Computational Neuroscience seminars

To understand brain function and develop artificial general intelligence it has become abundantly clear that there should be a close interaction among Neuroscience, machine learning and mathematics. There is a general hope that understanding the brain function will provide us with more powerful machine learning algorithms. On the other hand advances in machine learning are now providing the much needed tools to not only analyse brain activity data but also to design better experiments to expose brain function. Both neuroscience and machine learning explicitly or implicitly deal with high dimensional data and systems. Mathematics can provide powerful new tools to understand and quantify the dynamics of biological and artificial systems as they generate behavior that may be perceived as intelligent. In this meeting we bring together experts from Mathematics, Artificial Intelligence and Neuroscience for a three day long hybrid meeting. We will have talks on mathematical tools in particular Topology to understand high dimensional data, explainable AI, how AI can help neuroscience and to what extent the brain may be using algorithms similar to the ones used in modern machine learning. Finally we will wrap up with a discussion on some aspects of neural hardware that may not have been considered in machine learning.

Measuring the degree of consciousness an organism possesses has remained a longstanding challenge in Neuroscience. In part, this is due to the difficulty of finding the appropriate mathematical tools for describing such a subjective phenomenon. Current methods relate the level of consciousness to the complexity of neural activity, i.e., using the information contained in a stream of recorded signals they can tell whether the subject might be awake, asleep, or anaesthetised. Usually, the signals stemming from a complex system are correlated in time; the behaviour of the future depends on the patterns in the neural activity of the past. However these past-future relationships remain either hidden to, or not taken into account in the current measures of consciousness. These past-future correlations are likely to contain more information and thus can reveal a richer understanding about the behaviour of complex systems like a brain. Our work employs the "epsilon-machines” framework to account for the time correlations in neural recordings. In a nutshell, epsilon-machines reveal how much of the past neural activity is needed in order to accurately predict how the activity in the future will behave, and this is summarised in a single number called "statistical complexity". If a lot of past neural activity is required to predict the future behaviour, then can we say that the brain was more “awake" at the time of recording? Furthermore, if we read the recordings in reverse, does the difference between forward and reverse-time statistical complexity allow us to quantify the level of time asymmetry in the brain? Neuroscience predicts that there should be a degree of time asymmetry in the brain. However, this has never been measured. To test this, we used neural recordings measured from the brains of fruit flies and inferred the epsilon-machines. We found that the nature of the past and future correlations of neural activity in the brain, drastically changes depending on whether the fly was awake or anaesthetised. Not only does our study find that wakeful and anaesthetised fly brains are distinguished by how statistically complex they are, but that the amount of correlations in wakeful fly brains was much more sensitive to whether the neural recordings were read forward vs. backwards in time, compared to anaesthetised brains. In other words, wakeful fly brains were more complex, and time asymmetric than anaesthetised ones.

Vision begins in the eye, and what the “retina tells the brain” is a major interest in visual neuroscience. To deduce what the retina encodes (“tells”), computational models are essential. The most important models in the retina currently aim to understand the responses of the retinal output neurons – the ganglion cells. Typically, these models make simplifying assumptions about the neurons in the retinal network upstream of ganglion cells. One important assumption is linear spatial integration. In this talk, I first define what it means for a neuron to be spatially linear or nonlinear and how we can experimentally measure these phenomena. Next, I introduce the neurons upstream to retinal ganglion cells, with focus on bipolar cells, which are the connecting elements between the photoreceptors (input to the retinal network) and the ganglion cells (output). This pivotal position makes bipolar cells an interesting target to study the assumption of linear spatial integration, yet due to their location buried in the middle of the retina it is challenging to measure their neural activity. Here, I present bipolar cell data where I ask whether the spatial linearity holds under artificial and natural visual stimuli. Through diverse analyses and computational models, I show that bipolar cells are more complex than previously thought and that they can already act as nonlinear processing elements at the level of their somatic membrane potential. Furthermore, through pharmacology and current measurements, I illustrate that the observed spatial nonlinearity arises at the excitatory inputs to bipolar cells. In the final part of my talk, I address the functional relevance of the nonlinearities in bipolar cells through combined recordings of bipolar and ganglion cells and I show that the nonlinearities in bipolar cells provide high spatial sensitivity to downstream ganglion cells. Overall, I demonstrate that simple linear assumptions do not always apply and more complex models are needed to describe what the retina “tells” the brain.

