# Closing the Oracle Gap: Increment Vector Transformation for Class Incremental Learning

arXiv: https://arxiv.org/abs/2509.21898 · HTML: https://mlsanity.com/paper/2509.21898/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 54 of its 71 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Builds on (most cited first, 30 of 54)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Fine-Grained Visual Classification of Aircraft](https://mlsanity.com/paper/1306.5151/) (2013)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Learning to Prompt for Continual Learning](https://mlsanity.com/paper/2112.08654/) (2021)
- [Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence](https://mlsanity.com/paper/1801.10112/) (2018)
- [Large Scale Incremental Learning](https://mlsanity.com/paper/1905.13260/) (2019)
- [DualPrompt: Complementary Prompting for Rehearsal-free Continual Learning](https://mlsanity.com/paper/2204.04799/) (2022)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)
- [Merging Models with Fisher-Weighted Averaging](https://mlsanity.com/paper/2111.09832/) (2021)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [CODA-Prompt: COntinual Decomposed Attention-based Prompting for Rehearsal-Free Continual Learning](https://mlsanity.com/paper/2211.13218/) (2022)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [Dataless Knowledge Fusion by Merging Weights of Language Models](https://mlsanity.com/paper/2212.09849/) (2022)
- [What is being transferred in transfer learning?](https://mlsanity.com/paper/2008.11687/) (2020)
- [DER: Dynamically Expandable Representation for Class Incremental Learning](https://mlsanity.com/paper/2103.16788/) (2021)
- [Essentially No Barriers in Neural Network Energy Landscape](https://mlsanity.com/paper/1803.00885/) (2018)
- [S-Prompts Learning with Pre-trained Transformers: An Occam's Razor for Domain Incremental Learning](https://mlsanity.com/paper/2207.12819/) (2022)
- [Overcoming Catastrophic Forgetting by Incremental Moment Matching](https://mlsanity.com/paper/1703.08475/) (2017)
- [FOSTER: Feature Boosting and Compression for Class-Incremental Learning](https://mlsanity.com/paper/2204.04662/) (2022)
- [Mnemonics Training: Multi-Class Incremental Learning without Forgetting](https://mlsanity.com/paper/2002.10211/) (2020)
- [Understanding the Role of Training Regimes in Continual Learning](https://mlsanity.com/paper/2006.06958/) (2020)
- [SLCA: Slow Learner with Classifier Alignment for Continual Learning on a Pre-trained Model](https://mlsanity.com/paper/2303.05118/) (2023)
- [A Model or 603 Exemplars: Towards Memory-Efficient Class-Incremental Learning](https://mlsanity.com/paper/2205.13218/) (2022)
- [Finetune like you pretrain: Improved finetuning of zero-shot vision models](https://mlsanity.com/paper/2212.00638/) (2022)
- [Adaptive Aggregation Networks for Class-Incremental Learning](https://mlsanity.com/paper/2010.05063/) (2020)
- [Linear Mode Connectivity in Multitask and Continual Learning](https://mlsanity.com/paper/2010.04495/) (2020)
- [Always Be Dreaming: A New Approach for Data-Free Class-Incremental Learning](https://mlsanity.com/paper/2106.09701/) (2021)

## Abstract (arXiv)

Class Incremental Learning (CIL) aims to sequentially acquire knowledge of new classes without forgetting previously learned ones. Despite recent progress, current CIL methods still exhibit significant performance gaps compared to their oracle counterparts-models trained with full access to historical data. Inspired by recent insights on Linear Mode Connectivity (LMC), we revisit the geometric properties of oracle solutions in CIL and uncover a fundamental observation: these oracle solutions typically maintain low-loss linear connections to the optimum of previous tasks. Motivated by this finding, we propose Increment Vector Transformation (IVT), a novel plug-and-play framework designed to mitigate catastrophic forgetting during training. Rather than directly following CIL updates, IVT periodically teleports the model parameters to transformed solutions that preserve linear connectivity to previous task optimum. By maintaining low-loss along these connecting paths, IVT effectively ensures stable performance on previously learned tasks. The transformation is efficiently approximated using diagonal Fisher Information Matrices, making IVT suitable for both exemplar-free and exemplar-based scenarios, and compatible with various initialization strategies. Extensive experiments on CIFAR-100, FGVCAircraft, ImageNet-Subset, and ImageNet-Full demonstrate that IVT consistently enhances the performance of strong CIL baselines. Specifically, on CIFAR-100, IVT improves the last accuracy of the PASS baseline by +5.12% and reduces forgetting by 2.54%. For the CLIP-pre-trained SLCA baseline on FGVCAircraft, IVT yields gains of +14.93% in average accuracy and +21.95% in last accuracy. The code will be released.