Path integration is essential for spatial navigation. Experimental studies have identified neural correlates for path integration, but exactly how the neural system accomplishes this computation remains unresolved. Here, we adopt recurrent neural networks (RNNs) trained to perform a path integration task to explore this issue. After training, we borrow neuroscience prior knowledge and methods to unfold the black box of the trained model, including: clarifying neuron types based on their receptive fields, dissecting information flows between neuron groups by pruning their connections, and analyzing internal dynamics of neuron groups using the attractor framework. Intriguingly, we uncover a hierarchical information processing pathway embedded in the RNN model, along which velocity information of an agent is first forwarded to band cells, band and grid cells then coordinate to carry out path integration, and finally grid cells output the agent location. Inspired by the RNN-based study, we construct a neural circuit model, in which band cells form one-dimensional (1D) continuous attractor neural networks (CANNs) and serve as upstream neurons to support downstream grid cells to carry out path integration in the 2D space. Our study challenges the conventional view of considering grid cells as the principal velocity integrator, and supports a neural circuit model with the hierarchy of band and grid cells.

Object recognition is often viewed as a feedforward, bottom-up process in machine learning, but in real neural systems, object recognition is a complicated process which involves the interplay between two signal pathways. One is the parvocellular pathway (P-pathway), which is slow and extracts fine features of objects; the other is the magnocellular pathway (M-pathway), which is fast and extracts coarse features of objects. It has been suggested that the interplay between the two pathways endows the neural system with the capacity of processing visual information rapidly, adaptively, and robustly. However, the underlying computational mechanism remains largely unknown. In this study, we build a two-pathway model to elucidate the computational properties associated with the interactions between two visual pathways. Specifically, we model two visual pathways using two convolution neural networks: one mimics the P-pathway, referred to as FineNet, which is deep, has small-size kernels, and receives detailed visual inputs; the other mimics the M-pathway, referred to as CoarseNet, which is shallow, has large-size kernels, and receives blurred visual inputs. We show that CoarseNet can learn from FineNet through imitation to improve its performance, FineNet can benefit from the feedback of CoarseNet to improve its robustness to noise; and the two pathways interact with each other to achieve rough-to-fine information processing. Using visual backward masking as an example, we further demonstrate that our model can explain visual cognitive behaviors that involve the interplay between two pathways. We hope that this study gives us insight into understanding the interaction principles between two visual pathways.

Hippocampal place cells of freely moving rodents display an intriguing temporal organization in their responses known as `theta phase precession', in which individual neurons fire at progressively earlier phases in successive theta cycles as the animal traverses the place fields. Recent experimental studies found that in addition to phase precession, many place cells also exhibit accompanied phase procession, but the underlying neural mechanism remains unclear. Here, we propose a neural circuit model to elucidate the generation of both kinds of phase shift in place cells' firing. Specifically, we consider a continuous attractor neural network (CANN) with feedback inhibition, which is inspired by the reciprocal interaction between the hippocampus and the medial septum. The feedback inhibition induces intrinsic mobility of the CANN which competes with the extrinsic mobility arising from the external drive. Their interplay generates an oscillatory tracking state, that is, the network bump state (resembling the decoded virtual position of the animal) sweeps back and forth around the external moving input (resembling the physical position of the animal). We show that this oscillatory tracking naturally explains the forward and backward sweeps of the decoded position during the animal's locomotion. At the single neuron level, the forward and backward sweeps account for, respectively, theta phase precession and procession. Furthermore, by tuning the feedback inhibition strength, we also explain the emergence of bimodal cells and unimodal cells, with the former having co-existed phase precession and procession, and the latter having only significant phase precession. We hope that this study facilitates our understanding of hippocampal temporal coding and lays foundation for unveiling their computational functions.

