Tatsunori Hashimoto

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 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 the DPG is a powerful and flexible technique for shaping model properties using only synthetic training examples. We release the code for our project at https://github.com/TristanThrush/dataset-policy-gradients.

LLM self-play algorithms are notable in that, in principle, nothing bounds their learning: a Conjecturer model creates problems for a Solver, and both improve together. However, in practice, existing LLM self-play methods do not scale well with large amounts of compute, instead hitting learning plateaus. We argue this is because over long training runs, the Conjecturer learns to hack its reward, collapsing to artificially complex problems that do not help the Solver improve. To overcome this, we introduce Self-Guided Self-Play (SGS), a self-play algorithm in which the language model itself guides the Conjecturer away from degeneracy. In SGS, the model takes on three roles: Solver, Conjecturer, and a Guide that scores synthetic problems by their relevance to unsolved target problems and how clean and natural they are, providing supervision against Conjecturer collapse. Our core hypothesis is that language models can assess whether a subproblem is useful for achieving a goal. We evaluate the scaling properties of SGS by running training for significantly longer than prior works and by fitting scaling laws to cumulative solve rate curves. Applying SGS to formal theorem proving in Lean4, we find that it surpasses the asymptotic solve rate of our strongest RL baseline in fewer than 80 rounds of self-play.

Synthetic data augmentation has emerged as a promising solution when pre-training is constrained by data rather than compute. We study how to design synthetic data algorithms that achieve better loss scaling: not only lowering loss at finite compute but especially as compute approaches infinity. We first show that pre-training on web data mixed with synthetically generated rephrases improves i.i.d. validation loss on the web data, despite the synthetic data coming from an entirely different distribution. With optimal mixing and epoching, loss and benchmark accuracy improve without overfitting as the number of synthetic generations grows, plateauing near $1.48\times$ data efficiency at 32 rephrases per document. We find even better loss scaling under a new perspective: synthetic generations from the same document can form a single substantially longer *megadocument* instead of many short documents. We show two ways to construct megadocs: stitching synthetic rephrases from the same web document or stretching a document by inserting rationales. Both methods improve i.i.d. loss, downstream benchmarks, and especially long-context loss relative to simple rephrasing, increasing data efficiency from $1.48\times$ to $1.80\times$ at $32$ generations per document. Importantly, the improvement of megadocs over simple rephrasing widens as more synthetic data is generated. Our results show how to design synthetic data algorithms that benefit more from increasing compute when data-constrained.