Computational Neuroscience seminars

Neural systems are remarkably robust against various perturbations, a phenomenon that still requires a clear explanation. Here, we graphically illustrate how neural networks can become robust. We study spiking networks that generate low-dimensional representations, and we show that the neurons’ subthreshold voltages are confined to a convex region in a lower-dimensional voltage subspace, which we call a ‘bounding box.’ Any changes in network parameters (such as number of neurons, dimensionality of inputs, firing thresholds, synaptic weights, or transmission delays) can all be understood as deformations of this bounding box. Using these insights, we show that functionality is preserved as long as perturbations do not destroy the integrity of the bounding box. We suggest that the principles underlying robustness in these networks—low-dimensional representations, heterogeneity of tuning, and precise negative feedback—may be key to understanding the robustness of neural systems at the circuit level.

In behaving rodents, CA1 pyramidal neurons receive spatially-tuned depolarizing synaptic input while traversing a specific location within an environment called its place. Midbrain dopamine neurons participate in reinforcement learning, and bursts of action potentials riding a depolarizing wave of synaptic input signal rewards and reward expectation. Interestingly, slice electrophysiology in vitro shows that both types of cells exhibit a pronounced reduction in firing rate (adaptation) and even cessation of firing during sustained depolarization. We included a five state Markov model of NaV1.6 (for CA1) and NaV1.2 (for dopamine neurons) respectively, in computational models of these two types of neurons. Our simulations suggest that long-term inactivation of this channel is responsible for the adaptation in CA1 pyramidal neurons, in response to triangular depolarizing current ramps. We also show that the differential contribution of slow inactivation in two subpopulations of midbrain dopamine neurons can account for their different dynamic ranges, as assessed by their responses to similar depolarizing ramps. These results suggest long-term inactivation of the sodium channel is a general mechanism for adaptation.

Recent chronic imaging experiments in mice have revealed that the hippocampal code exhibits non-trivial turnover dynamics over long time scales. Specifically, the subset of cells which are active on any given session in a familiar environment changes over the course of days and weeks. While some cells transition into or out of the code after a few sessions, others are stable over the entire experiment. The mechanisms underlying this turnover are unknown. Here we show that the statistics of turnover are consistent with a model in which non-spatial inputs to CA1 pyramidal cells readily undergo plasticity, while spatially tuned inputs are largely stable over time. The heterogeneity in stability across the cell assembly, as well as the decrease in correlation of the population vector of activity over time, are both quantitatively fit by a simple model with Gaussian input statistics. In fact, such input statistics emerge naturally in a network of spiking neurons operating in the fluctuation-driven regime. This correspondence allows one to map the parameters of a large-scale spiking network model of CA1 onto the simple statistical model, and thereby fit the experimental data quantitatively. Importantly, we show that the observed drift is entirely consistent with random, ongoing synaptic turnover. This synaptic turnover is, in turn, consistent with Hebbian plasticity related to continuous learning in a fast memory system.

A central goal in neuroscience is to understand how orchestrated computations in the brain arise from the properties of single neurons and networks of such neurons. Answering this question requires theoretical advances that shine light into the ‘black box’ of neuronal networks. In this talk, I will demonstrate theoretical approaches that help describe how cognitive and behavioral task implementations emerge from structure in neural populations and from biologically plausible learning rules. First, I will introduce an analytic theory that connects geometric structures that arise from neural responses (i.e., neural manifolds) to the neural population’s efficiency in implementing a task. In particular, this theory describes how easy or hard it is to discriminate between object categories based on the underlying neural manifolds’ structural properties. Next, I will describe how such methods can, in fact, open the ‘black box’ of neuronal networks, by showing how we can understand a) the role of network motifs in task implementation in neural networks and b) the role of neural noise in adversarial robustness in vision and audition. Finally, I will discuss my recent efforts to develop biologically plausible learning rules for neuronal networks, inspired by recent experimental findings in synaptic plasticity. By extending our mathematical toolkit for analyzing representations and learning rules underlying complex neuronal networks, I hope to contribute toward the long-term challenge of understanding the neuronal basis of behaviors.

