# Parameter-Efficient Fine-Tuning for Continual Learning: A Neural Tangent Kernel Perspective

arXiv: https://arxiv.org/abs/2407.17120 · HTML: https://mlsanity.com/paper/2407.17120/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 95 of its 135 references that are in the map.
- First posted on arXiv 24 Jul 2024.

## Builds on (most cited first, 30 of 95)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [Scaling Up Visual and Vision-Language Representation Learning With Noisy Text Supervision](https://mlsanity.com/paper/2102.05918/) (2021)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Learning to Prompt for Vision-Language Models](https://mlsanity.com/paper/2109.01134/) (2021)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [Visual Prompt Tuning](https://mlsanity.com/paper/2203.12119/) (2022)
- [An Empirical Study of Training Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.02057/) (2021)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Natural Adversarial Examples](https://mlsanity.com/paper/1907.07174/) (2019)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [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)
- [iBOT: Image BERT Pre-Training with Online Tokenizer](https://mlsanity.com/paper/2111.07832/) (2021)
- [Few-Shot Parameter-Efficient Fine-Tuning is Better and Cheaper than In-Context Learning](https://mlsanity.com/paper/2205.05638/) (2022)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [CrossViT: Cross-Attention Multi-Scale Vision Transformer for Image Classification](https://mlsanity.com/paper/2103.14899/) (2021)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [AutoAugment: Learning Augmentation Policies from Data](https://mlsanity.com/paper/1805.09501/) (2018)
- [On Lazy Training in Differentiable Programming](https://mlsanity.com/paper/1812.07956/) (2018)

## Built on by (most cited first, 3 of 3)

- [Parameter Efficient Continual Learning with Dynamic Low-Rank Adaptation](https://mlsanity.com/paper/2505.11998/) (2025)
- [Efficient Parameter Adaptation for Multi-Modal Medical Image Segmentation and Prognosis](https://mlsanity.com/paper/2504.13645/) (2025)
- [Stable-Plastic Subspace Construction for Differentially Private Continual LoRA](https://mlsanity.com/paper/2610.17904/) (2026)

## Abstract (arXiv)

Parameter-efficient fine-tuning for continual learning (PEFT-CL) has shown promise in adapting pre-trained models to sequential tasks while mitigating catastrophic forgetting problem. However, understanding the mechanisms that dictate continual performance in this paradigm remains elusive. To unravel this mystery, we undertake a rigorous analysis of PEFT-CL dynamics to derive relevant metrics for continual scenarios using Neural Tangent Kernel (NTK) theory. With the aid of NTK as a mathematical analysis tool, we recast the challenge of test-time forgetting into the quantifiable generalization gaps during training, identifying three key factors that influence these gaps and the performance of PEFT-CL: training sample size, task-level feature orthogonality, and regularization. To address these challenges, we introduce NTK-CL, a novel framework that eliminates task-specific parameter storage while adaptively generating task-relevant features. Aligning with theoretical guidance, NTK-CL triples the feature representation of each sample, theoretically and empirically reducing the magnitude of both task-interplay and task-specific generalization gaps. Grounded in NTK analysis, our framework imposes an adaptive exponential moving average mechanism and constraints on task-level feature orthogonality, maintaining intra-task NTK forms while attenuating inter-task NTK forms. Ultimately, by fine-tuning optimizable parameters with appropriate regularization, NTK-CL achieves state-of-the-art performance on established PEFT-CL benchmarks. This work provides a theoretical foundation for understanding and improving PEFT-CL models, offering insights into the interplay between feature representation, task orthogonality, and generalization, contributing to the development of more efficient continual learning systems.