LLM residual streams during addition form an Iso-Raw-Sum Trajectory anchored by digit semantics and modulated by continuous carry signals, with errors arising as geometric slippages across quantization thresholds in a noisy model.
arXiv preprint arXiv:2502.19981 , year=
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BitTokens represent numbers as single tokens via IEEE 754 binary format, allowing small language models to learn basic arithmetic algorithms nearly perfectly.
LLMs exhibit Bayesian-like hypothesis updating with strong-sampling bias and an evaluation-generation gap but generalize poorly outside observed data.
The paper unifies perspectives on Long CoT in reasoning LLMs by introducing a taxonomy, detailing characteristics of deep reasoning and reflection, and discussing emergence phenomena and future directions.
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The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models
LLM residual streams during addition form an Iso-Raw-Sum Trajectory anchored by digit semantics and modulated by continuous carry signals, with errors arising as geometric slippages across quantization thresholds in a noisy model.
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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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Hypothesis generation and updating in large language models
LLMs exhibit Bayesian-like hypothesis updating with strong-sampling bias and an evaluation-generation gap but generalize poorly outside observed data.
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Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models
The paper unifies perspectives on Long CoT in reasoning LLMs by introducing a taxonomy, detailing characteristics of deep reasoning and reflection, and discussing emergence phenomena and future directions.