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Jiaxiang Li

Jiaxiang Li contributes to research discovery and scholarly infrastructure.

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Machine Learning Artificial Intelligence Computer Vision math.OC cond-mat.supr-con Data Structures and Algorithms eess.IV math.ST Robotics Statistics Theory

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preprint2026arXiv

A Tale of Two Problems: Multi-Task Bilevel Learning Meets Equality Constrained Multi-Objective Optimization

In recent years, bilevel optimization (BLO) has attracted significant attention for its broad applications in machine learning. However, most existing works on BLO remain confined to the single-task setting and rely on the lower-level strong convexity assumption, which significantly restricts their applicability to modern machine learning problems of growing complexity. In this paper, we make the first attempt to extend BLO to the multi-task setting under a relaxed lower-level general convexity (LLGC) assumption. To this end, we reformulate the multi-task bilevel learning (MTBL) problem with LLGC into an equality constrained multi-objective optimization (ECMO) problem. However, ECMO itself is a new problem that has not yet been studied in the literature. To address this gap, we first establish a new Karush-Kuhn-Tucker (KKT)-based Pareto stationarity as the convergence criterion for ECMO algorithm design. Based on this foundation, we propose a weighted Chebyshev (WC)-penalty algorithm that achieves a finite-time convergence rate of $O(ST^{-\frac{1}{2})$ to KKT-based Pareto stationarity in both deterministic and stochastic settings, where $S$ denotes the number of objectives, and $T$ is the total iterations. Moreover, by varying the preference vector over the $S$-dimensional simplex, our WC-penalty method systematically explores the Pareto front. Finally, solutions to the ECMO problem translate directly into solutions for the original MTBL problem, thereby closing the loop between these two foundational optimization frameworks.

preprint2026arXiv

Demystifying Manifold Constraints in LLM Pre-training

The empirical success of large language model (LLM) pre-training relies heavily on heuristic stabilization techniques, such as explicit normalization layers and weight decay. While recent constrained optimization approaches that explicitly restrict weights may improve numerical stability and performance, the mechanism and motivation for adding constraints still remain elusive. This paper systematically demystifies the role of explicit manifold constraints in LLM pre-training. By introducing the Msign-Aligned Constrained Riemannian Optimizer (MACRO)-a provably convergent, single-loop optimization framework-our study disentangles weight regularization heuristics from interacting mechanisms like RMS normalization and decoupled weight decay. Theoretical analyses and comprehensive empirical evaluations reveal that manifold constraints independently bound forward activation scales and enforce stable rotational equilibrium, thereby subsuming the roles of these heuristic mechanisms. Evaluations on large-scale LLM architectures demonstrate that MACRO achieves highly competitive performance while rigorously preserving the theoretical guarantees of exact Riemannian optimization.

preprint2026arXiv

Temporal Sampling Frequency Matters: A Capacity-Aware Study of End-to-End Driving Trajectory Prediction

End to end (E2E) autonomous driving trajectory prediction is often trained with camera frames sampled at the highest available temporal frequency, assuming that denser sampling improves performance. We question this assumption by treating temporal sampling frequency as an explicit training set design variable. Starting from high frequency E2E driving datasets, we construct frequency sweep training sets by temporally subsampling camera frames along each trajectory. For each model dataset pair, we train and evaluate the same model under a fixed protocol, so the frequency response reflects how prediction performance changes with sampling frequency. We analyze this response from a capacity aware perspective. Sparse sampling may miss driving relevant cues, while dense sampling may add redundant visual content and off manifold noise. For finite capacity models, this can create a driving irrelevant capacity burden. We evaluate three smaller E2E models and a larger VLA style AutoVLA model on Waymo, nuScenes, and PAVE. Results show model and dataset dependent frequency responses. Smaller E2E models often show non monotonic or near plateau trends and achieve their best 3 second ADE at lower or intermediate frequencies. In contrast, AutoVLA achieves its best 3 second ADE and FDE at the highest evaluated frequency on all three datasets. Iteration matched controls suggest that the advantage of lower or intermediate frequencies for smaller models is not explained only by unequal training update counts. These findings show that temporal sampling frequency should be reported and tuned, rather than fixed to the highest available value.

