Tao Zhong

Dongzhe Zheng, Tao Zhong, Christine Allen-Blanchette

In this paper, we study solution operators of physical field equations on geometric meshes from a function-space perspective. We reveal that Hodge orthogonality fundamentally resolves spectral interference by isolating unlearnable topological degrees of freedom from learnable geometric dynamics, enabling an additive approximation confined to structure-preserving subspaces. Building on Hodge theory and operator splitting, we derive a principled operator-level decomposition. The result is a Hybrid Eulerian-Lagrangian architecture with an algebraic-level inductive bias we call Hodge Spectral Duality (HSD). In our framework, we use discrete differential forms to capture topology-dominated components and an orthogonal auxiliary ambient space to represent complex local dynamics. Our method achieves superior accuracy and efficiency on geometric graphs with enhanced fidelity to physical invariants. Our code is available at https://github.com/ContinuumCoder/Hodge-Spectral-Duality

Tao Zhong, Dongzhe Zheng, Christine Allen-Blanchette

Sparse Mixture-of-Experts (MoE) layers route tokens through a handful of experts, and learning-free compression of these layers reduces inference cost without retraining. A subtle obstruction blocks every existing compressor in this family: three experts can each be pairwise compatible yet form an irreducible cycle when merged together, so any score that ranks experts on pairwise signals is structurally blind to which triples are jointly mergeable. We show the obstruction is a precise mathematical object, the harmonic kernel of the simplicial Laplacian on a 2-complex whose vertices are experts, whose edges carry KL merge barriers, and whose faces carry triplet barriers; Hodge-decomposing the edge-barrier signal isolates the kernel exactly. We turn the diagnostic into a selection objective: HodgeCover greedily covers the harmonic-critical edges and triplet-critical triangles, and a hybrid variant of HodgeCover pairs it with off-the-shelf weight pruning on survivors. On three open-weight Sparse MoE backbones under aggressive expert reduction, HodgeCover matches state-of-the-art learning-free baselines on the expert-reduction axis, leads on the aggressive-compression frontier of the hybrid axis, and uniquely balances retained mass across all four Hodge components. These results show that exposing the harmonic kernel of a learned MoE structure changes which compressor wins at the regime that matters most.

Xijun Li, Fangzhou Zhu, Hui-Ling Zhen et al.

In an era of digital ubiquity, efficient resource management and decision-making are paramount across numerous industries. To this end, we present a comprehensive study on the integration of machine learning (ML) techniques into Huawei Cloud's OptVerse AI Solver, which aims to mitigate the scarcity of real-world mathematical programming instances, and to surpass the capabilities of traditional optimization techniques. We showcase our methods for generating complex SAT and MILP instances utilizing generative models that mirror multifaceted structures of real-world problem. Furthermore, we introduce a training framework leveraging augmentation policies to maintain solvers' utility in dynamic environments. Besides the data generation and augmentation, our proposed approaches also include novel ML-driven policies for personalized solver strategies, with an emphasis on applications like graph convolutional networks for initial basis selection and reinforcement learning for advanced presolving and cut selection. Additionally, we detail the incorporation of state-of-the-art parameter tuning algorithms which markedly elevate solver performance. Compared with traditional solvers such as Cplex and SCIP, our ML-augmented OptVerse AI Solver demonstrates superior speed and precision across both established benchmarks and real-world scenarios, reinforcing the practical imperative and effectiveness of machine learning techniques in mathematical programming solvers.

Zehua Liu, Han Wu, Yuxuan Yao et al.

While most current approaches rely on further training techniques, such as fine-tuning or reinforcement learning, to enhance model capacities, model merging stands out for its ability of improving models without requiring any additional training. In this paper, we propose a unified framework for model merging based on low-rank estimation of task vectors without the need for access to the base model, named \textsc{LoRE-Merging}. Our approach is motivated by the observation that task vectors from fine-tuned models frequently exhibit a limited number of dominant singular values, making low-rank estimations less prone to interference. We implement the method by formulating the merging problem as an optimization problem. Extensive empirical experiments demonstrate the effectiveness of our framework in mitigating interference and preserving task-specific information, thereby advancing the state-of-the-art performance in model merging techniques.

Yixuan Li, Can Chen, Jiajun Li et al.

By exploiting the correlation between the structure and the solution of Mixed-Integer Linear Programming (MILP), Machine Learning (ML) has become a promising method for solving large-scale MILP problems. Existing ML-based MILP solvers mainly focus on end-to-end solution learning, which suffers from the scalability issue due to the high dimensionality of the solution space. Instead of directly learning the optimal solution, this paper aims to learn a reduced and equivalent model of the original MILP as an intermediate step. The reduced model often corresponds to interpretable operations and is much simpler, enabling us to solve large-scale MILP problems much faster than existing commercial solvers. However, current approaches rely only on the optimal reduced model, overlooking the significant preference information of all reduced models. To address this issue, this paper proposes a preference-based model reduction learning method, which considers the relative performance (i.e., objective cost and constraint feasibility) of all reduced models on each MILP instance as preferences. We also introduce an attention mechanism to capture and represent preference information, which helps improve the performance of model reduction learning tasks. Moreover, we propose a SetCover based pruning method to control the number of reduced models (i.e., labels), thereby simplifying the learning process. Evaluation on real-world MILP problems shows that 1) compared to the state-of-the-art model reduction ML methods, our method obtains nearly 20% improvement on solution accuracy, and 2) compared to the commercial solver Gurobi, two to four orders of magnitude speedups are achieved.