Activity dependent synaptic plasticity is considered to be a primary mechanism underlying learning and memory. Yet it is unclear whether plasticity rules such as STDP measured in vitro apply in vivo. Network models with STDP predict that activity patterns (e.g., place-cell spatial selectivity) should change much faster than observed experimentally. We address this gap by investigating a nonlinear calcium-based plasticity rule fit to experiments done in physiological conditions. In this model, LTP and LTD result from intracellular calcium transients arising almost exclusively from synchronous coactivation of pre- and postsynaptic neurons. We analytically approximate the full distribution of nonlinear calcium transients as a function of pre- and postsynaptic firing rates, and temporal correlations. This analysis directly relates activity statistics that can be measured in vivo to the changes in synaptic efficacy they cause. Our results highlight that both high-firing rates and temporal correlations can lead to significant changes to synaptic efficacy. Using a mean-field theory, we show that the nonlinear plasticity rule, without any fine-tuning, gives a stable, unimodal synaptic weight distribution characterized by many strong synapses which remain stable over long periods of time, consistent with electrophysiological and behavioral studies. Moreover, our theory explains how memories encoded by strong synapses can be preferentially stabilized by the plasticity rule. We confirmed our analytical results in a spiking recurrent network. Interestingly, although most synapses are weak and undergo rapid turnover, the fraction of strong synapses are sufficient for supporting realistic spiking dynamics and serve to maintain the network’s cluster structure. Our results provide a mechanistic understanding of how stable memories may emerge on the behavioral level from an STDP rule measured in physiological conditions. Furthermore, the plasticity rule we investigate is mathematically equivalent to other learning rules which rely on the statistics of coincidences, so we expect that our formalism will be useful to study other learning processes beyond the calcium-based plasticity rule.

We use the olfactory system and forebrain of (adult) zebrafish as a model to analyze how relevant information is extracted from sensory inputs, how information is stored in memory circuits, and how sensory inputs inform behavior. A series of recent findings provides evidence that inhibition has not only homeostatic functions in neuronal circuits but makes highly specific, instructive contributions to behaviorally relevant computations in different brain regions. These observations imply that the connectivity among excitatory and inhibitory neurons exhibits essential higher-order structure that cannot be determined without dense network reconstructions. To analyze such connectivity we developed an approach referred to as “dynamical connectomics” that combines 2-photon calcium imaging of neuronal population activity with EM-based dense neuronal circuit reconstruction. In the olfactory bulb, this approach identified specific connectivity among co-tuned cohorts of excitatory and inhibitory neurons that can account for the decorrelation and normalization (“whitening”) of odor representations in this brain region. These results provide a mechanistic explanation for a fundamental neural computation that strictly requires specific network connectivity.

In this talk I will present an account of how an agent designed or evolved to be intelligent may come to enjoy subjective experiences. First, the agent is stipulated to be capable of (meta)representing subjective ‘qualitative’ sensory information, in the sense that it can easily assess how exactly similar a sensory signal is to all other possible sensory signals. This information is subjective in the sense that it concerns how the different stimuli can be distinguished by the agent itself, rather than how physically similar they are. For this to happen, sensory coding needs to satisfy sparsity and smoothness constraints, which are known to facilitate metacognition and generalization. Second, this qualitative information can under some specific circumstances acquire an ‘assertoric force’. This happens when a certain self-monitoring mechanism decides that the qualitative information reliably tracks the current state of the world, and informs a general symbolic reasoning system of this fact. I will argue that the having of subjective conscious experiences amounts to nothing more than having qualitative sensory information acquiring an assertoric status within one’s belief system. When this happens, the perceptual content presents itself as reflecting the state of the world right now, in ways that seem undeniably rational to the agent. At the same time, without effort, the agent also knows what the perceptual content is like, in terms of how subjectively similar it is to all other possible precepts. I will discuss the computational benefits of this architecture, for which consciousness might have arisen as a byproduct.

To survive in a rapidly dynamic world, the brain predicts the future state of the world and proactively adjusts perception, attention and action. A key to efficient interaction is to predict and prepare to not only “where” and “what” things will happen, but also to “when”. I will present studies in healthy and neurological populations that investigated the cognitive architecture and neural basis of temporal anticipation. First, influential ‘entrainment’ models suggest that anticipation in rhythmic contexts, e.g. music or biological motion, uniquely relies on alignment of attentional oscillations to external rhythms. Using computational modeling and EEG, I will show that cortical neural patterns previously associated with entrainment in fact overlap with interval timing mechanisms that are used in aperiodic contexts. Second, temporal prediction and attention have commonly been associated with cortical circuits. Studying neurological populations with subcortical degeneration, I will present data that point to a double dissociation between rhythm- and interval-based prediction in the cerebellum and basal ganglia, respectively, and will demonstrate a role for the cerebellum in attentional control of perceptual sensitivity in time. Finally, using EEG in neurodegenerative patients, I will demonstrate that the cerebellum controls temporal adjustment of cortico-striatal neural dynamics, and use computational modeling to identify cerebellar-controlled neural parameters. Altogether, these findings reveal functionally and neural context-specificity and subcortical contributions to temporal anticipation, revising our understanding of dynamic cognition.