preprint2026arXiv

The Impact of Ionic Anharmonicity on Superconductivity in Metal-Stuffed B-C Clathrates

Metal-stuffed B$-$C compounds with sodalite clathrate structure have captured increasing attention due to their predicted exceptional superconductivity above liquid nitrogen temperature at ambient pressure. However, by neglecting the quantum lattice anharmonicity, the existing studies may result in an incomplete understanding of such a lightweight system. Here, using state-of-the-art ab initio methods incorporating quantum effects and machine learning potentials, we revisit the properties of a series of $XY$$\text{B}_{6}\text{C}_{6}$ clathrates where $X$ and $Y$ are metals. Our findings show that ionic quantum and anharmonic effects can harden the $E_g$ and $E_u$ vibrational modes, enabling the dynamical stability of 15 materials previously considered unstable in the harmonic approximation, including materials with previously unreported ($XY$)$^{1+}$ state, which is demonstrated here to be crucial to reach high critical temperatures. Further calculations based on the anisotropic Migdal-Eliashberg equation demonstrate that the $T_\text{c}$ values for KRb$\text{B}_{6}\text{C}_{6}$ and Rb$\text{B}_{3}\text{C}_{3}$ among these stabilized compounds are 102 and 115 K at 0 and 15 GPa, respectively, both being higher than $T_\text{c}$ of 92 K of KPb$\text{B}_{6}\text{C}_{6}$ at the anharmonic level. These record-high $T_\text{c}$ values, surpassing liquid nitrogen temperatures, emphasize the importance of anharmonic effects in stabilizing B-C clathrates with large electron-phonon coupling strength and advancing the search for high-$T_\text{c}$ superconductivity at (near) ambient pressure.

preprint2022arXiv

Playing Tic-Tac-Toe Games with Intelligent Single-pixel Imaging

Single-pixel imaging (SPI) is a novel optical imaging technique by replacing a two-dimensional pixelated sensor with a single-pixel detector and pattern illuminations. SPI have been extensively used for various tasks related to image acquisition and processing. In this work, a novel non-image-based task of playing Tic-Tac-Toe games interactively is merged into the framework of SPI. An optoelectronic artificial intelligent (AI) player with minimal digital computation can detect the game states, generate optimal moves and display output results mainly by pattern illumination and single-pixel detection. Simulated and experimental results demonstrate the feasibility of proposed scheme and its unbeatable performance against human players.

preprint2021arXiv

Stochastic Zeroth-order Riemannian Derivative Estimation and Optimization

We consider stochastic zeroth-order optimization over Riemannian submanifolds embedded in Euclidean space, where the task is to solve Riemannian optimization problem with only noisy objective function evaluations. Towards this, our main contribution is to propose estimators of the Riemannian gradient and Hessian from noisy objective function evaluations, based on a Riemannian version of the Gaussian smoothing technique. The proposed estimators overcome the difficulty of the non-linearity of the manifold constraint and the issues that arise in using Euclidean Gaussian smoothing techniques when the function is defined only over the manifold. We use the proposed estimators to solve Riemannian optimization problems in the following settings for the objective function: (i) stochastic and gradient-Lipschitz (in both nonconvex and geodesic convex settings), (ii) sum of gradient-Lipschitz and non-smooth functions, and (iii) Hessian-Lipschitz. For these settings, we analyze the oracle complexity of our algorithms to obtain appropriately defined notions of $ε$-stationary point or $ε$-approximate local minimizer. Notably, our complexities are independent of the dimension of the ambient Euclidean space and depend only on the intrinsic dimension of the manifold under consideration. We demonstrate the applicability of our algorithms by simulation results and real-world applications on black-box stiffness control for robotics and black-box attacks to neural networks.

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