# The Functionalizer: Lossless Functional Decomposition for Subword Tokenization

arXiv: https://arxiv.org/abs/2609.15991 · HTML: https://mlsanity.com/paper/2609.15991/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 32 references that are in the map.
- First posted on arXiv 7 Jul 2026.

## Builds on (most cited first, 14 of 14)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Neural Machine Translation of Rare Words with Subword Units](https://mlsanity.com/paper/1508.07909/) (2015)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [Subword Regularization: Improving Neural Network Translation Models with Multiple Subword Candidates](https://mlsanity.com/paper/1804.10959/) (2018)
- [ByT5: Towards a token-free future with pre-trained byte-to-byte models](https://mlsanity.com/paper/2105.13626/) (2021)
- [MEGABYTE: Predicting Million-byte Sequences with Multiscale Transformers](https://mlsanity.com/paper/2305.07185/) (2023)
- [MrT5: Dynamic Token Merging for Efficient Byte-level Language Models](https://mlsanity.com/paper/2410.20771/) (2024)
- [MorphBPE: A Morpho-Aware Tokenizer Bridging Linguistic Complexity for Efficient LLM Training Across Morphologies](https://mlsanity.com/paper/2502.00894/) (2025)
- [Naver Labs Europe's Systems for the WMT19 Machine Translation Robustness Task](https://mlsanity.com/paper/1907.06488/) (2019)
- [BPE Stays on SCRIPT: Structured Encoding for Robust Multilingual Pretokenization](https://mlsanity.com/paper/2505.24689/) (2025)
- [Don't Touch My Diacritics](https://mlsanity.com/paper/2410.24140/) (2024)
- [Tokens with Meaning: A Hybrid Tokenization Approach for Turkish](https://mlsanity.com/paper/2508.14292/) (2025)
- [Tokenization with Factorized Subword Encoding](https://mlsanity.com/paper/2306.07764/) (2023)

## Abstract (arXiv)

Standard subword tokenizers either treat every orthographic variation of a word (such as hello, Hello, HELLO, and H'ello) as unrelated vocabulary entries, which fragments the embedding space, or discard this variation through lossy normalization. We present the Functionalizer, a lossless pre-tokenizer framework that factors orthographic and structural variations into a compositional opcode/operand prefix stream before tokenization: a canonical base token (operand) prefixed by parametric transformation operators (opcodes) encoded in the Unicode Private Use Area. We introduce operators covering casing (CAPITALIZE), diacritics (13 dedicated opcodes), and character repetition (REPEAT, MULTIREPEAT), which are fully reversible. Across natural language and code corpora, the Functionalizer enables complete corpus coverage with significantly smaller vocabularies under unconstrained exhaustion conditions, reducing actual vocabulary slot requirements by up to 19.7%. Downstream evaluations on 98M-parameter GPT-2 models show that the Functionalizer improves Python code syntax validity (9.12% vs. 7.70%) while reducing duplicate n-gram repetition in natural language prose. These findings demonstrate that functional decomposition can be an effective mechanism for vocabulary-efficient, structurally aware language modeling, and motivate further validation at production scale.