Computational Neuroscience seminars

Resonance is defined as a maximal amplification of the response of a system to periodic inputs in a limited, intermediate input frequency band. Resonance may serve to optimize inter-neuronal communication, and has been observed at multiple levels of neuronal organization including membrane potential fluctuations, single neuron spiking, postsynaptic potentials, and neuronal networks. However, it is unknown how resonance observed at one level of neuronal organization (e.g., network) depends on the properties of the constituting building blocks, and whether, and if yes how, it affects the resonant and oscillatory properties upstream. One difficulty is the absence of a conceptual framework that facilitates the interrogation of resonant neuronal circuits and organizes the mechanistic investigation of network resonance in terms of the circuit components, across levels of organization. We address these issues by discussing a number of representative case studies. The dynamic mechanisms responsible for the generation of resonance involve disparate processes, including negative feedback effects, history-dependence, spiking discretization combined with subthreshold passive dynamics, combinations of these, and resonance inheritance from lower levels of organization. The band-pass filters associated with the observed resonances are generated by primarily nonlinear interactions of low- and high-pass filters. We identify these filters (and interactions) and we argue that these are the constitutive building blocks of a resonance framework. Finally, we discuss alternative frameworks and we show that different types of models (e.g., spiking neural networks and rate models) can show the same type of resonance by qualitative different mechanisms.

Research in our lab focuses on the circuit mechanisms underlying sensory computation. We use the mouse retina as a model system because it allows us to stimulate the circuit precisely with its natural input, patterns of light, and record its natural output, the spike trains of retinal ganglion cells. We harness the power of genetic manipulations and detailed information about cell types to uncover new circuits and discover their role in visual processing. Our methods include electrophysiology, computational modeling, and circuit tracing using a variety of imaging techniques.

To localize ourselves in an environment for spatial navigation, we rely on vision and self-motion inputs, which only provide noisy and partial information. It is unknown how the resulting uncertainty affects navigation behavior and neural representations. Here we show that spatial uncertainty underlies key effects of environmental geometry on navigation behavior and grid field deformations. We develop an ideal observer model, which continually updates probabilistic beliefs about its allocentric location by optimally combining noisy egocentric visual and self-motion inputs via Bayesian filtering. This model directly yields predictions for navigation behavior and also predicts neural responses under population coding of location uncertainty. We simulate this model numerically under manipulations of a major source of uncertainty, environmental geometry, and support our simulations by analytic derivations for its most salient qualitative features. We show that our model correctly predicts a wide range of experimentally observed effects of the environmental geometry and its change on homing response distribution and grid field deformation. Thus, our model provides a unifying, normative account for the dependence of homing behavior and grid fields on environmental geometry, and identifies the unavoidable uncertainty in navigation as a key factor underlying these diverse phenomena.

Solving complex planning problems efficiently and flexibly requires reusing expensive previous computations. The brain can do this, but how? I present a new theory that addresses this question and connects planning to hitherto distinct areas within cognitive neuroscience, such as entorhinal representation of cognitive maps and cognitive control.

The cerebellum resembles a feedforward, three-layer network of neurons in which the “hidden layer” consists of Purkinje cells (P-cells) and the output layer consists of deep cerebellar nucleus (DCN) neurons. In this analogy, the output of each DCN neuron is a prediction that is compared with the actual observation, resulting in an error signal that originates in the inferior olive. Efficient learning requires that the error signal reach the DCN neurons, as well as the P-cells that project onto them. However, this basic rule of learning is violated in the cerebellum: the olivary projections to the DCN are weak, particularly in adulthood. Instead, an extraordinarily strong signal is sent from the olive to the P-cells, producing complex spikes. Curiously, P-cells are grouped into small populations that converge onto single DCN neurons. Why are the P-cells organized in this way, and what is the membership criterion of each population? Here, I apply elementary mathematics from machine learning and consider the fact that P-cells that form a population exhibit a special property: they can synchronize their complex spikes, which in turn suppress activity of DCN neuron they project to. Thus complex spikes cannot only act as a teaching signal for a P-cell, but through complex spike synchrony, a P-cell population may act as a surrogate teacher for the DCN neuron that produced the erroneous output. It appears that grouping of P-cells into small populations that share a preference for error satisfies a critical requirement of efficient learning: providing error information to the output layer neuron (DCN) that was responsible for the error, as well as the hidden layer neurons (P-cells) that contributed to it. This population coding may account for several remarkable features of behavior during learning, including multiple timescales, protection from erasure, and spontaneous recovery of memory.

