Verified Neural Compressed Sensing
Rudy Bunel, Krishnamurthy Dvijotham, M. Pawan Kumar, Alessandro De, Palma, Robert Stanforth

TL;DR
This paper introduces the first neural networks with provable correctness for compressed sensing, verified automatically, enabling reliable sparse vector recovery beyond traditional methods.
Contribution
It presents a novel approach to train and verify neural networks that provably solve compressed sensing tasks with formal correctness guarantees.
Findings
Neural networks can provably recover sparse vectors in small dimensions.
Verification ensures neural network correctness without human input.
Network complexity adapts to problem difficulty, outperforming traditional methods.
Abstract
We develop the first (to the best of our knowledge) provably correct neural networks for a precise computational task, with the proof of correctness generated by an automated verification algorithm without any human input. Prior work on neural network verification has focused on partial specifications that, even when satisfied, are not sufficient to ensure that a neural network never makes errors. We focus on applying neural network verification to computational tasks with a precise notion of correctness, where a verifiably correct neural network provably solves the task at hand with no caveats. In particular, we develop an approach to train and verify the first provably correct neural networks for compressed sensing, i.e., recovering sparse vectors from a number of measurements smaller than the dimension of the vector. We show that for modest problem dimensions (up to 50), we can train…
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Taxonomy
TopicsSparse and Compressive Sensing Techniques · Photoacoustic and Ultrasonic Imaging · Electrical and Bioimpedance Tomography
MethodsFocus
