Train language models to think longer by incentivizing exploration of diverse reasoning paths.
Achieving effective test-time scaling requires models to engage in In-Context Exploration -- the intrinsic ability to generate, verify, and refine multiple reasoning hypotheses within a single continuous context. Grounded in State Coverage theory, our analysis identifies a critical bottleneck to enabling this capability: while broader state coverage requires longer reasoning trajectories, the probability of sampling such sequences decays exponentially during autoregressive generation, a phenomenon we term the ``Shallow Exploration Trap''. To bridge this gap, we propose Length-Incentivized Exploration(\method). This simple yet effective recipe explicitly encourages models to explore more via a length-based reward coupled with a redundancy penalty, thereby maximizing state coverage in two-step manner. Comprehensive experiments across different models (Qwen3, Llama) demonstrate that \method effectively incentivize in-context exploration. As a result, our method achieves an average improvement of 4.4\% on in-domain tasks and a 2.7\% gain on out-of-domain benchmarks.
Language models get stuck in shallow reasoning patterns despite having more tokens available for exploration.
Length-incentivized training enables models to explore diverse reasoning paths within a single response trajectory.
Count-based exploration using last-n-grams effectively measures and maximizes distinct reasoning patterns in model outputs.
Standard RL training doesn't naturally incentivize longer responses due to exponential decay in sampling probability.
State abstraction using last-n-grams may miss important distinctions in reasoning patterns beyond token sequences.
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