Zehua Liu, Han Wu, Xiaojin Fu et al.

Optimizers are crucial for the efficient training of Large Language Models (LLMs). While AdamW is the de facto standard, recent structure-aware optimizers like Muon have emerged, which regularize gradient updates by operating on entire weight matrices. The Muon optimizer balances the gradient updates along all the directions. However, Muon's reliance on the matrix sign function can lead to training instability, exhibits incompatibility when fine-tuning models pre-trained with AdamW. To address these limitations, we propose \textbf{REG}, a novel optimizer that replaces Muon's aggressive matrix sign operator with the Row-and-Column-Scaling (RACS) operator. Theoretically grounded in balancing a matrix, the RACS operator regularizes the update steps in a less drastic manner, making it simpler to implement and more compatible with established training dynamics. Through extensive empirical experiments on LLM training, we demonstrate that our REG optimizer not only achieves superior performance and stability over AdamW, but also maintains consistency with the AdamW training paradigm. This consistency is particularly evident during the fine-tuning stage, where REG optimizer avoids the performance degradation observed with Muon.

Yansen Zhang, Qingcan Kang, Yujie Chen et al.

Large language models (LLMs) have opened new paradigms in optimization modeling by enabling the generation of executable solver code from natural language descriptions. Despite this promise, existing approaches typically remain solver-driven: they rely on single-pass forward generation and apply limited post-hoc fixes based on solver error messages, leaving undetected semantic errors that silently produce syntactically correct but logically flawed models. To address this challenge, we propose SAC-Opt, a backward-guided correction framework that grounds optimization modeling in problem semantics rather than solver feedback. At each step, SAC-Opt aligns the original semantic anchors with those reconstructed from the generated code and selectively corrects only the mismatched components, driving convergence toward a semantically faithful model. This anchor-driven correction enables fine-grained refinement of constraint and objective logic, enhancing both fidelity and robustness without requiring additional training or supervision. Empirical results on seven public datasets demonstrate that SAC-Opt improves average modeling accuracy by 7.8\%, with gains of up to 21.9\% on the ComplexLP dataset. These findings highlight the importance of semantic-anchored correction in LLM-based optimization workflows to ensure faithful translation from problem intent to solver-executable code.

Tao Zhong, Mengzhe Geng, Shujie Hu et al.

Accurate recognition of dysarthric and elderly speech remains challenging to date. While privacy concerns have driven a shift from centralized approaches to federated learning (FL) to ensure data confidentiality, this further exacerbates the challenges of data scarcity, imbalanced data distribution and speaker heterogeneity. To this end, this paper conducts a systematic investigation of regularized FL techniques for privacy-preserving dysarthric and elderly speech recognition, addressing different levels of the FL process by 1) parameter-based, 2) embedding-based and 3) novel loss-based regularization. Experiments on the benchmark UASpeech dysarthric and DementiaBank Pitt elderly speech corpora suggest that regularized FL systems consistently outperform the baseline FedAvg system by statistically significant WER reductions of up to 0.55\% absolute (2.13\% relative). Further increasing communication frequency to one exchange per batch approaches centralized training performance.

Tao Zhong, Wonjik Kim, Masayuki Tanaka et al.

Consecutive LiDAR scans compose dynamic 3D sequences, which contain more abundant information than a single frame. Similar to the development history of image and video perception, dynamic 3D sequence perception starts to come into sight after inspiring research on static 3D data perception. This work proposes a spatio-temporal neural network for human segmentation with the dynamic LiDAR point clouds. It takes a sequence of depth images as input. It has a two-branch structure, i.e., the spatial segmentation branch and the temporal velocity estimation branch. The velocity estimation branch is designed to capture motion cues from the input sequence and then propagates them to the other branch. So that the segmentation branch segments humans according to both spatial and temporal features. These two branches are jointly learned on a generated dynamic point cloud dataset for human recognition. Our works fill in the blank of dynamic point cloud perception with the spherical representation of point cloud and achieves high accuracy. The experiments indicate that the introduction of temporal feature benefits the segmentation of dynamic point cloud.

Yue Sun, Kun Gao, Zhengwang Wu et al.

To better understand early brain growth patterns in health and disorder, it is critical to accurately segment infant brain magnetic resonance (MR) images into white matter (WM), gray matter (GM), and cerebrospinal fluid (CSF). Deep learning-based methods have achieved state-of-the-art performance; however, one of major limitations is that the learning-based methods may suffer from the multi-site issue, that is, the models trained on a dataset from one site may not be applicable to the datasets acquired from other sites with different imaging protocols/scanners. To promote methodological development in the community, iSeg-2019 challenge (http://iseg2019.web.unc.edu) provides a set of 6-month infant subjects from multiple sites with different protocols/scanners for the participating methods. Training/validation subjects are from UNC (MAP) and testing subjects are from UNC/UMN (BCP), Stanford University, and Emory University. By the time of writing, there are 30 automatic segmentation methods participating in iSeg-2019. We review the 8 top-ranked teams by detailing their pipelines/implementations, presenting experimental results and evaluating performance in terms of the whole brain, regions of interest, and gyral landmark curves. We also discuss their limitations and possible future directions for the multi-site issue. We hope that the multi-site dataset in iSeg-2019 and this review article will attract more researchers on the multi-site issue.