ReSyn: Autonomously Scaling Synthetic Environments for Reasoning Models

Reinforcement Learning (RL) has been shown to significantly boost reasoning capabilities of large language models (LLMs) in math, coding, and multi-hop reasoning tasks. However, RL fine-tuning requires abundant high-quality verifiable data, often sourced from human annotations, generated from frontier LLMs, or scored by LLM-based verifiers. All three have considerable limitations: human-annotated datasets are small and expensive to curate, LLM-generated data is hallucination-prone and costly, and LLM-based verifiers are inaccurate and slow. In this work, we investigate a cheaper alternative: RL fine-tuning on rule-generated synthetic data for multi-hop reasoning tasks. We discover that LLMs fine-tuned on synthetic data perform significantly better on popular real-world question-answering benchmarks, despite the synthetic data containing only fictional knowledge. On stratifying performance by question difficulty, we find that synthetic data teaches LLMs to compose knowledge -- a fundamental and generalizable reasoning skill. Our work highlights rule-generated synthetic reasoning data as a free and scalable resource to improve LLM reasoning capabilities.

Reinforcement Learning with Verifiable Rewards (RLVR) has substantially improved reasoning in formal domains such as mathematics and code, but extending these gains beyond STEM remains challenging. Extending RLVR beyond STEM is fundamentally constrained by the lack of high-quality verifiable training data. In this work, we introduce SUPERNOVA, a framework for curating RLVR data from natural instruction datasets, which are a rich source of expert-annotated data but are underexplored for RLVR training. Through 100+ controlled RL experiments, we systematically study how to utilize these dataset for RLVR and how data curation decisions affect downstream reasoning performance . In particular, we investigate three data designs: (a) source task selection, (b) task mixing, and (c) synthetic interventions. Our analysis reveals that source task selection has a significant impact on downstream reasoning performance. Moreover, selecting tasks based on their performance for individual target tasks outperforms strategies based on overall average performance and synthetic interventions do not improve reasoning. Guided by these insights, we construct SUPERNOVA, a high-quality RLVR dataset of 25K instances curated from natural instruction datasets. We show that training Qwen3-0.6B on SUPERNOVA outperforms the base Qwen3-0.6B, yielding a relative gain of 64.4pp on BigBench Extra Hard (BBEH), a challenging benchmark comprising 23 complex reasoning tasks. Importantly, we find that gains from SUPERNOVA generalize to unseen benchmarks, larger model scales, and newer model families. Overall, our findings provide practical insights for curating human-annotated resources to extend RLVR to general reasoning. Models, Data, Code at https://github.com/asuvarna31/supernova.

Reinforcement learning with verifiable rewards (RLVR) has become a leading paradigm for improving the reasoning ability of large language models through outcome-based supervision. However, verifiable rewards frequently become uninformative at the group level: when all sampled traces of a given prompt receive identical rewards, group-relative advantage estimation provides no gradient signal, even though the traces may differ substantially in reasoning quality. We propose Reasoning Arena, an adaptive training framework that routes such non-diverse reward groups to a judge system instead of discarding them. Beyond examining the final answer, Reasoning Arena constructs trace tournaments, where reasoning traces are compared head-to-head to expose finer-grained preferences within the group, converting reasoning quality into rich relative reward signals. To make reward estimation efficient, rather than exhaustively comparing every pair, each new trace is evaluated against a small, dynamically updated pool of previously generated traces as anchors to efficiently establish a relative ranking. We then fit a Bradley-Terry model on the incomplete comparison graph, enabling scalable RL integration without quadratic pairwise comparisons. Empirical results demonstrate that Reasoning Arena consistently outperforms the RLVR baseline by 7.6% on average in competition mathematics and coding benchmarks. By converting otherwise wasted zero-advantage samples into useful gradient updates, our method accelerates training by 27% to 41%, saving nearly 50% of generation compute, and substantially improves overall reasoning performance.