A neural network can forget along a graceful, human-like power-law curve — not only catastrophically — when feature overlap preserves the trace

The textbook AI failure mode is catastrophic forgetting: a network trained on task B abruptly overwrites task A. Kline (2025) shows the opposite regime is reachable. He trained an MLP on MNIST, then stopped presenting digit-8 examples, and measured a "recall probability" for class 8 — a softmax over the cosine similarity between the last hidden state and stored class prototypes. Instead of collapsing to zero, recall decayed gradually: starting near 0.29, falling to roughly 0.18, then flattening rather than vanishing. Fit to the data, the decay is a power law; Kline reports that "the forgetting curve measured from the MLP model closely follows a human-like memory curve." The trace never fully erased because 8 shares strokes with 6 and 9 — feature overlap keeps the representation partly supported even as retrieval fades.

The reconciliation with catastrophic forgetting is a regime distinction, not a refutation. Kline notes that "naïve networks update parameters via gradient descent and can overwrite representations for Task A almost immediately after learning Task B" — the abrupt failure is the disjoint-sequential-task regime. The graceful power-law curve appears instead under feature overlap and single-task representational drift. Which regime one observes depends on task geometry. The capture sourced that catastrophic-vs-graceful framing only to a Tier-4 web search, below the mechanism-claim floor; verification against primaries is routed to question-catastrophic-vs-graceful-forgetting-regime.

This extends the vault's neuro-AI-parallel cluster, where a plain optimizer reproduces a phenomenon usually attributed to biology: claim-critical-periods-arise-from-information-plasticity-not-biology and claim-deep-nets-have-critical-learning-periods-timed-like-animals make the same move for developmental critical periods, and Achille & Soatto frame that work as the Information-Bottleneck slogan "learning is forgetting" — a direct conceptual bridge to a literal forgetting curve. It sits in the same tension with backpropagation-gap: a non-biological learning mechanism reproducing a biological phenomenon. It is also the neural analogue of memory decay studied on the LLM side as context rot. The spacing effect Kline observes on top of this curve is treated separately in claim-spacing-effect-emerges-in-gradient-descent-unbidden.