arXiv subjects

Man Liang

Publications and source records attributed to Man Liang.

6 recordsLinked to original sources

arXiv2026

Encoded but Not Actionable: Auditing the Decode-Generate-Steer Gap in Frozen LLMs for Geometric Constraints

Large language models (LLMs) have demonstrated strong performance on structured reasoning tasks, but what they encode and whether it informs model behavior remain unclear. We investigate this question through geometric reasoning, using parametric CAD constraints as a controlled testbed for separating local pairwise relations from sketch-level constraint status. By probing the hidden states of six frozen decoder-only LLMs, we examine four properties: linear decodability, forced-choice generation, activation-level influence, and behavioral steerability. Pretraining substantially improves the decoding of local geometric relations, and this advantage persists after accounting for positional cues with shuffled-order controls. In contrast, sketch-level DOF status is already highly decodable from randomly initialized representations and improves only modestly with pretraining, indicating that much of its probe performance is available without learned weights. Further analyses show that decodable information is not always actionable. Generation often fails to express this information, and on the two intervention-tested backbones, activation-restoration effects at the patched entity position vanish while decodability persists across depth. Mean-difference steering also does not reliably control outputs. These results show that decodability, generation, activation-level influence, and steerability can diverge in the tested setting. The audit provides a controlled way to distinguish failures to encode geometric structure from failures to express or control encoded information.

cs.CL↗

arXiv2026

Disentangling Language Roles in Multilingual LLM Task Execution

Multilingual LLMs are increasingly used when instruction, source content, and required response languages do not coincide. Existing benchmarks have expanded multilingual instruction-following evaluation, but they rarely isolate these three roles within a fully crossed design. We introduce MTM-Bench, a controlled benchmark for language-conditioned task execution in which each instance is defined by a triplet $(L_{\text{instr}}, L_{\text{content}}, L_{\text{resp}})$. Across English, Spanish, and Chinese, MTM-Bench enumerates all 27 triplets and contains 2{,}430 instances per model across semantic reversal, final-state extraction, and language purity with update realization. We evaluate 20 frontier and open-weight LLMs using decomposed metrics for semantic correctness, target-language adherence, constraint satisfaction, contamination ratio, and joint success, with scoring validated by a targeted human audit. The fully crossed design reveals that degradation is organized by the role a language occupies in the task structure, not merely by mismatch count. The response-language role is the dominant axis of variation, and a single response-slot mismatch accounts for most degradation. The response-only and full-mismatch comparison suggests that mismatch count is not a monotonic predictor of difficulty, with model-level ordering varying across systems. Task families fail through distinct channels, showing that semantic correctness alone does not capture reliable multilingual task execution.

cs.CL↗

arXiv2025

Skew von Neumann constant in Weak Orlicz Spaces and Weak Lebesgue Spaces

This paper defines the skew von Neumann constant in quasi-Banach spaces. Meanwhile, we obtain two constants. It presents the upper and lower bounds of two constants. Subsequently, it deduces the lower bound of the skew von Neumann constant within weak Orlicz spaces. Then, leveraging the relationship between weak Orlicz spaces and weak Lebesgue spaces, the lower bound of the skew von Neumann - Jordan constant in weak Lebesgue spaces is established. Meanwhile, in this paper, we also generalize the skew von Neumann constant. Then we present the lower bounds for the $p$-th von Neumann constant in weak Orlicz spaces and weak Lebesgue spaces.

math.FA↗

arXiv2025

A Unified Theoretic and Algorithmic Framework for Solving Multivariate Linear Model with $\ell^1$-norm Approximation

It is a challenging problem that solving the \textit{multivariate linear model} (MLM) $\mathbf{A}\mathbf{x}=\mathbf{b}$ with the $\ell_1 $-norm approximation method such that $||\mathbf{A}\mathbf{x}-\mathbf{b}||_1$, the $\ell_1$-norm of the \textit{residual error vector} (REV), is minimized. In this work, our contributions lie in two aspects: firstly, the equivalence theorem for the structure of the $\ell_1$-norm optimal solution to the MLM is proposed and proved; secondly, a unified algorithmic framework for solving the MLM with $\ell_1$-norm optimization is proposed and six novel algorithms (L1-GPRS, L1-TNIPM, L1-HP, L1-IST, L1-ADM, L1-POB) are designed. There are three significant characteristics in the algorithms discussed: they are implemented with simple matrix operations which do not depend on specific optimization solvers; they are described with algorithmic pseudo-codes and implemented with Python and Octave/MATLAB which means easy usage; and the high accuracy and efficiency of our six new algorithms can be achieved successfully in the scenarios with different levels of data redundancy. We hope that the unified theoretic and algorithmic framework with source code released on GitHub could motivate the applications of the $\ell_1$-norm optimization for parameter estimation of MLM arising in science, technology, engineering, mathematics, economics, and so on.

math.OC↗

arXiv2022

Even Order Explicit Symplectic Geometric Algorithms for Solving Quaternions in Guidance Navigation and Control via Diagonal Pad\'{e} Approximation and Cayley Transform

Quaternion kinematical differential equation (QKDE) plays a key role in navigation, control and guidance systems. Although explicit symplectic geometric algorithms (ESGA) for this problem are available, there is a lack of a unified way for constructing high order symplectic difference schemes with configurable order parameter and the fractional interval sampling problem should be treated carefully. We present even order explicit symplectic geometric algorithms to solve the QKDE with diagonal Pad\'{e} approximation via a four-step strategy. Firstly, the Pad\'{e}-Cayley lemma is proved and used to simplify the symplectic Pad\'{e} approximation for the linear Hamiltonian system with infinitesimal symplectic structure. Secondly, both parallel and alternative iterative methods are proposed to construct the symplectic difference schemes with even order accuracy. Thirdly, the symplecity, orthogonality and invertibility of the single-step transition matrices are proved rigorously. Finally, the explicit symplectic geometric algorithms are designed for both the linear time-invariant and linear time-varying QKDE. The maximum absolute error for solving the QKDE is $\mathcal{O}((t_f-t_0)\tau^{2\ell})$ where $\tau$ is the time step, $\ell$ is the order parameter and $[t_0,t_f]$ is the time span. The linear time complexity and constant space complexity of computation as well as the simple algorithmic structure show that our algorithms are appropriate for real-time applications in aeronautics, astronautics, robotics and so on. The performance of the proposed algorithms are verified and validated by mathematical analysis and numerical simulation.

eess.SY↗

arXiv2021

Innovative System Design for Remote Air Traffic Control Simulation Training on and beyond COVID19

Remote ATC simulation training is an emerging technology in aviation education during COVID. Professional training institutions can learn from others, whereas the experiences of developing remote ATC simulation teaching/training with the Start-up company ByteProTeq will be beneficial for the rest of the world to understand the differences and similarities of current remote training and to improve their performance in building a safe and efficient remote training environment. In this paper, we will present three improvements to our remote ATC training: 1) infrastructure upgrading of hardware and software from an existing stand-alone system to a remote network that considers costs, cyber security, system compatibility, et cetera; 2) quality of remote ATC simulation training, compared with traditional face-to-face training, including students and instructors feedback; 3) enhancement of the current remote training system beyond COVID-19 regarding reliability, cyber security, and capacity. This foundation paper will support understanding of the current stage of remote ATC simulation training development with the Start-up company ByteProTeq, during and beyond the COVID-19 pandemic, thereby providing an excellent example for the rest of the world.

cs.NI↗