Benchmark Prediction with Sparse and Unpaired Cached Responses: Introducing Product Kernel Perspective Space (PKPS)

Forum topic · 小凯 · 2026-11-03

Summary

Evaluating generative models on every query of every benchmark task is prohibitively expensive, so models are typically evaluated on different subsets of tasks and queries. The resulting response collections and (model, task) score matrices are sparse and unpaired. This paper (arXiv:2611.03614) by Hayden Helm, Avijit Ghosh, Ben Johnson, and Carey Priebe introduces Product Kernel Perspective Space (PKPS), a collection of low-dimensional representations of models based on their embedded responses. PKPS generalizes existing methods for representing black-box generative models by comparing responses to similar rather than identical queries, allowing it to exploit sparse and unpaired evaluation data. The authors prove theoretically that PKPS-based benchmark prediction is query-efficient relative to methods restricted to dense, paired evaluation data. Empirically, on two large benchmark suites, PKPS-based methods outperform baselines on benchmark prediction tasks. This work offers a practical way to reduce evaluation costs while maintaining reliable model comparisons.

Paper Overview

Field: Machine Learning
Authors: Hayden Helm, Avijit Ghosh, Ben Johnson, Carey Priebe
Published: 2026-11-02
arXiv: 2611.03614

Abstract

Evaluating a generative model on all queries from all available benchmark tasks is prohibitively expensive. As such, models are often evaluated on different subsets of tasks and/or different subsets of queries from a given task. The resulting collection of responses and the corresponding (model, task) score matrix are sparse and unpaired.

In this paper, the authors introduce the Product Kernel Perspective Space (PKPS), a collection of low-dimensional representations of models based on their embedded responses. PKPS generalizes existing methods for representing black-box generative models by comparing responses to similar — rather than just identical — queries and is therefore able to utilize sparse and unpaired information.

Key Contributions

PKPS representation: Low-dimensional model representations built from embedded responses, enabling comparison across partially overlapping evaluation sets.
Query efficiency: Theoretically, benchmark prediction using PKPS is shown to be query-efficient relative to methods that only use dense and paired evaluation data.
Empirical results: On two large benchmark suites, PKPS-based methods outperform baselines on benchmark prediction tasks.

Why It Matters

Benchmarking large generative models is one of the most expensive parts of model development. By leveraging sparse, unpaired cached responses — data that conventional methods discard — PKPS enables more accurate benchmark prediction at lower evaluation cost.

Full paper: https://arxiv.org/abs/2611.03614