Understanding as No-Arbitrage: Bounded Dutch Books as a Definition and Training Objective for Language Models
Read the original on arXiv AI →The paper proposes measuring a language model’s understanding via no‑arbitrage, defining it as the inability of a bounded trader to profit from Dutch books against the model’s probabilities on logically related claims. It shows that full logical coherence is computationally infeasible, that standard next‑token training yields incoherent predictions across formats, and that uncertainty grows predictably along reasoning chains, creating arbitrage opportunities. The authors introduce Arbitr, a training framework that penalizes logical inconsistencies while maintaining accuracy, reducing exploitability by orders of magnitude and revealing a scaling illusion where large models appear coherent yet exhibit extreme unjustified confidence.
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