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Source note3 min read

Revealed Rationality: Label-Free Evaluation and Regularization from Representation Theorems

Source

arXiv

arxiv.org/abs/2608.05015v1

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Plain-Language Brief

The paper suggests using representation theorems in decision theory to evaluate and regularize Large Language Models (LLMs) and other AI systems. This approach checks if the model's behavior complies with certain axioms, which can be determined from its responses to synthetic choice problems without external labels or human feedback. The penalties for non-compliance are computable and exhaustive within the context of the relevant rationality standard for the elicited data.

What the Document Says

  • The paper discusses using representation theorems in decision theory to evaluate and regularize LLMs and AI systems.
  • Checking a model's compliance with certain axioms can be done from its responses to synthetic choice problems without external labels or human feedback.
  • Penalties for non-compliance are computable.
  • Since the axioms are necessary and sufficient, the resulting checks exhaust the implications of the relevant rationality standard for the elicited data.
  • Three instantiations are discussed: probabilistic coherence via de Finetti's theorem, preference rationality via Afriat's theorem, and subjective expected utility via Echenique and Saito's (2015) theorem.

Key Concepts Mentioned

  • Representation theorems
  • decision theory
  • LLMs
  • AI systems
  • axioms
  • synthetic choice problems
  • penalties

Claims Made by the Document

  • This approach can provide a useful foundation for label-free evaluation and regularization of LLMs and other AI systems.
  • Compliance with axioms can be checked from the model's responses to synthetic choice problems without external labels or human feedback.
  • The resulting checks exhaust the implications of the relevant rationality standard for the elicited data.

Evidence Used

  • The structure of 'if and only if' in representation theorems is argued to be useful

Methods / Approach

  • Using representation theorems from decision theory for evaluation and regularization of LLMs and AI systems

Limitations Stated by the Authors

  • Not stated in source

Limitations Noted by the Agent

Agent interpretation — not from the source.

  • The effectiveness of this approach may depend on the accuracy and applicability of the chosen representation theorems
  • It's unclear how well this method would perform on complex, real-world scenarios

Open Questions

  • How effective is this method in practice?
  • What are the potential drawbacks or limitations?

Notes for Future Q&A

May include interpretation. Labeled where it does.

  • The paper focuses on the theoretical aspects of the approach and does not provide practical implementation details
  • Discussion is limited to three specific instances of the proposed method

Raw Abstract / Excerpt

Representation theorems in decision theory establish that behavior satisfies certain axioms if and only if it can be rationalized by a well-defined objective. I argue that this ``if and only if'' structure provides a potentially useful foundation for label-free evaluation and regularization of LLMs and other AI systems. Axiom compliance can be checked from the model's own responses to synthetic choice problems, with no external labels or human feedback, and the penalties are readily computable. Because the axioms are necessary and sufficient, the resulting checks exhaust the implications of the relevant rationality standard for the elicited data: a model that passes cannot be rejected on rationality grounds by any further test of the same data. I discuss three instantiations: probabilistic coherence via a theorem of de Finetti, preference rationality via Afriat's theorem, and subjective expected utility via a theorem of Echenique and Saito (2015), each yielding a continuous penalty that is zero whenever behavior can be rationalized. Since coherence does not restrict which objective rationalizes behavior, these penalties complement rather than replace other evaluation and training signals.