Pith Number

pith:AWMSQSXD

pith:2026:AWMSQSXDDX6SNWCV64B6F4QOQS

not attested not anchored not stored refs resolved

A Calculus-Based Framework for Determining Vocabulary Size in End-to-End ASR

Sunil Kumar Kopparapu

Calculus locates the optimal vocabulary size for end-to-end ASR by fitting a cost curve and applying derivative tests.

arxiv:2605.14427 v1 · 2026-05-14 · cs.CL · cs.SD

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest 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.

C2weakest 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.

C3one 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.

References

13 extracted · 13 resolved · 0 Pith anchors

[1] A cost minimization approach to fix the vocabulary size in a tokenizer for an end-to-end ASR system, 2024

[2] Librispeech ASR corpus: train-clean-100, 2015

[3] D. C. Montgomery, E. A. Peck, and G. G. Vining,Introduction to Linear Regression Analysis, 5th ed. Hoboken, NJ: John Wiley & Sons,

[4] [Online]. Available: https://www.wiley.com/en-us/Introduction+ to+Linear+Regression+Analysis,+5th+Edition-p-9781119578727

[5] ESPnet: End-to-End Speech Processing Toolkit, 2018

Formal links

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Receipt and verification

First computed	2026-05-17T23:39:07.178032Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0599284ae31dfd26d855f703e2f20e8483234d8af7c4c39ed2544458fe2615f5

Aliases

arxiv: 2605.14427 · arxiv_version: 2605.14427v1 · doi: 10.48550/arxiv.2605.14427 · pith_short_12: AWMSQSXDDX6S · pith_short_16: AWMSQSXDDX6SNWCV · pith_short_8: AWMSQSXD

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/AWMSQSXDDX6SNWCV64B6F4QOQS \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 0599284ae31dfd26d855f703e2f20e8483234d8af7c4c39ed2544458fe2615f5

Canonical record JSON

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    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.CL",
    "submitted_at": "2026-05-14T06:19:42Z",
    "title_canon_sha256": "02173003b7a20c7ba5fa0b8df3d30825fb729eb4ed6a974c3aa1421b70248b53"
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