arXiv subjects

Andrey Bryutkin

Publications and source records attributed to Andrey Bryutkin.

4 recordsLinked to original sources

arXiv2026

Flow Reasoning Models: Turning Flows Into Efficient Recurrent Reasoners

Structured reasoning requires making and revising interdependent decisions to reach a globally consistent solution. Existing architectures struggle with this: autoregressive models commit sequentially and cannot revise earlier decisions, while masked diffusion models often require careful decoding schemes to coordinate interdependent predictions. We introduce Flow Reasoning Models (FRMs), a novel framework for structured reasoning that adapts continuous flows over discrete structured outputs with a simple recurrent refinement mechanism. By self-conditioning a flow model on its own past outputs, we turn one-shot denoising into iterative solution refinement. This lets FRMs make and revise decisions in parallel, efficiently coordinating interdependent choices across solutions. Yet conventional self-conditioning becomes unreliable at greater recurrent depth due to exposure bias between one-step training predictions and recursively generated inference states. We address this mismatch with Fixed-Point Forcing (FPF), which trains FRMs on states produced by their own inference dynamics while preserving the standard flow-matching objective. FRMs achieve solve rates of $99.5\%$, $100.0\%$, and $99.9\%$ on Sudoku-Extreme, Zebra, and Maze-Unique, respectively. On Sudoku-Extreme, FRMs achieve higher peak accuracy than the evaluated masked-diffusion and specialized reasoning baselines while remaining highly compute-efficient, matching the next-best method's $98.7\%$ peak solve rate with $44\times$ fewer inference FLOPs.

cs.AI↗

arXiv2025

Neural Triangular Transport Maps: A New Approach Towards Sampling in Lattice QCD

Lattice field theories are fundamental testbeds for computational physics; yet, sampling their Boltzmann distributions remains challenging due to multimodality and long-range correlations. While normalizing flows offer a promising alternative, their application to large lattices is often constrained by prohibitive memory requirements and the challenge of maintaining sufficient model expressivity. We propose sparse triangular transport maps that explicitly exploit the conditional independence structure of the lattice graph under periodic boundary conditions using monotone rectified neural networks (MRNN). We introduce a comprehensive framework for triangular transport maps that navigates the fundamental trade-off between \emph{exact sparsity} (respecting marginal conditional independence in the target distribution) and \emph{approximate sparsity} (computational tractability without fill-ins). Restricting each triangular map component to a local past enables site-wise parallel evaluation and linear time complexity in lattice size $N$, while preserving the expressive, invertible structure. Using $\phi^4$ in two dimensions as a controlled setting, we analyze how node labelings (orderings) affect the sparsity and performance of triangular maps. We compare against Hybrid Monte Carlo (HMC) and established flow approaches (RealNVP).

cs.LG↗

arXiv2025

Canonical Bayesian Linear System Identification

Standard Bayesian approaches for linear time-invariant (LTI) system identification are hindered by parameter non-identifiability; the resulting complex, multi-modal posteriors make inference inefficient and impractical. We solve this problem by embedding canonical forms of LTI systems within the Bayesian framework. We rigorously establish that inference in these minimal parameterizations fully captures all invariant system dynamics (e.g., transfer functions, eigenvalues, predictive distributions of system outputs) while resolving identifiability. This approach unlocks the use of meaningful, structure-aware priors (e.g., enforcing stability via eigenvalues) and ensures conditions for a Bernstein--von Mises theorem -- a link between Bayesian and frequentist large-sample asymptotics that is broken in standard forms. Extensive simulations with modern MCMC methods highlight advantages over standard parameterizations: canonical forms achieve higher computational efficiency, generate interpretable and well-behaved posteriors, and provide robust uncertainty estimates, particularly from limited data.

stat.ML↗

arXiv2024

HAMLET: Graph Transformer Neural Operator for Partial Differential Equations

We present a novel graph transformer framework, HAMLET, designed to address the challenges in solving partial differential equations (PDEs) using neural networks. The framework uses graph transformers with modular input encoders to directly incorporate differential equation information into the solution process. This modularity enhances parameter correspondence control, making HAMLET adaptable to PDEs of arbitrary geometries and varied input formats. Notably, HAMLET scales effectively with increasing data complexity and noise, showcasing its robustness. HAMLET is not just tailored to a single type of physical simulation, but can be applied across various domains. Moreover, it boosts model resilience and performance, especially in scenarios with limited data. We demonstrate, through extensive experiments, that our framework is capable of outperforming current techniques for PDEs.

cs.LG↗