A scale-dependent measure of system dimensionality

Predictions enable top-down pattern separation in the macaque face-processing hierarchy

Distinguishing faces requires well distinguishable neural activity patterns. Contextual information may separate neural representations, leading to enhanced identity recognition. Here, we use functional magnetic resonance imaging to investigate how predictions derived from contextual information affect the separability of neural activity patterns in the macaque face-processing system, a 3-level processing hierarchy in ventral visual cortex. We find that in the presence of predictions, early stages of this hierarchy exhibit well separable and high-dimensional neural geometries resembling those at the top of the hierarchy. This is accompanied by a systematic shift of tuning properties from higher to lower areas, endowing lower areas with higher-order, invariant representations instead of their feedforward tuning properties. Thus, top-down signals dynamically transform neural representations of faces into separable and high-dimensional neural geometries. Our results provide evidence how predictive context transforms flexible representational spaces to optimally use the computational resources provided by cortical processing hierarchies for better and faster distinction of facial identities.

A scalable spiking amygdala model that explains fear conditioning, extinction, renewal and generalization

The amygdala (AMY) is widely implicated in fear learning and fear behaviour, but it remains unclear how the many biological components present within AMY interact to achieve these abilities. Building on previous work, we hypothesize that individual AMY nuclei represent different quantities and that fear conditioning arises from error-driven learning on the synapses between AMY nuclei. We present a computational model of AMY that (a) recreates the divisions and connections between AMY nuclei and their constituent pyramidal and inhibitory neurons; (b) accommodates scalable high-dimensional representations of external stimuli; (c) learns to associate complex stimuli with the presence (or absence) of an aversive stimulus; (d) preserves feature information when mapping inputs to salience estimates, such that these estimates generalize to similar stimuli; and (e) induces a diverse profile of neural responses within each nucleus. Our model predicts (1) defensive responses and neural activities in several experimental conditions, (2) the consequence of artificially ablating particular nuclei and (3) the tendency to generalize defensive responses to novel stimuli. We test these predictions by comparing model outputs to neural and behavioural data from animals and humans. Despite the relative simplicity of our model, we find significant overlap between simulated and empirical data, which supports our claim that the model captures many of the neural mechanisms that support fear conditioning. We conclude by comparing our model to other computational models and by characterizing the theoretical relationship between pattern separation and fear generalization in healthy versus anxious individuals.

Low-dimensional criticality embedded in high-dimensional awake brain dynamics

Whether cortical neurons operate in a strongly or weakly correlated dynamical regime determines fundamental information processing capabilities and has fueled decades of debate. We offer a resolution of this debate; we show that two important dynamical regimes, typically considered incompatible, can coexist in the same local cortical circuit by separating them into two different subspaces. In awake mouse motor cortex, we find a low-dimensional subspace with large fluctuations consistent with criticality-a dynamical regime with moderate correlations and multi-scale information capacity and transmission. Orthogonal to this critical subspace, we find a high-dimensional subspace containing a desynchronized dynamical regime, which may optimize input discrimination. The critical subspace is apparent only at long timescales, which explains discrepancies among some previous studies. Using a computational model, we show that the emergence of a low-dimensional critical subspace at large timescales agrees with established theory of critical dynamics. Our results suggest that the cortex leverages its high dimensionality to multiplex dynamical regimes across different subspaces.

Physical effects of learning

Interacting many-body physical systems ranging from neural networks in the brain to folding proteins to self-modifying electrical circuits can learn to perform diverse tasks. This learning, both in nature and in engineered systems, can occur through evolutionary selection or through dynamical rules that drive active learning from experience. Here, we show that learning in linear physical networks with weak input signals leaves architectural imprints on the Hessian of a physical system. Compared to a generic organization of the system components, (a) the effective physical dimension of the response to inputs decreases, (b) the response of physical degrees of freedom to random perturbations (or system "susceptibility") increases, and (c) the low-eigenvalue eigenvectors of the Hessian align with the task. Overall, these effects embody the typical scenario for learning processes in physical systems in the weak input regime, suggesting ways of discovering whether a physical network may have been trained.

Disentangling Fact from Grid Cell Fiction in Trained Deep Path Integrators

Work on deep learning-based models of grid cells suggests that grid cells generically and robustly arise from optimizing networks to path integrate, i.e., track one's spatial position by integrating self-velocity signals. In previous work [27], we challenged this path integration hypothesis by showing that deep neural networks trained to path integrate almost always do so, but almost never learn grid-like tuning unless separately inserted by researchers via mechanisms unrelated to path integration. In this work, we restate the key evidence substantiating these insights, then address a response to [27] by authors of one of the path integration hypothesis papers [32]. First, we show that the response misinterprets our work, indirectly confirming our points. Second, we evaluate the response's preferred "unified theory for the origin of grid cells" in trained deep path integrators [31, 33, 34] and show that it is at best "occasionally suggestive," not exact or comprehensive. We finish by considering why assessing model quality through prediction of biological neural activity by regression of activity in deep networks [23] can lead to the wrong conclusions.

