Same Quantity, Different Answer: Numerical Representation Invariance in Language Models

arXiv:2609.25009 · cs.CL, cs.LG · Submitted 2026-07-27 · Read on arXiv

cs.CL, cs.LG

Submitted: 2026-07-27

Updated: 2026-07-27

Comments: 15 pages, 2 figures. Ancillary archive includes the frozen benchmark, evaluation and audit records, consensus raw responses, manifests, analysis code, and tests

Code: https://github.com/ggml-org/llama.cpp

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Accuracy — 10× in this paper · explained in 1 episode
• Benchmark — 10× in this paper · explained in 2 episodes
• Consistency — 10× in this paper · explained in 3 episodes
• Quantization — 6× in this paper · explained in 12 episodes
• Self-consistency — 6× in this paper · explained in 2 episodes
• Embeddings — 4× in this paper · explained in 2 episodes
• Tokenization — 4× in this paper · explained in 2 episodes
• Abstention — 3× in this paper · explained in 1 episode
• Generalization — 2× in this paper · explained in 13 episodes
• Hallucination — 2× in this paper · explained in 4 episodes
• International Conference on Learning Representations — 2× in this paper
• LLM judge — 2× in this paper · explained in 2 episodes
• Adam — 1× in this paper · explained in 2 episodes
• Domain Shift — 1× in this paper · explained in 4 episodes
• Provenance — 1× in this paper · explained in 4 episodes
• Trace — 1× in this paper · explained in 2 episodes
• Transformer — 1× in this paper · explained in 2 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Testing LLM Arithmetic Reasoning Generalization with Automatic Numeric-Remapping Attacks
• Metamorphic Testing of Large Language Models for Natural Language Processing
• gpt-oss-120b & gpt-oss-20b Model Card
• Tokenization counts: the impact of tokenization on arithmetic in frontier LLMs

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