From Source Reconstruction to Predictive State Preservation: An Information-Theoretic Framework for AI-Native Communication

Yi Wang; Linglong Dai

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arXiv · 2609.01131

From Source Reconstruction to Predictive State Preservation: An Information-Theoretic Framework for AI-Native Communication

Yi Wang·Linglong Dai

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Abstract

AI-native communication increasingly aims to support prediction rather than reproduce every detail of the source. This shift raises a basic question left implicit by conventional source coding: what should be preserved when the terminal goal is prediction? We take the source-induced predictive state as the fidelity object. It is the distribution of the specified future conditioned on the source observation and shared context. We show that this state is sufficient and minimal for exact predictive preservation. The terminal prediction loss then defines communication distortion as lost predictive performance rather than source reconstruction error. Under logarithmic loss, this distortion equals the conditional mutual information lost through communication. Using the receiver-side predictive state as a Bayes reference, we separate AI-receiver error into predictive value lost in communication, receiver-available value unusable by the model family, and family capability not realized by the deployed model. The same predictive state also suffices for matched compression. For finite-alphabet memoryless sources, access to the raw source gives no rate-distortion advantage over coding the state directly. Applying the same target-conditioned construction to sequential prediction reveals a dynamic boundary. A state induced by a fixed horizon is minimal for that horizon but may not support recursive updating as the target window shifts. Taking the entire future as the target yields a minimal full-future state that updates recursively and admits a Markov representation. Together, these results shift AI communication from source reconstruction to predictive-state preservation.

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Yi Wang, Linglong Dai. 2026-09-01. From Source Reconstruction to Predictive State Preservation: An Information-Theoretic Framework for AI-Native Communication. https://arxiv.org/abs/2609.01131

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