Many recent state-of-the-art results in language tasks were achieved using compound systems that perform multiple Language Model (LM) calls and aggregate their responses. However, there is little understanding of how the number of LM calls -- e.g., when asking the LM to answer each question multiple times and taking a majority vote -- affects such a compound system's performance. In this paper, we initiate the study of scaling properties of compound inference systems. We analyze, theoretically and empirically, how the number of LM calls affects the performance of Vote and Filter-Vote, two of the simplest compound system designs, which aggregate LM responses via majority voting, optionally applying LM filters. We find, surprisingly, that across multiple language tasks, the performance of both Vote and Filter-Vote can first increase but then decrease as a function of the number of LM calls. Our theoretical results suggest that this non-monotonicity is due to the diversity of query difficulties within a task: more LM calls lead to higher performance on easy queries, but lower performance on hard queries, and non-monotone behavior can emerge when a task contains both types of queries. This insight then allows us to compute, from a small number of samples, the number of LM calls that maximizes system performance, and define an analytical scaling model for both systems. Experiments show that our scaling model can accurately predict the performance of Vote and Filter-Vote systems and thus find the optimal number of LM calls to make.

Compound AI systems integrating multiple components, such as Large Language Models, specialized tools, and traditional machine learning models, are increasingly deployed to solve complex real-world tasks. However, optimizing compound systems remains challenging due to their non-differentiable structures and diverse configuration types across components, including prompts, hyperparameters, and model parameters. To address this challenge, we propose Optimas, a unified framework for effective optimization of compound systems. The core idea of Optimas is to maintain one Local Reward Function (LRF) per component, each satisfying a local-global alignment property, i.e., each component's local reward correlates with the global system performance. In each iteration, Optimas efficiently adapts the LRFs to maintain this property while simultaneously maximizing each component's local reward. This approach enables independent updates of heterogeneous configurations using the designated optimization method, while ensuring that local improvements consistently lead to performance gains. We present extensive evaluations across five real-world compound systems to demonstrate that Optimas outperforms strong baselines by an average improvement of 11.92%, offering a general and effective approach for improving compound systems. Our website is at https://optimas.stanford.edu.

Many recent state-of-the-art results in language tasks were achieved using compound systems that perform multiple Language Model (LM) calls and aggregate their responses. However, there is little understanding of how the number of LM calls -- e.g., when asking the LM to answer each question multiple times and taking a majority vote -- affects such a compound system's performance. In this paper, we initiate the study of scaling properties of compound inference systems. We analyze, theoretically and empirically, how the number of LM calls affects the performance of Vote and Filter-Vote, two of the simplest compound system designs, which aggregate LM responses via majority voting, optionally applying LM filters. We find, surprisingly, that across multiple language tasks, the performance of both Vote and Filter-Vote can first increase but then decrease as a function of the number of LM calls.

Modern retrieval systems do not rely on a single ranking model to construct their rankings. Instead, they generally take a cascading approach where a sequence of ranking models are applied in multiple re-ranking stages. Thereby, they balance the quality of the top-K ranking with computational costs by limiting the number of documents each model re-ranks. However, the cascading approach is not the only way models can interact to form a retrieval system. We propose the concept of compound retrieval systems as a broader class of retrieval systems that apply multiple prediction models. This encapsulates cascading models but also allows other types of interactions than top-K re-ranking. In particular, we enable interactions with large language models (LLMs) which can provide relative relevance comparisons. We focus on the optimization of compound retrieval system design which uniquely involves learning where to apply the component models and how to aggregate their predictions into a final ranking. This work shows how our compound approach can combine the classic BM25 retrieval model with state-of-the-art (pairwise) LLM relevance predictions, while optimizing a given ranking metric and efficiency target. Our experimental results show optimized compound retrieval systems provide better trade-offs between effectiveness and efficiency than cascading approaches, even when applied in a self-supervised manner. With the introduction of compound retrieval systems, we hope to inspire the information retrieval field to more out-of-the-box thinking on how prediction models can interact to form rankings.

Compound AI systems that combine multiple LLM calls, such as self-refine and multi-agent-debate, achieve strong performance on many AI tasks. We address a core question in optimizing compound systems: for each LLM call or module in the system, how should one decide which LLM to use? We show that these LLM choices have a large effect on quality, but the search space is exponential. We propose LLMSelector, an efficient framework for model selection in compound systems, which leverages two key empirical insights: (i) end-to-end performance is often monotonic in how well each module performs, with all other modules held fixed, and (ii) per-module performance can be estimated accurately by an LLM. Building upon these insights, LLMSelector iteratively selects one module and allocates to it the model with the highest module-wise performance, as estimated by an LLM, until no further gain is possible. LLMSelector is applicable to any compound system with a bounded number of modules, and its number of API calls scales linearly with the number of modules, achieving high-quality model allocation both empirically and theoretically. Experiments with popular compound systems such as multi-agent debate and self-refine using LLMs such as GPT-4o, Claude 3.5 Sonnet and Gemini 1.5 show that LLMSelector confers 5%-70% accuracy gains compared to using the same LLM for all modules.

AI caught everyone's attention in 2023 with Large Language Models (LLMs) that can be instructed to perform general tasks, such as translation or coding, just by prompting. This naturally led to an intense focus on models as the primary ingredient in AI application development, with everyone wondering what capabilities new LLMs will bring. As more developers begin to build using LLMs, however, we believe that this focus is rapidly changing: state-of-the-art AI results are increasingly obtained by compound systems with multiple components, not just monolithic models. For example, Google's AlphaCode 2 set state-of-the-art results in programming through a carefully engineered system that uses LLMs to generate up to 1 million possible solutions for a task and then filter down the set. AlphaGeometry, likewise, combines an LLM with a traditional symbolic solver to tackle olympiad problems.