arXiv subjects
Publications and source records attributed to Mian Huang.
Marton's inner bound, the best-known achievable region for a general discrete memoryless broadcast channel, was proposed by Katalin Marton in 1979, and whether it always achieves the capacity region has remained open since then. In this paper, we establish its strict sub-optimality: we show that the capacity region of some discrete memoryless broadcast channels can be strictly larger than Marton's inner bound.
This monograph develops elimination geometry (EG), a typed, native-loss, audit-oriented framework for studying when locally optimal objects can be realized by a shared deployment rule. Elimination and compression may erase distinctions required by prediction, inference, control, or representation. EG asks which distinctions are lost, whether the induced defect is visible to the declared task, and whether changing information, architecture, action space, or deployment domain can repair it. EG separates local solvability, global realizability, and finite-sample certifiability. It derives native defects from the original objective and distinguishes architecture obstruction from model approximation, generalization, and implementation error. The monograph synthesizes tools from geometry, optimization, information theory, statistics, and machine learning into interfaces for integrability, representation admissibility, resource constraints, observational overlap, and common deployment. Formal results address regular, coordination, singular, compositional, and resource-limited mechanisms with explicit antecedents and claim boundaries. Applications include sparse model selection, distribution-free prediction, observational treatment policies, routed expert and retrieval systems, and learned score fields. Obstruction-Aware Learning and Inference links structural diagnosis to finite-data authorization, mechanism-matched intervention, and independent validation. Reproducible synthetic and real-data studies illustrate how certificates can guide architecture repair while recording failed gates and unresolved cases. The framework requires the deployment contract, native endpoint, competing explanations, information and compute budgets, and validation rule to be fixed before a persistent performance floor is attributed to architecture.
We present two counterexamples to the \emph{Markovity Conjecture} of Gohari, Liu and Nair (ISIT 2025), which is a structural conjecture concerning the optimizers of the dual functional associated with Marton's inner bound and, if true, would greatly simplify the evaluation of Marton's inner bound. Both counterexamples are ternary-input broadcast channels with strictly positive transition probabilities and use the same nonrectangular $2\times2$ auxiliary structure. In each case, we exhibit an explicit non-Markov construction whose objective value is rigorously larger than that achievable by any construction satisfying the conjectured Markov structure. Both examples are obtained with the assistance of GPT-5.6 Sol and disprove the Markovity Conjecture.