arXiv subjects

Guy Rothblum

Publications and source records attributed to Guy Rothblum.

3 recordsLinked to original sources

arXiv2024

How to Verify Any (Reasonable) Distribution Property: Computationally Sound Argument Systems for Distributions

As statistical analyses become more central to science, industry and society, there is a growing need to ensure correctness of their results. Approximate correctness can be verified by replicating the entire analysis, but can we verify without replication? Building on a recent line of work, we study proof-systems that allow a probabilistic verifier to ascertain that the results of an analysis are approximately correct, while drawing fewer samples and using less computational resources than would be needed to replicate the analysis. We focus on distribution testing problems: verifying that an unknown distribution is close to having a claimed property. Our main contribution is a interactive protocol between a verifier and an untrusted prover, which can be used to verify any distribution property that can be decided in polynomial time given a full and explicit description of the distribution. If the distribution is at statistical distance $\varepsilon$ from having the property, then the verifier rejects with high probability. This soundness property holds against any polynomial-time strategy that a cheating prover might follow, assuming the existence of collision-resistant hash functions (a standard assumption in cryptography). For distributions over a domain of size $N$, the protocol consists of $4$ messages and the communication complexity and verifier runtime are roughly $\widetilde{O}\left(\sqrt{N} / \varepsilon^2 \right)$. The verifier's sample complexity is $\widetilde{O}\left(\sqrt{N} / \varepsilon^2 \right)$, and this is optimal up to $\polylog(N)$ factors (for any protocol, regardless of its communication complexity). Even for simple properties, approximately deciding whether an unknown distribution has the property can require quasi-linear sample complexity and running time. For any such property, our protocol provides a quadratic speedup over replicating the analysis.

cs.CC↗

arXiv2024

Models That Prove Their Own Correctness

How can we trust the correctness of a learned model on a particular input of interest? Model accuracy is typically measured on average over a distribution of inputs, giving no guarantee for any fixed input. This paper proposes a theoretically-founded solution to this problem: to train Self-Proving models that prove the correctness of their output to a verification algorithm $V$ via an Interactive Proof. Self-Proving models satisfy that, with high probability over an input sampled from a given distribution, the model generates a correct output and successfully proves its correctness to $V$. The soundness property of $V$ guarantees that, for every input, no model can convince $V$ of the correctness of an incorrect output. Thus, a Self-Proving model proves correctness of most of its outputs, while all incorrect outputs (of any model) are detected by $V$. We devise and analyze two generic methods for learning Self-Proving models: Transcript Learning (TL) which relies on access to transcripts of accepting interactions, and Reinforcement Learning from Verifier Feedback (RLVF) which trains a model by emulating interactions with the verifier.

cs.LG↗

arXiv2023

Samplable Anonymous Aggregation for Private Federated Data Analysis

We revisit the problem of designing scalable protocols for private statistics and private federated learning when each device holds its private data. Locally differentially private algorithms require little trust but are (provably) limited in their utility. Centrally differentially private algorithms can allow significantly better utility but require a trusted curator. This gap has led to significant interest in the design and implementation of simple cryptographic primitives, that can allow central-like utility guarantees without having to trust a central server. Our first contribution is to propose a new primitive that allows for efficient implementation of several commonly used algorithms, and allows for privacy accounting that is close to that in the central setting without requiring the strong trust assumptions it entails. {\em Shuffling} and {\em aggregation} primitives that have been proposed in earlier works enable this for some algorithms, but have significant limitations as primitives. We propose a {\em Samplable Anonymous Aggregation} primitive, which computes an aggregate over a random subset of the inputs and show that it leads to better privacy-utility trade-offs for various fundamental tasks. Secondly, we propose a system architecture that implements this primitive and perform a security analysis of the proposed system. Our design combines additive secret-sharing with anonymization and authentication infrastructures.

cs.CR↗