Brain-Inspired Capture: Evidence-Driven Neuromimetic Perceptual Simulation for Visual Decoding

Visual decoding of neurophysiological signals is a critical challenge for brain-computer interfaces (BCIs) and computational neuroscience. However, current approaches are often constrained by the systematic and stochastic gaps between neural and visual modalities, largely neglecting the intrinsic computational mechanisms of the Human Visual System (HVS). To address this, we propose Brain-Inspired Capture (BI-Cap), a neuromimetic perceptual simulation paradigm that aligns these modalities by emulating HVS processing. Specifically, we construct a neuromimetic pipeline comprising four biologically plausible dynamic and static transformations, coupled with Mutual Information (MI)-guided dynamic blur regulation to simulate adaptive visual processing. Furthermore, to mitigate the inherent non-stationarity of neural activity, we introduce an evidence-driven latent space representation. This formulation explicitly models uncertainty, thereby ensuring robust neural embeddings. Extensive evaluations on zero-shot brain-to-image retrieval across two public benchmarks demonstrate that BI-Cap substantially outperforms state-of-the-art methods, achieving relative gains of 9.2\% and 8.0\%, respectively. We have released the source code on GitHub through the link https://github.com/flysnow1024/BI-Cap.

Hypergraph Neural Diffusion: A PDE-Inspired Framework for Hypergraph Message Passing

Hypergraph neural networks (HGNNs) have shown remarkable potential in modeling high-order relationships that naturally arise in many real-world data domains. However, existing HGNNs often suffer from shallow propagation, oversmoothing, and limited adaptability to complex hypergraph structures. In this paper, we propose Hypergraph Neural Diffusion (HND), a novel framework that unifies nonlinear diffusion equations with neural message passing on hypergraphs. HND is grounded in a continuous-time hypergraph diffusion equation, formulated via hypergraph gradient and divergence operators, and modulated by a learnable, structure-aware coefficient matrix over hyperedge-node pairs. This partial differential equation (PDE) based formulation provides a physically interpretable view of hypergraph learning, where feature propagation is understood as an anisotropic diffusion process governed by local inconsistency and adaptive diffusion coefficient. From this perspective, neural message passing becomes a discretized gradient flow that progressively minimizes a diffusion energy functional. We derive rigorous theoretical guarantees, including energy dissipation, solution boundedness via a discrete maximum principle, and stability under explicit and implicit numerical schemes. The HND framework supports a variety of integration strategies such as non-adaptive-step (like Runge-Kutta) and adaptive-step solvers, enabling the construction of deep, stable, and interpretable architectures. Extensive experiments on benchmark datasets demonstrate that HND achieves competitive performance. Our results highlight the power of PDE-inspired design in enhancing the stability, expressivity, and interpretability of hypergraph learning.

Tackling Over-smoothing on Hypergraphs: A Ricci Flow-guided Neural Diffusion Approach

Hypergraph neural networks (HGNNs) have demonstrated strong capabilities in modeling complex higher-order relationships. However, existing HGNNs often suffer from over-smoothing as the number of layers increases and lack effective control over message passing among nodes. Inspired by the theory of Ricci flow in differential geometry, we theoretically establish that introducing discrete Ricci flow into hypergraph structures can effectively regulate node feature evolution and thereby alleviate over-smoothing. Building on this insight, we propose Ricci Flow-guided Hypergraph Neural Diffusion(RFHND), a novel message passing paradigm for hypergraphs guided by discrete Ricci flow. Specifically, RFHND is based on a PDE system that describes the continuous evolution of node features on hypergraphs and adaptively regulates the rate of information diffusion at the geometric level, preventing feature homogenization and producing high-quality node representations. Experimental results show that RFHND significantly outperforms existing methods across multiple benchmark datasets and demonstrates strong robustness, while also effectively mitigating over-smoothing.

D4PM: A Dual-branch Driven Denoising Diffusion Probabilistic Model with Joint Posterior Diffusion Sampling for EEG Artifacts Removal

Artifact removal is critical for accurate analysis and interpretation of Electroencephalogram (EEG) signals. Traditional methods perform poorly with strong artifact-EEG correlations or single-channel data. Recent advances in diffusion-based generative models have demonstrated strong potential for EEG denoising, notably improving fine-grained noise suppression and reducing over-smoothing. However, existing methods face two main limitations: lack of temporal modeling limits interpretability and the use of single-artifact training paradigms ignore inter-artifact differences. To address these issues, we propose D4PM, a dual-branch driven denoising diffusion probabilistic model that unifies multi-type artifact removal. We introduce a dual-branch conditional diffusion architecture to implicitly model the data distribution of clean EEG and artifacts. A joint posterior sampling strategy is further designed to collaboratively integrate complementary priors for high-fidelity EEG reconstruction. Extensive experiments on two public datasets show that D4PM delivers superior denoising. It achieves new state-of-the-art performance in EOG artifact removal, outperforming all publicly available baselines. The code is available at https://github.com/flysnow1024/D4PM.