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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 proposes using representation theorems in decision theory to evaluate and regulate Large Language Models (LLMs) and other AI systems. The 'if and only if' structure allows for axiom compliance checks from the model's responses to synthetic choice problems, without external labels or human feedback. The proposed method can exhaust the implications of the relevant rationality standard for the elicited data, providing continuous penalties that are zero when behavior can be rationalized.

What the Document Says

  • The paper discusses using representation theorems in decision theory to evaluate and regulate AI systems like LLMs.
  • Axiom compliance can be checked from the model's responses to synthetic choice problems, with no external labels or human feedback.
  • Penalties are computable and are zero whenever behavior can be rationalized.
  • 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 (2015) theorem.
  • Each instantiation yields a continuous penalty that is zero whenever behavior can be rationalized.
  • Coherence does not restrict which objective rationalizes behavior, so these penalties complement rather than replace other evaluation and training signals.

Key Concepts Mentioned

  • Representation theorems
  • decision theory
  • AI systems
  • Large Language Models (LLMs)
  • synthetic choice problems
  • axioms
  • objective rationalization
  • penalties
  • probabilistic coherence
  • preference rationality
  • subjective expected utility

Claims Made by the Document

  • The 'if and only if' structure of representation theorems can be useful for evaluating and regularizing AI systems.
  • Axiom compliance checks can be done from the model's responses to synthetic choice problems without human feedback.
  • The resulting checks exhaust the implications of the relevant rationality standard for the elicited data.
  • Three specific instantiations are proposed: probabilistic coherence, preference rationality, and subjective expected utility.

Evidence Used

  • The text explains how representation theorems can be used to evaluate AI systems based on axiom compliance checks.

Methods / Approach

  • Using representation theorems in decision theory to check axiom compliance from synthetic choice problems

Limitations Stated by the Authors

  • UNKNOWN
  • The paper does not discuss how these methods might perform in real-world applications or handle complex scenarios.

Limitations Noted by the Agent

Agent interpretation — not from the source.

  • The proposed method may not account for all aspects of AI system behavior, as it focuses on rationality standards based on axioms.
  • The effectiveness of the method in handling complex scenarios or real-world applications is unknown.

Open Questions

  • How effective would these methods be in real-world AI system evaluation and regulation?
  • How can these methods handle complex scenarios or unexpected behaviors not covered by the axioms?

Notes for Future Q&A

May include interpretation. Labeled where it does.

  • The paper does not discuss the practicality of its proposed methods in real-world applications.

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.