A key insight from the foraging literature is the importance of assessing the overall environmental quality — via global reward rate or similar measures, which capture the opportunity cost of time and can guide behavioral allocation toward relatively richer options. Meanwhile, the majority of research in decision neuroscience and computational psychiatry has focused instead on how choices are guided by much more local, event-locked evaluations: of individual situations, actions, or outcomes. I review a combination of research and theoretical speculation from my lab and others that emphasizes the role of foraging's average rewards and opportunity costs in a much larger range of decision problems, including risk, time discounting, vigor, cognitive control, and deliberation. The broad range of behaviors affected by this type of evaluation gives a new theoretical perspective on the effects of stress and autonomic mobilization, and on mood and the broad range of symptoms associated with mood disorders.

A central goal of vision science is to understand the principles underlying the perception and neural coding of the complex visual environment of our everyday experience. In the visual cortex, foundational work with artificial stimuli, and more recent work combining natural images and deep convolutional neural networks, have revealed much about the tuning of cortical neurons to specific image features. However, a major limitation of this existing work is its focus on single-neuron response strength to isolated images. First, during natural vision, the inputs to cortical neurons are not isolated but rather embedded in a rich spatial and temporal context. Second, the full structure of population activity—including the substantial trial-to-trial variability that is shared among neurons—determines encoded information and, ultimately, perception. In the first part of this talk, I will argue for a normative approach to study encoding of natural images in primary visual cortex (V1), which combines a detailed understanding of the sensory inputs with a theory of how those inputs should be represented. Specifically, we hypothesize that V1 response structure serves to approximate a probabilistic representation optimized to the statistics of natural visual inputs, and that contextual modulation is an integral aspect of achieving this goal. I will present a concrete computational framework that instantiates this hypothesis, and data recorded using multielectrode arrays in macaque V1 to test its predictions. In the second part, I will discuss how we are leveraging this framework to develop deep probabilistic algorithms for natural image and video segmentation.

Large-scale numerical simulations of brain circuit models are important for identifying hypotheses on brain functions and testing their consistency and plausibility. Similarly, spiking neural networks are also gaining traction in machine learning with the promise that neuromorphic hardware will eventually make them much more energy efficient than classical ANNs. In this session, we will present the GeNN (GPU-enhanced Neuronal Networks) framework, which aims to facilitate the use of graphics accelerators for computational models of large-scale spiking neuronal networks to address the challenge of efficient simulations. GeNN is an open source library that generates code to accelerate the execution of network simulations on NVIDIA GPUs through a flexible and extensible interface, which does not require in-depth technical knowledge from the users. GeNN was originally developed as a pure C++ and CUDA library but, subsequently, we have added a Python interface and OpenCL backend. We will briefly cover the history and basic philosophy of GeNN and show some simple examples of how it is used and how it interacts with other Open Source frameworks such as Brian2GeNN and PyNN.

The last twenty years have witnessed extraordinarily rapid progress in basic neuroscience, including breakthrough technologies such as optogenetics, and the collection of unprecedented amounts of neuroimaging, genetic and other data relevant to neuroscience and mental health. However, the translation of this progress into improved understanding of brain function and dysfunction has been comparatively slow. As a result, the development of therapeutics for mental health has stagnated too. One central challenge has been to extract meaning from these large, complex, multivariate datasets, which requires a shift towards systems-level mathematical and computational approaches. A second challenge has been reconciling different scales of investigation, from genes and molecules to cells, circuits, tissue, whole-brain, and ultimately behaviour. In this talk I will describe several strands of work using mathematical, statistical, and bioinformatic methods to bridge these gaps. Topics will include: using artificial neural networks to link the organization of large-scale brain connectivity to cognitive function; using multivariate statistical methods to link disease-related changes in brain networks to the underlying biological processes; and using network-based approaches to move from genetic insights towards drug discovey. Finally, I will discuss how simple organisms such as C. elegans can serve to inspire, test, and validate new methods and insights in networks neuroscience.