The brain performs probabilistic Bayesian inference to interpret the external world. The sampling-based view assumes that the brain represents the stimulus posterior distribution via samples of stochastic neuronal responses. Although the idea of sampling-based inference is appealing, it faces a critical challenge of whether stochastic sampling is fast enough to match the rapid computation of the brain. In this study, we explore how latent stimulus sampling can be accelerated in neural circuits. Specifically, we consider a canonical neural circuit model called continuous attractor neural networks (CANNs) and investigate how sampling-based inference of latent continuous variables is accelerated in CANNs. Intriguingly, we find that by including noisy adaptation in the neuronal dynamics, the CANN is able to speed up the sampling process significantly. We theoretically derive that the CANN with noisy adaptation implements the efficient sampling method called Hamiltonian dynamics with friction, where noisy adaption effectively plays the role of momentum. We theoretically analyze the sampling performances of the network and derive the condition when the acceleration has the maximum effect. Simulation results confirm our theoretical analyses. We further extend the model to coupled CANNs and demonstrate that noisy adaptation accelerates the sampling of the posterior distribution of multivariate stimuli. We hope that this study enhances our understanding of how Bayesian inference is realized in the brain.

Categorical relationships between objects are encoded as overlapped neural representations in the brain, where the more similar the objects are, the larger the correlations between their evoked neuronal responses. These representation correlations, however, inevitably incur interference when memories are retrieved. Here, we propose that neural feedback, which is widely observed in the brain but whose function remains largely unknown, contributes to disentangle neural correlations to improve information retrieval. We study a hierarchical neural network storing the hierarchical categorical information of objects, and information retrieval goes from rough-to-fine, aided by the push-pull neural feedback. We elucidate that the push and the pull components of the feedback suppress the interferences due to the representation correlations between objects from different and the same categories, respectively. Our model reproduces the push-pull phenomenon observed in neural data and sheds light on our understanding of the role of feedback in neural information processing.

Lévy flights describe a special class of random walks whose step sizes satisfy a power-law tailed distribution. As being an efficientsearching strategy in unknown environments, Lévy flights are widely observed in animal foraging behaviors. Recent studies further showed that human cognitive functions also exhibit the characteristics of Lévy flights. Despite being a general phenomenon, the neural mechanism at the circuit level for generating Lévy flights remains unresolved. Here, we investigate how Lévy flights can be achieved in attractor neural networks. To elucidate the underlying mechanism clearly, we first study continuous attractor neural networks (CANNs), and find that noisy neural adaptation, exemplified by spike frequency adaptation (SFA) in this work, can generate Lévy flights representing transitions of the network state in the attractor space. Specifically, the strength of SFA defines a travelling wave boundary, below which the network state displays local Brownian motion, and above which the network state displays long-jump motion. Noises in neural adaptation causes the network state to intermittently switch between these two motion modes, manifesting the characteristics of Lévy flights. We further extend the study to a general attractor neural network, and demonstrate that our model can explain the Lévy-flight phenomenon observed during free memory retrieval of humans. We hope that this study will give us insight into understanding the neural mechanism for optimal information processing in the brain.

Spatio-temporal information processing is fundamental in both brain functions and AI applications. Current strategies for spatio-temporal pattern recognition usually involve explicit feature extraction followed by feature aggregation, which requires a large amount of labeled data. In the present study, motivated by the subcortical visual pathway and early stages of the auditory pathway for motion and sound processing, we propose a novel brain-inspired computational model for generic spatio-temporal pattern recognition. The model consists of two modules, a reservoir module and a decision-making module. The former projects complex spatio-temporal patterns into spatially separated neural representations via its recurrent dynamics, the latter reads out neural representations via integrating information over time, and the two modules are linked together using known examples. Using synthetic data, we demonstrate that the model can extract the frequency and order information of temporal inputs. We apply the model to reproduce the looming pattern discrimination behavior as observed in experiments successfully. Furthermore, we apply the model to the gait recognition task, and demonstrate that our model accomplishes the recognition in an event-based manner and outperforms deep learning counterparts when training data is limited.

Experimental data has revealed that in addition to feedforward connections, there exist abundant feedback connections in a neural pathway. Although the importance of feedback in neural information processing has been widely recognized in the field, the detailed mechanism of how it works remains largely unknown. Here, we investigate the role of feedback in hierarchical information retrieval. Specifically, we consider a hierarchical network storing the hierarchical categorical information of objects, and information retrieval goes from rough to fine, aided by dynamical push-pull feedback from higher to lower layers. We elucidate that the push (positive) and pull (negative) feedbacks suppress the interferences due to neural correlations between different and the same categories, respectively, and their joint effect improves retrieval performance significantly. Our model agrees with the push-pull phenomenon observed in neural data and sheds light on our understanding of the role of feedback in neural information processing.