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Early Data Exposure Improves Robustness to Subsequent Fine-Tuning
Lawrence Feng, Gaurav R. Ghosal, Jacob Mitchell Springer, Ziqian Zhong, Aditi Raghunathan
TL;DR
The paper asks how to make post-trained capabilities survive later fine-tuning and studies upstream training choices in a three-stage language-model pipeline. It finds that early exposure to post-training data improves retention tradeoffs, while compute-matched allocation favors neither extreme; replay and dropout add complementary gains.
Problem
The paper asks how upstream training choices shape retention because capabilities acquired during post-training can be lost during later fine-tuning.
Source: §1 · pp. 1–2Method
Results
Early exposure improves the tradeoff between retained upstream capability and downstream fine-tuning loss, even when immediate post-training performance changes little or not at all.
Source: §1 · p. 2Takeaways & Limitations
Robustness to subsequent fine-tuning can be shaped through upstream training choices, with replay and dropout providing gains complementary to early exposure.
Source: §1 · p. 2Experiments limit early exposure to at most one pass over post-training data and study only one downstream adaptation method, not preference-based or reinforcement-learning fine-tuning.
Source: §6 · p. 11
Abstract
from arXiv · showhide
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.
1 Introduction
The paper asks how upstream training choices shape whether post-trained capabilities survive downstream fine-tuning, rather than focusing only on downstream fixes for forgetting. In a controlled three-stage pipeline, it finds that early exposure to post-training data improves retention tradeoffs, with replay and dropout offering complementary gains.
1 Introduction
- Training recipes with equivalent immediate post-training performance can differ substantially in how well their capabilities survive later adaptation.The paper therefore treats retention after subsequent fine-tuning, not immediate post-training performance alone, as a central question.Source: §1 · pp. 1–2
- The controlled setup models pretraining, post-training for a target capability, and downstream fine-tuning on a new objective.The study spans multiple post-training and downstream regimes, using 135M models and extending findings to 1B models.Source: §1 · p. 2, Figure 1 · p. 2
- Early exposure—mixing post-training data into pretraining—improves the tradeoff between retained capability and downstream fine-tuning loss across datasets and model sizes.This can hold even when early exposure has little or no visible effect on immediate post-training performance.Source: §1 · p. 2, Figure 2 · p. 3
- Under a fixed budget of post-training data, the best allocation between pretraining and post-training lies between the two extremes.The compute-matched experiments do not favor allocating all exposure to either stage.Source: §1 · p. 2
- Replay and dropout improve the tradeoff frontier and remain complementary to pretraining-time mixing.The paper evaluates them as interventions that shape how a capability is acquired, including whether their benefits persist through later fine-tuning.Source: §1 · p. 2
2 Related Works
Related work documents forgetting during sequential training and examines both downstream mitigation and upstream data-placement choices. This paper focuses on whether early exposure to post-training data can also improve robustness to later forgetting.
2 Related Works
- Prior work studies catastrophic forgetting across language-model training, safety fine-tuning, knowledge editing, and unlearning, while also examining how adaptation methods and pretraining duration shape forgetting.Examples include LoRA-style adaptation [Biderman et al., 2024] and longer pretraining [Springer et al., 2025].Source: §2 · p. 3
- Earlier pretraining interventions modify data through filtering or augmentation to improve safety [Maini et al., 2025; O’Brien et al., 2025], while Baek et al. (2026) report immediate in-domain gains from mixing post-training data.This work adds the question of whether such mixing improves robustness to forgetting during future training.Source: §2 · pp. 3–4
3 Preliminaries and Setting
The paper defines a three-stage training pipeline and evaluates how upstream choices affect downstream adaptation, retained post-training capability, and general pretraining performance. It compares loss frontiers across four experimental settings and two model scales.
