Neural activity in many sensory systems is organized on low-dimensional manifolds by means of convex receptive fields. Neural codes in these areas are constrained by this organization, as not every neural code is compatible with convex receptive fields. The same codes are also constrained by the structure of the underlying neural network. In my talk I will attempt to provide answers to the following natural questions: (i) How do recurrent circuits generate codes that are compatible with the convexity of receptive fields? (ii) How can we utilize the constraints imposed by the convex receptive field to understand the underlying stimulus space. To answer question (i), we describe the combinatorics of the steady states and fixed points of recurrent networks that satisfy the Dale’s law. It turns out the combinatorics of the fixed points are completely determined by two distinct conditions: (a) the connectivity graph of the network and (b) a spectral condition on the synaptic matrix. We give a characterization of exactly which features of connectivity determine the combinatorics of the fixed points. We also find that a generic recurrent network that satisfies Dale's law outputs convex combinatorial codes. To address question (ii), I will describe methods based on ideas from topology and geometry that take advantage of the convex receptive field properties to infer the dimension of (non-linear) neural representations. I will illustrate the first method by inferring basic features of the neural representations in the mouse olfactory bulb.

A long standing challenge in biological and artificial intelligence is to understand how new knowledge can be constructed from known building blocks in a way that is amenable for computation by neuronal circuits. Here we focus on the task of storage and recall of structured knowledge in long-term memory. Specifically, we ask how recurrent neuronal networks can store and retrieve multiple knowledge structures. We model each structure as a set of binary relations between events and attributes (attributes may represent e.g., temporal order, spatial location, role in semantic structure), and map each structure to a distributed neuronal activity pattern using a vector symbolic architecture (VSA) scheme. We then use associative memory plasticity rules to store the binarized patterns as fixed points in a recurrent network. By a combination of signal-to-noise analysis and numerical simulations, we demonstrate that our model allows for efficient storage of these knowledge structures, such that the memorized structures as well as their individual building blocks (e.g., events and attributes) can be subsequently retrieved from partial retrieving cues. We show that long-term memory of structured knowledge relies on a new principle of computation beyond the memory basins. Finally, we show that our model can be extended to store sequences of memories as single attractors.

Progress in deep learning has spawned great successes in many engineering applications. As a prime example, convolutional neural networks, a type of feedforward neural networks, are now approaching – and sometimes even surpassing – human accuracy on a variety of visual recognition tasks. In this talk, however, I will show that these neural networks and their recent extensions exhibit a limited ability to solve seemingly simple visual reasoning problems involving incremental grouping, similarity, and spatial relation judgments. Our group has developed a recurrent network model of classical and extra-classical receptive field circuits that is constrained by the anatomy and physiology of the visual cortex. The model was shown to account for diverse visual illusions providing computational evidence for a novel canonical circuit that is shared across visual modalities. I will show that this computational neuroscience model can be turned into a modern end-to-end trainable deep recurrent network architecture that addresses some of the shortcomings exhibited by state-of-the-art feedforward networks for solving complex visual reasoning tasks. This suggests that neuroscience may contribute powerful new ideas and approaches to computer science and artificial intelligence.

During primate evolution, prefrontal cortex (PFC) expanded substantially relative to other cortical areas. The expansion of PFC circuits likely supported the increased cognitive abilities of humans and anthropoids to sample information about their environment, evaluate that information, plan, and decide between different courses of action. What quantities do these circuits compute as information is being sampled towards and a decision is being made? And how can they be related to anatomical specialisations within and across PFC? To address this, we recorded PFC activity during value-based decision making using single unit recording in non-human primates and magnetoencephalography in humans. At a macrocircuit level, we found that value correlates differ substantially across PFC subregions. They are heavily shaped by each subregion’s anatomical connections and by the decision-maker’s current locus of attention. At a microcircuit level, we found that the temporal evolution of value correlates can be predicted using cortical recurrent network models that temporally integrate incoming decision evidence. These models reflect the fact that PFC circuits are highly recurrent in nature and have synaptic properties that support persistent activity across temporally extended cognitive tasks. Our findings build upon recent work describing economic decision making as a process of attention-weighted evidence integration across time.

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.

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.