Improving reduced-order models through nonlinear decoding of projection-dependent outputs

A fundamental hindrance to building data-driven reduced-order models (ROMs) is the poor topological quality of a low-dimensional data projection. This includes behavior such as overlapping, twisting, or large curvatures or uneven data density that can generate nonuniqueness and steep gradients in quantities of interest (QoIs). Here, we employ an encoder-decoder neural network architecture for dimensionality reduction. We find that nonlinear decoding of projection-dependent QoIs, when embedded in a dimensionality reduction technique, promotes improved low-dimensional representations of complex multiscale and multiphysics datasets. When data projection (encoding) is affected by forcing accurate nonlinear reconstruction of the QoIs (decoding), we minimize nonuniqueness and gradients in representing QoIs on a projection. This in turn leads to enhanced predictive accuracy of a ROM. Our findings are relevant to a variety of disciplines that develop data-driven ROMs of dynamical systems such as reacting flows, plasma physics, atmospheric physics, or computational neuroscience.

Common population codes produce extremely nonlinear neural manifolds

Populations of neurons represent sensory, motor, and cognitive variables via patterns of activity distributed across the population. The size of the population used to encode a variable is typically much greater than the dimension of the variable itself, and thus, the corresponding neural population activity occupies lower-dimensional subsets of the full set of possible activity states. Given population activity data with such lower-dimensional structure, a fundamental question asks how close the low-dimensional data lie to a linear subspace. The linearity or nonlinearity of the low-dimensional structure reflects important computational features of the encoding, such as robustness and generalizability. Moreover, identifying such linear structure underlies common data analysis methods such as Principal Component Analysis (PCA). Here, we show that for data drawn from many common population codes the resulting point clouds and manifolds are exceedingly nonlinear, with the dimension of the best-fitting linear subspace growing at least exponentially with the true dimension of the data. Consequently, linear methods like PCA fail dramatically at identifying the true underlying structure, even in the limit of arbitrarily many data points and no noise.

Dimension of Activity in Random Neural Networks

Neural networks are high-dimensional nonlinear dynamical systems that process information through the coordinated activity of many connected units. Understanding how biological and machine-learning networks function and learn requires knowledge of the structure of this coordinated activity, information contained, for example, in cross covariances between units. Self-consistent dynamical mean field theory (DMFT) has elucidated several features of random neural networks-in particular, that they can generate chaotic activity-however, a calculation of cross covariances using this approach has not been provided. Here, we calculate cross covariances self-consistently via a two-site cavity DMFT. We use this theory to probe spatiotemporal features of activity coordination in a classic random-network model with independent and identically distributed (i.i.d.) couplings, showing an extensive but fractionally low effective dimension of activity and a long population-level timescale. Our formulas apply to a wide range of single-unit dynamics and generalize to non-i.i.d. couplings. As an example of the latter, we analyze the case of partially symmetric couplings.

Low dimensional criticality embedded in high dimensional awake brain dynamics

Whether cortical neurons operate in a strongly or weakly correlated dynamical regime determines fundamental information processing capabilities and has fueled decades of debate. Here we offer a resolution of this debate; we show that two important dynamical regimes, typically considered incompatible, can coexist in the same local cortical circuit by separating them into two different subspaces. In awake mouse motor cortex, we find a low-dimensional subspace with large fluctuations consistent with criticality - a dynamical regime with moderate correlations and multi-scale information capacity and transmission. Orthogonal to this critical subspace, we find a high-dimensional subspace containing a desynchronized dynamical regime, which may optimize input discrimination. The critical subspace is apparent only at long timescales, which explains discrepancies among some previous studies. Using a computational model, we show that the emergence of a low-dimensional critical subspace at large timescale agrees with established theory of critical dynamics. Our results suggest that cortex leverages its high dimensionality to multiplex dynamical regimes across different subspaces.

Predicting in vitro single-neuron firing rates upon pharmacological perturbation using Graph Neural Networks

Modern Graph Neural Networks (GNNs) provide opportunities to study the determinants underlying the complex activity patterns of biological neuronal networks. In this study, we applied GNNs to a large-scale electrophysiological dataset of rodent primary neuronal networks obtained by means of high-density microelectrode arrays (HD-MEAs). HD-MEAs allow for long-term recording of extracellular spiking activity of individual neurons and networks and enable the extraction of physiologically relevant features at the single-neuron and population level. We employed established GNNs to generate a combined representation of single-neuron and connectivity features obtained from HD-MEA data, with the ultimate goal of predicting changes in single-neuron firing rate induced by a pharmacological perturbation. The aim of the main prediction task was to assess whether single-neuron and functional connectivity features, inferred under baseline conditions, were informative for predicting changes in neuronal activity in response to a perturbation with Bicuculline, a GABA A receptor antagonist. Our results suggest that the joint representation of node features and functional connectivity, extracted from a baseline recording, was informative for predicting firing rate changes of individual neurons after the perturbation. Specifically, our implementation of a GNN model with inductive learning capability (GraphSAGE) outperformed other prediction models that relied only on single-neuron features. We tested the generalizability of the results on two additional datasets of HD-MEA recordings-a second dataset with cultures perturbed with Bicuculline and a dataset perturbed with the GABA A receptor antagonist Gabazine. GraphSAGE models showed improved prediction accuracy over other prediction models. Our results demonstrate the added value of taking into account the functional connectivity between neurons and the potential of GNNs to study complex interactions between neurons.