Neurosymbolic systems rely on mathematical solvers to guarantee reasoning correctness, yet solvers are fundamentally blind to whether a formal translation maintains strict reference-equivalence to a designated formalization. We formalize this vulnerability as Verdict-Preserving-Unfaithfulness (VPU): a failure mode where an incorrect encoding executes successfully and matches the expected verdict. We theoretically prove that structural, verdict-only verification heuristics are mathematically bounded to chance-level detection on these deceptively valid traces. To resolve this, we introduce Generative Verification (GenV), which distills an offline Z3-equivalence oracle into a reference-free, continuous reference-equivalence score by repurposing the language model's native vocabulary space. Mechanistic analysis via decision-projected logit lenses and sparse autoencoders shows this generative readout natively extracts precise spatial error coordinates without explicit localization training. Empirically, our oracle-mined verifier (GenV+HN) achieves 0.961 AUROC in reference-equivalence verification, generalizes zero-shot across unseen translators and divergent formal styles, and yields an 11.3-point downstream accuracy gain in agentic test-time compute allocation.
Vikash Singh, Debargha Ganguly, Aman Goel et al.· 0 citations
This empirical study covers broad knowledge, symbolic reasoning, and competition mathematics, and it introduces an evaluation profile whose coordinates and simple functionals recover or bound common repeated-sampling metrics, and require compute accounting and uncertainty estimates that match the protocol.
Mohsen Hariri, Weicong Chen, Nahal Shahini et al.· 4 citations
Large language models can solve substantially harder reasoning problems with more inference-time compute. The term"test-time scaling,"however, now covers diverse inference algorithms that extend deliberation along a single trajectory, sample completed candidates and aggregate them through voting or verification, or search over unfinished partial states. These algorithms differ in their statistical structure, compute accounting, and failure modes. Treating these procedures as interchangeable under a single scalar"budget,"or reporting accuracy without the inference protocol that produced it, makes results difficult to compare across studies. We develop a systematic account of test-time scaling along three axes. First, we formalize test-time scaling as budgeted inference over the implicit prefix tree of an autoregressive model and distinguish three structural regimes: single-trajectory sequential scaling, leaf-level scaling with terminal reduction, and prefix-level scaling. Second, we treat the evaluated object as the entire inference system and develop evaluation principles that separate end-to-end system performance from candidate-bank diagnostics. We introduce an evaluation profile whose coordinates and simple functionals recover or bound common repeated-sampling metrics, and prescribe protocol-matched reporting of compute and uncertainty. Third, we specify reproducibility requirements for inference protocols, distinguishing exact replay from distributional reproducibility and identifying the artifacts needed to support each. We also organize the open-weight reasoning ecosystem by model-side and interface mechanisms, apply these principles to broad-knowledge, symbolic-reasoning, and competition-mathematics benchmarks, and assemble over 2 billion full reasoning traces for release with progressively richer verifier and token-level signals.
Mohsen Hariri, Weicong Chen, Nahal Shahini et al.· 4 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
