Large language models (LLMs) are now available from cloud API providers in various sizes and configurations. While this diversity offers a broad spectrum of choices, effectively leveraging the options to optimize computational cost and performance remains challenging. In this work, we present AutoMix, an approach that strategically routes queries to larger LMs, based on the approximate correctness of outputs from a smaller LM. Central to AutoMix are two key technical contributions. First, it has a few-shot self-verification mechanism, which estimates the reliability of its own outputs without requiring extensive training. Second, given that self-verification can be noisy, it employs a POMDP based router that can effectively select an appropriately sized model, based on answer confidence. Experiments across five language models and five challenging datasets show that Automix consistently surpasses strong baselines, reducing computational cost by over 50\% for comparable performance.

Recognition errors are common in human communication. Similar errors often lead to unwanted behaviour in dialogue systems or virtual assistants. In human communication, we can recover from them by repeating misrecognized words or phrases; however in human-machine communication this recovery mechanism is not available. In this paper, we attempt to bridge this gap and present a system that allows a user to correct speech recognition errors in a virtual assistant by repeating misunderstood words. When a user repeats part of the phrase the system rewrites the original query to incorporate the correction. This rewrite allows the virtual assistant to understand the original query successfully. We present an end-to-end 2-step attention pointer network that can generate the the rewritten query by merging together the incorrectly understood utterance with the correction follow-up. We evaluate the model on data collected for this task and compare the proposed model to a rule-based baseline and a standard pointer network. We show that rewriting the original query is an effective way to handle repetition-based recovery and that the proposed model outperforms the rule based baseline, reducing Word Error Rate by 19% relative at 2% False Alarm Rate on annotated data.