# PMF-CL: Pareto-Minimal-Forgetting Continual Learner for Conflicting Tasks

arXiv: https://arxiv.org/abs/2605.19145 · HTML: https://mlsanity.com/paper/2605.19145/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 39 of its 71 references that are in the map.
- First posted on arXiv 18 May 2026.

## Builds on (most cited first, 30 of 39)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Memory Aware Synapses: Learning what (not) to forget](https://mlsanity.com/paper/1711.09601/) (2017)
- [Efficient Lifelong Learning with A-GEM](https://mlsanity.com/paper/1812.00420/) (2018)
- [Dark Experience for General Continual Learning: a Strong, Simple Baseline](https://mlsanity.com/paper/2004.07211/) (2020)
- [A Survey on Multimodal Large Language Models](https://mlsanity.com/paper/2306.13549/) (2023)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks](https://mlsanity.com/paper/1901.08584/) (2019)
- [Online Continual Learning with Maximally Interfered Retrieval](https://mlsanity.com/paper/1908.04742/) (2019)
- [Gradient Projection Memory for Continual Learning](https://mlsanity.com/paper/2103.09762/) (2021)
- [Federated Continual Learning with Weighted Inter-client Transfer](https://mlsanity.com/paper/2003.03196/) (2020)
- [Federated Class-Incremental Learning](https://mlsanity.com/paper/2203.11473/) (2022)
- [Optimal Continual Learning has Perfect Memory and is NP-hard](https://mlsanity.com/paper/2006.05188/) (2020)
- [TRGP: Trust Region Gradient Projection for Continual Learning](https://mlsanity.com/paper/2202.02931/) (2022)
- [How catastrophic can catastrophic forgetting be in linear regression?](https://mlsanity.com/paper/2205.09588/) (2022)
- [Rehearsal revealed: The limits and merits of revisiting samples in continual learning](https://mlsanity.com/paper/2104.07446/) (2021)
- [Theory on Forgetting and Generalization of Continual Learning](https://mlsanity.com/paper/2302.05836/) (2023)
- [TARGET: Federated Class-Continual Learning via Exemplar-Free Distillation](https://mlsanity.com/paper/2303.06937/) (2023)
- [Beyond Not-Forgetting: Continual Learning with Backward Knowledge Transfer](https://mlsanity.com/paper/2211.00789/) (2022)
- [Federated Learning Meets Multi-objective Optimization](https://mlsanity.com/paper/2006.11489/) (2020)
- [Federated Continual Learning via Knowledge Fusion: A Survey](https://mlsanity.com/paper/2312.16475/) (2023)
- [A distillation-based approach integrating continual learning and federated learning for pervasive services](https://mlsanity.com/paper/2109.04197/) (2021)
- [Non-IID data and Continual Learning processes in Federated Learning: A long road ahead](https://mlsanity.com/paper/2111.13394/) (2021)
- [The Ideal Continual Learner: An Agent That Never Forgets](https://mlsanity.com/paper/2305.00316/) (2023)
- [Asynchronous Federated Continual Learning](https://mlsanity.com/paper/2304.03626/) (2023)

## Abstract (arXiv)

In the literature, many continual learning (CL) algorithms have been proposed to address the issue of catastrophic forgetting in ML models (i.e., learning new tasks leads to the loss of performance on previously learned tasks). Although all CL approaches use some form of memory to retain information about past tasks, a grounded understanding of what information needs to be stored to minimize catastrophic forgetting remains elusive. Recently, it has been recognized that under the strong assumption of the existence of a common global minimizer over all tasks, catastrophic forgetting can be completely avoided. However, in practice, tasks rarely have a common global minimizer, and a certain amount of forgetting is inevitable. In this paper, we propose a foundational reframing of CL as balancing conflicting tasks in hindsight from a multi-task learning (MTL) perspective. The approach is based on finding Pareto-optimal solutions, i.e., the solutions which, by definition, minimally forget the previous tasks in the Pareto sense. We derive a Pareto-minimal-forgetting CL (PMF-CL) algorithm for linear and basis-function regression. Our algorithm naturally extends to loss functions with quadratic upper bounds around their minimizers, despite consuming only a static memory footprint of O(d2) for d model parameters, independent of the number of sequentially occurring tasks T. In the quadratic-loss setting, we obtain exact hindsight Pareto-optimal guarantees on forgetting. In the quadratic-upper-bound setting, forgetting is provably bounded, with the tightness of the forgetting bound being directly determined by the tightness of the quadratic bound on the loss function. Our numerical results validate our theoretical claims of convergence to the Pareto-optimal solution, and demonstrate that we consistently out-perform prior empirical methods while occupying lesser memory.