Prismatic Synthesis: Gradient-based Data Diversification Boosts Generalization in LLM Reasoning

• URL: http://arxiv.org/abs/2505.20161v1
• Date: Mon, 26 May 2025 16:05:10 GMT
• Title: Prismatic Synthesis: Gradient-based Data Diversification Boosts Generalization in LLM Reasoning
• Authors: Jaehun Jung, Seungju Han, Ximing Lu, Skyler Hallinan, David Acuna, Shrimai Prabhumoye, Mostafa Patwary, Mohammad Shoeybi, Bryan Catanzaro, Yejin Choi,
• Abstract summary: We show that data diversity can be a strong predictor of generalization in language models.<n>We introduce G-Vendi, a metric that quantifies diversity via the entropy of model-induced gradients.<n>We present Prismatic Synthesis, a framework for generating diverse synthetic data.
• Score: 77.120955854093
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Effective generalization in language models depends critically on the diversity of their training data. Yet existing diversity metrics often fall short of this goal, relying on surface-level heuristics that are decoupled from model behavior. This motivates us to ask: What kind of diversity in training data actually drives generalization in language models -- and how can we measure and amplify it? Through large-scale empirical analyses spanning over 300 training runs, carefully controlled for data scale and quality, we show that data diversity can be a strong predictor of generalization in LLM reasoning -- as measured by average model performance on unseen out-of-distribution benchmarks. We introduce G-Vendi, a metric that quantifies diversity via the entropy of model-induced gradients. Despite using a small off-the-shelf proxy model for gradients, G-Vendi consistently outperforms alternative measures, achieving strong correlation (Spearman's $\rho \approx 0.9$) with out-of-distribution (OOD) performance on both natural language inference (NLI) and math reasoning tasks. Building on this insight, we present Prismatic Synthesis, a framework for generating diverse synthetic data by targeting underrepresented regions in gradient space. Experimental results show that Prismatic Synthesis consistently improves model performance as we scale synthetic data -- not just on in-distribution test but across unseen, out-of-distribution benchmarks -- significantly outperforming state-of-the-art models that rely on 20 times larger data generator than ours. For example, PrismMath-7B, our model distilled from a 32B LLM, outperforms R1-Distill-Qwen-7B -- the same base model trained on proprietary data generated by 671B R1 -- on 6 out of 7 challenging benchmarks.

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