Computational Neuroscience seminars

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 representations in neural circuits. In this talk, we will demonstrate theoretical approaches that help describe how cognitive and behavioral task implementations emerge from the structure in neural populations and from biologically plausible neural networks. First, we 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 a perceptron’s capacity for linearly classifying object categories based on the underlying neural manifolds’ structural properties. Next, we will describe how such methods can, in fact, open the ‘black box’ of distributed neuronal circuits in a range of experimental neural datasets. In particular, our method overcomes the limitations of traditional dimensionality reduction techniques, as it operates directly on the high-dimensional representations, rather than relying on low-dimensionality assumptions for visualization. Furthermore, this method allows for simultaneous multi-level analysis, by measuring geometric properties in neural population data, and estimating the amount of task information embedded in the same population. These geometric frameworks are general and can be used across different brain areas and task modalities, as demonstrated in the work of ours and others, ranging from the visual cortex to parietal cortex to hippocampus, and from calcium imaging to electrophysiology to fMRI datasets. Finally, we will discuss our recent efforts to fully extend this multi-level description of neural populations, by (1) investigating how single neuron properties shape the representation geometry in early sensory areas, and by (2) understanding how task-efficient neural manifolds emerge in biologically-constrained neural networks. By extending our mathematical toolkit for analyzing representations underlying complex neuronal networks, we hope to contribute to the long-term challenge of understanding the neuronal basis of tasks and behaviors.

Efficient navigation requires animals to track their position, velocity and heading direction (HD). Some animals’ behavior suggests that they also track uncertainties about these navigational variables, and make strategic use of these uncertainties, in line with a Bayesian computation. Ring-attractor networks have been proposed to estimate and track these navigational variables, for instance in the HD system of the fruit fly Drosophila. However, such networks are not designed to incorporate a notion of uncertainty, and therefore seem unsuited to implement dynamic Bayesian inference. Here, we close this gap by showing that specifically tuned ring-attractor networks can track both a HD estimate and its associated uncertainty, thereby approximating a circular Kalman filter. We identified the network motifs required to integrate angular velocity observations, e.g., through self-initiated turns, and absolute HD observations, e.g., visual landmark inputs, according to their respective reliabilities, and show that these network motifs are present in the connectome of the Drosophila HD system. Specifically, our network encodes uncertainty in the amplitude of a localized bump of neural activity, thereby generalizing standard ring attractor models. In contrast to such standard attractors, however, proper Bayesian inference requires the network dynamics to operate in a regime away from the attractor state. More generally, we show that near-Bayesian integration is inherent in generic ring attractor networks, and that their amplitude dynamics can account for close-to-optimal reliability weighting of external evidence for a wide range of network parameters. This only holds, however, if their connection strengths allow the network to sufficiently deviate from the attractor state. Overall, our work offers a novel interpretation of ring attractor networks as implementing dynamic Bayesian integrators. We further provide a principled theoretical foundation for the suggestion that the Drosophila HD system may implement Bayesian HD tracking via ring attractor dynamics.

Animals exhibit remarkable learning capabilities with little direct supervision. Likewise, self-supervised learning is an emergent paradigm in artificial intelligence, closing the performance gap to supervised learning. In the context of biology, self-supervised learning corresponds to a setting where one sense or specific stimulus may serve as a supervisory signal for another. After learning, the latter can be used to predict the former. On the implementation level, it has been demonstrated that such predictive learning can occur at the single neuron level, in compartmentalized neurons that separate and associate information from different streams. We demonstrate the power such self-supervised learning over unsupervised (Hebb-like) learning rules, which depend heavily on stimulus statistics, in two examples: First, in the context of animal navigation where predictive learning can associate internal self-motion information always available to the animal with external visual landmark information, leading to accurate path-integration in the dark. We focus on the well-characterized fly head direction system and show that our setting learns a connectivity strikingly similar to the one reported in experiments. The mature network is a quasi-continuous attractor and reproduces key experiments in which optogenetic stimulation controls the internal representation of heading, and where the network remaps to integrate with different gains. Second, we show that incorporating global gating by reward prediction errors allows the same setting to learn conditioning at the neuronal level with mixed selectivity. At its core, conditioning entails associating a neural activity pattern induced by an unconditioned stimulus (US) with the pattern arising in response to a conditioned stimulus (CS). Solving the generic problem of pattern-to-pattern associations naturally leads to emergent cognitive phenomena like blocking, overshadowing, saliency effects, extinction, interstimulus interval effects etc. Surprisingly, we find that the same network offers a reductionist mechanism for causal inference by resolving the post hoc, ergo propter hoc fallacy.

