University of Rochester

In Lean 4 theorem proving that depends on project context, failed proofs used to be discarded as a final filter result, and independent sampling restarted later attempts nearly from scratch. This search framework draws one candidate each from a general-purpose reasoning model and a Lean-specialized prover, uses compiler errors in a pairwise comparison to pick the current-best proof, accepts a revision only when the comparison judges it better, and resamples when refinement stagnates. On seven real Lean 4 projects from miniCTX-v2, within the pass@32 budget it improves average pass rate by 12.8 percentage points over the two base models' average pass@32 while cutting LLM calls by 21.9%.

In Lean 4 theorem proving that depends on project context, failed proofs used to be discarded as a final filter result, and independent sampling restarted later attempts nearly from scratch. This search framework draws one candidate each from a general-purpose reasoning model and a Lean-specialized prover, uses compiler errors in a pairwise comparison to pick the current-best proof, accepts a revision only when the comparison judges it better, and resamples when refinement stagnates. On seven real Lean 4 projects from miniCTX-v2, within the pass@32 budget it improves average pass rate by 12.8 percentage points over the two base models' average pass@32 while cutting LLM calls by 21.9%.

This study assembled a dataset of 32,847 webcam videos from 1,888 participants (727 with Parkinson's disease) across 16 standardized clinical tasks and systematically benchmarked seven video foundation models (VideoPrism, V-JEPA2 and its SSv2 variant, ViViT, VideoMAE, VideoMAEv2, and TimeSformer) using frozen embeddings with a linear classification head, finding that task saliency is highly model-dependent: VideoPrism excels in visual speech kinematics and facial expressivity, V-JEPA2 variants are superior for upper-limb motor tasks, and TimeSformer remains competitive for rhythmic tasks like finger tapping, with overall AUCs of 76.4–85.3%, accuracies of 71.5–80.6%, specificity up to 90.3%, and sensitivity of only 43.2–57.3%.

This study assembled a dataset of 32,847 webcam videos from 1,888 participants (727 with Parkinson's disease) across 16 standardized clinical tasks and systematically benchmarked seven video foundation models (VideoPrism, V-JEPA2 and its SSv2 variant, ViViT, VideoMAE, VideoMAEv2, and TimeSformer) using frozen embeddings with a linear classification head, finding that task saliency is highly model-dependent: VideoPrism excels in visual speech kinematics and facial expressivity, V-JEPA2 variants are superior for upper-limb motor tasks, and TimeSformer remains competitive for rhythmic tasks like finger tapping, with overall AUCs of 76.4–85.3%, accuracies of 71.5–80.6%, specificity up to 90.3%, and sensitivity of only 43.2–57.3%.