arXiv:2609.38287v1 Announce Type: cross
Abstract: Simulation-augmented generation (SAGE) is a recent technical proposal in which models simulate individuals' viewpoints at inference time in order to provide more representative answers to contentious user queries. A core challenge for SAGE is making inference-time simulation efficient without sacrificing representation quality. We introduce the first formalization of this problem, based upon an axiom from proportional clustering known as metric proportional justified representation+ (mPJR+) which is the strongest proportionality axiom known to always be satisfiable by centroid-based clustering. We prove that to proportionally represent the viewpoints of a population of $n_H$ humans on a given prompt, we need only create simulations of $n \ll n_H$ individuals, and at inference time, need only dynamically route to $k \ll n$ of those simulations based upon the prompt. This twofold reduction still yields approximate proportional representation guarantees for the entire population. Empirically, across two domains-political questions and personal advice-our proposed routing algorithm achieves higher mPJR+ satisfaction rates than $k$-means-based or random selection baselines.
Abstract: Simulation-augmented generation (SAGE) is a recent technical proposal in which models simulate individuals' viewpoints at inference time in order to provide more representative answers to contentious user queries. A core challenge for SAGE is making inference-time simulation efficient without sacrificing representation quality. We introduce the first formalization of this problem, based upon an axiom from proportional clustering known as metric proportional justified representation+ (mPJR+) which is the strongest proportionality axiom known to always be satisfiable by centroid-based clustering. We prove that to proportionally represent the viewpoints of a population of $n_H$ humans on a given prompt, we need only create simulations of $n \ll n_H$ individuals, and at inference time, need only dynamically route to $k \ll n$ of those simulations based upon the prompt. This twofold reduction still yields approximate proportional representation guarantees for the entire population. Empirically, across two domains-political questions and personal advice-our proposed routing algorithm achieves higher mPJR+ satisfaction rates than $k$-means-based or random selection baselines.
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