Current SNNs studies frequently ignore dendrites, the thin membranous extensions of biological neurons that receive and preprocess nearly all synaptic inputs in the brain. However, decades of experimental and theoretical research suggest that dendrites possess compelling computational capabilities that greatly influence neuronal and circuit functions. Notably, standard point-neuron networks cannot adequately capture most hallmark dendritic properties. Meanwhile, biophysically detailed neuron models are impractical for large-network simulations due to their complexity, and high computational cost. For this reason, we introduce Dendrify, a new theoretical framework combined with an open-source Python package (compatible with Brian2) that facilitates the development of bioinspired SNNs. Dendrify, through simple commands, can generate reduced compartmental neuron models with simplified yet biologically relevant dendritic and synaptic integrative properties. Such models strike a good balance between flexibility, performance, and biological accuracy, allowing us to explore dendritic contributions to network-level functions while paving the way for developing more realistic neuromorphic systems.

In this talk, we will examine human behavior from the perspective of the choices we make every day. We will study the role of the brain in enabling these decisions and discuss some simple computational models of decision making and the neural basis. Towards the end, we will have a short, interactive session to engage in some easy decisions that will help us discover our own biases.

Flexible computation is a hallmark of intelligent behavior. Yet, little is known about how neural networks contextually reconfigure for different computations. Humans are able to perform a new task without extensive training, presumably through the composition of elementary processes that were previously learned. Cognitive scientists have long hypothesized the possibility of a compositional neural code, where complex neural computations are made up of constituent components; however, the neural substrate underlying this structure remains elusive in biological and artificial neural networks. Here we identified an algorithmic neural substrate for compositional computation through the study of multitasking artificial recurrent neural networks. Dynamical systems analyses of networks revealed learned computational strategies that mirrored the modular subtask structure of the task-set used for training. Dynamical motifs such as attractors, decision boundaries and rotations were reused across different task computations. For example, tasks that required memory of a continuous circular variable repurposed the same ring attractor. We show that dynamical motifs are implemented by clusters of units and are reused across different contexts, allowing for flexibility and generalization of previously learned computation. Lesioning these clusters resulted in modular effects on network performance: a lesion that destroyed one dynamical motif only minimally perturbed the structure of other dynamical motifs. Finally, modular dynamical motifs could be reconfigured for fast transfer learning. After slow initial learning of dynamical motifs, a subsequent faster stage of learning reconfigured motifs to perform novel tasks. This work contributes to a more fundamental understanding of compositional computation underlying flexible general intelligence in neural systems. We present a conceptual framework that establishes dynamical motifs as a fundamental unit of computation, intermediate between the neuron and the network. As more whole brain imaging studies record neural activity from multiple specialized systems simultaneously, the framework of dynamical motifs will guide questions about specialization and generalization across brain regions.

Neuronal network computation and computation by avalanche supporting networks are of interest to the fields of physics, computer science (computation theory as well as statistical or machine learning) and neuroscience. Here we show that computation of complex Boolean functions arises spontaneously in threshold networks as a function of connectivity and antagonism (inhibition), computed by logic automata (motifs) in the form of computational cascades. We explain the emergent inverse relationship between the computational complexity of the motifs and their rank-ordering by function probabilities due to motifs, and its relationship to symmetry in function space. We also show that the optimal fraction of inhibition observed here supports results in computational neuroscience, relating to optimal information processing.

To move efficiently, animals must continuously work out their x,y,z positions with respect to real-world objects, and many animals have a pair of eyes to achieve this. How photoreceptors actively sample the eyes’ optical image disparity is not understood because this fundamental information-limiting step has not been investigated in vivo over the eyes’ whole sampling matrix. This integrative multiscale study will advance our current understanding of stereopsis from static image disparity comparison to a morphodynamic active sampling theory. It shows how photomechanical photoreceptor microsaccades enable Drosophila superresolution three-dimensional vision and proposes neural computations for accurately predicting these flies’ depth-perception dynamics, limits, and visual behaviors.