3 Preliminaries and Setting
- The pipeline proceeds from general-corpus pretraining, through post-training on a smaller target corpus, to downstream fine-tuning on a new objective.The post-training corpus is assumed to be much smaller than the pretraining corpus, reflecting a setting where targeted data is relatively scarce.Source: §3 · p. 4
3.1 Evaluation methodology
- Evaluation tracks downstream fine-tuning loss, retained post-training loss, and retained pretraining loss, using held-out validation loss and Pareto-optimal frontiers.The two main views compare retained post-training loss with downstream loss, and retained pretraining loss with retained post-training loss.Source: §3.1 · pp. 4–5, §3 · p. 4
3.2 Experimental instantiations
- The four experimental settings vary the post-training and downstream corpora while keeping the general pretraining corpus fixed to C4.They cover domain adaptation and instruction tuning, testing whether robustness patterns extend across downstream objectives.Source: §3.2 · p. 5, Table 1 · p. 5
3.3 Model scales and training budgets
- Experiments use 135M-parameter models and a 1B variant; post-training can run up to 2B tokens, followed by 200M-token downstream fine-tuning.Outside compute-matched experiments, post-training proceeds on Dpost with early stopping and no restriction on dataset repetitions.Source: §3.3 · p. 5
4 Experiments and Results
The experiments show that early exposure to post-training data improves retention after downstream fine-tuning, even when immediate post-training performance changes little. Under a fixed data budget the best retention occurs at a nonzero mixture, and replay and dropout provide complementary gains.
4.1 Immediate post-training performance does not reflect downstream retention
- As the mixture fraction rises, retained MusicPile loss after ChemPile fine-tuning improves while immediate MusicPile loss remains nearly constant.The result indicates that the retention benefit can be latent until subsequent fine-tuning.Source: Figure 3 · p. 6, §4.1 · p. 6
4.2 Early exposure and post-training play different roles under a fixed data budget
- With a fixed post-training-data budget, the best retained performance occurs at a nonzero mixture fraction, while reserving all data for Stage 2 gives the best immediate performance.Increasing the mixture fraction improves retained loss but worsens immediate post-training loss.Source: §4.2 · p. 7
4.3 Early exposure improves the loss frontier across hyperparameter sweeps
- Across four pipelines, early exposure improves the frontier between retained post-training performance and downstream fine-tuning loss, with a similar qualitative gain in 1B experiments.Mixing also improves the tradeoff between retaining broader pretraining capabilities and retaining the post-trained capability.Source: §4.3 · p. 7
4.4 Replay and dropout provide complementary gains
- Across both representative downstream settings, replay and dropout further improve the loss frontier beyond mixed pretraining alone.At 1B, replay has a weaker effect on the retained-post-training versus downstream-loss frontier, though it remains useful for preserving broader general-domain performance.Source: §4.4 · p. 8
- Replay and dropout complement rather than replace pretraining-time mixing, and the strongest frontiers combine these interventions.Mixing changes when the model first encounters the capability, while replay and dropout shape how it learns it during post-training.Source: §4.4 · pp. 8–9
5 Theoretical Analysis of Early Exposure
The theoretical analysis uses a two-layer linear model of pretraining, post-training, and downstream fine-tuning to explain how early exposure can make a capability less vulnerable to forgetting. Mixing enables specialized features that post-training can reuse and that downstream updates do not overwrite.
5 Theoretical Analysis of Early Exposure
- The theoretical account analyzes a three-task pipeline with a two-layer linear network, shared task singular vectors, and downstream inputs that exclude specialized features.The shared-vector assumption and inactive specialized dimensions in the downstream task specify the model setting for the forgetting result.Source: §5 · p. 9
5.1 Early exposure learns different features
- In the model, early exposure learns specialized features that unmixed pretraining does not learn.Linear networks learn features in descending singular-value order; mixing raises a specialized feature's effective singular value to αβ, so even a small α can suffice when β is large enough.Source: §5.1 · pp. 9–10
5.2 Post-training primarily reuses existing features
- Early exposure lets post-training reduce target-task loss using specialized features, whereas without it post-training modifies inconsistent features that also support general capabilities.The analysis predicts less degradation in C4 loss after post-training from an early-exposure checkpoint.Source: §5.2 · p. 10
5.3 Characterizing downstream forgetting behavior
- The analysis states that downstream fine-tuning increases post-training-task loss at least as much for the unmixed checkpoint as for the mixed checkpoint.Downstream updates overwrite inconsistent features but have zero projection along specialized features, allowing the mixed model's target-task improvement to persist.Source: §5.3 · p. 10
6 Conclusion
The conclusion frames retention after fine-tuning as an upstream training-design objective, because how and when a capability is learned shapes its durability. It also identifies boundaries of the experiments, including limited exposure levels and a single downstream adaptation method.
