# Pathway-based Progressive Inference (PaPI) for Energy-Efficient Continual Learning

arXiv: https://arxiv.org/abs/2506.17848 · HTML: https://mlsanity.com/paper/2506.17848/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 24 references that are in the map.
- First posted on arXiv 21 Jun 2025.

## Builds on (most cited first, 14 of 14)

- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Experience Replay for Continual Learning](https://mlsanity.com/paper/1811.11682/) (2018)
- [PackNet: Adding Multiple Tasks to a Single Network by Iterative Pruning](https://mlsanity.com/paper/1711.05769/) (2017)
- [Once-for-All: Train One Network and Specialize it for Efficient Deployment](https://mlsanity.com/paper/1908.09791/) (2019)
- [Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence](https://mlsanity.com/paper/1801.10112/) (2018)
- [Green AI](https://mlsanity.com/paper/1907.10597/) (2019)
- [Understanding the Role of Training Regimes in Continual Learning](https://mlsanity.com/paper/2006.06958/) (2020)
- [Online Meta-Learning](https://mlsanity.com/paper/1902.08438/) (2019)
- [Routing Networks: Adaptive Selection of Non-linear Functions for Multi-Task Learning](https://mlsanity.com/paper/1711.01239/) (2017)
- [A PAC-Bayesian bound for Lifelong Learning](https://mlsanity.com/paper/1311.2838/) (2013)

## Abstract (arXiv)

Continual learning systems face the dual challenge of preventing catastrophic forgetting while maintaining energy efficiency, particularly in resource-constrained environments. This paper introduces Pathway-based Progressive Inference (PaPI), a novel theoretical framework that addresses these challenges through a mathematically rigorous approach to pathway selection and adaptation. We formulate continual learning as an energy-constrained optimization problem and provide formal convergence guarantees for our pathway routing mechanisms. Our theoretical analysis demonstrates that PaPI achieves an O(K) improvement in the stability-plasticity trade-off compared to monolithic architectures, where K is the number of pathways. We derive tight bounds on forgetting rates using Fisher Information Matrix analysis and prove that PaPI's energy consumption scales with the number of active parameters rather than the total model size. Comparative theoretical analysis shows that PaPI provides stronger guarantees against catastrophic forgetting than Elastic Weight Consolidation (EWC) while maintaining better energy efficiency than both EWC and Gradient Episodic Memory (GEM). Our experimental validation confirms these theoretical advantages across multiple benchmarks, demonstrating PaPI's effectiveness for continual learning in energy-constrained settings. Our codes are available at https://github.com/zser092/PAPIFILES.