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Causally Sufficient and Necessary Feature Expansion for Class-Incremental Learning

Zhen Zhang, Jielei Chu, Tianrui Li

TL;DR

A Probability of Necessity and Sufficiency (PNS)-based regularization method to guide feature expansion in CIL, which quantifies both the causal completeness of intra-task representations and the separability of inter-task representations.

Abstract

Current expansion-based methods for Class Incremental Learning (CIL) effectively mitigate catastrophic forgetting by freezing old features. However, such task-specific features learned from the new task may collide with the old features. From a causal perspective, spurious feature correlations are the main cause of this collision, manifesting in two scopes: (i) guided by empirical risk minimization (ERM), intra-task spurious correlations cause task-specific features to rely on shortcut features. These non-robust features are vulnerable to interference, inevitably drifting into the feature space of other tasks; (ii) inter-task spurious correlations induce semantic confusion between visually similar classes across tasks. To address this, we propose a Probability of Necessity and Sufficiency (PNS)-based regularization method to guide feature expansion in CIL. Specifically, we first extend the definition of PNS to expansion-based CIL, termed CPNS, which quantifies both the causal completeness of intra-task representations and the separability of inter-task representations. We then introduce a dual-scope counterfactual generator based on twin networks to ensure the measurement of CPNS, which simultaneously generates: (i) intra-task counterfactual features to minimize intra-task PNS risk and ensure causal completeness of task-specific features, and (ii) inter-task interfering features to minimize inter-task PNS risk, ensuring the separability of inter-task representations. Theoretical analyses confirm its reliability. The regularization is a plug-and-play method for expansion-based CIL to mitigate feature collision. Extensive experiments demonstrate the effectiveness of the proposed method.

Causally Sufficient and Necessary Feature Expansion for Class-Incremental Learning

TL;DR

A Probability of Necessity and Sufficiency (PNS)-based regularization method to guide feature expansion in CIL, which quantifies both the causal completeness of intra-task representations and the separability of inter-task representations.

Abstract

Current expansion-based methods for Class Incremental Learning (CIL) effectively mitigate catastrophic forgetting by freezing old features. However, such task-specific features learned from the new task may collide with the old features. From a causal perspective, spurious feature correlations are the main cause of this collision, manifesting in two scopes: (i) guided by empirical risk minimization (ERM), intra-task spurious correlations cause task-specific features to rely on shortcut features. These non-robust features are vulnerable to interference, inevitably drifting into the feature space of other tasks; (ii) inter-task spurious correlations induce semantic confusion between visually similar classes across tasks. To address this, we propose a Probability of Necessity and Sufficiency (PNS)-based regularization method to guide feature expansion in CIL. Specifically, we first extend the definition of PNS to expansion-based CIL, termed CPNS, which quantifies both the causal completeness of intra-task representations and the separability of inter-task representations. We then introduce a dual-scope counterfactual generator based on twin networks to ensure the measurement of CPNS, which simultaneously generates: (i) intra-task counterfactual features to minimize intra-task PNS risk and ensure causal completeness of task-specific features, and (ii) inter-task interfering features to minimize inter-task PNS risk, ensuring the separability of inter-task representations. Theoretical analyses confirm its reliability. The regularization is a plug-and-play method for expansion-based CIL to mitigate feature collision. Extensive experiments demonstrate the effectiveness of the proposed method.
Paper Structure (32 sections, 5 theorems, 42 equations, 7 figures, 7 tables, 1 algorithm)

This paper contains 32 sections, 5 theorems, 42 equations, 7 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problem Formulation
  4. Feature Expansion of Task-Specific Models
  5. Causal Analysis of expansion-based CIL
  6. Method
  7. Probability of Sufficient and Necessary Cause
  8. Definition of PNS in expansion-based CIL
  9. Causal Identifiability of CPNS
  10. CPNS Risk Modeling
  11. Overall Objective and Optimization Strategy
  12. Experiments
  13. Experimental Setup
  14. Performance Results
  15. Performance Experiments on Fine-grained Dataset.
  16. ...and 17 more sections

Key Result

Theorem 3.3

Given the monotonicity assumption, the CPNS is identifiable and defined by the difference in interventional distributions, robust to latent confounding: First, the identifiability of intra-task PNS: Second, the identifiability of inter-task PNS: where $do(\cdot)$ denotes the causal intervention operator.

Figures (7)

  • Figure 1: (a) Illustration of feature suppression and collision. ERM and diversity strategy drives the model to learn shortcut features (e.g., ear vs. eyes) for semantically similar classes, leading to a fragmented feature space. (b) CKA feature similarity analysis. Our method possesses high similarity in shallow layers (indicating shared causal semantics) while maintaining discriminability in deep layers.
  • Figure 2: Structural Causal Model (SCM) for expansion-based CIL. Left: causal generating mechanism, Right: the learning process.
  • Figure 3: Accuracy curves for CPNS on various scenarios and baselines.
  • Figure 4: Hyperparameter sensitivity analysis on CI FAR-100 10-10.
  • Figure 5: Training time and accuracy of different methods in the CIFAR-100 10-10 scenario.
  • ...and 2 more figures

Theorems & Definitions (12)

  • Definition 3.1: Probability of Necessity and Sufficiency (PNS) pearl2009causalityyang2023invariant
  • Definition 3.2: Probability of Necessity and Sufficiency in Expansion-based CIL (CPNS)
  • Theorem 3.3: Causal Identifiability of CPNS under Monotonicity
  • Definition 3.4: Double-range counterfactual modeling
  • Theorem 3.5: CPNS risk
  • Theorem 1.1: Causal Identifiability of CPNS under Monotonicity
  • proof
  • Proposition 1.2
  • proof
  • Definition 1.3: Binary Simplification for Inter-task Monotonicity
  • ...and 2 more