Orthogonal Approximate Message Passing Algorithms for Rectangular Spiked Matrix Models with Rotationally Invariant Noise

We propose an orthogonal approximate message passing (OAMP) algorithm for signal estimation in the rectangular spiked matrix model with general rotationally invariant (RI) noise. We establish a rigorous state evolution that exactly characterizes the high-dimensional dynamics of the algorithm. Building on this framework, we derive an optimal variant of OAMP that minimizes the predicted mean-squared error at each iteration. For the special case of i.i.d. Gaussian noise, the fixed point of the proposed OAMP algorithm coincides with that of the standard AMP algorithm. For general RI noise models, we conjecture that the optimal OAMP algorithm is statistically optimal within a broad class of iterative methods, and achieves Bayes-optimal performance in certain regimes.

Orthogonal Approximate Message Passing with Optimal Spectral Initializations for Rectangular Spiked Matrix Models

We propose an orthogonal approximate message passing (OAMP) algorithm for signal estimation in the rectangular spiked matrix model with general rotationally invariant (RI) noise. We establish a rigorous state evolution that precisely characterizes the algorithm's high-dimensional dynamics and enables the construction of iteration-wise optimal denoisers. Within this framework, we accommodate spectral initializations under minimal assumptions on the empirical noise spectrum. In the rectangular setting, where a single rank-one component typically generates multiple informative outliers, we further propose a procedure for combining these outliers under mild non-Gaussian signal assumptions. For general RI noise models, the predicted performance of the proposed optimal OAMP algorithm agrees with replica-symmetric predictions for the associated Bayes-optimal estimator, and we conjecture that it is statistically optimal within a broad class of iterative estimation methods.

InterMoE: Individual-Specific 3D Human Interaction Generation via Dynamic Temporal-Selective MoE

Generating high-quality human interactions holds significant value for applications like virtual reality and robotics. However, existing methods often fail to preserve unique individual characteristics or fully adhere to textual descriptions. To address these challenges, we introduce InterMoE, a novel framework built on a Dynamic Temporal-Selective Mixture of Experts. The core of InterMoE is a routing mechanism that synergistically uses both high-level text semantics and low-level motion context to dispatch temporal motion features to specialized experts. This allows experts to dynamically determine the selection capacity and focus on critical temporal features, thereby preserving specific individual characteristic identities while ensuring high semantic fidelity. Extensive experiments show that InterMoE achieves state-of-the-art performance in individual-specific high-fidelity 3D human interaction generation, reducing FID scores by 9% on the InterHuman dataset and 22% on InterX.

BezierSeg: Parametric Shape Representation for Fast Object Segmentation in Medical Images

Delineating the lesion area is an important task in image-based diagnosis. Pixel-wise classification is a popular approach to segmenting the region of interest. However, at fuzzy boundaries such methods usually result in glitches, discontinuity, or disconnection, inconsistent with the fact that lesions are solid and smooth. To overcome these undesirable artifacts, we propose the BezierSeg model which outputs bezier curves encompassing the region of interest. Directly modelling the contour with analytic equations ensures that the segmentation is connected, continuous, and the boundary is smooth. In addition, it offers sub-pixel accuracy. Without loss of accuracy, the bezier contour can be resampled and overlaid with images of any resolution. Moreover, a doctor can conveniently adjust the curve's control points to refine the result. Our experiments show that the proposed method runs in real time and achieves accuracy competitive with pixel-wise segmentation models.