Our ability to understand ongoing events depends critically on general knowledge about how different kinds of situations work (schemas), and also on recollection of specific instances of these situations that we have previously experienced (episodic memory). The consensus around this general view masks deep questions about how these two memory systems interact to support event understanding: How do we build our library of schemas? and how exactly do we use episodic memory in the service of event understanding? Given rich, continuous inputs, when do we store and retrieve episodic memory “snapshots”, and how are they organized so as to ensure that we can retrieve the right snapshots at the right time? I will develop predictions about how these processes work using memory augmented neural networks (i.e., neural networks that learn how to use episodic memory in the service of task performance), and I will present results from relevant fMRI and behavioral studies.

Norepinephrine (NE) is a neuromodulator that is released from projections of the locus coeruleus via extra-synaptic vesicle exocytosis. Tonic fluctuations in NE are involved in brain states, such as sleep, arousal, and attention. Previously, NE in the PFC was thought to be a homogenous field created by bulk release, but it remains unknown whether phasic (fast, short-term) fluctuations in NE can produce a spatially heterogeneous field, which could then structure cell firing at a fine spatial scale. To understand how spatiotemporal dynamics of norepinephrine (NE) release in the prefrontal cortex affect neuronal firing, we performed a novel in-vivo two-photon imaging experiment in layer ⅔ of the prefrontal cortex using a green fluorescent NE sensor and a red fluorescent Ca2+ sensor, which allowed us to simultaneously observe fine-scale neuronal and NE dynamics in the form of spatially localized fluorescence time series. Using generalized linear modeling, we found that the local NE field differs from the global NE field in transient periods of decorrelation, which are influenced by proximal NE release events. We used optical flow and pattern analysis to show that release and reuptake events can occur at the same location but at different times, and differential recruitment of release and reuptake sites over time is a potential mechanism for creating a heterogeneous NE field. Our generalized linear models predicting cellular dynamics show that the heterogeneous local NE field, and not the global field, drives cell firing dynamics. These results point to the importance of local, small-scale, phasic NE fluctuations for structuring cell firing. Prior research suggests that these phasic NE fluctuations in the PFC may play a role in attentional shifts, orienting to sensory stimuli in the environment, and in the selective gain of priority representations during stress (Mather, Clewett et al. 2016) (Aston-Jones and Bloom 1981).

Natural perception relies inherently on inferring causal structure in the environment. However, the neural mechanisms and functional circuits that are essential for representing and updating the hidden causal structure during multisensory processing are unknown. To address this, monkeys were trained to infer the probability of a potential common source from visual and proprioceptive signals on the basis of their spatial disparity in a virtual reality system. The proprioceptive drift reported by monkeys demonstrated that they combined historical information and current multisensory signals to estimate the hidden common source and subsequently updated both the causal structure and sensory representation. Single-unit recordings in premotor and parietal cortices revealed that neural activity in premotor cortex represents the core computation of causal inference, characterizing the estimation and update of the likelihood of integrating multiple sensory inputs at a trial-by-trial level. In response to signals from premotor cortex, neural activity in parietal cortex also represents the causal structure and further dynamically updates the sensory representation to maintain consistency with the causal inference structure. Thus, our results indicate how premotor cortex integrates historical information and sensory inputs to infer hidden variables and selectively updates sensory representations in parietal cortex to support behavior. This dynamic loop of frontal-parietal interactions in the causal inference framework may provide the neural mechanism to answer long-standing questions regarding how neural circuits represent hidden structures for body-awareness and agency.

