arXiv subjects

Divya Shyamal

Publications and source records attributed to Divya Shyamal.

3 recordsLinked to original sources

arXiv2026

SCATR: Simple Calibrated Test-Time Ranking

Test-time scaling (TTS) improves large language models (LLMs) by allocating additional compute at inference time. In practice, TTS is often achieved through parallel scaling: generating multiple candidate responses and selecting the best via a Best-of-N (BoN) strategy. Its effectiveness therefore hinges on the scoring function. Learned scorers such as process reward models (PRMs) can be strong, but they are expensive to train and run. Lightweight confidence heuristics based on token log-probabilities are much cheaper, yet we find that they often perform substantially worse. To improve on lightweight confidence heuristics without incurring the full cost of stronger learned scorers, we introduce SCATR, a simple and efficient BoN ranking method that learns a lightweight scorer from a small calibration set using hidden representations from the base model. Across coding and mathematical reasoning benchmarks, SCATR improves over prior confidence-based baselines by up to 9%. Relative to LoRA fine-tuning on the same calibration data, it achieves comparable accuracy with up to 8000x fewer trainable parameters and much lower compute, reducing training and inference latency by up to 150x and 1000x, respectively. SCATR is also competitive with strong PRM baselines, and in several settings improves accuracy by up to 7.8% on math and 4.2% on coding while enabling up to 1000x faster inference. Overall, SCATR offers a strong accuracy-efficiency trade-off for scalable test-time selection.

cs.LG↗

arXiv2025

Probabilistic Factorial Experimental Design for Combinatorial Interventions

A combinatorial intervention, consisting of multiple treatments applied to a single unit with potentially interactive effects, has substantial applications in fields such as biomedicine, engineering, and beyond. Given $p$ possible treatments, conducting all possible $2^p$ combinatorial interventions can be laborious and quickly becomes infeasible as $p$ increases. Here we introduce probabilistic factorial experimental design, formalized from how scientists perform lab experiments. In this framework, the experimenter selects a dosage for each possible treatment and applies it to a group of units. Each unit independently receives a random combination of treatments, sampled from a product Bernoulli distribution determined by the dosages. Additionally, the experimenter can carry out such experiments over multiple rounds, adapting the design in an active manner. We address the optimal experimental design problem within an intervention model that imposes bounded-degree interactions between treatments. In the passive setting, we provide a closed-form solution for the near-optimal design. Our results prove that a dosage of $\tfrac{1}{2}$ for each treatment is optimal up to a factor of $1+O(\tfrac{\ln(n)}{n})$ for estimating any $k$-way interaction model, regardless of $k$, and imply that $O\big(kp^{3k}\ln(p)\big)$ observations are required to accurately estimate this model. For the multi-round setting, we provide a near-optimal acquisition function that can be numerically optimized. We also explore several extensions of the design problem and finally validate our findings through simulations.

cs.LG↗

arXiv2024

Matching Algorithms in the Sparse Stochastic Block Model

The stochastic block model (SBM) is a generalization of the Erdős--Rényi model of random graphs that describes the interaction of a finite number of distinct communities. In sparse Erdős--Rényi graphs, it is known that a linear-time algorithm of Karp and Sipser achieves near-optimal matching sizes asymptotically almost surely, giving a law-of-large numbers for the matching sizes of such graphs in terms of solutions to an ODE. We provide an extension of this analysis, identifying broad ranges of stochastic block model parameters for which the Karp--Sipser algorithm achieves near-optimal matching sizes, but demonstrating that it cannot perform optimally on general SBM instances. We also consider the problem of constructing a matching online, in which the vertices of one half of a bipartite stochastic block model arrive one-at-a-time, and must be matched as they arrive. We show that the competitive ratio lower bound of 0.837 found by Mastin and Jaillet for the Erdős--Rényi case is tight whenever the expected degrees in all communities are equal. We propose several linear-time algorithms for online matching in the general stochastic block model, but prove that despite very good experimental performance, none of these achieve online asymptotic optimality.

cs.DS↗