# Geometry-Anchored Transport Framework for Exemplar-Free Class-Incremental Learning

arXiv: https://arxiv.org/abs/2606.25347 · HTML: https://mlsanity.com/paper/2606.25347/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 38 references that are in the map.
- First posted on arXiv 24 Jun 2026.

## Builds on (most cited first, 25 of 25)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence](https://mlsanity.com/paper/1801.10112/) (2018)
- [Overcoming catastrophic forgetting with hard attention to the task](https://mlsanity.com/paper/1801.01423/) (2018)
- [Class-incremental learning: survey and performance evaluation on image classification](https://mlsanity.com/paper/2010.15277/) (2020)
- [Online Continual Learning in Image Classification: An Empirical Survey](https://mlsanity.com/paper/2101.10423/) (2021)
- [Semantic Drift Compensation for Class-Incremental Learning](https://mlsanity.com/paper/2004.00440/) (2020)
- [Class-Incremental Continual Learning into the eXtended DER-verse](https://mlsanity.com/paper/2201.00766/) (2022)
- [FeTrIL: Feature Translation for Exemplar-Free Class-Incremental Learning](https://mlsanity.com/paper/2211.13131/) (2022)
- [PyCIL: A Python Toolbox for Class-Incremental Learning](https://mlsanity.com/paper/2112.12533/) (2021)
- [ACIL: Analytic Class-Incremental Learning with Absolute Memorization and Privacy Protection](https://mlsanity.com/paper/2205.14922/) (2022)
- [On the Stability-Plasticity Dilemma of Class-Incremental Learning](https://mlsanity.com/paper/2304.01663/) (2023)
- [Elastic Feature Consolidation for Cold Start Exemplar-Free Incremental Learning](https://mlsanity.com/paper/2402.03917/) (2024)
- [Resurrecting Old Classes with New Data for Exemplar-Free Continual Learning](https://mlsanity.com/paper/2405.19074/) (2024)
- [Exemplar-free Continual Representation Learning via Learnable Drift Compensation](https://mlsanity.com/paper/2407.08536/) (2024)
- [DS-AL: A Dual-Stream Analytic Learning for Exemplar-Free Class-Incremental Learning](https://mlsanity.com/paper/2403.17503/) (2024)
- [Adapting to Continuous Covariate Shift via Online Density Ratio Estimation](https://mlsanity.com/paper/2302.02552/) (2023)
- [Task-recency bias strikes back: Adapting covariances in Exemplar-Free Class Incremental Learning](https://mlsanity.com/paper/2409.18265/) (2024)
- [Overcoming Recency Bias of Normalization Statistics in Continual Learning: Balance and Adaptation](https://mlsanity.com/paper/2310.08855/) (2023)
- [Predicting the Susceptibility of Examples to Catastrophic Forgetting](https://mlsanity.com/paper/2406.09935/) (2024)
- [Semantic Shift Estimation via Dual-Projection and Classifier Reconstruction for Exemplar-Free Class-Incremental Learning](https://mlsanity.com/paper/2503.05423/) (2025)
- [Measuring Representational Shifts in Continual Learning: A Linear Transformation Perspective](https://mlsanity.com/paper/2505.20970/) (2025)
- [Class-Incremental Mixture of Gaussians for Deep Continual Learning](https://mlsanity.com/paper/2307.04094/) (2023)

## Abstract (arXiv)

Exemplar-free class-incremental learning (EFCIL) requires stable decision boundaries within a shifting feature space. While maintaining class-conditional Gaussian statistics provides a principled classification strategy, these parametric summaries remain sensitive to anisotropic representation drift. Existing methods often transport these statistics across tasks using a decoupled, post-hoc paradigm: optimizing a backbone without explicit geometric constraints can distort the legacy manifold, limiting the precision of retroactive alignment. In this paper, we formulate feature transport as an endogenous training constraint rather than a separate post-task step, presenting the Geometry-Anchored Transport Framework. First, we derive an Analytic Geometric Anchor via Mahalanobis-aligned regression to mitigate macroscopic anisotropic drift. Second, we introduce a Topology-Aware Evolution objective that regularizes localized manifold degradation while calibrating a residual network against the analytic prior. By coupling manifold evolution with transport constraints during the primary training phase, our framework mitigates evaluation errors without requiring decoupled fine-tuning. Experiments across CIFAR-100, TinyImageNet, and ImageNet-100 demonstrate that the proposed framework consistently improves upon existing post-hoc alternatives under strict exemplar-free constraints.