arXiv subjects

Senhan Yao

Publications and source records attributed to Senhan Yao.

6 recordsLinked to original sources

arXiv2026

Uniform Testability Implies Asymmetric Testability

We prove a filtration-level conversion from uniform fixed-time testing to all-sample one-sided error control and uniform future-tail control. Given an adapted deterministic binary test whose worst-case fixed-time error tends to zero, the construction selects update times with prescribed summable error budgets and holds each selected decision until the next update. For every prescribed significance level, the construction yields a test that controls Type I error at every sample size; from each update time onward, the probability of any subsequent error is bounded uniformly over each hypothesis class by the remaining budget. Hence the test is uniformly consistent and eventually correct almost surely under both hypotheses. Applying the conversion to finite-alphabet coordinate processes proves the first implication in Ryabko's Conjecture 5.2.

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arXiv2026

Independence Is Not Always Consistently Testable

We study the problem of testing independence between the coordinate processes of a jointly stationary ergodic binary process from finite observations. We prove that no test is pointwise consistent in probability: any procedure whose power tends to one against every dependent law must have nonvanishing false-positive probability on some independent stationary ergodic law along infinitely many sample sizes. Quantitatively, for some jointly stationary ergodic law with independent coordinate processes, the false-positive probability has limsup at least $1/2$. Thus, even under stationarity and ergodicity, independence cannot be consistently decided from increasingly long finite samples. The proof combines a diagonal construction with rare markers that create detectable dependence at selected scales while converging to a limiting process whose coordinates are independent.

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arXiv2026

Weak but Not Strong Asymptotic Testability

We construct two fixed disjoint families $H_0,H_1$ of stationary ergodic binary process distributions for which a weakly asymptotically consistent test exists, but no strongly asymptotically consistent test exists. The construction combines a synchronizing binary suspension code, an independent i.i.d marker process, and countably many independent slowly switching two-state Markov chains. In particular, this disproves the asymptotic-consistency branch of a conjecture of Ryabko.

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arXiv2026

Invariance Entropy in the Dust

We answer negatively two natural general forms of Kawan's questions on invariance entropy for control systems, open for more than fifteen years, by a single construction. We show that finite strict invariance entropy need not coincide with ordinary invariance entropy, and that strict invariance entropy need not be lower semicontinuous under Hausdorff perturbations of the initial set. The construction is a continuous-time control system in which a Cantor coordinate stores an infinite symbolic instruction, an exponentially contracting coordinate makes late mismatches geometrically invisible, and a compact matching graph forces exact symbolic agreement. It identifies a source of information complexity not generated by dynamical expansion, but by the persistence of exact viability constraints under thin invariant geometry and by the order of limits in invariance entropy.

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arXiv2026

A Less Conservative Sufficient Condition for PID Stabilization of Scalar Second-Order Nonlinear Uncertain Systems

This letter studies robust set-point regulation of scalar second-order nonlinear uncertain systems using a classical PID controller with constant gains. The scalar second-order model provides a minimal prototype for nonlinear mechanical and electromechanical dynamics, while its velocity-dependent term captures uncertainties such as physical damping and friction. For a positive velocity-derivative bound, existing Lyapunov sufficient conditions certify fixed-gain PID parameter regions that remain separated from the boundary associated with the necessary condition obtained from the worst-case linear model. To reduce this conservatism, this letter proposes an endpoint-balanced quadratic-plus-integral Lyapunov certificate. The key idea is to choose the quadratic cross-term coefficient so that the mixed-term penalty is balanced at the two endpoints of the admissible effective-damping interval before extracting the scalar PID inequality. The resulting condition guarantees global asymptotic regulation for the full derivative-bounded uncertainty class. When the velocity-derivative bound is positive, the proposed condition certifies a fixed-gain PID region that strictly contains those certified by Zhao--Guo and Zhang--Guo. When this bound is zero, the corresponding boundary coincides with that necessary boundary. At the level of Lyapunov analysis, the construction reduces the uniform mixed-term penalty over the entire effective-damping interval.

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arXiv2025

On the Fundamental Limit of the Stochastic Gradient Identification Algorithm Under Non-Persistent Excitation

Stochastic gradient (SG) methods are fundamental to system identification and machine learning, enabling online parameter estimation in large-scale and streaming-data settings. As a classical identification method, the SG algorithm has been extensively studied for decades. Under non-persistent excitation, the strongest currently available convergence result assumes that the condition number of the Fisher information matrix is $O((\log r_n)^\alpha)$, where $r_n = 1 + \sum_{i=1}^n \|\varphi_i\|^2$. Existing theory establishes strong consistency when $\alpha \le 1/3$, whereas the same condition with $\alpha > 1$ is insufficient to guarantee strong consistency. We prove that strong consistency holds throughout the range $0 \le \alpha < 1$. The proof is based on a new algebraic framework that yields substantially sharper matrix norm bounds. This result nearly resolves the four-decade-old Chen--Guo conjecture by establishing strong consistency throughout the previously open range $1/3 < \alpha < 1$.

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