Gradient-based learning drives robust representations in recurrent neural networks by balancing compression and expansion

The cognitive critical brain: Modulation of criticality in perception-related cortical regions

The constantly evolving world necessitates a brain that can swiftly adapt and respond to rapid changes. The brain, conceptualized as a system performing cognitive functions through collective neural activity, has been shown to maintain a resting state characterized by near-critical neural dynamics, positioning it to effectively respond to external stimuli. However, how near-criticality is dynamically modulated during task performance remains insufficiently understood. In this study, we utilized the prototypical Ising Hamiltonian model to investigate the modulation of near-criticality in neural activity at the cortical subsystem level during perceptual tasks. Specifically, we simulated 2D-Ising models in silico using structural MRI data and empirically estimated the system's state in vivo using functional MRI data. We first replicated previous findings that the resting state is typically near-critical as captured by the Ising model. Importantly, we observed heterogeneous changes in criticality across cortical subsystems during a naturalistic movie-watching task, with visual and auditory regions fine-tuned closer to criticality. A more fine-grained analysis of the ventral temporal cortex during an object recognition task further revealed that only regions selectively responsive to a specific object category were tuned closer to criticality when processing that object category. In conclusion, our study provides empirical evidence from the domain of perception supporting the cognitive critical brain hypothesis that modulating the criticality of subsystems within the brain's hierarchical and modular organization may be a fundamental mechanism for achieving diverse cognitive functions.

Chaotic recurrent neural networks for brain modelling: A review

Even in the absence of external stimuli, the brain is spontaneously active. Indeed, most cortical activity is internally generated by recurrence. Both theoretical and experimental studies suggest that chaotic dynamics characterize this spontaneous activity. While the precise function of brain chaotic activity is still puzzling, we know that chaos confers many advantages. From a computational perspective, chaos enhances the complexity of network dynamics. From a behavioural point of view, chaotic activity could generate the variability required for exploration. Furthermore, information storage and transfer are maximized at the critical border between order and chaos. Despite these benefits, many computational brain models avoid incorporating spontaneous chaotic activity due to the challenges it poses for learning algorithms. In recent years, however, multiple approaches have been proposed to overcome this limitation. As a result, many different algorithms have been developed, initially within the reservoir computing paradigm. Over time, the field has evolved to increase the biological plausibility and performance of the algorithms, sometimes going beyond the reservoir computing framework. In this review article, we examine the computational benefits of chaos and the unique properties of chaotic recurrent neural networks, with a particular focus on those typically utilized in reservoir computing. We also provide a detailed analysis of the algorithms designed to train chaotic RNNs, tracing their historical evolution and highlighting key milestones in their development. Finally, we explore the applications and limitations of chaotic RNNs for brain modelling, consider their potential broader impacts beyond neuroscience, and outline promising directions for future research.

A transient high-dimensional geometry affords stable conjunctive subspaces for efficient action selection

Flexible action selection requires cognitive control mechanisms capable of mapping the same inputs to different output actions depending on the context. From a neural state-space perspective, this requires a control representation that separates similar input neural states by context. Additionally, for action selection to be robust and time-invariant, information must be stable in time, enabling efficient readout. Here, using EEG decoding methods, we investigate how the geometry and dynamics of control representations constrain flexible action selection in the human brain. Participants performed a context-dependent action selection task. A forced response procedure probed action selection different states in neural trajectories. The result shows that before successful responses, there is a transient expansion of representational dimensionality that separated conjunctive subspaces. Further, the dynamics stabilizes in the same time window, with entry into this stable, high-dimensional state predictive of individual trial performance. These results establish the neural geometry and dynamics the human brain needs for flexible control over behavior.

Practice Reshapes the Geometry and Dynamics of Task-tailored Representations

Extensive practice makes task performance more efficient and precise, leading to automaticity. However, theories of automaticity differ on which levels of task representations (e.g., low-level features, stimulus-response mappings, or high-level conjunctive memories of individual events) change with practice, despite predicting the same pattern of improvement (e.g., power law of practice). To resolve this controversy, we built on recent theoretical advances in understanding computations through neural population dynamics. Specifically, we hypothesized that practice optimizes the neural representational geometry of task representations to minimally separate the highest-level task contingencies needed for successful performance. This involves efficiently reaching conjunctive neural states that integrate task-critical features nonlinearly while abstracting over non-critical dimensions. To test this hypothesis, human participants (n = 40) engaged in extensive practice of a simple, context-dependent action selection task over 3 days while recording EEG. During initial rapid improvement in task performance, representations of the highest-level, context-specific conjunctions of task-features were enhanced as a function of the number of successful episodes. Crucially, only enhancement of these conjunctive representations, and not lower-order representations, predicted the power-law improvement in performance. Simultaneously, over sessions, these conjunctive neural states became more stable earlier in time and more aligned, abstracting over redundant task features, which correlated with offline performance gain in reducing switch costs. Thus, practice optimizes the dynamic representational geometry as task-tailored neural states that minimally tesselate the task space, taming their high-dimensionality.

A Transient High-dimensional Geometry Affords Stable Conjunctive Subspaces for Efficient Action Selection

Flexible action selection requires cognitive control mechanisms capable of mapping the same inputs to different output actions depending on the context. From a neural state-space perspective, this requires a control representation that separates similar input neural states by context. Additionally, for action selection to be robust and time-invariant, information must be stable in time, enabling efficient readout. Here, using EEG decoding methods, we investigate how the geometry and dynamics of control representations constrain flexible action selection in the human brain. Participants performed a context-dependent action selection task. A forced response procedure probed action selection different states in neural trajectories. The result shows that before successful responses, there is a transient expansion of representational dimensionality that separated conjunctive subspaces. Further, the dynamics stabilizes in the same time window, with entry into this stable, high-dimensional state predictive of individual trial performance. These results establish the neural geometry and dynamics the human brain needs for flexible control over behavior.

