Computational Neuroscience seminars

Cognitive control guides behavior by controlling what, where, and how information is represented in the brain. Perhaps the most well-studied form of cognitive control has been ‘attention’, which controls how external sensory stimuli are represented in the brain. In contrast, the neural mechanisms controlling the selection of representations held ‘in mind’, in working memory, are unknown. In this talk, I will present evidence that the prefrontal cortex controls working memory by selectively enhancing and transforming the contents of working memory. In particular, I will show how the neural representation of the content of working memory changes over time, moving between different ‘subspaces’ of the neural population. These dynamics may play a critical role in controlling what and how neural representations are acted upon.

In this talk, we propose to decipher the activity of neural networks via a “multiply and conquer” approach. This approach considers limit networks made of infinitely many replicas with the same basic neural structure. The key point is that these so-called replica-mean-field networks are in fact simplified, tractable versions of neural networks that retain important features of the finite network structure of interest. The finite size of neuronal populations and synaptic interactions is a core determinant of neural dynamics, being responsible for non-zero correlation in the spiking activity and for finite transition rates between metastable neural states. Theoretically, we develop our replica framework by expanding on ideas from the theory of communication networks rather than from statistical physics to establish Poissonian mean-field limits for spiking networks. Computationally, we leverage our original replica approach to characterize the stationary spiking activity of various network models via reduction to tractable functional equations. We conclude by discussing perspectives about how to use our replica framework to probe nontrivial regimes of spiking correlations and transition rates between metastable neural states.

Several species of insects have been observed to perform accurate path integration, constantly updating a vector memory of their location relative to a starting position, which they can use to take a direct return path. Foraging insects such as bees and ants are also able to store and recall the vectors to return to food locations, and to take novel shortcuts between these locations. Other insects, such as dung beetles, are observed to integrate multimodal directional cues in a manner well described by vector addition. All these processes appear to be functions of the Central Complex, a highly conserved and strongly structured circuit in the insect brain. Modelling this circuit, at the single neuron level, suggests it has general capabilities for vector encoding, vector memory, vector addition and vector rotation that can support a wide range of directed and navigational behaviours.

We recorded and analyzed the population activity of hundreds of neurons in the medial premotor areas (MPC) of rhesus monkeys performing an isochronous tapping task guided by brief flashing stimuli or auditory tones. The animals showed a strong bias towards visual metronomes, with rhythmic tapping that was more precise and accurate than for auditory metronomes. The population dynamics in state space as well as the corresponding neural sequences shared the following properties across modalities: the circular dynamics of the neural trajectories and the neural sequences formed a regenerating loop for every produced interval, producing a relative time representation; the trajectories converged in similar state space at tapping times while the moving bumps restart at this point, resetting the beat-based clock; the tempo of the synchronized tapping was encoded by a combination of amplitude modulation and temporal scaling in the neural trajectories. In addition, the modality induced a displacement in the neural trajectories in auditory and visual subspaces without greatly altering time keeping mechanism. These results suggest that the interaction between the amodal internal representation of pulse within MPC and a modality specific external input generates a neural rhythmic clock whose dynamics define the temporal execution of tapping using auditory and visual metronomes.

In the first half of my talk, I will discuss our recent work on the midbrain dopamine system. The hypothesis that midbrain dopamine neurons broadcast an error signal for the prediction of reward is among the great successes of computational neuroscience. However, our recent results contradict a core aspect of this theory: that the neurons uniformly convey a scalar, global signal. I will review this work, as well as our new efforts to update models of the neural basis of reinforcement learning with our data. In the second half of my talk, I will discuss our recent findings of state-dependent decision-making mechanisms in the striatum.

Artificial neural networks simplify complex biological circuits into tractable models for computational exploration and experimentation. However, the simplification of artificial models also undermines their applicability to real brain dynamics. Typical efforts to address this mismatch add complexity to increasingly unwieldy models. Here, we take a different approach; by reducing the complexity of a biological cortical culture, we aim to distil the essential factors of neuronal dynamics and plasticity. We leverage recent advances in growing neurons from human induced pluripotent stem cells (hiPSCs) to analyse ex vivo cortical cultures with only two distinct excitatory and inhibitory neuron populations. Over 6 weeks of development, we record from thousands of neurons using high-density microelectrode arrays (HD-MEAs) that allow access to individual neurons and the broader population dynamics. We compare these dynamics to two-population artificial networks of single-compartment neurons with random sparse connections and show that they produce similar dynamics. Specifically, our model captures the firing and bursting statistics of the cultures. Moreover, tightly integrating models and cultures allows us to evaluate the impact of changing architectures over weeks of development, with and without external stimuli. Broadly, the use of simplified cortical cultures enables us to use the repertoire of theoretical neuroscience techniques established over the past decades on artificial network models. Our approach of deriving neural networks from human cells also allows us, for the first time, to directly compare neural dynamics of disease and control. We found that cultures e.g. from epilepsy patients tended to have increasingly more avalanches of synchronous activity over weeks of development, in contrast to the control cultures. Next, we will test possible interventions, in silico and in vitro, in a drive for personalised approaches to medical care. This work starts bridging an important theoretical-experimental neuroscience gap for advancing our understanding of mammalian neuron dynamics.