Inhibitory neurons take on many forms and functions. How this diversity contributes to memory function is not completely known. Previous formal studies indicate inhibition differentiated by local and global connectivity in associative memory networks functions to rescale the level of retrieval of excitatory assemblies. However, such studies lack biological details such as a distinction between types of neurons (excitatory and inhibitory), unrealistic connection schemas, and non-sparse assemblies. In this study, we present a rate-based cortical model where neurons are distinguished (as excitatory, local inhibitory, or global inhibitory), connected more realistically, and where memory items correspond to sparse excitatory assemblies. We use this model to study how local-global inhibition balance can alter memory retrieval in associative memory structures, including naturalistic and artificial structures. Experimental studies have reported inhibitory neurons and their sub-types uniquely respond to specific stimuli and can form sophisticated, joint excitatory-inhibitory assemblies. Our model suggests such joint assemblies, as well as a distribution and rebalancing of overall inhibition between two inhibitory sub-populations – one connected to excitatory assemblies locally and the other connected globally – can quadruple the range of retrieval across related memories. We identify a possible functional role for local-global inhibitory balance to, in the context of choice or preference of relationships, permit and maintain a broader range of memory items when local inhibition is dominant and conversely consolidate and strengthen a smaller range of memory items when global inhibition is dominant. This model therefore highlights a biologically-plausible and behaviourally-useful function of inhibitory diversity in memory.

Predictive coding represents a promising framework for understanding brain function, postulating that the brain continuously inhibits predictable sensory input, ensuring a preferential processing of surprising elements. A central aspect of this view on cortical computation is its hierarchical connectivity, involving recurrent message passing between excitatory bottom-up signals and inhibitory top-down feedback. Here we use computational modelling to demonstrate that such architectural hard-wiring is not necessary. Rather, predictive coding is shown to emerge as a consequence of energy efficiency, a fundamental requirement of neural processing. When training recurrent neural networks to minimise their energy consumption while operating in predictive environments, the networks self-organise into prediction and error units with appropriate inhibitory and excitatory interconnections and learn to inhibit predictable sensory input. We demonstrate that prediction units can reliably be identified through biases in their median preactivation, pointing towards a fundamental property of prediction units in the predictive coding framework. Moving beyond the view of purely top-down driven predictions, we demonstrate via virtual lesioning experiments that networks perform predictions on two timescales: fast lateral predictions among sensory units and slower prediction cycles that integrate evidence over time. Our results, which replicate across two separate data sets, suggest that predictive coding can be interpreted as a natural consequence of energy efficiency. More generally, they raise the question which other computational principles of brain function can be understood as a result of physical constraints posed by the brain, opening up a new area of bio-inspired, machine learning-powered neuroscience research.

Our group focuses on brain computation, physiology and evolution, with a particular focus on network dynamics, sleep (evolution and mechanistic underpinnings), cortical computation (through the study of ancestral cortices), and sensorimotor processing. This talk will describe our recent results on the remarkable camouflage behavior of cuttlefish (action) and on brain activity in REM and NonREM in lizards (sleep). Both topics will focus on aspects of circuit dynamics.

Panelists: - Surya Ganguli, Matteo Carandini, Anna Schapiro,Blake Richards. Moderator: Konrad Kording

Recently, the field of computational neuroscience has seen an explosion of the use of trained recurrent network models (RNNs) to model patterns of neural activity. These RNN models are typically characterized by tuned recurrent interactions between rate 'units' whose dynamics are governed by smooth, continuous differential equations. However, the response of biological single neurons is better described by all-or-none events - spikes - that are triggered in response to the processing of their synaptic input by the complex dynamics of their membrane. One line of research has attempted to resolve this discrepancy by linking the average firing probability of a population of simplified spiking neuron models to rate dynamics similar to those used for RNN units. However, challenges remain to account for complex temporal dependencies in the biological single neuron response and for the heterogeneity of synaptic input across the population. Here, we make progress by showing how to derive dynamic rate equations for a population of spiking neurons with multi-timescale adaptation properties - as this was shown to accurately model the response of biological neurons - while they receive independent time-varying inputs, leading to plausible asynchronous activity in the network. The resulting rate equations yield an insightful segregation of the population's response into dynamics that are driven by the mean signal received by the neural population, and dynamics driven by the variance of the input across neurons, with respective timescales that are in agreement with slice experiments. Further, these equations explain how input variability can shape log-normal instantaneous rate distributions across neurons, as observed in vivo. Our results help interpret properties of the neural population response and open the way to investigating whether the more biologically plausible and dynamically complex rate model we derive could provide useful inductive biases if used in an RNN to solve specific tasks.

