[2606.00132] Foundation-Preserving Adaptation via Generalized Rayleigh-Quotient Optimization
[Submitted on 28 May 2026]
Title:Foundation-Preserving Adaptation via Generalized Rayleigh-Quotient Optimization
View a PDF of the paper titled Foundation-Preserving Adaptation via Generalized Rayleigh-Quotient Optimization, by Dongjun Kim and 4 other authors
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Abstract:While finetuning effectively adapts foundation models to specialized downstream tasks, it can degrade nontarget capabilities acquired during pretraining. Existing forgetting aware methods typically seek safer updates through specialized initialization or fixed constraints, but do not regulate the adaptation preservation trade-off during training. We propose Foundation Preserving LoRA (FoLoRA), a forgetting aware optimization framework. Guided by a first order preservation condition, FoLoRA defines a forgetting penalty over pretraining-proxy activations and a task utility over downstream task activations. It then scores update directions by task utility per unit forgetting penalty via a generalized Rayleigh quotient. The resulting spectral coordinate system enables direction wise gated Adam updates, attenuating low utility to penalty directions during training. To estimate the forgetting penalty, FoLoRA constructs pretraining proxy calibration data by sampling from the pretrained model rather than relying on a single proxy dataset. Experiments on math, code, and instruction following adaptation show that FoLoRA achieves the strongest preservation adaptation balance over baselines, improving target task performance with best aggregate preservation of non target capabilities.
Subjects:
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
Cite as: arXiv:2606.00132 [cs.LG]
(or arXiv:2606.00132v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.00132
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Dongjun Kim [view email] [v1] Thu, 28 May 2026 21:22:31 UTC (1,246 KB)
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