High-Value Training Data from Noisy, Diverse Sources

Single-stage fine-tuning is pervasive, yet catastrophic forgetting persists when the source pre-training data is inaccessible. Data weighting affords a natural lever to modulate sample influence. Yet existing weighting methods lack a principled mechanism to explicitly arbitrate knowledge retention against new-task adaptation, and provide no unified differentiable objective to accommodate auxiliary signals such as sample diversity and sample characteristics. This is because current schemes privilege one goal over the other, and no explicit gradient-compatible encoding exists for such signals. To address this, we propose DRIVE, a principled and efficient weight assignment framework. It derives per-sample weights via a unified differentiable objective where three coupled signals co-evolve: Shapley additivity splits contribution into anti-forgetting and adaptation components, which are reshaped by a covariance-based diversity term and stabilized by a sample-characteristic prior. Far from a mere combination, this yields an end-to-end gradient-based scheme balancing stability against plasticity. Theoretically, we prove that DRIVE enjoys superior stability-plasticity guarantees over existing weighting schemes and enhances parameter estimation robustness. Empirically, it attains superior overall performance, faster convergence, and stronger robustness. Code at https://github.com/luciabcd/DRIVE.

What are the limits of controlling language models via synthetic training data? We develop a reinforcement learning (RL) primitive, the Dataset Policy Gradient (DPG), which can precisely optimize synthetic data generators to produce a dataset of targeted examples. When used for supervised fine-tuning (SFT) of a target model, these examples cause the target model to do well on a differentiable metric of our choice. Our approach achieves this by taking exact data attribution via higher-order gradients and using those scores as policy gradient rewards. We prove that this procedure closely approximates the true, intractable gradient for the synthetic data generator. To illustrate the potential of DPG, we show that, using only SFT on generated examples, we can cause the target model's LM head weights to (1) embed a QR code, (2) embed the pattern $\texttt{67}$, and (3) have lower $\ell^2$ norm. We additionally show that we can cause the generator to (4) rephrase inputs in a new language and (5) produce a specific UUID, even though neither of these objectives is conveyed in the generator's input prompts. These findings suggest that DPG is a powerful and flexible technique for shaping model properties using only synthetic training examples.

Foundation models are routinely released to the public, yet the data recipes used to train them -- such as domain mixture weights that determine how different sources are sampled -- are rarely disclosed. This creates an access asymmetry: researchers study the resulting models but lack visibility into the training distribution that produces them. Prior works for inferring training data, such as membership inference, detect at the level of individual samples and thus cannot characterize the global composition of the training corpus. We introduce WARP, a framework that recovers a fine-tuned model's training mixtures directly from its released weights. WARP interpolates between the base and fine-tuned models using model merging, generating pseudo-checkpoints that approximate the missing training trajectory and expose a geometric footprint of the training data in the weight space. From these simulated footprints, WARP extracts geometric features and maps them to domain proportions using either a parameter-free softmax readout or an MLP projector trained on synthetic mixtures. In controlled experiments with BERT and GPT-2, WARP recovers domain mixtures with an average MAE as low as 0.046 and 0.104 respectively, outperforming membership inference and a variant with access to the true training trajectory.