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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2511.01202 |
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| _version_ | 1866909034473324544 |
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| author | Bai, Bo |
| author_facet | Bai, Bo |
| contents | Despite the empirical successes of Large Language Models (LLMs), the prevailing paradigm is heuristic and experiment-driven, tethered to massive compute and data, while a first-principles theory remains absent. This treatise develops a Semantic Information Theory at the confluence of statistical physics, signal processing, and classical information theory, organized around a single paradigm shift: replacing the classical BIT - a microscopic substrate devoid of semantic content - with the macroscopic TOKEN as the atomic carrier of meaning and reasoning. Within this framework we recast attention and the Transformer as energy-based models, and interpret semantic embedding as vectorization on the semantic manifold. Modeling the LLM as a stateful channel with feedback, we adopt Massey's directed information as the native causal measure of autoregressive generation, from which we derive a *directed rate-distortion function for pre-training, a directed rate-reward function for RL-based post-training, and a sub-martingale account of inference-time semantic information flow. This machinery makes precise the identification of next-token prediction with Granger causal inference, and sharpens the limits of LLM reasoning against Pearl's Ladder of Causation - affirming that *whereas the BIT defined the Information Epoch, the TOKEN will define the AI Epoch. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01202 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Forget BIT, It is All about TOKEN: Towards Semantic Information Theory for LLMs Bai, Bo Information Theory Artificial Intelligence Despite the empirical successes of Large Language Models (LLMs), the prevailing paradigm is heuristic and experiment-driven, tethered to massive compute and data, while a first-principles theory remains absent. This treatise develops a Semantic Information Theory at the confluence of statistical physics, signal processing, and classical information theory, organized around a single paradigm shift: replacing the classical BIT - a microscopic substrate devoid of semantic content - with the macroscopic TOKEN as the atomic carrier of meaning and reasoning. Within this framework we recast attention and the Transformer as energy-based models, and interpret semantic embedding as vectorization on the semantic manifold. Modeling the LLM as a stateful channel with feedback, we adopt Massey's directed information as the native causal measure of autoregressive generation, from which we derive a *directed rate-distortion function for pre-training, a directed rate-reward function for RL-based post-training, and a sub-martingale account of inference-time semantic information flow. This machinery makes precise the identification of next-token prediction with Granger causal inference, and sharpens the limits of LLM reasoning against Pearl's Ladder of Causation - affirming that *whereas the BIT defined the Information Epoch, the TOKEN will define the AI Epoch. |
| title | Forget BIT, It is All about TOKEN: Towards Semantic Information Theory for LLMs |
| topic | Information Theory Artificial Intelligence |
| url | https://arxiv.org/abs/2511.01202 |