary orders for the flexible production of long and complex motor sequences.

Rational thoughts in neural codes

First, we describe a new method for inferring the mental model of an animal performing a natural task. We use probabilistic methods to compute the most likely mental model based on an animal’s sensory observations and actions. This also reveals dynamic beliefs that would be optimal according to the animal’s internal model, and thus provides a practical notion of “rational thoughts.” Second, we construct a neural coding framework by which these rational thoughts, their computational dynamics, and actions can be identified within the manifold of neural activity. We illustrate the value of this approach by training an artificial neural network to perform a generalization of a widely used foraging task. We analyze the network’s behaviour to find rational thoughts, and successfully recover the neural properties that implemented those thoughts, providing a way of interpreting the complex neural dynamics of the artificial brain. Joint work with Zhengwei Wu, Minhae Kwon, Saurabh Daptardar, and Paul Schrater.

Multi-layer network learning in an electric fish

The electrosensory lobe (ELL) in mormyrid electric fish is a cerebellar-like structure that cancels the sensory effects of self-generated electric fields, allowing prey to be detected. Like the cerebellum, the ELL involves two stages of processing, analogous to the Purkinje cells and cells of the deep cerebellar nuclei. Through the work of Curtis Bell and others, a model was previously developed to describe the output stage of the ELL, but the role of the Purkinje-cell analogs, the medium ganglion (MG) cells, in the circuit had remained mysterious. I will present a complete, multi-layer circuit description of the ELL, developed in collaboration with Nate Sawtell and Salomon Muller, that reveals a novel role for the MG cells. The resulting model provides an example of how a biological system solves well-known problems associated with learning in multi-layer networks, and it reveals that ELL circuitry is organization on the basis of learning rather than by the response properties of neurons.

Neural manifolds for the stable control of movement

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.

Inferring Brain Rhythm Circuitry and Burstiness

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.

Recurrent network models of adaptive and maladaptive learning

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.

Burst-dependent synaptic plasticity can coordinate learning in hierarchical circuits

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.

Sleep, semantic memory, and creative problem solving

Creative thought relies on the reorganisation of existing knowledge. Sleep is known to be important for creative thinking, but there is a debate about which sleep stage is most relevant, and why. I will address this issue by proposing that Rapid Eye Movement sleep, or 'REM', and Non-REM sleep facilitate creativity in different ways. Memory replay mechanisms in Non-REM can abstract rules from corpuses of learned information, while replay in REM may promote novel associations. I propose that the iterative interleaving of REM and Non-REM across a night boosts the formation of complex knowledge frameworks, and allows these frameworks to be restructured - thus facilitating creative thought. My talk will discuss experiments exploring these hypotheses, and the mechanisms for these processes.