Time perception is fundamental in our daily life. An important feature of time perception is temporal scaling (TS): the ability to generate temporal sequences (e.g., movements) with different speeds. However, it is largely unknown about the mathematical principle underlying TS in the brain.

The information processing in the brain and embodied agents form a sensory-action loop to interact with the world. An important step in the loop is motion planning which selects motor actions based on the current world state and task need. In goal-directed navigation, the brain chooses and generates motor actions to bring the current state into the goal state. It is unclear about the neural circuit mechanism of motor action selection, nor its underlying theory. The present study formulates the motion planning as a Lie group operator search problem, and uses the 1D rotation group as an example to provide insight into general operator search in neural circuits.

In sampling-based Bayesian models of brain function, neural activities are assumed to be samples from probability distributions that the brain uses for probabilistic computation. However, a comprehensive understanding of how mechanistic models of neural dynamics can sample from arbitrary distributions is still lacking. We use tools from functional analysis and stochastic differential equations to explore the minimum architectural requirements for $\textit{recurrent}$ neural circuits to sample from complex distributions. We first consider the traditional sampling model consisting of a network of neurons whose outputs directly represent the samples ($\textit{sampler-only}$ network). We argue that synaptic current and firing-rate dynamics in the traditional model have limited capacity to sample from a complex probability distribution. We show that the firing rate dynamics of a recurrent neural circuit with a separate set of output units can sample from an arbitrary probability distribution. We call such circuits $\textit{reservoir-sampler networks}$ (RSNs). We propose an efficient training procedure based on denoising score matching that finds recurrent and output weights such that the RSN implements Langevin sampling. We empirically demonstrate our model's ability to sample from several complex data distributions using the proposed neural dynamics and discuss its applicability to developing the next generation of sampling-based Bayesian brain models.

Attractor networks require neuronal connections to be highly structured in order to maintain attractor states that represent information, while excitation and inhibition balanced networks (E-INNs) require neuronal connections to be random and sparse to generate irregular neuronal firings. Despite being regarded as canonical models of neural circuits, both types of networks are usually studied in isolation, and it remains unclear how they coexist in the brain, given their very different structural demands. In this study, we investigate the compatibility of continuous attractor neural networks (CANNs) and E-INNs. In line with recent experimental data, we find that a neural circuit can exhibit both the traits of CANNs and E-INNs if the neuronal synapses consist of two sets: one set is strong and fast for irregular firing, and the other set is weak and slow for attractor dynamics. Our results from simulations and theoretical analysis reveal that the network also exhibits enhanced performance compared to the case of using only one set of synapses, with accelerated convergence of attractor states and retained E-I balanced condition for localized input. We also apply the network model to solve a real-world tracking problem and demonstrate that it can track fast-moving objects well. We hope that this study provides insight into how structured neural computations are realized by irregular firings of neurons.

Major Depressive Disorder (MDD), affecting millions worldwide, exhibits complex pathophysiology manifested through disrupted brain network dynamics. Although graph neural networks that leverage neuroimaging data have shown promise in depression diagnosis, existing approaches are predominantly data-driven and operate largely as black-box models, lacking neurobiological interpretability. Here, we present NH-GCAT (Neurocircuitry-Inspired Hierarchical Graph Causal Attention Networks), a novel framework that bridges neuroscience domain knowledge with deep learning by explicitly and hierarchically modeling depression-specific mechanisms at different spatial scales. Our approach introduces three key technical contributions: (1) at the local brain regional level, we design a residual gated fusion module that integrates temporal blood oxygenation level dependent (BOLD) dynamics with functional connectivity patterns, specifically engineered to capture local depression-relevant low-frequency neural oscillations; (2) at the multi-regional circuit level, we propose a hierarchical circuit encoding scheme that aggregates regional node representations following established depression neurocircuitry organization, and (3) at the multi-circuit network level, we develop a variational latent causal attention mechanism that leverages a continuous probabilistic latent space to infer directed information flow among critical circuits, characterizing disease-altered whole-brain inter-circuit interactions. Rigorous leave-one-site-out cross-validation on the REST-meta-MDD dataset demonstrates NH-GCAT's state-of-the-art performance in depression classification, achieving a sample-size weighted-average accuracy of 73.3\% and an AUROC of 76.4\%, while simultaneously providing neurobiologically meaningful explanations.

Experience constantly shapes neural circuits through a variety of plasticity mechanisms. While the functional roles of some plasticity mechanisms are well-understood, it remains unclear how changes in neural excitability contribute to learning. Here, we develop a normative interpretation of intrinsic plasticity (IP) as a key component of unsupervised learning. We introduce a novel generative mixture model that accounts for the class-specific statistics of stimulus intensities, and we derive a neural circuit that learns the input classes and their intensities. We will analytically show that inference and learning for our generative model can be achieved by a neural circuit with intensity-sensitive neurons equipped with a specific form of IP. Numerical experiments verify our analytical derivations and show robust behavior for artificial and natural stimuli. Our results link IP to non-trivial input statistics, in particular the statistics of stimulus intensities for classes to which a neuron is sensitive. More generally, our work paves the way toward new classification algorithms that are robust to intensity variations.

Population activity measurement by calcium imaging can be combined with cellular resolution optogenetic activity perturbations to enable the mapping of neural connectivity in vivo .

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/