Context Channel Capacity: An Information-Theoretic Framework for Understanding Catastrophic Forgetting
Catastrophic forgetting remains a central challenge in continual learning (CL), yet lacks a unified information-theoretic explanation for why some architectures forget catastrophically while others do not. We introduce \emph{Context Channel Capacity} ($C_\mathrm{ctx}$), the mutual information between a CL architecture's context signal and its generated parameters, and prove that zero forgetting requires $C_\mathrm{ctx} \geq H(T)$, where $H(T)$ is the task identity entropy. We establish an \emph{Impossibility Triangle} -- zero forgetting, online learning, and finite parameters cannot be simultaneously satisfied by sequential state-based learners -- and show that conditional regeneration ar...
| Authors | Ran Cheng |
|---|---|
| Primary category | cs.LG |
| Published | 8 March 2026 |
| Last updated at source | 8 March 2026 |
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