arXiv subjects

Oleg Kiriukhin

Publications and source records attributed to Oleg Kiriukhin.

8 recordsLinked to original sources

arXiv2026

Towards Robust Speech Deepfake Detection via Human-Inspired Reasoning

The modern generative audio models can be used by an adversary in an unlawful manner, specifically, to impersonate other people to gain access to private information. To mitigate this issue, speech deepfake detection (SDD) methods started to evolve. Unfortunately, current SDD methods generally suffer from the lack of generalization to new audio domains and generators. More than that, they lack interpretability, especially human-like reasoning that would naturally explain the attribution of a given audio to the bona fide or spoof class and provide human-perceptible cues. In this paper, we propose HIR-SDD, a novel SDD framework that combines the strengths of Large Audio Language Models (LALMs) with the chain-of-thought reasoning derived from the novel proposed human-annotated dataset. Experimental evaluation demonstrates both the effectiveness of the proposed method and its ability to provide reasonable justifications for predictions.

cs.SD↗

arXiv2026

A Polynomial Recovery Criterion for Forced Commutativity in the Matrix Square-Root Fiber of a Square-Free Cubic Polynomial

Let $k$ be an algebraically closed field of characteristic different from $2$ and $3$, and let $f(t)=t^3+at+b\in k[t]$ be square-free. For $X\in M_m(k)$ set $A=f(X)$. This paper studies the full matrix equation $Y^2=A$, without imposing $[X,Y]=0$. Existence is the classical square-root problem for the fixed matrix $A$. The only obstruction is the nilpotent square-root pairing criterion on the zero-primary component of $A$. The main result is a fiberwise commutativity classification: if the fiber $\{Y\in M_m(k):Y^2=A\}$ is nonempty, then every such $Y$ commutes with $X$ if and only if $X\in k[A]$. The forward direction restricts the classical centralizer criterion of Thompson (1969) to the square root fiber. The new content is the converse: when $X\notin k[A]$, an explicit square root $Y$ of $A$ with $[X,Y]\ne 0$ is exhibited. The witnesses arise from nonzero spectral collision under $f$, critical nilpotent collapse, or a multicolor zero-primary fiber.

math.AG↗

arXiv2026

Orbit-Level Transfer Matrix for the 3D Fourier-Galerkin Navier-Stokes System on the Periodic Torus: Explicit Orbit-Triad Incidence Bounds and Deterministic Row-Sum Estimates

I study the cubic Fourier-Galerkin truncation of the three-dimensional (3D) incompressible Navier-Stokes equations on the periodic torus after reduction by the full octahedral symmetry group $O_h$. The nonlinear interaction is encoded by a state-dependent orbit-level transfer matrix $M_N(u)$, and the main discrete problem is to estimate orbit-triad incidences in shell slices of translated cubes. Using a face-normalized decomposition, I reduce the local counting problem to the classical two-squares representation function and obtain an incidence bound of order $N^{4+\varepsilon}$ by the shell-counting argument developed in this manuscript. I also derive the exact orbit-level enstrophy identity, the algebraic decomposition $M_N(u)=A_N(u)+V_N(u)$, and deterministic Sobolev row-sum bounds for the raw matrix $M_N(u)$ in the stated range of exponents. These results give an orbit-level description of nonlinear transfer in the truncated system.

math.AP↗

arXiv2026

Entropy-Rate Selection for Partially Observed Processes

I formulate an entropy-rate maximization problem at the observable level for stochastic processes observed through an information-reducing observation map. For a visible stationary law, the map determines an observational fiber of hidden stationary laws generating that law. In the finite-state finite-memory setting, retained visible constraints determine a feasible class of stationary $(r+1)$-block laws, and the entropy maximizer is defined as the entropy-rate maximizer on this class. The paper formulates entropy-rate maximization on feasible classes induced by partial observability and develops a structural theory for the resulting maximizer. I prove existence and uniqueness of the maximizer, with uniqueness under a fixed-context-marginal hypothesis and, more generally, via a strict-concavity characterization by row proportionality. Two global characterization regimes are central: a fixed one-point marginal yields the i.i.d. maximizer, and a fixed $r$-block law yields the $(r-1)$-step Markov extension. The gap functional equals a conditional mutual information and vanishes exactly at the maximizing completion. I also derive optimality conditions, local geometry of the maximizer, a latent random-mapping realization that leaves the visible law unchanged, and a local empirical consistency theorem, and illustrate the framework by an aliased hidden-state example.

cs.IT↗

arXiv2026

Variable-Length Markov Chains on Finite Quivers: Boundary-Window Identifiability, Exact Depth, and Local Rank Comparison

