HSRM: Hidden-State Reward Models for Test-Time Verification

Large language models can often generate plausible mathematical reasoning traces, but reliably identifying the correct solution among multiple candidates remains a key challenge. Existing test-time reasoning pipelines typically rely on text-based verifiers that re-read each generated solution, making verification an expensive component of inference. Prior work has shown, however, that LLMs often encode correctness-related signals in their internal representations, including awareness of when their own answers are likely to be wrong. Building on this observation, we introduce HSRM, a lightweight hidden-state reward model that verifies candidate solutions by directly reading the generator's internal representations rather than re-processing its text. HSRM extracts hidden states from a frozen generator at reasoning-step boundaries and uses a small Transformer encoder to rank candidates. It is trained from self-generated trajectories with outcome labels, requiring neither human-written process supervision nor a large pretrained verifier. Across four mathematical reasoning benchmarks, HSRM matches or outperforms a 55M-parameter text-only energy verifier in 15 of 16 generator--dataset settings while using only about 2M parameters, providing an efficient alternative to text-only verification by reusing representations already computed during generation.

Prefix-Denoising Consistency: Test-Time Verification for Diffusion Language Models

Diffusion Language Models (DLMs) have recently become increasingly competitive with autoregressive (AR) models, and even outperform them on certain tasks. Unlike AR models, DLMs produce output through iterative denoising without a left-to-right order. To further improve the performance of DLMs, we introduce PDC (\emph{Prefix-Denoising Consistency}), a test-time self-verification method for DLMs. PDC exploits a distinctive test-time signal in DLMs under prefix conditioned regeneration, correct trajectories are more stable and reproducible than incorrect ones. Concretely, given an initially generated sample, PDC splits the sentence at an intermediate position and regenerates the remaining tokens conditioned on the fixed prefix. Across mathematical reasoning and commonsense reasoning benchmarks, PDC consistently improves upon the initial sample, outperforms independent generations under a computational constrained comparison, and is robust to different unmasking strategies and parameter settings. These results highlight prefix-conditioned regeneration as an effective DLM-specific primitive for test-time verification.

Test-Time Verification for Text-to-SQL via Outcome Reward Models

Improving the reliability of large language models (LLMs) at inference time is a central challenge in structured reasoning tasks such as Text-to-SQL. Common test-time inference strategies, including Best-of-N sampling and Majority Voting, rely on heuristic signals such as execution success or output frequency, which provide limited semantic discrimination across candidate outputs. In this work, we study Outcome Reward Models (ORMs) as learned semantic scoring functions for test-time verification in Text-to-SQL. While ORMs have been previously explored for test-time scaling and alignment, their application to structured query generation remains underexplored. We introduce GradeSQL, a scalable framework for training task-specific ORMs via automated candidate generation and execution-based labeling, enabling verifier training without manual annotation. We integrate ORMs into a verification-driven Best-of-N pipeline and evaluate our approach on the BIRD and Spider benchmarks across multiple open-source LLM families. ORM-based selection consistently outperforms execution-based Best-of-N and Majority Voting, with gains of up to +4.33% on BIRD and +2.10% on Spider. We further show that ORMs scale effectively with larger candidate sets and yield stronger improvements on complex queries. Overall, our results demonstrate that ORM-based verification provides a simple, effective, and scalable alternative to heuristic test-time selection strategies for Text-to-SQL. Code datasets and models are publicly available.