I will build from Niccolo's discussion of the Blockhead argument to argue that having an FeedForward Network (FN) responding like an recurrent network (RN) in a consciousness experiment is not enough to convince us the two are the same with regards to the posession of mental states and conscious experience. I will then argue that a robust functional equivalence between FFN and RN is akso not supported by the mathematical work on the Universal Approximator theorem, and is also unlikely to hold, as a conjecture, given data in cognitive neuroscience; I will argue that an equivalence of RN and FFN may only apply to static functions between input/output layers and not to the temporal patterns or to the network's reactions to structural perturbations. Finally, I review data indicating that consciousness has functional characteristics, such as a flexible control of behavior, and that cognitive/brain dynamics reveal interacting top-down and bottom-up processes, which are necessary for the mediation of such control processes.

Gradient-based optimization powered by the backpropagation algorithm proved to be the pivotal method in the training of non-spiking artificial neural networks. At the same time, spiking neural networks hold the promise for efficient processing of real-world sensory data by communicating using discrete events in continuous time. We derive the backpropagation algorithm for a recurrent network of spiking (leaky integrate-and-fire) neurons with hard thresholds and show that the backward dynamics amount to an event-based backpropagation of errors through time. Our derivation uses the jump conditions for partial derivatives at state discontinuities found by applying the implicit function theorem, allowing us to avoid approximations or substitutions. We find that the gradient exists and is finite almost everywhere in weight space, up to the null set where a membrane potential is precisely tangent to the threshold. Our presented algorithm, EventProp, computes the exact gradient with respect to a general loss function based on spike times and membrane potentials. Crucially, the algorithm allows for an event-based communication scheme in the backward phase, retaining the potential advantages of temporal sparsity afforded by spiking neural networks. We demonstrate the optimization of spiking networks using gradients computed via EventProp and the Yin-Yang and MNIST datasets with either a spike time-based or voltage-based loss function and report competitive performance. Our work supports the rigorous study of gradient-based optimization in spiking neural networks as well as the development of event-based neuromorphic architectures for the efficient training of spiking neural networks. While we consider the leaky integrate-and-fire model in this work, our methodology generalises to any neuron model defined as a hybrid dynamical system.

Homeostatic plasticity plays a key role in stabilizing neural network activity. But what is its role in neural information processing? We showed analytically how homeostasis changes collective dynamics and consequently information flow - depending on the input to the network. We then studied how input and homeostasis on a recurrent network of LIF neurons impacts information flow and task performance. We showed how we can tune the working point of the network, and found that, contrary to previous assumptions, there is not one optimal working point for a family of tasks, but each task may require its own working point.

During primate evolution, prefrontal cortex (PFC) expanded substantially relative to other cortical areas. The expansion of PFC circuits likely supported the increased cognitive abilities of humans and anthropoids to plan, evaluate, and decide between different courses of action. But what do these circuits compute as a decision is being made, and how can they be related to anatomical specialisations within and across PFC? To address this, we recorded PFC activity during value-based decision making using single unit recording in non-human primates and magnetoencephalography in humans. At a macrocircuit level, we found that value correlates differ substantially across PFC subregions. They are heavily shaped by each subregion’s anatomical connections and by the decision-maker’s current locus of attention. At a microcircuit level, we found that the temporal evolution of value correlates can be predicted using cortical recurrent network models that temporally integrate incoming decision evidence. These models reflect the fact that PFC circuits are highly recurrent in nature and have synaptic properties that support persistent activity across temporally extended cognitive tasks. Our findings build upon recent work describing economic decision making as a process of attention-weighted evidence integration across time.

Many networks in the brain are sparsely connected, and the brain eliminates synapses during development and learning. How could the brain decide which synapses to prune? In a recurrent network, determining the importance of a synapse between two neurons is a difficult computational problem, depending on the role that both neurons play and on all possible pathways of information flow between them. Noise is ubiquitous in neural systems, and often considered an irritant to be overcome. In the first part of this talk, I will suggest that noise could play a functional role in synaptic pruning, allowing the brain to probe network structure and determine which synapses are redundant. I will introduce a simple, local, unsupervised plasticity rule that either strengthens or prunes synapses using only synaptic weight and the noise-driven covariance of the neighboring neurons. For a subset of linear and rectified-linear networks, this rule provably preserves the spectrum of the original matrix and hence preserves network dynamics even when the fraction of pruned synapses asymptotically approaches 1. The plasticity rule is biologically-plausible and may suggest a new role for noise in neural computation. Time permitting, I will then turn to the problem of extracting structure from neural population data sets using dimensionality reduction methods. I will argue that nonlinear structures naturally arise in neural data and show how these nonlinearities cause linear methods of dimensionality reduction, such as Principal Components Analysis, to fail dramatically in identifying low-dimensional structure.