# HEDP: A Hybrid Energy-Distance Prompt-based Framework for Domain Incremental Learning

arXiv: https://arxiv.org/abs/2605.05776 · HTML: https://mlsanity.com/paper/2605.05776/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 42 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 27 of 27)

- [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)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [Learning to Prompt for Vision-Language Models](https://mlsanity.com/paper/2109.01134/) (2021)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [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)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Large Scale Incremental Learning](https://mlsanity.com/paper/1905.13260/) (2019)
- [DyTox: Transformers for Continual Learning with DYnamic TOken eXpansion](https://mlsanity.com/paper/2111.11326/) (2021)
- [CORe50: a New Dataset and Benchmark for Continuous Object Recognition](https://mlsanity.com/paper/1705.03550/) (2017)
- [S-Prompts Learning with Pre-trained Transformers: An Occam's Razor for Domain Incremental Learning](https://mlsanity.com/paper/2207.12819/) (2022)
- [Co2L: Contrastive Continual Learning](https://mlsanity.com/paper/2106.14413/) (2021)
- [Continual Pre-training of Language Models](https://mlsanity.com/paper/2302.03241/) (2023)
- [Revisiting Class-Incremental Learning with Pre-Trained Models: Generalizability and Adaptivity are All You Need](https://mlsanity.com/paper/2303.07338/) (2023)
- [Continual Learning with Pre-Trained Models: A Survey](https://mlsanity.com/paper/2401.16386/) (2024)
- [Self-Supervised Models are Continual Learners](https://mlsanity.com/paper/2112.04215/) (2021)
- [Latent Replay for Real-Time Continual Learning](https://mlsanity.com/paper/1912.01100/) (2019)
- [Continual Learning and Catastrophic Forgetting](https://mlsanity.com/paper/2403.05175/) (2024)
- [A Continual Deepfake Detection Benchmark: Dataset, Methods, and Essentials](https://mlsanity.com/paper/2205.05467/) (2022)
- [Isolation and Impartial Aggregation: A Paradigm of Incremental Learning without Interference](https://mlsanity.com/paper/2211.15969/) (2022)
- [Energy-based Latent Aligner for Incremental Learning](https://mlsanity.com/paper/2203.14952/) (2022)
- [A Unified Approach to Domain Incremental Learning with Memory: Theory and Algorithm](https://mlsanity.com/paper/2310.12244/) (2023)
- [Continual Learning at the Edge: Real-Time Training on Smartphone Devices](https://mlsanity.com/paper/2105.13127/) (2021)
- [CP-Prompt: Composition-Based Cross-modal Prompting for Domain-Incremental Continual Learning](https://mlsanity.com/paper/2407.21043/) (2024)
- [MoP-CLIP: A Mixture of Prompt-Tuned CLIP Models for Domain Incremental Learning](https://mlsanity.com/paper/2307.05707/) (2023)

## Abstract (arXiv)

Domain Incremental Learning is a critical scenario that requires models to continuously adapt to new data domains without retraining. However, domain shifts often cause severe performance degradation. To address this, we propose Hybrid Energy-Distance Prompt, a domain-incremental framework inspired by Helmholtz free energy. HEDP introduces an energy regularization loss to enhance the separability of domain representations and a hybrid energy-distance weighted mechanism that fuses energy-based and distance-based cues to improve domain selection and generalization. Experiments on multiple benchmarks, including CORe50, show that HEDP achieves superior performance on unseen domains with a 2.57% accuracy gain, effectively mitigating catastrophic forgetting and enhancing open-world adaptability. Our code is hrefhttps://github.com/dannis97500/HEDP/available here.