Contrastive Decoding Improves Reasoning in Large Language Models
O'Brien, Sean, Mike Lewis · arXiv (Cornell University) · 2023
This record contains the camera-ready paper “LLM Inference in Normal Form: A TRoT-Based Unification.”We show that many inference-time methods for large language models (LLMs)—e.g., MBR/eMBR decoding, Conformal prediction gates, Verifier/Judge ensembles, Self-RAG, Chain/Tree/Graph-of-Thought, and Verifier-Sandwich (VS)—admit a single normal form derived from the Theory of Relativity of Theories (TRoT). Our formulation uses enriched category theory over the Lawvere cost quantale (tropical (min,+) semiring): left/right Kan extensions \Lan/\Ran\Lan/\Ran\Lan/\Ran, residuation (elementwise residuals), masking and nuclei (1-Lipschitz projectors). In this normal form, generation/lifts (K3), safety consolidation (K4), and auditing (K6–K10 RAVE) become GraphBLAS-style sparse operators with explicit stability and auditability contracts. Provable guarantees Implementation equivalence (normal form): common decoding “tricks” map to \Lan\Lan\Lan → Obs → \Ran\Ran\Ran with the same outputs under masking/nucleus conditions. Stability: \Lan\Lan\Lan and the residual are 1-Lipschitz in ℓ∞\ell_\inftyℓ∞. Approximation bounds: geometric truncation error q\*k+11−q\*\frac{q_\*^{k+1}}{1-q_\*}1−q\*q\*k+1; soft-min (log-sum-exp) gap k logdmaxλcost\frac{k\,\log d_{\max}}{\lambda_{\text{cost}}}λcostklogdmax (with join ≡ numeric infimum in Cost polarity). Auditing: a deterministic spending schedule ∑tαt≤αglobal\sum_t\alpha_t\le\alpha_{\text{global}}∑tαt≤αglobal with test-(super)martingale e-processes gives time-uniform FWER control; LR/mixture-LR constructions yield valid e-values. Implementation blueprint (GPU/GraphBLAS-ready) \Lan\Lan\Lan: sparse SpMV/SpGEMM on (min,+); \Ran\Ran\Ran: elementwise residual → max-reduce; Numerics: log-domain + row-wise max-shift; masks send forbidden entries to +∞+\infty+∞. Reproducibility log (minimum fields): seed; model/revision; tokenizer; prompts; forward map JJJ; transport KKK; masks; λcost\lambda_{\text{cost}}λcost; kkk; effective dmaxd_{\max}dmax; \Lan/\Ran\Lan/\Ran\Lan/\Ran kernel + build flags; hardware/BLAS; e-process updates (et,Mt)(e_t,M_t)(et,Mt); Conformal calibration snapshots.