6 Conclusion
- Early exposure, post-training replay, and post-training regularization shift the retention–adaptation frontier, with effects described as largely complementary rather than substitutable.The conclusion argues that robustness should be designed into upstream training rather than treated only as a downstream problem.Source: §6 · p. 11
- Experiments introduce at most one pass over post-training data during pretraining and study only one downstream adaptation method, not preference-based or reinforcement-learning fine-tuning.The paper also reports additional LoRA experiments in Appendix B.3.Source: §6 · p. 11
- The authors call for testing overlap levels, wider exposure amounts, heavy data repetition, and larger models with longer training runs.They also propose investigating whether later objectives or regularizers can approximate early exposure's representational effect without changing the pretraining corpus.Source: §6 · p. 11
Contributions
Lawrence Feng led the project and conducted its main experiments, while Gaurav R. Ghosal originated the investigation of pretraining's role in catastrophic forgetting. Ghosal, Ziqian Zhong, Jacob Mitchell Springer, and Aditi Raghunathan also contributed throughout the project.
Contributions
- Lawrence Feng led the project and conducted all the main experiments.Source: Contributions · p. 15
- Gaurav R. Ghosal seeded the investigation of pretraining's role in catastrophic forgetting.Source: Contributions · p. 15
- Gaurav R. Ghosal, Ziqian Zhong, Jacob Mitchell Springer, and Aditi Raghunathan contributed to project direction, experimental design, and paper writing.Source: Contributions · p. 15
A.1 SmolLM2-1B model architecture
Across the appendix experiments, mixing post-training data into pretraining generally improves fine-tuning–retention frontiers, with complementary effects from dropout and replay. Results vary by downstream setting and intervention, and frontier ordering is established early in Stage 3.
B.1 135M dropout and replay frontiers with retained pretraining loss (C4)
- At 135M, adding dropout or replay to mixed pretraining lowers retained pretraining loss at matched retained post-training loss.Without mixing, both interventions shift the fine-tuning–retention frontier toward the lower left; mixed pretraining improves both FFT and LoRA frontiers, with FFT generally better at matched upstream configurations.Source: Figure 5 · p. 19, Figure 6 · p. 19, Figure 7 · p. 20
B.3 135M LoRA experiments
- At 135M, FFT generally attains a better fine-tuning–retention tradeoff than LoRA at matched upstream configurations; mixed pretraining improves both FFT and LoRA frontiers in both downstream settings.Each panel shows four frontiers from sweeps of Stage 2 post-training hyperparameters and Stage 3 fine-tuning learning rates.Source: Figure 7 · p. 20
B.4.1 Mixing frontiers
- At 1B, mixed pretraining improves the MusicPile frontier, while for FLAN it improves pretraining-versus-retention but not noticeably retention-versus-fine-tuning.The mixed frontier also dominates when Tulu-3-SFT is used as the post-training corpus.Source: Figure 8 · p. 21, Figure 9 · p. 21, Figure 10 · p. 22
B.4.2 Upstream dropout and replay at 1B parameters
- At 1B, dropout further improves the mixed-pretraining frontier, replay alone tracks it closely, and their combination yields the best frontier overall.Without mixing, dropout shifts the frontier beyond the unmixed baseline, replay has little effect, and the combination behaves similarly to dropout alone.Source: Figure 11 · p. 23, Figure 13 · p. 24
- At 1B, replay preserves and can slightly improve C4 retention, whereas swept dropout rates often degrade it; the combined intervention inherits that degradation.The authors attribute dropout’s C4-retention degradation to insufficient tuning of the dropout rate.Source: Figure 12 · p. 23
B.4.3 Sensitivity to the Stage 3 fine-tuning budget
- At 1B, intervention-frontier ordering emerges early in Stage 3 and persists to the final checkpoint, making the comparisons insensitive to the exact fine-tuning budget.The sweep covers 6% to 100% of the Stage 3 budget.Source: Figure 14 · p. 25
B.5 Additional Plots on the Latent Effect of Early Exposure
- Paired models with and without early exposure cluster near ΔLim ≈ 0 while often showing substantially negative ΔLret, so similar immediate performance can precede different retention.The plotted differences compare immediate and retained post-training performance for pairs differing only in early exposure.Source: Figure 15 · p. 26
B.6 Base-Model Familiarity Predicts Robustness to Forgetting in OLMo-2-7B
In a frozen OLMo-2-7B model, examples with lower base-model loss show less forgetting after SFT fine-tuning on ChemPile. The paper uses base-model loss as a proxy for prior familiarity, not as a direct manipulation of pretraining exposure.