Variable-length Markov chains on finite quivers provide a natural framework for context-dependent stochastic growth under incidence constraints. I study quiver-valued variable-length Markov chains observed through finite boundary windows and develop a first-order theory of visible-depth identifiability via stationary visible one-step transition laws and their restricted differentials on prescribed tangent blocks. For visible depth $m$, the main object is the stationary one-step informative map $q_{\mathcal{Q}}^{(m)}$. In the edge-homogeneous regime, once the local visible support is fixed and the representation hypothesis holds, all admissible visible depths encode the same edge-level extension law and hence have the same first-order rank. In the exact-depth regime of context length $r$, the depth-$r$ boundary process is the canonical finite-state Markov chain, smaller visible windows are deterministic truncations, and every coarser informative map factors $C^1$-smoothly through the depth-$r$ informative map on the relevant affine transition-array neighborhood. Hence rank cannot increase beyond depth $r$. After quotienting a tangent block by directions already invisible at depth $r$, I characterize strict coarse-depth loss exactly by coarse rank deficiency, equivalently by strict rank drop from depth $r$ to depth $m$ on the original block. I also give subspace-based and global selected-coordinate criteria, a global one-coordinate branching criterion, and an explicit depth-two example. Under full fine-depth rank and strict coordinate-rank loss at every smaller depth, a global coordinate-rank theorem yields $m_*(T,θ_0)=r$. Reduced local coordinates remove stochastic redundancies, first-order criteria are invariant under $C^1$ reparameterization, and the statistical and LAN consequences remain conditional on additional estimation and likelihood-level hypotheses.

math.PR↗

arXiv2026

A Strict Gap Between Relaxed and Partition-Constrained Spectral Compression in a Six-State Lumpable Markov Chain

This paper studies a finite reversible lumpable Markov chain for which relaxed spectral compression yields a larger determinant than partition-constrained compression. For a symmetric six-state lumpable chain and the positive operator $T=P^2$, I compare the relaxed benchmark \begin{equation*} \mathfrak D^{\mathrm{rel}}_3(T):=\sup_{U^*U=I_3}\det(U^*TU) \end{equation*} and the partition-constrained benchmark \begin{equation*} \sup_{\mathcal A\,\mathrm{3\text{-}partition}}\det Q_{\mathcal A}(T), \qquad Q_{\mathcal A}(T)=H_{\mathcal A}^*TH_{\mathcal A}. \end{equation*} Here the partition-constrained benchmark is the compression induced by normalized indicator vectors of genuine partitions of the state space. I derive closed formulas for the two analytically central partition families, prove strict upper bounds for both in a local-mode-dominated regime, and combine these bounds with an exhaustive enumeration of all $90$ partitions into three nonempty cells in an explicit six-state model. For this model, one obtains a strict global gap: \begin{equation*} \sup_{\mathcal A}\det Q_{\mathcal A}(T)<\mathfrak D^{\mathrm{rel}}_3(T). \end{equation*} Thus, in this model, indicator-based partition frames are strictly weaker than relaxed orthonormal frames even after global partition-constrained optimization.

math.PR↗

arXiv2026

Orbit-Level Stretching in Cubic Fourier-Galerkin Navier-Stokes: Sharp Incidence, Spectral Decay, and a Continuation Criterion

I study orbit-level enstrophy stretching in a cubic Fourier-Galerkin truncation of the three-dimensional incompressible Navier-Stokes equations, reduced by the full octahedral symmetry group $O_h$. The nonlinear transfer compresses to an orbit-level matrix whose symmetric part $V_N$ governs net enstrophy growth. I reduce the stretching problem to an orbit--triad incidence estimate and close it by a face-normalized decomposition and a two-squares argument, establishing the sharp bound \begin{equation} c\,N^3\le\max_α\sum_β\sqrt{Γ_{αβ}}\le C\,N^{3}. \end{equation} A weighted-incidence refinement then yields, in the isotropic unit-energy ensemble, \begin{equation} \mathbb{E}\,ρ(V_N)\le C\, N^{-3/2}\to 0, \qquad \mathbb{E}\,ν_c^*(N)\le C\, N^{-7/2}\to 0, \end{equation} where $ν_c^*(N)=ρ(V_N)/N^2$ is the orbit-level critical-threshold ratio. For Sobolev-class data with ${ \left\lVert u \right\rVert}_{H^s}\le M$ and $s>2$, a stronger deterministic bound ${{ \left\lVert V_N \right\rVert} }_\infty\le C_s M^3$ holds uniformly in $N$, with $ν_c^*(N)\to 0$ for all $s>3/2$. A comparison with Tao's averaged Navier-Stokes construction shows that the orbit-level subcriticality is a structural property of the true nonlinearity that is violated by known blowup mechanisms. Monte Carlo experiments at $N=1,\ldots,8$ under both isotropic and Kolmogorov-spectrum ensembles confirm the decay, with $ρ(V_N)\sim N^{-2.6}$ far exceeding the proven upper bound. Tracking these bounds along the Galerkin evolution yields an orbit-level continuation criterion for the strong solution: global regularity holds if and only if $\int_0^T { \left\lVert V_N \right\rVert}_\infty\,dt$ remains bounded uniformly in $N$.

math.AP↗

arXiv2026

Probabilistic Verification of Voice Anti-Spoofing Models

Recent advances in generative models have amplified the risk of malicious misuse of speech synthesis technologies, enabling adversaries to impersonate target speakers and access sensitive resources. Although speech deepfake detection has progressed rapidly, most existing countermeasures lack formal robustness guarantees or fail to generalize to unseen generation techniques. We propose PV-VASM, a probabilistic framework for verifying the robustness of voice anti-spoofing models (VASMs). PV-VASM estimates the probability of misclassification under text-to-speech (TTS), voice cloning (VC), and parametric signal transformations. The approach is model-agnostic and enables robustness verification against unseen speech synthesis techniques and input perturbations. We derive a theoretical upper bound on the error probability and validate the method across diverse experimental settings, demonstrating its effectiveness as a practical robustness verification tool.

cs.SD↗