e3: Learning to Explore Enables Extrapolation of Test-Time Compute for LLMs
This addresses the challenge of test-time compute scaling for LLMs, offering a method to enhance reasoning performance on difficult tasks beyond training limits, though it is incremental in refining existing paradigms.
The paper tackles the problem of enabling large language models (LLMs) to extrapolate beyond their training compute budget for improved reasoning on hard problems, achieving a 1.7B model that sets new state-of-the-art scores on benchmarks like AIME'25 and HMMT'25 and extrapolates to twice the training token budget.
Test-time scaling offers a promising path to improve LLM reasoning by utilizing more compute at inference time; however, the true promise of this paradigm lies in extrapolation (i.e., improvement in performance on hard problems as LLMs keep "thinking" for longer, beyond the maximum token budget they were trained on). Surprisingly, we find that most existing reasoning models do not extrapolate well. We show that one way to enable extrapolation is by training the LLM to perform in-context exploration: training the LLM to effectively spend its test time budget by chaining operations (such as generation, verification, refinement, etc.), or testing multiple hypotheses before it commits to an answer. To enable in-context exploration, we identify three key ingredients as part of our recipe e3: (1) chaining skills that the base LLM has asymmetric competence in, e.g., chaining verification (easy) with generation (hard), as a way to implement in-context search; (2) leveraging "negative" gradients from incorrect traces to amplify exploration during RL, resulting in longer search traces that chains additional asymmetries; and (3) coupling task difficulty with training token budget during training via a specifically-designed curriculum to structure in-context exploration. Our recipe e3 produces the best known 1.7B model according to AIME'25 and HMMT'25 scores, and extrapolates to 2x the training token budget. Our e3-1.7B model not only attains high pass@1 scores, but also improves pass@k over the base model.