Epiplexity Guided Data Selection and Generation for Out-of-Distribution Generalization
Authors: Ellen Su, Andres Potapczynski, Shikai Qiu, Edward Hughes, Andrew Gordon Wilson
Abstract
Modern systems are increasingly expected to transfer across tasks not specified during training. What data facilitates generalization in these new, unanticipated settings? One hypothesis is that data with more structural information could contain shared circuits and subprograms that could be recycled in a wider array of downstream settings. Epiplexity, a recently proposed measure of the structural information a compute-bounded learner can extract from data, provides a mechanism to reason about this relationship. In this paper, we show how to operationalize epiplexity as an online training signal for data selection and synthetic data generation. For selection, we fit scaling laws to the training loss curves of natural data domains to predict the expected epiplexity gain as a function of training tokens, and use this signal to adaptively determine the sampling weights over domains during training. For synthetic data generation, we define a generator's reward as the change in learner epiplexity over a buffer of previously generated data and use REINFORCE policy gradients to guide the generator toward an epiplexity-maximizing distribution. In both cases, higher epiplexity predicts improved downstream performance on zero-shot and fine-tuning based tasks, supporting the hypothesis that data rich in structural information yield representations that transfer across domains.
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.
Synthetic data is useful only when the added samples fill missing parts of the training distribution that matter for the downstream task. We introduce LiBaGS, a lightweight, generator-agnostic method for targeted synthetic training data selection. LiBaGS scores candidate synthetic samples by combining decision-boundary proximity, predictive uncertainty, real-data density, and support validity, so that selected samples are both informative and likely to remain on the real data manifold. We then use a boundary-gap allocation rule that targets sparse but realistic decision-boundary neighborhoods, rather than simply adding more data or selecting only the most uncertain candidates. LiBaGS also learns when enough synthetic samples have been added through a marginal-value stopping rule, assigns softer labels near ambiguous boundaries, and uses a diversity objective to avoid redundant near-duplicate selections. Experiments show that LiBaGS improves accuracy over classical oversampling, hard augmentation, uncertainty and density ablations, and targeted-generation selection criteria.
Large Language Models have demonstrated remarkable progress in general-purpose capabilities and can achieve strong performance in specific domains through fine-tuning on domain-specific data. However, acquiring high-quality data for target domains remains a significant challenge. Existing data synthesis approaches follow a deductive paradigm, heavily relying on explicit domain descriptions expressed in natural language and careful prompt engineering, limiting their applicability in real-world scenarios where domains are difficult to describe or formally articulate. In this work, we tackle the underexplored problem of domain-specific data synthesis through an inductive paradigm, where the target domain is defined only through a set of reference examples, particularly when domain characteristics are difficult to articulate in natural language. We propose a novel framework, DOMINO, that learns a minimal sufficient domain representation from reference samples and leverages it to guide the generation of domain-aligned synthetic data. DOMINO integrates prompt tuning with a contrastive disentanglement objective to separate domain-level patterns from sample-specific noise, mitigating overfitting while preserving core domain characteristics. Theoretically, we prove that DOMINO expands the support of the synthetic data distribution, ensuring greater diversity. Empirically, on challenging coding benchmarks where domain definitions are implicit, fine-tuning on data synthesized by DOMINO improves Pass@1 accuracy by up to 4.63% over strong, instruction-tuned backbones, demonstrating its effectiveness and robustness. This work establishes a new paradigm for domain-specific data synthesis, enabling practical and scalable domain adaptation without manual prompt design or natural language domain specifications.