Why Do Neural Networks Forget: A Study of Collapse in Continual Learning

Catastrophic forgetting is commonly interpreted as the irreversible erasure of previously acquired knowledge during sequential learning. In this work, we investigate an alternative perspective: that forgetting may arise not from complete destruction of task representations but from a loss of accessibility to preserved information. We introduce a three-level framework separating knowledge storage, representation, and accessibility, and evaluate each component through a series of continual-learning experiments on sequential CIFAR-100 classification using ResNet-18. Our analysis combines checkpoint persistence, linear probing, representation geometry, classifier-reset recovery, and layer-wise recoverability experiments. We observe complete behavioral forgetting of earlier tasks, with task accuracy collapsing from 54.8% to 0%, while linear probe performance retains approximately 76% of the original representational information. Furthermore, retraining only the final classifier restores 75.7% of the original task performance without modifying the backbone network. Layer-wise analysis reveals that early and intermediate layers preserve highly recoverable task information despite severe degradation at later stages. Projection-energy and principal-angle analyses indicate that retained knowledge persists as distributed high-dimensional representations rather than through preservation of a small dominant subspace. These findings suggest that catastrophic forgetting is better characterized as an accessibility failure than complete representational erasure, and that substantial task-relevant information remains embedded within neural representations even after functional forgetting has occurred.

Accuracy degradation is the standard metric for Catastrophic Forgetting (CF), however, it records only whether forgetting occurred or not. It saturates at the extremes and collapses discretely at task boundaries, hiding the internal structure of what is being forgotten. We introduce six softmax-derived metrics spanning true-label rank (TLR), predictive confidence, and distributional divergence that characterize forgetting continuously, each normalized to [0, 1] with no modification to training. On CIFAR-100, these metrics carry information where accuracy does not: at 0% accuracy, the Confusion Margin spans an IQR of [0.32, 0.50] across classes that accuracy treats identically. We demonstrate that this richer signal is actionable in mitigating catastrophic forgetting. Per-sample metric scores used as loss weights reduce forgetting by 1.3 percentage points over uniform experience replay (ER) on CIFAR-100. Furthermore, the slope of a metric over a small window provides a stable sampling criterion: at a small-window size (e.g. 3 epochs), accuracy-trend degrades to 34.79% (std. = 2.32) while log-TLR achieves 41.07% (std. = 0.57). This gap is structural since reliable small-window trend estimation requires a continuous signal. On TinyImageNet, log-TLR trend sampling reduces forgetting by 7.7 percentage points over the ER baseline.

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 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 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 Wrong-Context Probing (P5), a practical diagnostic protocol for measuring $C_\mathrm{ctx}$, and extend the framework to CIFAR-10 via a novel 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: architecture over algorithm -- the context pathway must be structurally unbypassable.