Lévy flights describe aspecial class of random walks whose step sizes satisfy a power-lawtaileddistribution.

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.

Large language model (LLM)-based agentic frameworks increasingly adopt the paradigm of dynamically generating task-specific agents. We suggest that not only agents but also specialized software modules for scientific and engineering tasks can be generated on demand. We demonstrate this concept in the field of solid mechanics. There, so-called constitutive models are required to describe the relationship between mechanical stress and body deformation. Constitutive models are essential for both the scientific understanding and industrial application of materials. However, even recent data-driven methods of constitutive modeling, such as constitutive artificial neural networks (CANNs), still require substantial expert knowledge and human labor. We present a framework in which an LLM generates a CANN on demand, tailored to a given material class and dataset provided by the user. The framework covers LLM-based architecture selection, integration of physical constraints, and complete code generation. Evaluation on three benchmark problems demonstrates that LLM-generated CANNs achieve accuracy comparable to or greater than manually engineered counterparts, while also exhibiting reliable generalization to unseen loading scenarios and extrapolation to large deformations. These findings indicate that LLM-based generation of physics-constrained neural networks can substantially reduce the expertise required for constitutive modeling and represent a step toward practical end-to-end automation.

The brain's Path Integration (PI) mechanism offers substantial guidance and inspiration for Brain-Inspired Navigation (BIN). However, the PI capability constructed by the Continuous Attractor Neural Networks (CANNs) in most existing BIN studies exhibits significant computational redundancy, and its operational efficiency needs to be improved; otherwise, it will not be conducive to the practicality of BIN technology. To address this, this paper proposes an efficient PI approach using representation learning models to replicate CANN neurodynamic patterns. This method successfully replicates the neurodynamic patterns of CANN-modeled Head Direction Cells (HDCs) and Grid Cells (GCs) using lightweight Artificial Neural Networks (ANNs). These ANN-reconstructed HDC and GC models are then integrated to achieve brain-inspired PI for Dead Reckoning (DR). Benchmark tests in various environments, compared with the well-known NeuroSLAM system, demonstrate that this work not only accurately replicates the neurodynamic patterns of navigation cells but also matches NeuroSLAM in positioning accuracy. Moreover, efficiency improvements of approximately 17.5% on the general-purpose device and 40~50% on the edge device were observed, compared with NeuroSLAM. This work offers a novel implementation strategy to enhance the practicality of BIN technology and holds potential for further extension.

We propose Grid-like Code Quantization (GCQ), a brain-inspired method for compressing observation-action sequences into discrete representations using grid-like patterns in attractor dynamics. Unlike conventional vector quantization approaches that operate on static inputs, GCQ performs spatiotemporal compression through an action-conditioned codebook, where codewords are derived from continuous attractor neural networks and dynamically selected based on actions. This enables GCQ to jointly compress space and time, serving as a unified world model. The resulting representation supports long-horizon prediction, goal-directed planning, and inverse modeling. Experiments across diverse tasks demonstrate GCQ's effectiveness in compact encoding and downstream performance. Our work offers both a computational tool for efficient sequence modeling and a theoretical perspective on the formation of grid-like codes in neural systems.

To extract motion information, the brain needs to compensate for time delays that are ubiquitous in neural signal transmission and processing. Here we propose a simple yet effective mechanism to implement anticipative tracking in neural systems. The proposed mechanism utilizes the property of spike-frequency adaptation (SFA), a feature widely observed in neuronal responses. We employ continuous attractor neural networks (CANNs) as the model to describe the tracking behaviors in neural systems. Incorporating SFA, a CANN exhibits intrinsic mobility, manifested by the ability of the CANN to support self-sustained travelling waves. In tracking a moving stimulus, the interplay between the external drive and the intrinsic mobility of the network determines the tracking performance. Interestingly, we find that the regime of anticipation effectively coincides with the regime where the intrinsic speed of the travelling wave exceeds that of the external drive. Depending on the SFA amplitudes, the network can achieve either perfect tracking, with zero-lag to the input, or perfect anticipative tracking, with a constant leading time to the input. Our model successfully reproduces experimentally observed anticipative tracking behaviors, and sheds light on our understanding of how the brain processes motion information in a timely manner.

To extract motion information, the brain needs to compensate for time delays that are ubiquitous in neural signal transmission and processing. Here we propose a simple yet effective mechanism to implement anticipative tracking in neural systems. The proposed mechanism utilizes the property of spike-frequency adaptation (SFA), a feature widely observed in neuronal responses. We employ continuous attractor neural networks (CANNs) as the model to describe the tracking behaviors in neural systems. Incorporating SFA, a CANN exhibits intrinsic mobility, manifested by the ability of the CANN to hold self-sustained travelling waves. In tracking a moving stimulus, the interplay between the external drive and the intrinsic mobility of the network determines the tracking performance. Interestingly, we find that the regime of anticipation effectively coincides with the regime where the intrinsic speed of the travelling wave exceeds that of the external drive. Depending on the SFA amplitudes, the network can achieve either perfect tracking, with zero-lag to the input, or perfect anticipative tracking, with a constant leading time to the input. Our model successfully reproduces experimentally observed anticipative tracking behaviors, and sheds light on our understanding of how the brain processes motion information in a timely manner.