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arXiv 2603.07415cs.LGcs.AIcs.ITmath.IT

上下文通道容量:一种理解灾难性遗忘的信息论框架

Context Channel Capacity: An Information-Theoretic Framework for Understanding Catastrophic Forgetting

Ran Cheng

AI总结:

本文提出上下文通道容量框架,通过信息论解释持续学习中的灾难性遗忘问题,证明零遗忘需满足C_ctx ≥ H(T),并展示HyperNetworks通过重新定义参数为函数值实现零遗忘,同时提出Wrong-Context Probing诊断协议和梯度上下文编码器改进方法。

摘要:

灾难性遗忘仍然是持续学习(CL)中的核心挑战,但缺乏统一的信息论解释来说明为什么某些架构会灾难性地遗忘,而其他架构则不会。我们引入了上下文通道容量(C_ctx),即持续学习架构的上下文信号与其生成参数之间的互信息,并证明零遗忘需要C_ctx ≥ H(T),其中H(T)是任务身份熵。我们建立了一个不可能三角形——零遗忘、在线学习和有限参数无法同时由基于状态的顺序学习者满足,并展示了条件再生架构(HyperNetworks)通过将参数重新定义为函数值而非状态来绕过这个三角形。我们验证了该框架在8种持续学习方法上对Split-MNIST的适用性(1,130多个实验,持续86天,每个种子4次),证明C_ctx完美预测遗忘行为:C_ctx = 0的方法(NaiveSGD、EWC、SI、LwF、CFlow)表现出灾难性遗忘(6-97%),而C_ctx ≈ 1的方法(HyperNetwork)实现零遗忘(98.8% ACC)。我们进一步提出Wrong-Context Probing(P5),一种实用的诊断协议用于测量C_ctx,并通过一种新的梯度上下文编码器将框架扩展到CIFAR-10,从而缩小了Oracle差距从23.3pp到0.7pp。一个系统化的15多个闭合研究方向的分类——包括Hebbian null结果(冻结随机特征优于学习特征)、CFlow的θ₀-记忆现象以及S_N对列专业化的对称障碍——为社区提供了精确诊断的负面结果。我们的核心设计原则:架构优先于算法——上下文路径必须在结构上不可绕过。

英文摘要:

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 architectures (HyperNetworks) bypass this triangle by redefining parameters as function values rather than states. We validate this framework across 8 CL methods on Split-MNIST (1,130+ experiments over 86 days, 4 seeds each), showing that $C_\mathrm{ctx}$ perfectly predicts forgetting behavior: methods with $C_\mathrm{ctx} = 0$ (NaiveSGD, EWC, SI, LwF, CFlow) exhibit catastrophic forgetting (6--97\%), while methods with $C_\mathrm{ctx} \approx 1$ (HyperNetwork) achieve zero forgetting (98.8\% ACC). We further propose \emph{Wrong-Context Probing} (P5), a practical diagnostic protocol for measuring $C_\mathrm{ctx}$, and extend the framework to CIFAR-10 via a novel \emph{Gradient Context Encoder} that closes the oracle gap from 23.3pp to 0.7pp. A systematic taxonomy of 15+ closed research directions -- including the Hebbian null result (frozen random features outperform learned features), CFlow's $θ_0$-memorizer phenomenon, and the $S_N$ symmetry barrier to column specialization -- provides the community with precisely diagnosed negative results. Our central design principle: \emph{architecture over algorithm} -- the context pathway must be structurally unbypassable.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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