# Routing without Forgetting

arXiv: https://arxiv.org/abs/2603.09576 · HTML: https://mlsanity.com/paper/2603.09576/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 46 references that are in the map.
- First posted on arXiv 10 Mar 2026.

## Builds on (most cited first, 30 of 34)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [Visual Prompt Tuning](https://mlsanity.com/paper/2203.12119/) (2022)
- [Efficient Lifelong Learning with A-GEM](https://mlsanity.com/paper/1812.00420/) (2018)
- [Learning to Prompt for Continual Learning](https://mlsanity.com/paper/2112.08654/) (2021)
- [Dark Experience for General Continual Learning: a Strong, Simple Baseline](https://mlsanity.com/paper/2004.07211/) (2020)
- [Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence](https://mlsanity.com/paper/1801.10112/) (2018)
- [DualPrompt: Complementary Prompting for Rehearsal-free Continual Learning](https://mlsanity.com/paper/2204.04799/) (2022)
- [Gradient based sample selection for online continual learning](https://mlsanity.com/paper/1903.08671/) (2019)
- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [CODA-Prompt: COntinual Decomposed Attention-based Prompting for Rehearsal-Free Continual Learning](https://mlsanity.com/paper/2211.13218/) (2022)
- [Online Continual Learning with Maximally Interfered Retrieval](https://mlsanity.com/paper/1908.04742/) (2019)
- [On Tiny Episodic Memories in Continual Learning](https://mlsanity.com/paper/1902.10486/) (2019)
- [FOSTER: Feature Boosting and Compression for Class-Incremental Learning](https://mlsanity.com/paper/2204.04662/) (2022)
- [New Insights on Reducing Abrupt Representation Change in Online Continual Learning](https://mlsanity.com/paper/2104.05025/) (2021)
- [InfLoRA: Interference-Free Low-Rank Adaptation for Continual Learning](https://mlsanity.com/paper/2404.00228/) (2024)
- [Revisiting Class-Incremental Learning with Pre-Trained Models: Generalizability and Adaptivity are All You Need](https://mlsanity.com/paper/2303.07338/) (2023)
- [Using Hindsight to Anchor Past Knowledge in Continual Learning](https://mlsanity.com/paper/2002.08165/) (2020)
- [A Model or 603 Exemplars: Towards Memory-Efficient Class-Incremental Learning](https://mlsanity.com/paper/2205.13218/) (2022)
- [Class-Incremental Continual Learning into the eXtended DER-verse](https://mlsanity.com/paper/2201.00766/) (2022)
- [Expandable Subspace Ensemble for Pre-Trained Model-Based Class-Incremental Learning](https://mlsanity.com/paper/2403.12030/) (2024)
- [Large-scale Unsupervised Semantic Segmentation](https://mlsanity.com/paper/2106.03149/) (2021)
- [PCR: Proxy-based Contrastive Replay for Online Class-Incremental Continual Learning](https://mlsanity.com/paper/2304.04408/) (2023)
- [Divide and not forget: Ensemble of selectively trained experts in Continual Learning](https://mlsanity.com/paper/2401.10191/) (2024)

## Abstract (arXiv)

Continual learning in transformers is commonly addressed through parameter-efficient adaptation: prompts, adapters, or LoRA modules are specialized per task while the backbone remains frozen. Although effective in controlled multi-epoch settings, these approaches rely on gradual gradient-based specialization and struggle in Online Continual Learning (OCL), where data arrive as a non-stationary stream and each sample may be observed only once. We recast continual learning in transformers as a routing problem: under strict online constraints, the model must dynamically select the appropriate representational subspace for each input without explicit task identifiers or repeated optimization. We thus introduce Routing without Forgetting (RwF), a transformer architecture augmented with energy-based associative retrieval layers inspired by Modern Hopfield Networks. Instead of storing or merging task-specific prompts, RwF generates dynamic prompts through single-step associative retrieval over the transformer token embeddings at each layer. Retrieval corresponds to the closed-form minimization of a strictly convex free-energy functional, enabling input-conditioned routing within each forward pass, independently of iterative gradient refinement. Across challenging class-incremental benchmarks, RwF improves over existing prompt-based methods. On Split-ImageNet-R and Split-ImageNet-S, RwF outperforms prior prompt-based approaches by a large margin, even in few-shot learning regimes. These results indicate that embedding energy-based associative routing directly within the transformer backbone provides a principled and effective foundation for OCL.