One of the fundamental functions of the brain is to flexibly plan and control movement production at different timescales to efficiently shape structured behaviors. I will present a model that clarifies how these complex computations could be performed in the mammalian brain, with an emphasis on the learning of an extendable library of autonomous motor motifs and the flexible stringing of these motifs in motor sequences. To build this model, we took advantage of the fact that the anatomy of the circuits involved is well known. Our results show how these architectural constraints lead to a principled understanding of how strategically positioned plastic connections located within motif-specific thalamocortical loops can interact with cortical dynamics that are shared across motifs to create an efficient form of modularity. This occurs because the cortical dynamics can be controlled by the activation of as few as one thalamic unit, which induces a low-rank perturbation of the cortical connectivity, and significantly expands the range of outputs that the network can produce. Finally, our results show that transitions between any motifs can be facilitated by a specific thalamic population that participates in preparing cortex for the execution of the next motif. Taken together, our model sheds light on the neural network mechanisms that can generate flexible sequencing of varied motor motifs.

Biological brains possess an exceptional ability to infer relevant behavioral responses to a wide range of stimuli from only a few examples. This capacity to generalize beyond the training set has been proven particularly challenging to realize in artificial systems. How neural processes enable this capacity to extrapolate to novel stimuli is a fundamental open question. A prominent but underexplored hypothesis suggests that generalization is facilitated by a low-dimensional organization of collective neural activity, yet evidence for the underlying neural mechanisms remains wanting. Combining network modeling, theory and neural data analysis, we tested this hypothesis in the framework of flexible timing tasks, which rely on the interplay between inputs and recurrent dynamics. We first trained recurrent neural networks on a set of timing tasks while minimizing the dimensionality of neural activity by imposing low-rank constraints on the connectivity, and compared the performance and generalization capabilities with networks trained without any constraint. We then examined the trained networks, characterized the dynamical mechanisms underlying the computations, and verified their predictions in neural recordings. Our key finding is that low-dimensional dynamics strongly increases the ability to extrapolate to inputs outside of the range used in training. Critically, this capacity to generalize relies on controlling the low-dimensional dynamics by a parametric contextual input. We found that this parametric control of extrapolation was based on a mechanism where tonic inputs modulate the dynamics along non-linear manifolds in activity space while preserving their geometry. Comparisons with neural recordings in the dorsomedial frontal cortex of macaque monkeys performing flexible timing tasks confirmed the geometric and dynamical signatures of this mechanism. Altogether, our results tie together a number of previous experimental findings and suggest that the low-dimensional organization of neural dynamics plays a central role in generalizable behaviors.

Neurons in the brain communicate through action potentials (spikes) that are transmitted through chemical synapses. Throughout the last decades, the question how networks of spiking neurons represent and process information has remained an important challenge. Some progress has resulted from a recent family of supervised learning rules (tempotrons) for models of spiking neurons. However, these studies have viewed synaptic transmission as static and characterized synaptic efficacies as scalar quantities that change only on slow time scales of learning across trials but remain fixed on the fast time scales of information processing within a trial. By contrast, signal transduction at chemical synapses in the brain results from complex molecular interactions between multiple biochemical processes whose dynamics result in substantial short-term plasticity of most connections. Here we study the computational capabilities of spiking neurons whose synapses are dynamic and plastic, such that each individual synapse can learn its own dynamics. We derive tempotron learning rules for current-based leaky-integrate-and-fire neurons with different types of dynamic synapses. Introducing ordinal synapses whose efficacies depend only on the order of input spikes, we establish an upper capacity bound for spiking neurons with dynamic synapses. We compare this bound to independent synapses, static synapses and to the well established phenomenological Tsodyks-Markram model. We show that synaptic dynamics in principle allow the storage capacity of spiking neurons to scale with the number of input spikes and that this increase in capacity can be traded for greater robustness to input noise, such as spike time jitter. Our work highlights the feasibility of a novel computational paradigm for spiking neural circuits with plastic synaptic dynamics: Rather than being determined by the fixed number of afferents, the dimensionality of a neuron's decision space can be scaled flexibly through the number of input spikes emitted by its input layer.

Statistics of natural scenes are not uniform - their structure varies dramatically from ground to sky. It remains unknown whether these non-uniformities are reflected in the large-scale organization of the early visual system and what benefits such adaptations would confer. By deploying an efficient coding argument, we predict that changes in the structure of receptive fields across visual space increase the efficiency of sensory coding. To test this experimentally, developed a simple, novel imaging system that is indispensable for studies at this scale. In agreement with our predictions, we could show that receptive fields of retinal ganglion cells change their shape along the dorsoventral axis, with a marked surround asymmetry at the visual horizon. Our work demonstrates that, according to principles of efficient coding, the panoramic structure of natural scenes is exploited by the retina across space and cell-types.

