Grow, Don't Overwrite: Fine-tuning Without Forgetting

Dyah Adila; Hanna Mazzawi; Benoit Dherin; Xavier Gonzalvo

cs.LGMar 9, 2026

Grow, Don't Overwrite: Fine-tuning Without Forgetting

Authors: Dyah Adila, Hanna Mazzawi, Benoit Dherin, Xavier Gonzalvo

Organizations: University of Wisconsin-Madison · Google Research

Abstract

Adapting pre-trained models to specialized tasks often leads to catastrophic forgetting, where new knowledge overwrites foundational capabilities. Existing methods either compromise performance on the new task or struggle to balance training stability with efficient reuse of pre-trained knowledge. We introduce a novel function-preserving expansion method that resolves this dilemma. Our technique expands model capacity by replicating pre-trained parameters within transformer submodules and applying a scaling correction that guarantees the expanded model is mathematically identical to the original at initialization, enabling stable training while exploiting existing knowledge. Empirically, our method eliminates the trade-off between plasticity and stability, matching the performance of full fine-tuning on downstream tasks without any degradation of the model's original capabilities. Furthermore, we demonstrate the modularity of our approach, showing that by selectively expanding a small subset of layers we can achieve the same performance as full fine-tuning at a fraction of the computational cost.

Figures & tables

Panel of Figure 1 — Figure 1: (a) We double the MLP’s hidden dimension by duplicating the up-projection weights ( $W_{n}^{(1)}$ ) and compensating in the down-projection layer ( $W_{n}^{(2)}$ ) to preserve the original function. (b) In the G-Freeze variant, only new parameters (darker shades) are trained. In the G-Train variant, the entire up-projection matrix is trained while the down-projection matrix is frozen, as indicated by the snowflake symbol.

Panel of Figure 2 — Figure 2: SFT (blue) shows severe degradation on the original domain (top plots), particularly for tasks with large domain shifts like translation and entailment. Our method (green, orange) maintain original performance while matching or exceeding the baseline on the new fine-tuning tasks (bottom plots).

Panel of Figure 3 — Figure 3: Full performance can be achieved with a fraction of the trainable parameters. Growing a targeted subset of 10 layers (green) consistently matches the performance of growing all layers (orange).

Panel of Figure 4 — Figure 4: Performance scales with the number of grown layers $N$ . New task performance (bottom) improves as $N$ increases, an effect most significant on the more complex MathQA task (b).

Panel of Figure 5 — Figure 5: The effective rank of weight update matrix. Brighter colors in the colorbar indicate a higher rank. The x-axis is the layer index, the y-axis is the training stage–with the earliest stages at the top and the latest at the bottom. Cognitively demanding tasks like MathQA, involve high-rank weight updates in almost all layers.

Dataset	Method	# Intersecting Heads ( $\uparrow$ )	FV Similarity ( $\uparrow$ )
Entailment	SFT	2/10	0.28
Entailment	Ours	5/10	0.95
Translation	SFT	3/10	0.58
Translation	Ours	5/10	0.76

Table 1: Substantially Preserves Model Function Vector

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

Symbol	Definition
$M_{0}$	pretrained model
$\theta_{0}$	pretrained model parameters
$M_{T}$	finetuned model
$\theta_{T}$	finetuned model parameters
$\mathcal{L}_{T}$	finetuning task loss
$\mathcal{D}_{T}$	downstream task dataset

Appendix

Table 2: Glossary of variables and symbols used in this paper.

Panel of Figure 6 — Figure 6: Our results hold on larger models.

Panel of Figure 7 — Figure 7: Comparison with zero initialization

Panel of Figure 8 — Figure 8: Comparison with growing attention head module

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Open paper AskPDF arXiv

How can we train models whose post-trained capabilities survive subsequent fine-tuning? Rather than focusing on downstream interventions to mitigate forgetting of upstream capabilities, we study how upstream training choices - that is, the manner in which a capability is acquired - shape how robustly that capability is retained. We investigate this question in a controlled three-stage language-model pipeline: pretraining, post-training to acquire a target capability, and downstream fine-tuning on a new objective. Across 135M and 1B models, two post-training domains, and two downstream fine-tuning tasks, we find that immediate post-training performance does not reliably predict retention after subsequent fine-tuning: training recipes that look equivalent immediately after post-training can retain the target capability very differently after subsequent fine-tuning. In particular, early exposure - mixing post-training data into pretraining - consistently improves the frontier between retained upstream performance and downstream performance. In compute-matched experiments, where the target data must be allocated between pretraining and post-training, we find that the optimum lies at neither extreme. Together with our other empirical and theoretical findings, this supports the view that post-training drives immediate specialization while early exposure improves robustness to later forgetting. Replay and dropout, typically used to mitigate forgetting as it occurs during fine-tuning, provide complementary gains to early exposure when applied during post-training. Our findings suggest that robustness to subsequent fine-tuning should be treated as a first-class objective of upstream training, addressed preventatively through choices like early exposure rather than reactively during fine-tuning itself.

Abstract

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