# A Triadic Suffix Tokenization Scheme for Numerical Reasoning

arXiv: https://arxiv.org/abs/2604.11582 · HTML: https://mlsanity.com/paper/2604.11582/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 8 of its 11 references that are in the map.
- First posted on arXiv 13 Apr 2026.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 8 of 8)

- [Tokenization counts: the impact of tokenization on arithmetic in frontier LLMs](https://mlsanity.com/paper/2402.14903/) (2024)
- [Number Cookbook: Number Understanding of Language Models and How to Improve It](https://mlsanity.com/paper/2411.03766/) (2024)
- [NumeroLogic: Number Encoding for Enhanced LLMs' Numerical Reasoning](https://mlsanity.com/paper/2404.00459/) (2024)
- [Exposing Numeracy Gaps: A Benchmark to Evaluate Fundamental Numerical Abilities in Large Language Models](https://mlsanity.com/paper/2502.11075/) (2025)
- [Regress, Don't Guess -- A Regression-like Loss on Number Tokens for Language Models](https://mlsanity.com/paper/2411.02083/) (2024)
- [Scaling Behavior for Large Language Models regarding Numeral Systems: An Example using Pythia](https://mlsanity.com/paper/2409.17391/) (2024)
- [Efficient numeracy in language models through single-token number embeddings](https://mlsanity.com/paper/2510.06824/) (2025)
- [Estimating Numbers without Regression](https://mlsanity.com/paper/2310.06204/) (2023)

## Abstract (arXiv)

Standard subword tokenization methods fragment numbers inconsistently, causing large language models (LLMs) to lose positional and decimal structure - a primary driver of errors in arithmetic and scientific reasoning. We introduce Triadic Suffix Tokenization (TST), a deterministic scheme that partitions digits into three-digit triads and annotates each triad with an explicit magnitude marker. Critically, the scheme defines a fixed, one-to-one mapping between suffixes and orders of magnitude for the integer part (thousands, millions, billions, etc.) and a parallel system of replicated markers for fractional depth (tenths, thousandths, millionths, etc.). Unlike approaches that rely on positional inference, this method provides a consistent gradient signal, which should ensure stable convergence. Two implementation variants are proposed: (1) a vocabulary-based approach that adds at most 10,000 fixed tokens to an existing vocabulary, covering 33 orders of magnitude (10-15 to 1018); and (2) a suffix-marker approach that uses a small set of special tokens to denote magnitude dynamically. Both variants preserve exact digits while making order-of-magnitude relationships transparent at the token level. While we focus on 3-digit groups (Triadic), the framework is inherently scalable to any group size for precise vocabulary optimization. Furthermore, it allows for linear vocabulary expansion to accommodate arbitrary precision and range. TST is architecture-agnostic and can be integrated as a drop-in preprocessing step. Experimental validation is deferred to future work.