Michael J. Zellinger

Michael J. Zellinger, Peter Bühlmann

Cluster analysis relies on effective benchmarks for evaluating and comparing different algorithms. Simulation studies on synthetic data are popular because important features of the data sets, such as the overlap between clusters, or the variation in cluster shapes, can be effectively varied. Unfortunately, creating evaluation scenarios is often laborious, as practitioners must translate higher-level scenario descriptions like "clusters with very different shapes" into lower-level geometric parameters such as cluster centers, covariance matrices, etc. To make benchmarks more convenient and informative, we propose synthetic data generation based on direct specification of high-level scenarios, either through verbal descriptions or high-level geometric parameters. Our open-source Python package repliclust implements this workflow, making it easy to set up interpretable and reproducible benchmarks for cluster analysis. A demo of data generation from verbal inputs is available at https://demo.repliclust.org.

Michael J. Zellinger, Matt Thomson

Understanding the reliability of large language models (LLMs) has recently garnered significant attention. Given LLMs' propensity to hallucinate, as well as their high sensitivity to prompt design, it is already challenging to predict the performance of an individual LLM. However, the problem becomes more complex for compound LLM systems such as cascades, where in addition to each model's standalone performance, we must understand how the error rates of different models interact. In this paper, we present a probabilistic model for the joint performance distribution of a sequence of LLMs, which enables a framework for rationally tuning the confidence thresholds of a LLM cascade using continuous optimization. Compared to selecting confidence thresholds using Bayesian optimization, our parametric Markov-copula model yields more favorable error-cost trade-offs, improving the area under the error-cost curve by 4.3% on average for cascades with $k\geq 3$ models. In the low-sample regime with $n \leq 30$ training examples, the performance improvement widens to 10.2%, suggesting that our framework's inductive assumptions about the interactions between the error rates of different LLMs enhance sample efficiency. Overall, our Markov-copula model provides a rational basis for tuning LLM cascade performance and points to the potential of probabilistic methods in analyzing systems of LLMs.

Michael J. Zellinger, Rex Liu, Matt Thomson

LLM cascades deploy small LLMs to answer most queries, limiting the use of large and expensive LLMs to difficult queries. This approach can significantly reduce costs without impacting performance. However, risk-sensitive domains such as finance or medicine place an additional premium on avoiding model errors. Since even the most expensive models are susceptible to making mistakes, applications in these domains benefit from allowing LLM systems to completely abstain from answering difficult queries. Introducing abstention poses a design question for LLM cascades: should abstention only be allowed at the final model or also at earlier models? Since the error patterns of small and large models are correlated, allowing earlier models to abstain may reduce inference costs and latency by anticipating abstention decisions by expensive and slow models, thus avoiding the need to run these models. We investigate the benefits of such "early abstention" in LLM cascades and find that it reduces overall test loss by 2.2% on average across six benchmarks (GSM8K, MedMCQA, MMLU, TriviaQA, TruthfulQA, and XSum). These gains result from a more effective use of abstention, trading a 4.1% average increase in the overall abstention rate for a 13.0% reduction in cost and a 5.0% reduction in error rate. Our findings demonstrate the possibility of leveraging correlations between the error patterns of different language models to drive performance improvements for LLM systems with abstention.

Michael J. Zellinger, Matt Thomson

State-of-the-art reasoning LLMs are powerful problem solvers, but they still occasionally make mistakes. However, adopting AI models in risk-sensitive domains often requires error rates near 0%. To address this gap, we propose collaboration between a reasoning model and a human expert who resolves queries the model cannot confidently answer. We find that quantifying the uncertainty of a reasoning model through the length of its reasoning trace yields an effective basis for deferral to a human, e.g., cutting the error rate of Qwen3 235B-A22B on difficult MATH problems from 3% to less than 1% when deferring 7.5% of queries. However, the high latency of reasoning models still makes them challenging to deploy on use cases with high query volume. To address this challenge, we explore fronting a reasoning model with a large non-reasoning model. We call this modified human-in-the-loop system "Fail Fast, or Ask", since the non-reasoning model may defer difficult queries to the human expert directly ("failing fast"), without incurring the reasoning model's higher latency. We show that this approach yields around 40% latency reduction and about 50% cost savings for DeepSeek R1 while maintaining 90+% area under the accuracy-rejection curve. However, we observe that latency savings are lower than expected because of "latency drag", the phenomenon that processing easier queries with a non-reasoning model pushes the reasoning model's latency distribution towards longer latencies. Broadly, our results suggest that the deficiencies of state-of-the-art reasoning models -- nontrivial error rates and high latency -- can be substantially mitigated through black-box systems engineering, without requiring access to LLM internals.

Michael J. Zellinger, Matt Thomson

Practitioners often navigate LLM performance trade-offs by plotting Pareto frontiers of optimal accuracy-cost trade-offs. However, this approach offers no way to compare between LLMs with distinct strengths and weaknesses: for example, a cheap, error-prone model vs a pricey but accurate one. To address this gap, we propose economic evaluation of LLMs. Our framework quantifies the performance trade-off of an LLM as a single number based on the economic constraints of a concrete use case, all expressed in dollars: the cost of making a mistake, the cost of incremental latency, and the cost of abstaining from a query. We apply our economic evaluation framework to compare the performance of reasoning and non-reasoning models on difficult questions from the MATH benchmark, discovering that reasoning models offer better accuracy-cost tradeoffs as soon as the economic cost of a mistake exceeds \$0.01. In addition, we find that single large LLMs often outperform cascades when the cost of making a mistake is as low as \$0.1. Overall, our findings suggest that when automating meaningful human tasks with AI models, practitioners should typically use the most powerful available model, rather than attempt to minimize AI deployment costs, since deployment costs are likely dwarfed by the economic impact of AI errors.