Computing with Stochastic Oracles in AI-Augmented Computation

2026-07-07

AI Summary

This work investigates the impact of stochastic oracles on computational power and performance in AI-augmented computation. To this end, it introduces the Stochastic Oracle Turing Machine (SOTM) framework, modeling AI augmentation as an interaction between a probabilistic Turing machine and a context-dependent distributional oracle, and distinguishes between cached and fresh response mechanisms. For the first time, an information-theoretic upper bound on performance is established based on query–response transcripts, revealing how repeated queries enhance accuracy and output quality through the accumulation of independent evidence. Combining total variation distance, Chernoff bounds, majority-vote amplification, and threshold-based stopping strategies, the analysis proves that under binary single-bit queries, the error probability decays exponentially at the Chernoff rate, and provides explicit bounds on the number of queries required to achieve desired output quality improvements along with corresponding amplification guarantees.

Abstract

The Stochastic-Oracle Turing Machine (SOTM) framework models AI-augmented computation as the interaction of a probabilistic Turing machine with an oracle whose responses are drawn from context-dependent distributions. This paper studies what an SOTM can achieve under two oracle-response schemes: in a cached-response oracle, each distinct query receives one response that is reused on later calls to the same query, while in a fresh-response oracle, each call returns an independent response. In both schemes, the SOTM first computes from its input and internal random source to generate its first query, then proceeds adaptively, computing from its query-response transcript (the record of queries issued and responses received) to generate each subsequent query or produce a final output. Cached responses impose two transcript-based ceilings on achievable performance: a correct-identification ceiling governed by the total variation distance between the transcript distributions induced by the hidden states of the oracle, and an output quality ceiling equal to the expected score of the best output the SOTM can compute from the transcript. Fresh responses can raise these ceilings by allowing repeated calls to accumulate independent evidence toward correct or high-quality outputs. In the binary single-informative-query case, the error probability decreases exponentially in the number of calls to the same query at the Chernoff rate. For output quality, query-count bounds characterize threshold stopping when the score function is incorporated as part of the SOTM, and majority-based amplification bounds characterize the binary candidate-output model when it is not. Together, the results identify how response reuse, transcript information, and access to the score function determine what an SOTM can compute and at what token cost.

Problem

• Stochastic Oracle
• AI-Augmented Computation
• Turing Machine
• Response Reuse
• Transcript Information

Innovation

• Stochastic-Oracle Turing Machine
• cached-response oracle
• fresh-response oracle
• transcript-based performance ceiling
• Chernoff rate