Memory consolidation is the process by which recent experiences are assimilated into long-term memory. In animals, this process requires the offline replay of sequences observed during online exploration in the hippocampus. Recent experimental work has found that salient but task-irrelevant stimuli are systematically excluded from these replay epochs, suggesting that replay samples from an abstracted model of the world, rather than verbatim previous experiences. We find that this phenomenon can be explained parsimoniously and biologically plausibly by a Hebbian spike time-dependent plasticity rule at inhibitory synapses. Using spiking networks at three levels of abstraction–leaky integrate-and-fire, biophysically detailed, and abstract binary–we show that this rule enables efficient inference of a model of the structure of the world. While plasticity has previously mainly been studied at excitatory synapses, we find that plasticity at excitatory synapses alone is insufficient to accomplish this type of structural learning. We present theoretical results in a simplified model showing that in the presence of Hebbian excitatory and inhibitory plasticity, the replayed sequences form a statistical estimator of a latent sequence, which converges asymptotically to the ground truth. Our work outlines a direct link between the synaptic and cognitive levels of memory consolidation, and highlights a potential conceptually distinct role for inhibition in computing with SNNs.

The spike-threshold nonlinearity is a fundamental, yet enigmatic, component of biological computation — despite its role in many theories, it has evaded definitive characterisation. Indeed, much classic work has attempted to limit the focus on spiking by smoothing over the spike threshold or by approximating spiking dynamics with firing-rate dynamics. Here, we take a novel perspective that captures the full potential of spike-based computation. Based on previous studies of the geometry of efficient spike-coding networks, we consider a population of neurons with low-rank connectivity, allowing us to cast each neuron’s threshold as a boundary in a space of population modes, or latent variables. Each neuron divides this latent space into subthreshold and suprathreshold areas. We then demonstrate how a network of inhibitory (I) neurons forms a convex, attracting boundary in the latent coding space, and a network of excitatory (E) neurons forms a concave, repellant boundary. Finally, we show how the combination of the two yields stable dynamics at the crossing of the E and I boundaries, and can be mapped onto a constrained optimization problem. The resultant EI networks are balanced, inhibition-stabilized, and exhibit asynchronous irregular activity, thereby closely resembling cortical networks of the brain. Moreover, we demonstrate how such networks can be tuned to either suppress or amplify noise, and how the composition of inhibitory convex and excitatory concave boundaries can result in universal function approximation. Our work puts forth a new theory of biologically-plausible computation in balanced spiking networks, and could serve as a novel framework for scalable and interpretable computation with spikes.

A central problem in biological learning is how information about the outcome of a decision or behavior can be used to reliably guide learning across distributed neural circuits while obeying biological constraints. This “credit assignment” problem is commonly solved in artificial neural networks through supervised gradient descent and the backpropagation algorithm. In contrast, biological learning is typically modelled using unsupervised Hebbian learning rules. While these rules only use local information to update synaptic weights, and are sometimes combined with weight constraints to reflect a diversity of excitatory (only positive weights) and inhibitory (only negative weights) cell types, they do not prescribe a clear mechanism for how to coordinate learning across multiple layers and propagate error information accurately across the network. In recent years, several groups have drawn inspiration from the known dendritic non-linearities of pyramidal neurons to propose new learning rules and network architectures that enable biologically plausible multi-layer learning by processing error information in segregated dendrites. Meanwhile, recent experimental results from the hippocampus have revealed a new form of plasticity—Behavioral Timescale Synaptic Plasticity (BTSP)—in which large dendritic depolarizations rapidly reshape synaptic weights and stimulus selectivity with as little as a single stimulus presentation (“one-shot learning”). Here we explore the implications of this new learning rule through a biologically plausible implementation in a rate neuron network. We demonstrate that regulation of dendritic spiking and BTSP by top-down feedback signals can effectively coordinate plasticity across multiple network layers in a simple pattern recognition task. By analyzing hidden feature representations and weight trajectories during learning, we show the differences between networks trained with standard backpropagation, Hebbian learning rules, and BTSP.

