Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
Can Generative AI Solve Your In-Context Learning Problem? A Martingale Perspective
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Proposes the generative predictive p-value, which lets posterior predictive checks run on conditional generative models (e.g., Llama-2, Gemma-2) by sampling dataset completions from the model's predictive distribution, to decide whether a CGM can solve an in-context learning problem.
Problem
Assessing whether a conditional generative model is an appropriate Bayesian model for an in-context learning problem, when only the predictive distribution (not the likelihood or posterior) of the CGM is accessible.
Approach
Replace sampling from the latent-explanation posterior with ancestral (predictive resampling) generation of a large dataset completion from the CGM predictive, then compute posterior-predictive-style p-values on that completion; a martingale argument (Doob's theorem) shows the infinite-completion version equals the standard posterior predictive p-value.
Key results
- On OOD tabular tasks with NLL discrepancy, the generative predictive p-value gives non-trivial OOD predictors across all significance levels (M=40, N-n=200).
- For Llama-2 7B in-capability vs out-of-capability text tasks, the NLL discrepancy gives accuracy above 0.5 across significance levels.
- The NLL discrepancy's p-values correlate with response RMSE (lower p-value, higher error), yielding substantially lower risk than NLML at matched accuracy in tabular experiments.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the generative predictive p-value under either the NLL or NLML discrepancy to predict out-of-capability tasks | Llama-2 7B · Natural language ICL: RTE and MQP vs. SST2 and AG News | accuracy: >0.5 | Helped |
| Use the generative predictive p-value under either the NLL or NLML discrepancy to predict OOD tasks | Llama-2 regression model · Generative fill: MNIST and CIFAR-10 vs. SVHN | accuracy: > 0.66\bar{6} | Helped |
| Use NLML instead of NLL as the discrepancy | Generative predictive p-value capability predictor · Tabular, natural language, and imaging ICL tasks | precision | Helped |
| Use NLL instead of NLML as the discrepancy | Generative predictive p-value capability predictor · Tabular, natural language, and imaging ICL tasks | recall | Helped |
| Use NLL with significance level α=0.05 rather than NLML at an evaluated significance level | Generative predictive p-value capability predictor · Tabular, natural language, and imaging ICL tasks | accuracy: α=0.05 | Helped |
| Use the NLL discrepancy rather than NLML | Generative predictive p-value capability predictor · In-distribution polynomial tabular tasks | risk | Helped |
| Use NLL rather than NLML to calculate the p-value | Generative predictive p-value · In-distribution polynomial tabular tasks | association between p-value and response RMSE | Helped |
| Increase the generated completion size N-n | Generative predictive p-value · Reference Bayesian polynomial regression and OOD ReLU-NN tasks | approximation to reference NLL p-value: N-n = 2; 100 | Helped |
| Increase the in-context dataset size n | NLML discrepancy capability predictor · Tabular and natural language ICL tasks | recall | Mixed |
| Use NLL rather than NLML to assess capability | Generative predictive p-value · In-distribution polynomial tabular tasks | ability to indicate sufficient in-context examples | Helped |
Surprising findings
- The NLML discrepancy's recall is sensitive to the number of in-context examples n and can misclassify out-of-capability tasks as solvable at small alpha or small n.
- The NLML-based p-value does not correlate with RMSE, while the NLL-based one does, indicating NLML cannot tell whether there are enough examples.
Limitations
- Finite completion size N introduces estimation error relative to the ideal posterior predictive p-value; formal error analysis left to future work.
- Theory requires identifiability and measurability conditions that may not hold for contemporary LLMs.
- Empirical evaluation uses only Llama-2 7B and Gemma-2 9B and small synthetic or narrow benchmarks.
Experimental setup
Datasets: SVHN MNIST CIFAR-10 SST2 AG News Medical Questions Pairs (MQP) RTE synthetic polynomial, ReLU-NN and RBF-GP regression tasks
Benchmarks: SST2 AG News MQP RTE SVHN MNIST CIFAR-10 synthetic tabular OOD regression tasks
Metrics: precision recall F1 accuracy FPR RMSE-based risk
Baselines: NLML discrepancy (posterior predictive p-value style) posterior predictive p-value
Builds on: posterior predictive checks Doob's theorem for estimators predictive resampling Bayesian model criticism
Closest papers by meaning
- In-Context Learning through the Bayesian Prism (ICLR 2024 · similarity 0.88)
- Estimating the Hallucination Rate of Generative AI (NeurIPS 2024 · similarity 0.88)
- Is In-Context Learning in Large Language Models Bayesian? A Martingale Perspective (ICML 2024 · similarity 0.86)
- Can Transformers Learn Full Bayesian Inference in Context? (ICML 2025 · similarity 0.86)
- Technical Debt in In-Context Learning: Diminishing Efficiency in Long Context (NeurIPS 2025 · similarity 0.85)
- In-Context Learning Strategies Emerge Rationally (NeurIPS 2025 · similarity 0.85)
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