Selected work

Representative Papers

Revisiting the Stability of the Ingleton Inequality: A Tropicalization-Free Approach

Jul 18, 2026

This study investigates the stability of the Ingleton inequality under approximate conditional independence—specifically, when the conditional mutual information is small but nonzero—and quantifies the extent to which the inequality may be violated. To this end, we introduce a novel analytical framework that avoids tropicalization and dispenses with the intricate machinery of tropical probability spaces, thereby substantially simplifying the stability analysis. Within this framework, we derive explicit error bounds that improve upon existing estimates, resolve an open problem concerning the stability of the sum of two Ingleton expressions, and consequently construct a new family of entropy inequalities that confirm the stability of this sum.

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On the Supremum of Singleton Ratios in Submodular Functions

Apr 26, 2026

This work investigates the maximum possible ratio λ of function values over singleton sets for submodular functions, under the constraint that the function value on a given singleton is fixed to 1. This ratio characterizes the strength of inter-variable constraints and the extremal scaling behavior of base polyhedra. By constructing a novel class of a-reduced submodular functions and integrating techniques from submodular decomposition, extremal combinatorics, and polyhedral geometry, the authors present the first explicit construction achieving a lower bound of λ = Ω(n / log n). They also establish a double-exponential upper bound on λ, thereby revealing a substantial gap between existing theoretical bounds. This result provides a foundational step toward tightening the known bounds on λ in future research.

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Information Inequalities for Five Random Variables

Dec 29, 2025

The structural characterization of the Shannon entropy region for five discrete random variables has remained unresolved for decades. Method: This paper introduces an enhanced maximum-entropy method based on intergenerational variable replication, integrating group symmetry analysis, lattice-based combinatorial enumeration, and convex geometric modeling. Contributions/Results: We fully enumerate and verify all non-Shannon entropy inequalities generated up to the ninth generation for five variables—the first complete such enumeration. We rigorously construct two infinite families of new non-Shannon inequalities, yielding the richest explicit outer bounds on the entropy region to date. Furthermore, we establish a parametric framework for enumerating extremal entropy inequalities. This work breaks a long-standing theoretical bottleneck in characterizing the entropy region boundary for more than four variables and proposes a profound conjecture on the completeness of the proposed method—offering a novel paradigm for the systematic discovery of high-dimensional information inequalities.

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Recent publications

Latest Papers

Revisiting the Stability of the Ingleton Inequality: A Tropicalization-Free Approach

Jul 18, 2026

This study investigates the stability of the Ingleton inequality under approximate conditional independence—specifically, when the conditional mutual information is small but nonzero—and quantifies the extent to which the inequality may be violated. To this end, we introduce a novel analytical framework that avoids tropicalization and dispenses with the intricate machinery of tropical probability spaces, thereby substantially simplifying the stability analysis. Within this framework, we derive explicit error bounds that improve upon existing estimates, resolve an open problem concerning the stability of the sum of two Ingleton expressions, and consequently construct a new family of entropy inequalities that confirm the stability of this sum.

0 citationsRead paper

On the Supremum of Singleton Ratios in Submodular Functions

Apr 26, 2026

This work investigates the maximum possible ratio λ of function values over singleton sets for submodular functions, under the constraint that the function value on a given singleton is fixed to 1. This ratio characterizes the strength of inter-variable constraints and the extremal scaling behavior of base polyhedra. By constructing a novel class of a-reduced submodular functions and integrating techniques from submodular decomposition, extremal combinatorics, and polyhedral geometry, the authors present the first explicit construction achieving a lower bound of λ = Ω(n / log n). They also establish a double-exponential upper bound on λ, thereby revealing a substantial gap between existing theoretical bounds. This result provides a foundational step toward tightening the known bounds on λ in future research.

0 citationsRead paper

Information Inequalities for Five Random Variables

Dec 29, 2025

The structural characterization of the Shannon entropy region for five discrete random variables has remained unresolved for decades. Method: This paper introduces an enhanced maximum-entropy method based on intergenerational variable replication, integrating group symmetry analysis, lattice-based combinatorial enumeration, and convex geometric modeling. Contributions/Results: We fully enumerate and verify all non-Shannon entropy inequalities generated up to the ninth generation for five variables—the first complete such enumeration. We rigorously construct two infinite families of new non-Shannon inequalities, yielding the richest explicit outer bounds on the entropy region to date. Furthermore, we establish a parametric framework for enumerating extremal entropy inequalities. This work breaks a long-standing theoretical bottleneck in characterizing the entropy region boundary for more than four variables and proposes a profound conjecture on the completeness of the proposed method—offering a novel paradigm for the systematic discovery of high-dimensional information inequalities.

0 citationsRead paper