Despite their remarkable progress across diverse domains, Large Language Models (LLMs) consistently fail at simple character-level tasks, such as counting letters in words, due to a fundamental limitation: tokenization. In this work, we frame this limitation as a problem of low mutual information and analyze it in terms of concept emergence. Using a suite of 19 synthetic tasks that isolate character-level reasoning in a controlled setting, we show that such capabilities emerge slowly, suddenly, and only late in training. We further show that percolation-based models of concept emergence explain these patterns, suggesting that learning character composition is not fundamentally different from learning commonsense knowledge. To address this bottleneck, we propose a lightweight architectural modification that significantly improves character-level reasoning while preserving the inductive advantages of subword models. Together, our results bridge low-level perceptual gaps in tokenized LMs and provide a principled framework for understanding and mitigating their structural blind spots. We make our code publicly available.
TBD
If you found our work useful, please cite our paper:
@misc{cosma2025strawberry,
title={The Strawberry Problem: Emergence of Character-level Understanding in Tokenized Language Models},
author={Adrian Cosma and Stefan Ruseti and Emilian Radoi and Mihai Dascalu},
year={2025},
eprint={2505.14172},
archivePrefix={arXiv},
primaryClass={cs.CL},
url={https://arxiv.org/abs/2505.14172},
}
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