# Causally Sufficient and Necessary Feature Expansion for Class-Incremental Learning

arXiv: https://arxiv.org/abs/2603.09145 · HTML: https://mlsanity.com/paper/2603.09145/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 62 references that are in the map.
- First posted on arXiv 10 Mar 2026.

## Builds on (most cited first, 30 of 33)

- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Large Scale Incremental Learning](https://mlsanity.com/paper/1905.13260/) (2019)
- [Progress & Compress: A scalable framework for continual learning](https://mlsanity.com/paper/1805.06370/) (2018)
- [Class-incremental learning: survey and performance evaluation on image classification](https://mlsanity.com/paper/2010.15277/) (2020)
- [Filter Pruning via Geometric Median for Deep Convolutional Neural Networks Acceleration](https://mlsanity.com/paper/1811.00250/) (2018)
- [DER: Dynamically Expandable Representation for Class Incremental Learning](https://mlsanity.com/paper/2103.16788/) (2021)
- [Counterfactual Visual Explanations](https://mlsanity.com/paper/1904.07451/) (2019)
- [DyTox: Transformers for Continual Learning with DYnamic TOken eXpansion](https://mlsanity.com/paper/2111.11326/) (2021)
- [Semantic Drift Compensation for Class-Incremental Learning](https://mlsanity.com/paper/2004.00440/) (2020)
- [FOSTER: Feature Boosting and Compression for Class-Incremental Learning](https://mlsanity.com/paper/2204.04662/) (2022)
- [Class-Incremental Learning: A Survey](https://mlsanity.com/paper/2302.03648/) (2023)
- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [A Model or 603 Exemplars: Towards Memory-Efficient Class-Incremental Learning](https://mlsanity.com/paper/2205.13218/) (2022)
- [Interventional Causal Representation Learning](https://mlsanity.com/paper/2209.11924/) (2022)
- [Weakly supervised causal representation learning](https://mlsanity.com/paper/2203.16437/) (2022)
- [Rademacher Complexity for Adversarially Robust Generalization](https://mlsanity.com/paper/1810.11914/) (2018)
- [Diffusion Visual Counterfactual Explanations](https://mlsanity.com/paper/2210.11841/) (2022)
- [Multi-View Causal Representation Learning with Partial Observability](https://mlsanity.com/paper/2311.04056/) (2023)
- [Prototypical Verbalizer for Prompt-based Few-shot Tuning](https://mlsanity.com/paper/2203.09770/) (2022)
- [Transport-based Counterfactual Models](https://mlsanity.com/paper/2108.13025/) (2021)
- [Counterfactual Samples Synthesizing and Training for Robust Visual Question Answering](https://mlsanity.com/paper/2110.01013/) (2021)
- [Invariant Learning via Probability of Sufficient and Necessary Causes](https://mlsanity.com/paper/2309.12559/) (2023)
- [Resolving Task Confusion in Dynamic Expansion Architectures for Class Incremental Learning](https://mlsanity.com/paper/2212.14284/) (2022)
- [Task-Agnostic Guided Feature Expansion for Class-Incremental Learning](https://mlsanity.com/paper/2503.00823/) (2025)

## Abstract (arXiv)

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.