Transition to chaos separates learning regimes and relates to measure of consciousness in recurrent neural networks

Recurrent neural networks exhibit chaotic dynamics when the variance in their connection strengths exceed a critical value. Recent work indicates connection variance also modulates learning strategies; networks learn "rich" representations when initialized with low coupling and "lazier" solutions with larger variance. Using Watts-Strogatz networks of varying sparsity, structure, and hidden weight variance, we find that the critical coupling strength dividing chaotic from ordered dynamics also differentiates rich and lazy learning strategies. Training moves both stable and chaotic networks closer to the edge of chaos, with networks learning richer representations before the transition to chaos. In contrast, biologically realistic connectivity structures foster stability over a wide range of variances. The transition to chaos is also reflected in a measure that clinically discriminates levels of consciousness, the perturbational complexity index (PCIst). Networks with high values of PCIst exhibit stable dynamics and rich learning, suggesting a consciousness prior may promote rich learning. The results suggest a clear relationship between critical dynamics, learning regimes and complexity-based measures of consciousness.

Chaotic neural dynamics facilitate probabilistic computations through sampling

Cortical neurons exhibit highly variable responses over trials and time. Theoretical works posit that this variability arises potentially from chaotic network dynamics of recurrently connected neurons. Here, we demonstrate that chaotic neural dynamics, formed through synaptic learning, allow networks to perform sensory cue integration in a sampling-based implementation. We show that the emergent chaotic dynamics provide neural substrates for generating samples not only of a static variable but also of a dynamical trajectory, where generic recurrent networks acquire these abilities with a biologically plausible learning rule through trial and error. Furthermore, the networks generalize their experience in the stimulus-evoked samples to the inference without partial or all sensory information, which suggests a computational role of spontaneous activity as a representation of the priors as well as a tractable biological computation for marginal distributions. These findings suggest that chaotic neural dynamics may serve for the brain function as a Bayesian generative model.

Emergent neural dynamics and geometry for generalization in a transitive inference task

Relational cognition-the ability to infer relationships that generalize to novel combinations of objects-is fundamental to human and animal intelligence. Despite this importance, it remains unclear how relational cognition is implemented in the brain due in part to a lack of hypotheses and predictions at the levels of collective neural activity and behavior. Here we discovered, analyzed, and experimentally tested neural networks (NNs) that perform transitive inference (TI), a classic relational task (if A > B and B > C, then A > C). We found NNs that (i) generalized perfectly, despite lacking overt transitive structure prior to training, (ii) generalized when the task required working memory (WM), a capacity thought to be essential to inference in the brain, (iii) emergently expressed behaviors long observed in living subjects, in addition to a novel order-dependent behavior, and (iv) expressed different task solutions yielding alternative behavioral and neural predictions. Further, in a large-scale experiment, we found that human subjects performing WM-based TI showed behavior inconsistent with a class of NNs that characteristically expressed an intuitive task solution. These findings provide neural insights into a classical relational ability, with wider implications for how the brain realizes relational cognition.

Quantifying and Maximizing the Information Flux in Recurrent Neural Networks

Free-running recurrent neural networks (RNNs), especially probabilistic models, generate an ongoing information flux that can be quantified with the mutual information I[x→(t),x→(t+1)] between subsequent system states x→. Although previous studies have shown that I depends on the statistics of the network's connection weights, it is unclear how to maximize I systematically and how to quantify the flux in large systems where computing the mutual information becomes intractable. Here, we address these questions using Boltzmann machines as model systems. We find that in networks with moderately strong connections, the mutual information I is approximately a monotonic transformation of the root-mean-square averaged Pearson correlations between neuron pairs, a quantity that can be efficiently computed even in large systems. Furthermore, evolutionary maximization of I[x→(t),x→(t+1)] reveals a general design principle for the weight matrices enabling the systematic construction of systems with a high spontaneous information flux. Finally, we simultaneously maximize information flux and the mean period length of cyclic attractors in the state-space of these dynamical networks. Our results are potentially useful for the construction of RNNs that serve as short-time memories or pattern generators.

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.

Behavioral Classification of Sequential Neural Activity Using Time Varying Recurrent Neural Networks

Shifts in data distribution across time can strongly affect early classification of time-series data. When decoding behavior from neural activity, early detection of behavior may help in devising corrective neural stimulation before the onset of behavior. Recurrent Neural Networks (RNNs) are common models for sequence data. However, standard RNNs are not able to handle data with temporal distributional shifts to guarantee robust classification across time. To enable the network to utilize all temporal features of the neural input data, and to enhance the memory of an RNN, we propose a novel approach: RNNs with time-varying weights, here termed Time-Varying RNNs (TV-RNNs). These models are able to not only predict the class of the time-sequence correctly but also lead to accurate classification earlier in the sequence than standard RNNs. In this work, we focus on early sequential classification of brain-wide neural activity across time using TV-RNNs applied to a variety of neural data from mice and humans, as subjects perform motor tasks. Finally, we explore the contribution of different brain regions on behavior classification using SHapley Additive exPlanation (SHAP) value, and find that the somatosensory and premotor regions play a large role in behavioral classification.