Understanding Catastrophic Interference: On the Identifibility of Latent Representations

TL;DR

The paper tackles catastrophic forgetting by treating it as a latent-variable identifiability problem between partial-task aware and all-task aware data-generating processes. It proves that forgetting can be quantified by the distance between PTA and ATA latent representations and mitigated by identifying and aligning their shared latent variables through a two-stage training procedure (MLE latent recovery followed by KL-based alignment). The ICON framework leverages flow-based networks to model PTA and ATA, provides identifiability guarantees under stated assumptions, and demonstrates superior performance on synthetic data and real-world benchmarks (CIFAR-100 and ImageNet-100) compared with state-of-the-art methods. This work bridges theory and practice, offering a principled approach to continual learning through latent-variable identifiability with practical strategies for real-world continual adaptation.

Abstract

Catastrophic interference, also known as catastrophic forgetting, is a fundamental challenge in machine learning, where a trained learning model progressively loses performance on previously learned tasks when adapting to new ones. In this paper, we aim to better understand and model the catastrophic interference problem from a latent representation learning point of view, and propose a novel theoretical framework that formulates catastrophic interference as an identification problem. Our analysis demonstrates that the forgetting phenomenon can be quantified by the distance between partial-task aware (PTA) and all-task aware (ATA) setups. Building upon recent advances in identifiability theory, we prove that this distance can be minimized through identification of shared latent variables between these setups. When learning, we propose our method \ourmeos with two-stage training strategy: First, we employ maximum likelihood estimation to learn the latent representations from both PTA and ATA configurations. Subsequently, we optimize the KL divergence to identify and learn the shared latent variables. Through theoretical guarantee and empirical validations, we establish that identifying and learning these shared representations can effectively mitigate catastrophic interference in machine learning systems. Our approach provides both theoretical guarantees and practical performance improvements across both synthetic and benchmark datasets.

Figures (4)

• Figure 1: The illustration of our definition of subspace identification in Def. \ref{['def:iden']}. Given two space of latent variables of PTA setup $\overline{\mathcal{Z}}^{\mathbf{t}}\ni\overline{{\mathbf{z}}}^{\mathbf{t}}$ and ATA approach $\tilde{\mathcal{Z}}^{\mathbf{t}}\ni\tilde{{\mathbf{z}}}^{\mathbf{t}}$, we aim to identify their intersection ${\mathbf{z}}^{\mathbf{t}}\in\mathcal{Z}^{\mathbf{t}} = \overline{\mathcal{Z}}^{\mathbf{t}} \cap \tilde{\mathcal{Z}}^{\mathbf{t}}$.
• Figure 2: Visualization of latent space distributions across three tasks under PTA (blue) and ATA (red) setups from our simulations. The top row shows representations without optimizing the KL divergence in Eq. \ref{['eq:kl_divergence']}, displaying significant disparity between PTA and ATA. The bottom row demonstrates improved alignment through our proposed KL-based identification approach, illustrating effective mitigation of catastrophic forgetting across sequential tasks. For clear visualizations, each figure displays 1,000 uniformly sampled points $\hat{\overline{{\mathbf{z}}}}^{\mathbf{t}}$ and $\hat{\tilde{{\mathbf{z}}}}^{\mathbf{t}}$, respectively.
• Figure 3: Visualization of latent space distributions across Tasks 1, 4, and 7 on ImageNet-100 dataset, comparing representations from PTA (blue) and ATA (red) frameworks. The top row shows results without using KL divergence optimization in Eq. \ref{['eq:kl_divergence']}, where significant distribution misalignment indicates catastrophic forgetting as training progresses through tasks. The bottom row demonstrates our ICON with KL divergence optimization, exhibiting substantially improved alignment. For visualization clarity, each subfigure displays 1,000 uniformly sampled points from the estimated latent representations $\hat{\overline{\mathbf{z}}}^t$ (PTA framework) and $\hat{\tilde{\mathbf{z}}}^t$ (ATA framework).
• Figure 4: Visualization of latent space distributions across Tasks 1, 4, and 7 on CIFAR-100 benchmark.