{"paper":{"title":"A Calculus-Based Framework for Determining Vocabulary Size in End-to-End ASR","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Calculus locates the optimal vocabulary size for end-to-end ASR by fitting a cost curve and applying derivative tests.","cross_cats":["cs.SD"],"primary_cat":"cs.CL","authors_text":"Sunil Kumar Kopparapu","submitted_at":"2026-05-14T06:19:42Z","abstract_excerpt":"In hybrid automatic speech recognition (ASR) systems, the vocabulary size is unambiguous, typically determined by the number of phones, bi-phones, or tri-phones present in the language. In contrast, end-to-end ASR systems derive their vocabulary, often referred to as tokens from the text corpus used for training. The choice and, more importantly, the size of this vocabulary is a critical hyper-parameter in training end-to-end ASR systems. Tokenization algorithms such as Byte Pair Encoding (BPE), WordPiece, and Unigram Language Model (ULM) use the vocabulary size as an input hyper-parameter to "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We demonstrate the utility and usefulness of our approach by applying it on a standard Librispeech corpus and show that the optimal choice of vocabulary size hyper-parameter improves the performance of the ASR.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That a curve fitted to the cost function data will have a differentiable minimum identifiable by first and second derivative tests, and that this mathematical optimum will produce measurably better ASR performance on held-out data.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Curve fitting and calculus derivative tests on a tokenization cost function identify an optimal vocabulary size that improves end-to-end ASR performance on Librispeech.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Calculus locates the optimal vocabulary size for end-to-end ASR by fitting a cost curve and applying derivative tests.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"0263389b0e2f1f4f5a9ce1d1aa57a6db9bc901f89cc3a1ef46fe4dfa89981426"},"source":{"id":"2605.14427","kind":"arxiv","version":1},"verdict":{"id":"26ff0e22-fde7-496a-9abf-2f629b64ff3a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:04:22.903529Z","strongest_claim":"We demonstrate the utility and usefulness of our approach by applying it on a standard Librispeech corpus and show that the optimal choice of vocabulary size hyper-parameter improves the performance of the ASR.","one_line_summary":"Curve fitting and calculus derivative tests on a tokenization cost function identify an optimal vocabulary size that improves end-to-end ASR performance on Librispeech.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That a curve fitted to the cost function data will have a differentiable minimum identifiable by first and second derivative tests, and that this mathematical optimum will produce measurably better ASR performance on held-out data.","pith_extraction_headline":"Calculus locates the optimal vocabulary size for end-to-end ASR by fitting a cost curve and applying derivative tests."},"references":{"count":13,"sample":[{"doi":"","year":2024,"title":"A cost minimization approach to fix the vocabulary size in a tokenizer for an end-to-end ASR system,","work_id":"295ba0f9-2df3-4fd3-84ba-1b1b0387f424","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2015,"title":"Librispeech ASR corpus: train-clean-100,","work_id":"b03979c8-8ea1-4017-b0f8-cc645a16dc58","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"D. C. Montgomery, E. A. Peck, and G. G. Vining,Introduction to Linear Regression Analysis, 5th ed. Hoboken, NJ: John Wiley & Sons,","work_id":"9e3877dc-f7ff-4fa7-96d4-f209f9c0815e","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"[Online]. Available: https://www.wiley.com/en-us/Introduction+ to+Linear+Regression+Analysis,+5th+Edition-p-9781119578727","work_id":"35b01cf2-232b-4065-bef3-9f43e92c481e","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2018,"title":"ESPnet: End-to-End Speech Processing Toolkit,","work_id":"92255ea1-947e-4e96-893b-e43fea4ae518","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":13,"snapshot_sha256":"35122c0ddecccc217d28bd53e50eefe054468204824bea12868252fd02889c45","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"52f25b64deb19bf9bbee5b9e3f360954a18137e16abd22fb38093c77b6f4bdba"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}