Low-dimensional population dynamics can be observed in neural activity recorded from the prefrontal cortex (PFC) of subjects performing simple cognitive tasks. Many studies have shown that recurrent neural networks (RNNs) trained on the same tasks can reproduce qualitatively these state space trajectories, and have used them as models of how neuronal dynamics implement task computations. The PFC is also viewed as a conductor that organizes the communication between cortical areas and provides contextual information. It is then not clear what is its role in solving simple cognitive tasks. Do the low-dimensional trajectories observed in the PFC really correspond to the computations that it performs? Or do they indirectly reflect the computations occurring within the cortical areas projecting to the PFC? To address these questions, we modelled cortical areas with a modular RNN and equipped it with a PFC-like cognitive system. When trained on cognitive tasks, this multi-system brain model can reproduce the low-dimensional population responses observed in neuronal activity as well as classical RNNs. Qualitatively different mechanisms can emerge from the training process when varying some details of the architecture such as the time constants. In particular, there is one class of models where it is the dynamics of the cognitive system that is implementing the task computations, and another where the cognitive system is only necessary to provide contextual information about the task rule as task performance is not impaired when preventing the system from accessing the task inputs. These constitute two different hypotheses about the causal role of the PFC in solving simple cognitive tasks, which could motivate further experiments on the brain.

Spike Timing Dependent Plasticity (STDP) is argued to modulate synaptic strength depending on the timing of pre- and postsynaptic spikes. Physiological experiments identified a variety of temporal kernels: Hebbian, anti-Hebbian and symmetrical LTP/LTD. In this work we present a novel plasticity model, the Voltage-Dependent Pathway Model (VDP), which is able to replicate those distinct kernel types and intermediate versions with varying LTP/LTD ratios and symmetry features. In addition, unlike previous models it retains these characteristics for different neuron models, which allows for comparison of plasticity in different neuron types. The plastic updates depend on the relative strength and activation of separately modeled LTP and LTD pathways, which are modulated by glutamate release and postsynaptic voltage. We used the 15 neuron type parametrizations in the GLIF5 model presented by Teeter et al. (2018) in combination with the VDP to simulate a range of standard plasticity protocols including standard STDP experiments, frequency dependency experiments and low frequency stimulation protocols. Slight variation in kernel stability and frequency effects can be identified between the neuron types, suggesting that the neuron type may have an effect on the effective learning rule. This plasticity model builds a middle ground between biophysical and phenomenological models allowing not just for the combination with more complex and biophysical neuron models, but is also computationally efficient so can be used in network simulations. Therefore it offers the possibility to explore the functional role of the different kernel types and electrophysiological differences in heterogeneous networks in future work.

Decision-making in noisy environments with constant sensory evidence involves integrating sequentially-sampled evidence, a strategy formalized by diffusion models which is supported by decades behavioral and neural findings. By contrast, it is unknown whether this strategy is also used during decision-making when the underlying sensory evidence is expected to change. Here, we trained monkeys to identify the dominant color of a dynamically refreshed checkerboard pattern that doesn't become informative until after a variable delay. Animals' behavioral responses were briefly suppressed after an abrupt change in evidence, and many neurons in the frontal eye field displayed a corresponding dip in activity at this time, similar to the dip frequently observed after stimulus onset. Generalized drift-diffusion models revealed that behavior and neural activity were consistent with a brief suppression of motor output without a change in evidence accumulation itself, in contrast to the popular belief that evidence accumulation is paused or reset. These results suggest that a brief interruption in motor preparation is an important strategy for dealing with changing evidence during perceptual decision making.

The world around us is complex, but at the same time full of meaningful regularities. We can detect, learn and exploit these regularities automatically in an unsupervised manner i.e. without any direct instruction or explicit reward. For example, we effortlessly estimate the average tallness of people in a room, or the boundaries between words in a language. These regularities and prior knowledge, once learned, can affect the way we acquire and interpret new information to build and update our internal model of the world for future decision-making processes. Despite the ubiquity of passively learning from the structured information in the environment, the mechanisms that support learning from real-world experience are largely unknown. By combing sophisticated cognitive tasks in human and rats, neuronal measurements and perturbations in rat and network modelling, we aim to build a multi-level description of how sensory history is utilised in inferring regularities in temporally extended tasks. In this talk, I will specifically focus on a comparative rat and human model, in combination with neural network models to study how past sensory experiences are utilized to impact working memory and decision making behaviours.

It is common for animals to use self-generated movements to actively sense the surrounding environment. For instance, rodents rhythmically move their whiskers to explore the space close to their body. The mouse whisker system has become a standard model to study active sensing and sensorimotor integration through feedback loops. In this work, we developed a bioinspired spiking neural network model of the sensorimotor peripheral whisker system, modelling trigeminal ganglion, trigeminal nuclei, facial nuclei, and central pattern generator neuronal populations. This network was embedded in a virtual mouse robot, exploiting the Neurorobotics Platform, a simulation platform offering a virtual environment to develop and test robots driven by brain-inspired controllers. Eventually, the peripheral whisker system was properly connected to an adaptive cerebellar network controller. The whole system was able to drive active whisking with learning capability, matching neural correlates of behaviour experimentally recorded in mice.