Guiying Yan

Feixue Shao, Guangze Shi, Xueyu Liu et al.

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.

Zhiheng Zhou, Mengyao Zhou, Xixun Lin et al.

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.

Ziyang Zhao, Haoran Xiong, Zicheng Ye et al.

LDPC codes have attracted significant attention because of their superior performance close to the Shannon limit. Elementary trapping sets are the main cause of the error floor phenomenon in LDPC codes. We consider typical graphs related to trapping sets, including theta graphs, dumbbell graphs, and short cycles with chords. Based on the Turán numbers of $θ(2,2,2)$, $θ(1,3,3)$ and $D(4,4;0)$, we prove that any $(a,b)$-ETS with $g=8$ variable-regular $γ$ satisfies the inequality $b\geq aγ-\frac{a(\sqrt{24a-23}-1)}{4}$, provided that any two 8-cycles in the Tanner graph do not share common variable node. In addition, we can also eliminate ETSs by removing certain short-cycle structures with chords. The minimum sizes of ETSs obtained through these methods are significantly increased. To assess practical impact , we analyze spectral radii of the ETSs and construct QC-LDPC codes to show frame error rates in the error floor region.

Wen-Xuan Lang, Guiying Yan, Zhi-Ming Ma

In classical information theory, both the form and performance of the optimal detector for additive noise channels can be precisely derived, based on the assumption that the channel noise follows a specific probability distribution or a mixture of known distributions, or that the exact distribution exists but is unknown. In this paper, we extend the analyses of detectors for additive noise channel to the situation where the probability model for analyzing channels is uncertain, utilizing nonlinear expectation theory. We consider two types of distribution uncertainties: one with no mean uncertainty but with variance uncertainty, and another with both mean and variance uncertainties. We derive the optimal detectors for binary input additive noise channel under the nonlinear expectation optimal criterion for both scenarios and provide their explicit forms. Our findings reveal that mean uncertainty significantly influences the form of the optimal detector, whereas variance uncertainty does not. Additionally, we propose an estimation method for the uncertain parameters of the channel noise. Finally, we present theoretical analyses and simulated performance results of the newly derived optimal detectors, and compare these results with the performance of optimal detector under classical information theory, which assumes a deterministic probability model. The results of experiments show that our new detection methods outperform conventional methods in most scenarios with uncertain probability models, showing the practical relevance of our theoretical contributions.

Mengyao Zhou, Zhiheng Zhou, Xiao Han et al.

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.

Qingqing Peng, Dongxu Chang, Guiying Yan et al.

In this study, we investigate the characteristics of scheduling sequences that enable efficient decoding of generalized low-density parity-check (GLDPC) codes under the layered message-passing algorithm. In particular, we show that scheduling sequences leading to higher decoding efficiency should prioritize the update of constraint nodes corresponding to subcodes with larger minimum distance, fewer minimum-weight codewords, and shorter code length. Based on these characteristics, we design a scheduling algorithm, which further demonstrates the effectiveness of these characteristics through simulation experiments.

Dengyi Zhao, Zhiheng Zhou, Guiying Yan et al.

Accurately characterizing higher-order interactions of brain regions and extracting interpretable organizational patterns from Functional Magnetic Resonance Imaging data is crucial for brain disease diagnosis. Current graph-based deep learning models primarily focus on pairwise or triadic patterns while neglecting signed higher-order interactions, limiting comprehensive understanding of brain-wide communication. We propose HOI-Brain, a novel computational framework leveraging signed higher-order interactions and organizational patterns in fMRI data for brain disease diagnosis. First, we introduce a co-fluctuation measure based on Multiplication of Temporal Derivatives to detect higher-order interactions with temporal resolution. We then distinguish positive and negative synergistic interactions, encoding them in signed weighted simplicial complexes to reveal brain communication insights. Using Persistent Homology theory, we apply two filtration processes to these complexes to extract signed higher-dimensional neural organizations spatiotemporally. Finally, we propose a multi-channel brain Transformer to integrate heterogeneous topological features. Experiments on Alzheimer' s disease, Parkinson' s syndrome, and autism spectrum disorder datasets demonstrate our framework' s superiority, effectiveness, and interpretability. The identified key brain regions and higher-order patterns align with neuroscience literature, providing meaningful biological insights.