Can Generative AI Solve Your In-Context Learning Problem? A Martingale Perspective (2412.06033v1)

Abstract: This work is about estimating when a conditional generative model (CGM) can solve an in-context learning (ICL) problem. An in-context learning (ICL) problem comprises a CGM, a dataset, and a prediction task. The CGM could be a multi-modal foundation model; the dataset, a collection of patient histories, test results, and recorded diagnoses; and the prediction task to communicate a diagnosis to a new patient. A Bayesian interpretation of ICL assumes that the CGM computes a posterior predictive distribution over an unknown Bayesian model defining a joint distribution over latent explanations and observable data. From this perspective, Bayesian model criticism is a reasonable approach to assess the suitability of a given CGM for an ICL problem. However, such approaches -- like posterior predictive checks (PPCs) -- often assume that we can sample from the likelihood and posterior defined by the Bayesian model, which are not explicitly given for contemporary CGMs. To address this, we show when ancestral sampling from the predictive distribution of a CGM is equivalent to sampling datasets from the posterior predictive of the assumed Bayesian model. Then we develop the generative predictive $p$-value, which enables PPCs and their cousins for contemporary CGMs. The generative predictive $p$-value can then be used in a statistical decision procedure to determine when the model is appropriate for an ICL problem. Our method only requires generating queries and responses from a CGM and evaluating its response log probability. We empirically evaluate our method on synthetic tabular, imaging, and natural language ICL tasks using LLMs.

• The paper introduces a martingale predictive framework that assesses when conditional generative models are ideal for solving in-context learning tasks.
• It leverages ancestral sampling and discrepancy functions to translate Bayesian model criticism into actionable predictive p-values across various data types.
• Empirical evaluations on tabular, image, and text datasets confirm the method’s robustness in gauging generative model capability for diverse ICL challenges.

Estimating Conditional Generative Model Capability in In-Context Learning: A Martingale Perspective

The paper under review delineates a methodology for assessing when a conditional generative model (CGM) is appropriate for solving an in-context learning (ICL) problem using a martingale perspective. This paper provides a significant extension of Bayesian model criticism to contemporary generative AI systems, laying the groundwork for a structured and empirical testing mechanism to gauge model suitability for specific ICL tasks.

The exploration centers on leveraging ancestral sampling to equate data generation from CGMs with the posterior predictive distributions expected in Bayesian models. The authors introduce a generative predictive p-value as a mechanism to integrate posterior predictive checks (PPCs) with modern CGMs, where direct sampling from explicit likelihoods is intractable. This approach requires merely generating queries and responses from a CGM and computing the log probabilities of these responses, thereby making it feasible with contemporary deep learning models that often encapsulate complex, implicit distributions.

The paper provides a comprehensive evaluation of the proposed method across diverse domains—tabular data, image recognition, and natural language processing using established LLMs such as Llama-2 and Gemma-2. The empirical analysis confirms that the generative predictive p-value is a robust predictor of model capability across all tested domains. Notably, the p-value calculation using different discrepancy functions indicates model limitations in data length and complexity, thus serving as a potential measure of model capability in handling varied data distributions and tasks.

Among the key theoretical advancements is the formalization of a martingale predictive framework. The authors prove the theoretical equivalence of the posterior and martingale predictive p-values—the cornerstone that underpins the entire methodology. This ensures that the empirical approaches maintain their fidelity to the underlying theoretical constructs of Bayesian inference.

Major Findings and Contributions

1. Martingale Perspective in ICL: The paper rigorously defines an ICL task and establishes conditions under which a CGM may be deployed adeptly for solving ICL problems through posterior predictive distribution equivalence.
2. Generation of Predictive p-Values: By generating sequences from the CGM predictive distribution, the authors construct approximate infinite datasets, allowing for the translation of complex Bayesian model constructs to actionable predictors in generative AI systems.
3. Comprehensive Empirical Validation: A wide-ranging set of benchmarks, including real-world tasks, confirm the robustness of the generative predictive p-value as a measure of CGM capability. The statistical metrics used affirm model suitability across domain-specific nuances.
4. Discrepancy Function Insights: Analysis elucidates that using different discrepancy functions offers insight into model data efficiency and task complexity. The NLL discrepancy provides valuable information about data sufficiency, whereas NLML caters to computational efficiency needs.

Implications and Future Directions

This paper effectively bridges the conceptual gap between traditional Bayesian model criticism and modern generative methods, providing researchers a new toolset to assess model capability in nuanced and dynamic ICL contexts. Practically, it aids in optimizing model selection and fine-tuning, potentially enhancing the deployment of generative models in resource-sensitive applications.

For future research, addressing specific limitations in the generation of large sequence datasets and refining the computational efficiency of such models hold potential. Moreover, extending this framework to other novel tasks in generative AI, where latent distributions elude explicit formulation, could offer exciting advancements in AI reliability and capability across industries.

Conclusion

This paper adeptly navigates the intricacies of Bayesian model criticism in the context of modern CGMs, equipping the community with a rigorous framework for determining model capability. The empirical findings underscore the method’s applicability, offering new insights into model-data alignment across diverse tasks. The methodological fidelity and expansive evaluations provided here will undoubtedly catalyze further exploration and refinement in generative AI capabilities, with broad implications spanning multiple domains of artificial intelligence research.