The accumulation and storage of information in memory is a fundamental computation underlying animal behavior. In many brain regions and task paradigms, ranging from motor control to navigation to decision-making, such accumulation is accomplished through neural integrator circuits that enable external inputs to move a system’s population-wide patterns of neural activity along a continuous attractor. In the first portion of the talk, I will discuss our efforts to dissect the circuit mechanisms underlying a neural integrator from a rich array of anatomical, physiological, and perturbation experiments. In the second portion of the talk, I will show how the accumulation and storage of information in long-term memory may also be described by attractor dynamics, but now within the space of synaptic weights rather than neural activity. Altogether, this work suggests a conceptual unification of seemingly distinct short- and long-term memory processes.

Conventionally, neurons are thought to be cellular units that process synaptic inputs into synaptic spikes. However, it is well known that neurons can also spike spontaneously and display a rich repertoire of firing properties with no apparent functional relevance e.g. in in vitro cortical slice preparations. In this talk, I will propose a hypothesis according to which intrinsic excitability in neurons may be a survival mechanism to minimize toxic byproducts of the cell’s energy metabolism. In neurons, this toxicity can arise when mitochondrial ATP production stalls due to limited ADP. Under these conditions, electrons deviate from the electron transport chain to produce reactive oxygen species, disrupting many cellular processes and challenging cell survival. To mitigate this, neurons may engage in ADP-producing metabolic spikes. I will explore the validity of this hypothesis using computational models that illustrate the implications of synaptic and metabolic spiking, especially in the context of substantia nigra pars compacta dopaminergic neurons and their degeneration in Parkinson's disease.

Neural circuits exhibit complex activity patterns, both spontaneously and in response to external stimuli. Information encoding and learning in neural circuits depend on the ability of time-varying stimuli to control spontaneous network activity. In particular, variability arising from the sensitivity to initial conditions of recurrent cortical circuits can limit the information conveyed about the sensory input. Spiking and firing rate network models can exhibit such sensitivity to initial conditions that are reflected in their dynamic entropy rate and attractor dimensionality computed from their full Lyapunov spectrum. I will show how chaos in both spiking and rate networks depends on biophysical properties of neurons and the statistics of time-varying stimuli. In spiking networks, increasing the input rate or coupling strength aids in controlling the driven target circuit, which is reflected in both a reduced trial-to-trial variability and a decreased dynamic entropy rate. With sufficiently strong input, a transition towards complete network state control occurs. Surprisingly, this transition does not coincide with the transition from chaos to stability but occurs at even larger values of external input strength. Controllability of spiking activity is facilitated when neurons in the target circuit have a sharp spike onset, thus a high speed by which neurons launch into the action potential. I will also discuss chaos and controllability in firing-rate networks in the balanced state. For these, external control of recurrent dynamics strongly depends on correlations in the input. This phenomenon was studied with a non-stationary dynamic mean-field theory that determines how the activity statistics and the largest Lyapunov exponent depend on frequency and amplitude of the input, recurrent coupling strength, and network size. This shows that uncorrelated inputs facilitate learning in balanced networks. The results highlight the potential of Lyapunov spectrum analysis as a diagnostic for machine learning applications of recurrent networks. They are also relevant in light of recent advances in optogenetics that allow for time-dependent stimulation of a select population of neurons.

Sensory systems reliably process incoming stimuli in spite of changes in context. Most recent models accredit this context invariance to an extraction of increasingly complex sensory features in hierarchical feedforward networks. Here, we study how context-invariant representations can be established by feedback rather than feedforward processing. We show that feedforward neural networks modulated by feedback can dynamically generate invariant sensory representations. The required feedback can be implemented as a slow and spatially diffuse gain modulation. The invariance is not present on the level of individual neurons, but emerges only on the population level. Mechanistically, the feedback modulation dynamically reorients the manifold of neural activity and thereby maintains an invariant neural subspace in spite of contextual variations. Our results highlight the importance of population-level analyses for understanding the role of feedback in flexible sensory processing.