{"paper":{"title":"Geometry-Aware Decoding with Wasserstein-Regularized Truncation and Mass Penalties for Large Language Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Wasserstein distance over token embeddings yields a closed-form truncation rule that balances mass and entropy in LLM decoding.","cross_cats":["cs.LG"],"primary_cat":"cs.CL","authors_text":"Arash Gholami Davoodi, Navid Rezazadeh, Pouya Pezeshkpour, Seyed Pouyan Mousavi Davoudi","submitted_at":"2026-02-10T22:36:48Z","abstract_excerpt":"Large language models (LLMs) must balance diversity and creativity against logical coherence in open-ended generation. Existing truncation-based samplers are effective but largely heuristic, relying mainly on probability mass and entropy while ignoring semantic geometry of the token space. We present Top-W, a geometry-aware truncation rule that uses Wasserstein distance-defined over token-embedding geometry-to keep the cropped distribution close to the original, while explicitly balancing retained probability mass against the entropy of the kept set. Our theory yields a simple closed-form stru"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Our theory yields a simple closed-form structure for the fixed-potential subset update... achieving up to 33.7% improvement.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That Wasserstein distance defined over token-embedding geometry meaningfully captures semantic relationships required for logical coherence during open-ended generation.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Top-W applies Wasserstein-regularized truncation on token-embedding geometry to create a closed-form optimal crop for LLM sampling that outperforms prior methods by up to 33.7% on GSM8K, GPQA, AlpacaEval, and MT-Bench.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Wasserstein distance over token embeddings yields a closed-form truncation rule that balances mass and entropy in LLM decoding.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1adc735ef44b66f27ea7aaec6156e20a3a54abd46bc97bd55d16eac574e88f77"},"source":{"id":"2602.10346","kind":"arxiv","version":2},"verdict":{"id":"32b662c8-6905-47ec-afd7-966a0301f4c3","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T05:05:01.174568Z","strongest_claim":"Our theory yields a simple closed-form structure for the fixed-potential subset update... achieving up to 33.7% improvement.","one_line_summary":"Top-W applies Wasserstein-regularized truncation on token-embedding geometry to create a closed-form optimal crop for LLM sampling that outperforms prior methods by up to 33.7% on GSM8K, GPQA, AlpacaEval, and MT-Bench.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That Wasserstein distance defined over token-embedding geometry meaningfully captures semantic relationships required for logical coherence during open-ended generation.","pith_extraction_headline":"Wasserstein distance over token embeddings yields a closed-form truncation rule that balances mass and entropy in LLM decoding."},"references":{"count":21,"sample":[{"doi":"","year":null,"title":"Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone","work_id":"feef9556-a016-493c-abd2-0c97a23a7ebf","ref_index":1,"cited_arxiv_id":"2404.14219","is_internal_anchor":true},{"doi":"","year":2007,"title":"Mirostat: A perplexity-controlled neural text decoding algorithm","work_id":"adf6dca4-9ef0-4476-8003-87f72f5b99c9","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1901,"title":"Lan- guage models are few-shot learners.Advances in neural information processing systems, 33:1877–1901,","work_id":"ed7e2043-f7e9-45d2-8c60-61778195b799","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"DoLa: Decoding by Contrasting Layers Improves Factuality in Large Language Models","work_id":"0f1b9a7a-0623-4efc-bed3-6dd997054681","ref_index":4,"cited_arxiv_id":"2309.03883","is_internal_anchor":true},{"doi":"","year":null,"title":"Training Verifiers to Solve Math Word Problems","work_id":"acab1aa8-b4d6-40e0-a3ee-25341701dca2","ref_index":5,"cited_arxiv_id":"2110.14168","is_internal_anchor":true}],"resolved_work":21,"snapshot_sha256":"2efd99269372ebe9905f81d5eb95d97ec9cd1bb7285edd28853f5e623163a823","internal_anchors":12},"formal_canon":{"evidence_count":2,"snapshot_sha256":"ea470f9d7b1f7e895f2961c66cae3348c4867833af2643ae7ad6e74bbb2cddb7"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}