Technical Summary: Catastrophic Forgetting as Accessibility Collapse

Problem Statement

The paper addresses catastrophic forgetting in deep neural networks, a phenomenon where performance on previously learned tasks collapses rapidly as new tasks are learned sequentially. The prevailing assumption in the field is that this collapse represents the irreversible destruction or erasure of learned knowledge representations. The authors challenge this interpretation, proposing that the observed accuracy collapse may not reflect the loss of underlying knowledge, but rather a failure in accessing that knowledge. The central research question is whether catastrophic forgetting implies the network has lost the knowledge itself or merely the ability to utilize it through its current decision pathway.

Methodology

The authors employ a "pure forgetting" experimental setup to create a clean benchmark for analyzing knowledge persistence without the interference of continual learning (CL) mitigation strategies.

• Dataset & Protocol: Experiments utilize Split CIFAR-100, partitioned into 10 sequential tasks of 10 classes each.
• Architecture: A ResNet-18 model is trained from random initialization.
• Training Conditions: The model is trained sequentially using standard cross-entropy loss and SGD. Crucially, no replay, no regularization, and no CL methods are applied. This ensures that any retention of knowledge is intrinsic to the network's dynamics rather than enforced by external constraints.
• Evaluation Framework: The authors introduce a Three-Level Framework to distinguish between:
  1. Knowledge Storage: Validity of saved checkpoints.
  2. Knowledge Representation: Information encoded in frozen intermediate features.
  3. Knowledge Accessibility: Functional output accuracy.
• Diagnostic Metrics:
  • Accessibility Gap (AG): Defined as $AG = LP_{final} - ACC_{final}$, quantifying the discrepancy between linear probe accuracy (representational knowledge) and task accuracy (functional performance).
  • Projection Energy (PE): A geometric metric measuring the fraction of final representation energy remaining within the original task subspace.
  • Principal Angle Analysis: Used to measure geometric drift between checkpoint and final model subspaces.
• Key Experiments:
  • Linear Probing: Training linear classifiers on frozen features from various layers to measure retained information.
  • Classifier Reset: Freezing the entire backbone of the "forgotten" model and training a new linear head on the original task data to test recoverability.
  • Layer-wise Analysis: Examining retention and recoverability at each residual block (Layers 1–4).
  • Parameter-Space Recovery: Testing if moving weights toward a stored checkpoint can restore accuracy.

Key Results

1. Complete Accuracy Collapse vs. Representation Retention

After sequential training on 10 tasks, Task 0's output accuracy collapses completely to 0.000. However, the internal state of the network retains significant information:

• Linear Probe Retention: A linear probe trained on the final model's Layer 4 features achieves 0.468 accuracy, which is 76% of the checkpoint-level probe accuracy (0.616).
• Accessibility Gap: The AG for Task 0 is 0.468, demonstrating a massive divergence between functional performance and internal representational quality.

2. Layer-Wise Asymmetry

Forgetting is not uniform across the network:

• Early Layers (1 & 2): These layers show 103% and 104% retention of their original probe accuracy, respectively. In some cases, subsequent task training appears to refine low-level features, improving their discriminative power for earlier tasks.
• Late Layers (4 & Classifier): Degradation is concentrated almost entirely in Layer 4 (76% retention) and the final classifier layer (0% retention).

3. Recoverability via Classifier Reset

When the backbone of the "forgotten" model is frozen and a new linear head is trained on Task 0 data:

• The model recovers 0.415 accuracy.
• This represents 75.7% of the original Task 0 performance (0.548), proving that the majority of task-relevant information remains encoded and is recoverable without modifying the backbone.
• Layer-wise Recoverability Hierarchy: Recoverable accuracy decreases monotonically from Layer 1 (122% of original) to Layer 4 (85%) to the full backbone reset (75.7%), indicating that information loss accumulates as representations propagate forward.

4. Geometric Findings

• Distributed Encoding: Projection Energy analysis reveals that retained information is not concentrated in a small set of dominant principal directions. Instead, it is distributed across high-dimensional subspaces.
• Subspace Rotation: Principal angle analysis shows a mean angle of 79° between the checkpoint and final model subspaces (approaching orthogonality). Despite this severe geometric rotation, linear probe retention remains high, suggesting that representational preservation is a high-dimensional phenomenon not captured by low-rank subspace overlap.
• Negative Result: Parameter-space geometric recovery (moving weights toward a stored checkpoint) was found to be ineffective under these experimental conditions.

Significance and Claims

The paper proposes the Accessibility Collapse Hypothesis, which reframes catastrophic forgetting not as the structural destruction of representations, but as a localized breakdown of functional accessibility concentrated at the final readout layer.

• Paradigm Shift: The authors argue that the field should shift from a prevention-oriented paradigm (constraining updates to preserve parameters) to a repair-oriented paradigm. Since representations naturally persist in a distributed, high-dimensional form, interventions should focus on adaptive, context-dependent readout mechanisms or lightweight task-specific routing heads rather than rigid regularization.
• Diagnostic Utility: The introduction of the Accessibility Gap and Projection Energy provides formal tools to distinguish between representational erasure and accessibility failure, offering a more nuanced view of knowledge persistence.
• Empirical Foundation: By demonstrating that 75.7% of task performance can be recovered simply by retraining the linear head, the work establishes that substantial task-relevant information survives sequential training even in the absence of any continual learning safeguards.

The paper concludes that catastrophic forgetting is primarily an alignment failure between the network's internal representations and its output pathway, rather than a loss of the representations themselves.