B.6 Base-Model Familiarity Predicts Robustness to Forgetting in OLMo-2-7B
- The study uses per-example base-model loss as a familiarity proxy because exposure cannot be manipulated in the frozen public model.The SFT checkpoint is fine-tuned on 52M ChemPile tokens, and response-token loss is measured on 50,000 Tulu-3-SFT examples before and after fine-tuning.Source: §B.6 · p. 27
- For OLMo-2-7B, forgetting rises with base-model loss, and the trend remains within a narrow slice of SFT-model loss.The restricted slice contains 1,237 examples; the caption reports qualitatively identical trends in other slices.Source: Figure 16 · p. 27
C.1 Preliminaries and Setup
- Invariant features have equal singular values across pretraining, post-training, and fine-tuning tasks; specialized directions have no covariance in pretraining or downstream data.The setup also distinguishes inconsistent features, where task singular values differ.Source: §C.1 · p. 28
- The analysis assumes downstream inputs do not activate specialized features and that post-training and fine-tuning diverge on inconsistent features.Mixed training is modeled as a distribution combining pretraining and post-training data.Source: §C.1 · p. 28
C.2 Analysis of Initial Pretraining
The two-layer linear analysis compares which features mixed and unmixed pretraining learn. Under its stated setup, mixing learns specialized features that unmixed pretraining does not.
C.2 Analysis of Initial Pretraining
- The analysis assumes a near-zero, nonzero initialization and tasks with a joint decomposition; its cited feature-learning result orders learned features by singular value.The passage identifies this ordering as the basis for comparing mixed and unmixed pretraining.Source: §C.2 · p. 29
- Mixing post-training data during pretraining learns specialized features, while unmixed pretraining learns only shared and inconsistent features.The analysis characterizes features through singular values and vectors and applies sequential feature-learning results to the two pretraining conditions.Source: §C.2 · p. 30
C.3 Analysis of Post-Training
In the idealized linear analysis, post-training can use features already present at initialization but cannot create absent ones. This permits mixed and unmixed starting points to reduce post-training loss through different feature pathways.
C.3 Analysis of Post-Training
- The post-training analysis assumes bounded parameters and learning rates, regularized loss, and a sufficient number of post-training steps.Sufficient steps are defined using a lower bound involving the minimum nonzero post-training singular value.Source: §C.3 · pp. 30–31
- Post-training from the mixed checkpoint can use specialized features, whereas the unmixed checkpoint relies on shared features to reduce post-training loss.The theorem compares these idealized initializations after sufficient post-training; the proof notes that zero singular values remain zero throughout optimization.Source: §C.3 · pp. 31–32
C.4 Analysis of Downstream Adaptation
The analysis compares the change in Dpost loss after downstream fine-tuning from mixed and unmixed initializations. It finds a larger change for the unmixed initialization, while specialized directions with no Dft covariance remain unchanged.
C.4 Analysis of Downstream Adaptation
- Specialized features along directions with zero Dft covariance remain unchanged during downstream adaptation.The input covariance projects gradient updates to zero along those directions.Source: §C.4 · p. 32
- The theorem reports ∆unmixed > ∆mixed for the Dpost-loss change after K downstream gradient steps.The proof establishes ∆mixed = 0 and ∆unmixed > 0 under its stated conditions.Source: §C.4 · pp. 32–33
- In the mixed case, unchanged invariant and specialized features imply ∆mixed = 0.The proof attributes specialized-feature stability to Lemma C.16.Source: §C.4 · p. 32