Data quality remains a critical bottleneck in developing capable, competitive models. Researchers have explored many ways to generate top quality samples. Some works rely on rejection sampling: generating lots of synthetic samples and filtering out low-quality samples. Other works rely on larger or closed-source models to extract model weaknesses, necessary skills, or a curriculum off of which to base data generation. These works have one common limitation: there is no quantitative approach to measure the impact of the generated samples on the downstream learner. Active learning literature provides exactly this, in the form of acquisition functions. Acquisition functions measure the informativeness and/or influence of data, providing interpretable, model-centric signals. Inspired by this, we propose AcquisitionSynthesis: using acquisition functions as reward models to train language models to generate higher-quality synthetic data. We conduct experiments on classic verifiable tasks of math, medical question-answering, and coding. Our experimental results indicate that (1) student models trained with AcquisitionSynthesis data achieve good performance on in-distribution tasks (2-7% gain) and is more robust to catastrophic forgetting, and (2) AcquisitionSynthesis models can generate data for other models and for low-to-high resource training paradigms. By leveraging acquisition rewards, we seek to demonstrate a principled path toward model-aware self-improvement that surpasses static datasets.
Can a language model improve from plain text sampled from itself, with no prompts, no teacher, no verifier, and no reward model? Yes, but only when the synthetic corpus is compatible with the student, a relational property of the source-student pair rather than an intrinsic property of the data. We call this the latent capability resurfacing hypothesis: weak self-training can amplify capabilities already present in the pretrained model, but only under this compatibility condition. We study this in the minimal setting of prompt-free unconditional self-training, where base language models are fine-tuned on text generated from the BOS token alone, with no task specification or external supervision. We report three findings. First, synthetic utility is relational rather than intrinsic: self-generated data is the most effective source, same-lineage transfer outperforms stronger but differently trained sources, and cross-family transfer is substantially weaker. Second, common intrinsic proxies fail: neither benchmark-level semantic similarity nor average per-token likelihood under the student predicts which corpora help. Third, this regime produces a surprising byproduct. In controlled Pythia experiments, capability and verbatim memorization decouple: benchmark utility is preserved or improved while held-out exact-match extraction drops by over 95 percent, with no forget set, privacy objective, or targeted unlearning. Together, these results suggest that prompt-free self-training works by amplifying what the student already knows, not by importing structure from the data. They also reveal a regime in which capability and verbatim memorization can be separated without any explicit unlearning objective.
Language models are increasingly taught from synthetic question--answer (QA) supervision: a model generates questions about a document, answers them from the same text, and the resulting pairs are used to fine-tune, distill, or compress knowledge into another model. We show that this generation step is not neutral preprocessing. It is an implicit policy that both selects which evidence becomes training signal and decides how that evidence is answered, and it is fragile at both stages. When choosing what to ask, generators do not scan a document uniformly. Coverage saturates early and concentrates on salient spans, diverse prompts converge on the same regions, and what looks question-worthy is driven by local presentation. As a result, salient artifacts such as poorly cleaned markup can hijack question generation across model families and scales. When answering, the model that produces the supervision tends to obey instruction-like passages embedded in the text. This compliance depends on the intent and surface form of the passage rather than its strictness, and is worst under task conflict, where larger models comply more often. These failure modes arise from choices made during QA generation, so they can be reduced without changing the training loop. Tying each question to a fixed target reduces biased selection, and filtering instruction-like spans before answering lowers mean injection compliance from 88% to 13% in our evaluation while retaining nearly all clean text.
Synthetic data becomes crucial for large language model training, but its effectiveness is highly inconsistent. We provide an information-theoretic account of this inconsistency: synthetic data improves a model only when the generation-training loop is information-open, i.e., shaped by external signals (verifiers, environments, or rubrics) that inject task-relevant information beyond the model's current distribution. When the loop is information-closed (relying on the model's own outputs without such signals), the data processing inequality ensures that task-relevant information can only decrease, making collapse a predicted outcome. Among information-open pipelines, both efficiency and generalization hinge on the meta-level of supervision: a coarser signal such as binary correctness treats all acceptable outputs as equivalent, so the behavior it teaches is not tied to any particular domain or surface form and generalizes naturally across tasks and domains. These observations lead to a guiding thesis: learning preferentially converges to the most information-efficient signal component available, which accelerates learning when that component is the intended one, but causes reward hacking when a spurious pattern happens to be simpler.