arXiv subjects

Shaocheng Liu

Publications and source records attributed to Shaocheng Liu.

5 recordsLinked to original sources

arXiv2026

Automated Proving of Shannon-Type Entropy Inequalities via Fine-Tuned Language Models and Guided Tree Search

Proving Shannon-type entropy inequalities is a fundamental task in information theory that often requires constructing non-trivial linear combinations of known constraints, which is a combinatorial search problem that scales poorly with the number of random variables. We investigate whether small-scale large language models (0.6B--1.7B parameters), fine-tuned on atomic proof steps and combined with guided beam search, can automate this process. On a held-out test set of 60 inequalities spanning n=10 to 15 variables, our 0.6B fine-tuned model achieves an 85\% proof success rate with tree search. GPT-5.5 solves 1.7\% samples under zero-shot prompting while Psitip solves 33.3\% samples. A systematic ablation study across training context length (4096 vs.\ 8192 tokens) and data distribution (n=9-skewed vs not skewed) reveals that a 4096-token not skewed training distribution yields the best performance, with extended context and skewed data providing no marginal benefit. We further identify two dominant failure modes -- format failures and step quality degradation -- and verify that the beam-scoring heuristic is essential via a controlled ablation (random scoring reduces success from 83\% to 23\%).

cs.IT↗

arXiv2025

Entropy Functions on Two-Dimensional Faces of Polymatroidal Region of Degree Four: Part II: Information Theoretic Constraints Breed New Combinatorial Structures

Characterization of entropy functions is of fundamental importance in information theory. By imposing constraints on their Shannon outer bound, i.e., the polymatroidal region, one obtains the faces of the region and entropy functions on them with special structures. In this series of two papers, we characterize entropy functions on the $2$-dimensional faces of the polymatroidal region $\Gamma_4$. In Part I, we formulated the problem, enumerated all $59$ types of $2$-dimensional faces of $\Gamma_4$ by a algorithm, and fully characterized entropy functions on $49$ types of them. In this paper, i.e., Part II, we will characterize entropy functions on the remaining $10$ types of faces, among which $8$ types are fully characterized and $2$ types are partially characterized. To characterize these types of faces, we introduce some new combinatorial design structures which are interesting in themselves.

cs.IT↗

arXiv2025

Functional perturbation theory under axisymmetry: Simplified formulae and their uses for tokamaks

In strictly axisymmetric configurations of tokamaks, field-line tracing reduces from a three-dimensional ODE system to a two-dimensional one, where Poincar\'e-Bendixson theorem applies and guarantees the nonexistence of chaos. The formulae of functional perturbation theory (FPT) mostly simplify to compact closed-form expressions to allow the computation to finish instantly, which could improve and accelerate the existing plasma control systems by detangling the plasma dynamics from the magnetic topology change. FPT can conveniently calculate how the key geometric objects of magnetic topology: 1. the divertor X-point(s) and the magnetic axis, 2. the last closed flux surface (LCFS) 3. flux surfaces change under perturbation. For example, when the divertor X-point shifts outwards, the LCFS there must expand accordingly, but not necessarily for other places of the LCFS, which could also contract, depending on the perturbation. FPT can not only facilitate adaptive control of plasma, but also enable utilizing as much as possible space in the vacuum vessel by weakening the plasma-wall interaction (PWI) via tuning the eigenvalues of $\mathcal{DP}^m$ of the divertor X-point(s), such that the field line connection lengths in the scrape-off layer (SOL) are long enough to achieve detachment. Increasing flux expansion $f_x$ is another option for detachment and can also be facilitated by FPT. Apart from the edge, FPT can also benefit the understanding of the plasma core. Since the magnetic axis O-point would also shift under perturbation and the shift is known by FPT, the O-point can be controlled without full knowledge of the plasma response, which shall not significantly change the tendency.

physics.plasm-ph↗

arXiv2024

Symmetric Entropy Regions of Degrees Six and Seven

In this paper, we classify all G-symmetric almost entropic regions according to their Shannon-tightness, that is, whether they can be fully characterized by Shannon-type inequalities, where G is a permutation group of degree 6 or 7.

cs.IT↗

arXiv2023

Entropy Functions on Two-Dimensional Faces of Polymatroidal Region of Degree Four: Part I: Problem Formulation and More

Characterization of entropy functions is of fundamental importance in information theory. By imposing constraints on their Shannon outer bound, i.e., the polymatroidal region, one obtains the faces of the region and entropy functions on them with special structures. In this series of two papers, we characterize entropy functions on the 2-dimensional faces of the polymatroidal region of degree 4. In Part I, we formulate the problem, enumerate all 59 types of 2-dimensional faces of the region by an algorithm, and fully characterize entropy functions on 49 types of them. Among them, those non-trivial cases are mainly characterized by the graph-coloring technique. The entropy functions on the remaining 10 types of faces will be characterized in Part II, among which 8 types are fully characterized, and 2 types are partially characterized.

cs.IT↗