Jiahe Feng

ZhiMing Li, JiaHe Feng

We study eigendecomposition on $SO(n)$ under streaming observations $C_k = C_{\mathrm{sig}} + σ_k^2 I + E_k$, where the isotropic background $σ_k^2 I$ may be time-varying and arbitrarily large. Standard algorithms couple their stability to $\lVert C_k \rVert_2 \approx σ^2$, forcing step sizes, contraction rates, and iteration counts to degrade with the noise floor. We observe that $σ^2 I$ lies in the center of the matrix algebra and therefore *should never enter* the eigenspace dynamics. We construct a discrete double-bracket flow whose skew-symmetric generator $Ω= [A, \operatorname{diag}(A)]$ operates in the tangent Lie algebra $\mathfrak{so}(n)$, where scalar multiples of the identity vanish by antisymmetry. The resulting trajectory, Lyapunov function, and maximal stable step size $η_{\max} = 1/L_C$ depend exclusively on the trace-free signal $C_e$ -- achieving pointwise, pathwise $σ^2$-invariance. We establish input-to-state stability with a noise ball governed solely by trace-free perturbations, prove global convergence via strict-saddle geometry and a discrete Łojasiewicz argument, and extend the framework to top-$k$ eigentracking on the Stiefel manifold $\operatorname{St}(k,n)$ at cost $k$ matrix-vector products per step.

Timing Li, Bing Cao, Jiahe Feng et al.

Image fusion synthesizes complementary information from multiple sources, mitigating the inherent limitations of unimodal imaging systems. Accurate image registration is essential for effective multi-source data fusion. However, existing registration methods, often based on image translation in Euclidean space, fail to handle cross-modal misalignment effectively, resulting in suboptimal alignment and fusion quality. To overcome this limitation, we explore image alignment in non-Euclidean space and propose a Hyperbolic Cycle Alignment Network (Hy-CycleAlign). To the best of our knowledge, Hy-CycleAlign is the first image registration method based on hyperbolic space. It introduces a dual-path cross-modal cyclic registration framework, in which a forward registration network aligns cross-modal inputs, while a backward registration network reconstructs the original image, forming a closed-loop registration structure with geometric consistency. Additionally, we design a Hyperbolic Hierarchy Contrastive Alignment (H$^{2}$CA) module, which maps images into hyperbolic space and imposes registration constraints, effectively reducing interference caused by modality discrepancies. We further analyze image registration in both Euclidean and hyperbolic spaces, demonstrating that hyperbolic space enables more sensitive and effective multi-modal image registration. Extensive experiments on misaligned multi-modal images demonstrate that our method significantly outperforms existing approaches in both image alignment and fusion. Our code will be publicly available.

Ye Li, Jiahe Feng, Yuan Meng et al.

Diffusion Policy (DP) excels in embodied control but suffers from high inference latency and computational cost due to multiple iterative denoising steps. The temporal complexity of embodied tasks demands a dynamic and adaptable computation mode. Static and lossy acceleration methods, such as quantization, fail to handle such dynamic embodied tasks, while speculative decoding offers a lossless and adaptive yet underexplored alternative for DP. However, it is non-trivial to address the following challenges: how to match the base model's denoising quality at lower cost under time-varying task difficulty in embodied settings, and how to dynamically and interactively adjust computation based on task difficulty in such environments. In this paper, we propose Temporal-aware Reinforcement-based Speculative Diffusion Policy (TS-DP), the first framework that enables speculative decoding for DP with temporal adaptivity. First, to handle dynamic environments where task difficulty varies over time, we distill a Transformer-based drafter to imitate the base model and replace its costly denoising calls. Second, an RL-based scheduler further adapts to time-varying task difficulty by adjusting speculative parameters to maintain accuracy while improving efficiency. Extensive experiments across diverse embodied environments demonstrate that TS-DP achieves up to 4.17 times faster inference with over 94% accepted drafts, reaching an inference frequency of 25 Hz and enabling real-time diffusion-based control without performance degradation.

Zewen Sun, Ruoxiang Huang, Jiahe Feng et al.

Enhancing interrogation capabilities in Traditional Chinese Medicine (TCM) diagnosis through multi-turn dialogues and knowledge graphs presents a significant challenge for modern AI systems. Current large language models (LLMs), despite their advancements, exhibit notable limitations in medical applications, particularly in conducting effective multi-turn dialogues and proactive questioning. These shortcomings hinder their practical application and effectiveness in simulating real-world diagnostic scenarios. To address these limitations, we propose DoPI, a novel LLM system specifically designed for the TCM domain. The DoPI system introduces a collaborative architecture comprising a guidance model and an expert model. The guidance model conducts multi-turn dialogues with patients and dynamically generates questions based on a knowledge graph to efficiently extract critical symptom information. Simultaneously, the expert model leverages deep TCM expertise to provide final diagnoses and treatment plans. Furthermore, this study constructs a multi-turn doctor-patient dialogue dataset to simulate realistic consultation scenarios and proposes a novel evaluation methodology that does not rely on manually collected real-world consultation data. Experimental results show that the DoPI system achieves an accuracy rate of 84.68 percent in interrogation outcomes, significantly enhancing the model's communication ability during diagnosis while maintaining professional expertise.