GeoMin Matches Fully Supervised AI Reasoning Using Only 10% of Labeled Data
GeoMin uses geometric distribution modeling to squeeze full reasoning gains from just 10% of labeled training data, beating fully supervised RLVR models.
- GeoMin is a new semi-supervised RLVR method that matches fully supervised reasoning model performance using only 10% of labeled data.
- It beats the strongest semi-supervised baselines by +4.1% on reasoning benchmarks by modeling geometric feature distributions of correct vs. incorrect rollouts.
- Unlike prior methods (e.g., TraPO), GeoMin uses global feature-space geometry rather than coarse pass-rate trajectories to filter unreliable unlabeled training samples.
- The two-stage pipeline first anchors correct/incorrect rollout distributions from labeled data, then mines reliable unlabeled samples using that prior.
- Designed for verifiable-answer domains (math, code, logic); does not apply to open-ended generation tasks without ground-truth answers.
- No code or model weights have been publicly released alongside the paper yet.
Training a reasoning model with reinforcement learning is expensive -- not in compute, but in annotation. Every question needs a verified ground-truth answer, and at scale, that cost becomes a serious bottleneck. A new paper introduces GeoMin, a semi-supervised approach that sidesteps this problem by modeling the geometry of feature distributions to decide which unlabeled training examples are actually trustworthy -- and which ones will quietly poison your model.
The annotation trap
RLVR (Reinforcement Learning with Verifiable Rewards) enables the emergence of robust reasoning capabilities in models, often with minimal human supervision for intermediate steps. The key idea is simple: instead of labeling every reasoning step, you just check whether the final answer is correct. The reasoning capabilities observed in models like DeepSeek-R1 appear to be emergent byproducts of optimizing for verifiable outcomes, not explicitly trained behaviors.
But even verifying final answers requires labeled data -- and lots of it. Although supervised RLVR has achieved great success, its reliance on golden answers incurs high annotation costs. To address this, the community has explored unsupervised RLVR techniques that rely solely on unlabeled data. The most common trick is majority voting: treat the most frequent answer across multiple model rollouts as the pseudo-label.
Recent work has explored unsupervised RLVR methods that derive rewards solely from the model's internal consistency, such as through entropy and majority voting. While seemingly promising, these methods often suffer from model collapse in the later stages of training, which may arise from the reinforcement of incorrect reasoning patterns in the absence of external supervision. In other words, if the model is confidently wrong, majority voting just makes it more confidently wrong.
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