Tianyou Liu | Searcharxiv

arXiv2026

.tmu: A Low-Entropy Tree-Structured Representation for LLM-Assisted Scientific Writing

As large language models (LLMs) increasingly assist scientific writing, the limitations and token costs of generating TeX become increasingly visible. This paper analyzes TeX's architectural mismatch with LLM workflows, stemming from its lack of an explicit structural representation, to illustrate its limitations on generated semantics and error localization. As an alternative, we introduce .tmu, a low-entropy tree-structured representation. With its efficient data structure and clear contextual boundaries, .tmu outperforms .tex in the above aspects. Experiments across four LLMs provide evidence for this claim in most evaluated settings. Furthermore, we show that due to its lower information entropy, fine-tuning LLMs on .tmu achieves approximately 43% lower final training loss than on .tex. Our work provides a more scalable and LLM-friendly data representation for LLM-assisted scientific writing.

cs.CL↗

arXiv2020

Fast non-convex low-rank matrix decomposition for separation of potential field data using minimal memory

A fast non-convex low-rank matrix decomposition method for potential field data separation is proposed. The singular value decomposition of the large size trajectory matrix, which is also a block Hankel matrix, is obtained using a fast randomized singular value decomposition algorithm in which fast block Hankel matrix-vector multiplications are implemented with minimal memory storage. This fast block Hankel matrix randomized singular value decomposition algorithm is integrated into the \texttt{Altproj} algorithm, which is a standard non-convex method for solving the robust principal component analysis optimization problem. The improved algorithm avoids the construction of the trajectory matrix. Hence, gravity and magnetic data matrices of large size can be computed. Moreover, it is more efficient than the traditional low-rank matrix decomposition method, which is based on the use of an inexact augmented Lagrange multiplier algorithm. The presented algorithm is also robust and, hence, algorithm-dependent parameters are easily determined. The improved and traditional algorithms are contrasted for the separation of synthetic gravity and magnetic data matrices of different sizes. The presented results demonstrate that the improved algorithm is not only computationally more efficient but it is also more accurate. Moreover, it is possible to solve far larger problems. As an example, for the adopted computational environment, matrices of sizes larger than $205 \times 205$ generate "out of memory" exceptions with the traditional method, but a matrix of size $2001\times 2001$ can be calculated in $1062.29$s with the new algorithm. Finally, the improved method is applied to separate real gravity and magnetic data in the Tongling area, Anhui province, China. Areas which may exhibit mineralizations are inferred based on the separated anomalies.

physics.geo-ph↗