BitTokens represent numbers as single tokens via IEEE 754 binary format, allowing small language models to learn basic arithmetic algorithms nearly perfectly.
Exposing numeracy gaps: A benchmark to evaluate fundamental numerical abilities in large language models.arXiv preprint arXiv:2502.11075
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Evaluations of 53 LLMs on 14 basic math tasks show reasoning models use ~18x more tokens with sometimes lower accuracy, non-monotonic gains from extended budgets, and sharp performance drops under token constraints.
Triadic Suffix Tokenization groups digits into triads with fixed magnitude suffixes to make order-of-magnitude relationships explicit at the token level for LLMs.
citing papers explorer
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Efficient numeracy in language models through single-token number embeddings
BitTokens represent numbers as single tokens via IEEE 754 binary format, allowing small language models to learn basic arithmetic algorithms nearly perfectly.
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Do LLMs Overthink Basic Math Reasoning? Benchmarking the Accuracy-Efficiency Tradeoff in Language Models
Evaluations of 53 LLMs on 14 basic math tasks show reasoning models use ~18x more tokens with sometimes lower accuracy, non-monotonic gains from extended budgets, and sharp performance drops under token constraints.
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A Triadic Suffix Tokenization Scheme for Numerical Reasoning
Triadic Suffix Tokenization groups digits into triads with fixed magnitude suffixes to make order-of-magnitude relationships explicit at the token level for LLMs.