An object’s colour, brightness and pattern are all influenced by its surroundings, and a number of visual phenomena and “illusions” have been discovered that highlight these often dramatic effects. Explanations for these phenomena range from low-level neural mechanisms to high-level processes that incorporate contextual information or prior knowledge. Importantly, few of these phenomena can currently be accounted for when measuring an object’s perceived colour. Here we ask to what extent colour appearance is predicted by a model based on the principle of coding efficiency. The model assumes that the image is encoded by noisy spatio-chromatic filters at one octave separations, which are either circularly symmetrical or oriented. Each spatial band’s lower threshold is set by the contrast sensitivity function, and the dynamic range of the band is a fixed multiple of this threshold, above which the response saturates. Filter outputs are then reweighted to give equal power in each channel for natural images. We demonstrate that the model fits human behavioural performance in psychophysics experiments, and also primate retinal ganglion responses. Next we systematically test the model’s ability to qualitatively predict over 35 brightness and colour phenomena, with almost complete success. This implies that contrary to high-level processing explanations, much of colour appearance is potentially attributable to simple mechanisms evolved for efficient coding of natural images, and is a basis for modelling the vision of humans and other animals.

This session is a double feature of the Cologne Theoretical Neuroscience Forum and the Institute of Neuroscience and Medicine (INM-6) Computational and Systems Neuroscience of the Jülich Research Center.

Which nodes in a brain network causally influence one another, and how do such interactions utilize the underlying structural connectivity? One of the fundamental goals of neuroscience is to pinpoint such causal relations. Conventionally, these relationships are established by manipulating a node while tracking changes in another node. A causal role is then assigned to the first node if this intervention led to a significant change in the state of the tracked node. In this presentation, I use a series of intuitive thought experiments to demonstrate the methodological shortcomings of the current ‘causation via manipulation’ framework. Namely, a node might causally influence another node, but how much and through which mechanistic interactions? Therefore, establishing a causal relationship, however reliable, does not provide the proper causal understanding of the system, because there often exists a wide range of causal influences that require to be adequately decomposed. To do so, I introduce a game-theoretical framework called Multi-perturbation Shapley value Analysis (MSA). Then, I present our work in which we employed MSA on an Echo State Network (ESN), quantified how much its nodes were influencing each other, and compared these measures with the underlying synaptic strength. We found that: 1. Even though the network itself was sparse, every node could causally influence other nodes. In this case, a mere elucidation of causal relationships did not provide any useful information. 2. Additionally, the full knowledge of the structural connectome did not provide a complete causal picture of the system either, since nodes frequently influenced each other indirectly, that is, via other intermediate nodes. Our results show that just elucidating causal contributions in complex networks such as the brain is not sufficient to draw mechanistic conclusions. Moreover, quantifying causal interactions requires a systematic and extensive manipulation framework. The framework put forward here benefits from employing neural network models, and in turn, provides explainability for them.

Spiking recurrent neural networks (RNNs) are a promising tool for solving a wide variety of complex cognitive and motor tasks, due to their rich temporal dynamics and sparse processing. However training spiking RNNs on dedicated neuromorphic hardware is still an open challenge. This is due mainly to the lack of local, hardware-friendly learning mechanisms that can solve the temporal credit assignment problem and ensure stable network dynamics, even when the weight resolution is limited. These challenges are further accentuated, if one resorts to using memristive devices for in-memory computing to resolve the von-Neumann bottleneck problem, at the expense of a substantial increase in variability in both the computation and the working memory of the spiking RNNs. In this talk, I will present our recent work where we introduced a PyTorch simulation framework of memristive crossbar arrays that enables accurate investigation of such challenges. I will show that recently proposed e-prop learning rule can be used to train spiking RNNs whose weights are emulated in the presented simulation framework. Although e-prop locally approximates the ideal synaptic updates, it is difficult to implement the updates on the memristive substrate due to substantial device non-idealities. I will mention several widely adapted weight update schemes that primarily aim to cope with these device non-idealities and demonstrate that accumulating gradients can enable online and efficient training of spiking RNN on memristive substrates.

