Difficulty filtering selects training problems by how often a starting model solves them. In RLVR, problems solved almost always or never provide little policy-gradient signal, so training commonly retains problems solved 20–80% of the time. section 7.3.3 section 7.5
A practical offline filtering pipeline is:
- Sample multiple completions for every candidate prompt, such as 16 responses. section 7.3.3
- Verify each completion with a correctness signal, such as answer matching or another verifier. section 7.3.3 section 7.5
- Estimate difficulty from the fraction of correct completions and retain prompts within the desired range, commonly 20–80%. section 7.3.3
Offline filtering chooses the training pool before large-scale RL. Online filtering or a difficulty curriculum instead selects problems during training, presents suitable questions per batch, or postpones harder problems to later stages for greater stability. section 7.3.3
Why the middle matters
A prompt the starting policy answers correctly on every sampled completion offers no useful contrast between strategies; a prompt it never answers correctly offers no successful behavior to reinforce. A prompt with mixed correct and incorrect completions supplies the variation needed for policy-gradient learning. section 7.3.3