I am working on color vision in Drosophila, identifying behaviors that involve color vision and understanding the neural circuits supporting them (Longden 2016). I have a long-term interest in understanding how neural computations operate reliably under changing circumstances, be they external changes in the sensory context, or internal changes of state such as hunger and locomotion. On internal state-modulation of sensory processing, I have shown how hunger alters visual motion processing in blowflies (Longden et al. 2014), and identified a role for octopamine in modulating motion vision during locomotion (Longden and Krapp 2009, 2010). On responses to external cues, I have shown how one kind of uncertainty in the motion of the visual scene is resolved by the fly (Saleem, Longden et al. 2012), and I have identified novel cells for processing translation-induced optic flow (Longden et al. 2017). I like working with colleagues who use different model systems, to get at principles of neural operation that might apply in many species (Ding et al. 2016, Dyakova et al. 2015). I like work motivated by computational principles - my background is computational neuroscience, with a PhD on models of memory formation in the hippocampus (Longden and Willshaw, 2007).

Optogenetics is a powerful tool that allows experimentalists to perturb neural circuits. What can we learn about a network from observing its response to perturbations? I will first describe the results of optogenetic activation of inhibitory neurons in mice cortex, and show that the results are consistent with inhibition stabilization. I will then move to experiments in which excitatory neurons are activated optogenetically, with or without visual inputs, in mice and monkeys. In some conditions, these experiments show a surprising result that the distribution of firing rates is not significantly changed by stimulation, even though firing rates of individual neurons are strongly modified. I will show in which conditions a network model of excitatory and inhibitory neurons can reproduce this feature.

Environmental boundaries anchor cognitive maps that support memory. However, trapezoidal boundary geometry distorts the regular firing patterns of entorhinal grid cells proposedly providing a metric for cognitive maps. Here, we test the impact of trapezoidal boundary geometry on human spatial memory using immersive virtual reality. Consistent with reduced regularity of grid patterns in rodents and a grid-cell model based on the eigenvectors of the successor representation, human positional memory was degraded in a trapezoid compared to a square environment; an effect particularly pronounced in the trapezoid’s narrow part. Congruent with spatial frequency changes of eigenvector grid patterns, distance estimates between remembered positions were persistently biased; revealing distorted memory maps that explained behavior better than the objective maps. Our findings demonstrate that environmental geometry affects human spatial memory similarly to rodent grid cell activity — thus strengthening the putative link between grid cells and behavior along with their cognitive functions beyond navigation.

The idea that perception in humans relies on some form of probabilistic computations has become very popular over the last decades. It has been extremely difficult however to characterize the extent and the nature of the probabilistic representations and operations that are manipulated by neural populations in the human cortex. Several theoretical works suggest that probabilistic representations are present from low-level sensory areas to high-level areas. According to this view, the neural dynamics implements some forms of probabilistic message passing (i.e. neural sampling, probabilistic population coding, etc.) which solves the problem of perceptual inference. Here I will present recent experimental evidence that human and non-human primate perception implements some form of message passing. I will first review findings showing probabilistic integration of sensory evidence across space and time in primate visual cortex. Second, I will show that the confidence reports in a hierarchical task reveal that uncertainty is represented both at lower and higher levels, in a way that is consistent with probabilistic message passing both from lower to higher and from higher to lower representations. Finally, I will present behavioral and neural evidence that human perception takes into account pairwise correlations in sequences of sensory samples in agreement with the message passing hypothesis, and against standard accounts such as accumulation of sensory evidence or predictive coding.

The theory of predictive processing posits that the brain computes expectations to process information predictively. Empirical evidence in support of this theory, however, is scarce and largely limited to sensory areas. Here, we report a precise and adaptive mechanism in the frontal cortex of non-human primates consistent with predictive processing of temporal events. We found that the speed of neural dynamics is precisely adjusted according to the average time of an expected stimulus. This speed adjustment, in turn, enables neurons to encode stimuli in terms of deviations from expectation. This lawful relationship was evident across multiple experiments and held true during learning: when temporal statistics underwent covert changes, neural responses underwent predictable changes that reflected the new mean. Together, these results highlight a precise mathematical relationship between temporal statistics in the environment and neural activity in the frontal cortex that may serve as a mechanism for predictive temporal processing.

The visual system is characterized by multiple mirrored visuotopic maps, with each repetition corresponding to a different visual area. In this work we explore whether such visuotopic organization can emerge as a result of minimizing the total wire length between neurons connected in a deep hierarchical network. Our results show that networks with purely feedforward connectivity typically result in a single visuotopic map, and in certain cases no visuotopic map emerges. However, when we modify the network by introducing lateral connections, with sufficient lateral connectivity among neurons within layers, multiple visuotopic maps emerge, where some connectivity motifs yield mirrored alternations of visuotopic maps–a signature of biological visual system areas. These results demonstrate that different connectivity profiles have different emergent organizations under the minimum total wire length hypothesis, and highlight that characterizing the large-scale spatial organizing of tuning properties in a biological system might also provide insights into the underlying connectivity.

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.

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.

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.

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.