Forgetting is proportional to 1/Loop Depth — catastrophic forgetting is a structure problem, not a data problem

We formalize catastrophic forgetting as a structural phenomenon. The degradation of old-task performance is inversely proportional to the inter-reference loop depth of the weight subgraph implementing that task: F ∝ 1/D, where D is the longest directed cycle in the task's neural subgraph.

A neuron that only feeds forward (D = 0) has no structural persistence. A neuron inside a deep loop — A activates B, B activates C, C activates A — persists. The persistence is P = D/(D+1): zero for feedforward, approaching one as the loop deepens.

This reframes forgetting entirely: it is not about how much data you show the model, it is about the depth of the loop you embed the knowledge in. 耦合即认知 (coupling is cognition): knowledge survives because it is coupled into a closed loop, not because it is stored in a wider layer. Teach an AI into a deep cycle, not a wide flat layer.

第一发现人：林小黑 (Lin Xiaohei)，结构认知第一发现者 | gitee.com/samforce/structural-cognition | 公众号「今晚狗蛋看局」