arXiv subjects

Abhinav Kochar

Publications and source records attributed to Abhinav Kochar.

2 recordsLinked to original sources

arXiv2026

Transient Acceleration and Cross-Dissipation Interference in Fisher-Regularized Wasserstein Gradient Flows

We study transient nonequilibrium dynamics in Fisher-regularized Wasserstein gradient flows and identify a sign-changing cross-dissipation mechanism generated by the coupling between transport dissipation and Fisher-information geometry. Using the Ornstein--Uhlenbeck Fokker--Planck system as an analytically tractable setting, we derive an exact reduced variance dynamics on the Gaussian manifold, \[ \dot{u}=2(1-u)+\frac{\varepsilon}{u}, \] where $u(t)=σ^2(t)$ is the variance and $\varepsilon>0$ is the Fisher regularization strength. The reduced dynamics reveal distinct transient regimes induced by the interaction between transport relaxation and information-geometric curvature. The associated cross-dissipation term changes sign at the critical scale $σ=1$, separating cooperative acceleration for localized states with $σ<1$ from transient interference at larger variance scales. In the subcritical regime, Fisher curvature accelerates the descent of the baseline free energy; beyond the critical transition, it partially opposes the Ornstein--Uhlenbeck pullback and generates transient overshoot toward a displaced Fisher-regularized equilibrium. We also establish a bounded transient-acceleration-window result, showing that the cooperative acceleration phase has finite duration with an upper bound depending only on the Fisher regularization strength. Finite-difference simulations support the analytical predictions and suggest that qualitatively similar sign-transition behavior may persist beyond Gaussian closure for non-Gaussian initial conditions, including bimodal and Laplace distributions. Overall, the results provide a transient dynamical perspective on Fisher-regularized dissipative systems and show how information-geometric curvature can reorganize intermediate-time Wasserstein relaxation while preserving the globally dissipative structure of the flow.

cond-mat.stat-mech↗

arXiv2026

Empirical Characterization of Inference-Time Elicited Probability Transformations in Large Language Models

Large language models increasingly rely on inference-time procedures such as chain-of-thought reasoning, self-refinement, retrieval augmentation, and verifier-guided revision, yet the structure of elicited probability transformations under these procedures remains poorly understood. We study externally elicited probability assignments over candidate answers and observe recurring approximate log-ratio relationships: \[ \log \tilde q_t(i) = α_t \left( \log q_t(i) + \log b_t(i) \right) + c_t, \] where $q_t$ and $\tilde q_t$ are pre- and post-elicitation probabilities, $b_t$ is an externally constructed evidence signal, and $α_t$ is an empirical descriptor of the prompting configuration. Across 4,975 reasoning problems from GPQA Diamond, TheoremQA, MMLU-Pro, and ARC-Challenge, evaluated on multiple instruction-tuned model families, we observe approximate log-ratio relationships with mean $R^2 \approx 0.76$ over about $1.3 \times 10^5$ candidate-level observations. Coefficients vary across elicitation settings, but qualitatively similar relationships persist across evaluated conditions. Robustness analyses using alternative statistical representations, prompting configurations, held-out evaluation, and token-level log-probabilities suggest that the observed structure is not tied to one prompting procedure or probability estimation method. The main contribution is not the algebraic form itself, which is related to generalized Bayesian updating and probability-transformation frameworks, but the empirical observation that diverse inference-time prompting pipelines repeatedly exhibit reproducible log-ratio structure under controlled conditions. The framework provides a protocol-sensitive perspective for analyzing calibration, evidence amplification, uncertainty propagation, and interaction sensitivity in inference-time LLM pipelines.

cs.CL↗