Many decisions under uncertainty entail dynamic belief updating: multiple pieces of evidence informing about the state of the environment are accumulated across time to infer the environmental state, and choose a corresponding action. Traditionally, this process has been conceptualized as a linear and perfect (i.e., without loss) integration of sensory information along purely feedforward sensory-motor pathways. Yet, natural environments can undergo hidden changes in their state, which requires a non-linear accumulation of decision evidence that strikes a tradeoff between stability and flexibility in response to change. How this adaptive computation is implemented in the brain has remained unknown. In this talk, I will present an approach that my laboratory has developed to identify evidence accumulation signatures in human behavior and neural population activity (measured with magnetoencephalography, MEG), across a large number of cortical areas. Applying this approach to data recorded during visual evidence accumulation tasks with change-points, we find that behavior and neural activity in frontal and parietal regions involved in motor planning exhibit hallmarks signatures of adaptive evidence accumulation. The same signatures of adaptive behavior and neural activity emerge naturally from simulations of a biophysically detailed model of a recurrent cortical microcircuit. The MEG data further show that decision dynamics in parietal and frontal cortex are mirrored by a selective modulation of the state of early visual cortex. This state modulation is (i) specifically expressed in the alpha frequency-band, (ii) consistent with feedback of evolving belief states from frontal cortex, (iii) dependent on the environmental volatility, and (iv) amplified by pupil-linked arousal responses during evidence accumulation. Together, our findings link normative decision computations to recurrent cortical circuit dynamics and highlight the adaptive nature of decision-related long-range feedback processing in the brain.

Change is ubiquitous in living beings. In particular, the connectome and neural representations can change. Nevertheless behaviors and memories often persist over long times. In a standard model, associative memories are represented by assemblies of strongly interconnected neurons. For faithful storage these assemblies are assumed to consist of the same neurons over time. We propose a contrasting memory model with complete temporal remodeling of assemblies, based on experimentally observed changes of synapses and neural representations. The assemblies drift freely as noisy autonomous network activity or spontaneous synaptic turnover induce neuron exchange. The exchange can be described analytically by reduced, random walk models derived from spiking neural network dynamics or from first principles. The gradual exchange allows activity-dependent and homeostatic plasticity to conserve the representational structure and keep inputs, outputs and assemblies consistent. This leads to persistent memory. Our findings explain recent experimental results on temporal evolution of fear memory representations and suggest that memory systems need to be understood in their completeness as individual parts may constantly change.

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.

Working memory involves the short-term maintenance of information and is critical in many tasks. The neural circuit dynamics underlying working memory remain poorly understood, with different aspects of prefrontal cortical (PFC) responses explained by different putative mechanisms. By mathematical analysis, numerical simulations, and using recordings from monkey PFC, we investigate a critical but hitherto ignored aspect of working memory dynamics: information loading. We find that, contrary to common assumptions, optimal information loading involves inputs that are largely orthogonal, rather than similar, to the persistent activities observed during memory maintenance. Using a novel, theoretically principled metric, we show that PFC exhibits the hallmarks of optimal information loading and we find that such dynamics emerge naturally as a dynamical strategy in task-optimized recurrent neural networks. Our theory unifies previous, seemingly conflicting theories of memory maintenance based on attractor or purely sequential dynamics, and reveals a normative principle underlying the widely observed phenomenon of dynamic coding in PFC.

To generate brain circuits that are both flexible and stable requires the coordination of powerful developmental mechanisms acting at different scales, including activity-dependent synaptic plasticity and changes in single neuron properties. The brain prepares to efficiently compute information and reliably generate behavior during early development without any prior sensory experience but through patterned spontaneous activity. After the onset of sensory experience, ongoing activity continues to modify sensory circuits, and plays an important functional role in the mature brain. Using quantitative data analysis, experiment-driven theory and computational modeling, I will present a framework for how neural circuits are built and organized during early postnatal development into functional units, and how they are modified by intact and perturbed sensory-evoked activity. Inspired by experimental data from sensory cortex, I will then show how neural circuits use the resulting non-random connectivity to flexibly gate a network’s response, providing a mechanism for routing information.