Model Stealing for Any Low-Rank Language Model (2411.07536v1)

Abstract: Model stealing, where a learner tries to recover an unknown model via carefully chosen queries, is a critical problem in machine learning, as it threatens the security of proprietary models and the privacy of data they are trained on. In recent years, there has been particular interest in stealing LLMs. In this paper, we aim to build a theoretical understanding of stealing LLMs by studying a simple and mathematically tractable setting. We study model stealing for Hidden Markov Models (HMMs), and more generally low-rank LLMs. We assume that the learner works in the conditional query model, introduced by Kakade, Krishnamurthy, Mahajan and Zhang. Our main result is an efficient algorithm in the conditional query model, for learning any low-rank distribution. In other words, our algorithm succeeds at stealing any LLM whose output distribution is low-rank. This improves upon the previous result by Kakade, Krishnamurthy, Mahajan and Zhang, which also requires the unknown distribution to have high "fidelity", a property that holds only in restricted cases. There are two key insights behind our algorithm: First, we represent the conditional distributions at each timestep by constructing barycentric spanners among a collection of vectors of exponentially large dimension. Second, for sampling from our representation, we iteratively solve a sequence of convex optimization problems that involve projection in relative entropy to prevent compounding of errors over the length of the sequence. This is an interesting example where, at least theoretically, allowing a machine learning model to solve more complex problems at inference time can lead to drastic improvements in its performance.

• The paper introduces an algorithm that efficiently learns any low-rank distribution from conditional queries.
• It employs barycentric spanners and convex optimization with relative entropy projections to minimize cumulative sampling errors.
• The theoretical guarantees, including polynomial query complexity, highlight inherent security risks in proprietary language models.

Overview of "Model Stealing for Any Low-Rank LLM"

The paper "Model Stealing for Any Low-Rank LLM," authored by Allen Liu and Ankur Moitra, addresses the increasingly significant issue of model stealing within the field of machine learning. As proprietary models such as LLMs become integral to various applications, the potential threat of these models being reverse-engineered through strategic queries poses serious security risks. This paper is particularly focused on formalizing and addressing the theoretical underpinnings of model stealing in the context of Hidden Markov Models (HMMs) and more generally low-rank LLMs.

Problem Statement and Methodology

The core problem that the paper seeks to address is whether it is possible to efficiently reverse-engineer or steal a LLM purely from access to its outputs upon specific queries, a task that is highly relevant given the desire for both security and functionality transfer (as in model distillation). The authors place their framework within the conditional query model. In this setup, they aim to recover low-rank distributions efficiently using a mathematically grounded approach.

The paper's primary contribution is an algorithm that can learn any low-rank distribution from conditional queries, improving upon previous works that had more restrictive conditions. The authors target two technical challenges: representing conditional distributions via barycentric spanners among vectors, and employing convex optimization with relative entropy projections to counteract cumulative errors in sequential sampling. This suggests significant performance improvements in theoretical model performance by allowing machine learning models to solve more complex problems at inference time.

Key Results

A central result of the paper is a theorem demonstrating that given conditional query access to an unknown low-rank distribution, the proposed algorithm can produce an approximately accurate learned model with efficiency. This is significant for it posits that low-rank characterizations are adept at both understanding model complexity and facilitating effective model stealing. The authors bolster their theoretical insights with rigorous performance guarantees related to polynomial query complexity and successful sampling algorithm implementation, all within the formal assumptions of the conditional model.

Implications and Future Directions

The findings in this paper have both theoretical and practical ramifications. Theoretically, the authors advance our understanding of model stealing by positing that model complexity, specifically rank, dictates its susceptibility to theft via conditional queries. This work opens pathways toward analyzing machine learning models' structural vulnerability and framing defensive strategies within an increasingly adversarial AI landscape.

Practically, given the increasing deployment of proprietary models, understanding and mitigating risks associated with unintended model function replication becomes imperative. The proposed framework and algorithm offer a foundation on which defenses against model stealing may be developed—an essential consideration for service providers protecting sensitive model parameters and underlying datasets.

Future research may extend these insights to broader classes of models beyond the field of low-rank or HMM structures, offering potential advancements in both AI security strategies and model interpretation methodologies. Moreover, as AI continues evolving, elaborate hybrid models that incorporate various complex elements besides those found in HMMs could benefit from adapted techniques based on the foundational ideas presented.

In conclusion, "Model Stealing for Any Low-Rank LLM" provides an illuminating exposition on model theft risk, delivering a mathematically precise set of tools to paper and address this emerging threat. As machine learning models grow in complexity and applicability, such theoretical groundwork will prove invaluable in paralleling technological advances with comprehensive security preparedness.