Biologically plausible spiking neural networks (SNNs) are an emerging architecture for deep learning tasks due to their energy efficiency when implemented on neuromorphic hardware. However, many of the biological features are at best irrelevant and at worst counterproductive when evaluated in the context of task performance and suitability for neuromorphic hardware. In this talk, I will present an alternative paradigm to design deep learning architectures with good task performance in real-world benchmarks while maintaining all the advantages of SNNs. We do this by focusing on two main features – event-based computation and activity sparsity. Starting from the performant gated recurrent unit (GRU) deep learning architecture, we modify it to make it event-based and activity-sparse. The resulting event-based GRU (EGRU) is extremely efficient for both training and inference. At the same time, it achieves performance close to conventional deep learning architectures in challenging tasks such as language modelling, gesture recognition and sequential MNIST.

Understanding the nature of neural representation is a central challenge of neuroscience. One common approach to this challenge is to compute receptive fields by correlating neural activity with external variables drawn from sensory signals. But these receptive fields are only meaningful to the experimenter, not the organism, because only the experimenter has access to both the neural activity and knowledge of the external variables. To understand neural representation more directly, recent methodological advances have sought to capture the intrinsic geometry of sensory driven neural responses without external reference. To date, this approach has largely been restricted to low-dimensional stimuli as in spatial navigation. In this talk, I will discuss recent work from my lab examining the intrinsic geometry of sensory representations in a model vocal communication system, songbirds. From the assumption that sensory systems capture invariant relationships among stimulus features, we conceptualized the space of natural birdsongs to lie on the surface of an n-dimensional hypersphere. We computed composite receptive field models for large populations of simultaneously recorded single neurons in the auditory forebrain and show that solutions to these models define convex regions of response probability in the spherical stimulus space. We then define a combinatorial code over the set of receptive fields, realized in the moment-to-moment spiking and non-spiking patterns across the population, and show that this code can be used to reconstruct high-fidelity spectrographic representations of natural songs from evoked neural responses. Notably, we find that topological relationships among combinatorial codewords directly mirror acoustic relationships among songs in the spherical stimulus space. That is, the time-varying pattern of co-activity across the neural population expresses an intrinsic representational geometry that mirrors the natural, extrinsic stimulus space. Combinatorial patterns across this intrinsic space directly represent complex vocal communication signals, do not require computation of receptive fields, and are in a form, spike time coincidences, amenable to biophysical mechanisms of neural information propagation.

The brain efficiently performs nonlinear computations through its intricate networks of spiking neurons, but how this is done remains elusive. While recurrent spiking networks implementing linear computations can be directly derived and easily understood (e.g., in the spike coding network (SCN) framework), the connectivity required for nonlinear computations can be harder to interpret, as they require additional non-linearities (e.g., dendritic or synaptic) weighted through supervised training. Here we extend the SCN framework to directly implement any polynomial dynamical system. This results in networks requiring multiplicative synapses, which we term the multiplicative spike coding network (mSCN). We demonstrate how the required connectivity for several nonlinear dynamical systems can be directly derived and implemented in mSCNs, without training. We also show how to precisely carry out higher-order polynomials with coupled networks that use only pair-wise multiplicative synapses, and provide expected numbers of connections for each synapse type. Overall, our work provides an alternative method for implementing nonlinear computations in spiking neural networks, while keeping all the attractive features of standard SCNs such as robustness, irregular and sparse firing, and interpretable connectivity. Finally, we discuss the biological plausibility of mSCNs, and how the high accuracy and robustness of the approach may be of interest for neuromorphic computing.

Memory is a key component of biological neural systems that enables the retention of information over a huge range of temporal scales, ranging from hundreds of milliseconds up to years. While Hebbian plasticity is believed to play a pivotal role in biological memory, it has so far been analyzed mostly in the context of pattern completion and unsupervised learning. Here, we propose that Hebbian plasticity is fundamental for computations in biological neural systems. We introduce a novel spiking neural network (SNN) architecture that is enriched by Hebbian synaptic plasticity. We experimentally show that our memory-equipped SNN model outperforms state-of-the-art deep learning mechanisms in a sequential pattern-memorization task, as well as demonstrate superior out-of-distribution generalization capabilities compared to these models. We further show that our model can be successfully applied to one-shot learning and classification of handwritten characters, improving over the state-of-the-art SNN model. We also demonstrate the capability of our model to learn associations for audio to image synthesis from spoken and handwritten digits. Our SNN model further presents a novel solution to a variety of cognitive question answering tasks from a standard benchmark, achieving comparable performance to both memory-augmented ANN and SNN-based state-of-the-art solutions to this problem. Finally we demonstrate that our model is able to learn from rewards on an episodic reinforcement learning task and attain near-optimal strategy on a memory-based card game. Hence, our results show that Hebbian enrichment renders spiking neural networks surprisingly versatile in terms of their computational as well as learning capabilities. Since local Hebbian plasticity can easily be implemented in neuromorphic hardware, this also suggests that powerful cognitive neuromorphic systems can be build based on this principle.