Reconstructing Trust Embeddings from Siamese Trust Scores: A Direct-Sum Approach with Fixed-Point Semantics

TL;DR

This paper presents a method to reconstruct high-dimensional trust embeddings from one-dimensional trust scores, demonstrating its accuracy, fixed-point properties, and privacy implications in distributed-security systems.

Contribution

It introduces a direct-sum estimator for reconstructing trust embeddings from trust scores, with theoretical guarantees and practical validation, highlighting privacy risks and countermeasures.

Findings

Reconstructed embeddings preserve inter-device geometry.

Reconstruction accuracy linked to score-sequence length.

Publishing trust scores can leak behavioral information.

Abstract

We study the inverse problem of reconstructing high-dimensional trust embeddings from the one-dimensional Siamese trust scores that many distributed-security frameworks expose. Starting from two independent agents that publish time-stamped similarity scores for the same set of devices, we formalise the estimation task, derive an explicit direct-sum estimator that concatenates paired score series with four moment features, and prove that the resulting reconstruction map admits a unique fixed point under a contraction argument rooted in Banach theory. A suite of synthetic benchmarks (20 devices x 10 time steps) confirms that, even in the presence of Gaussian noise, the recovered embeddings preserve inter-device geometry as measured by Euclidean and cosine metrics; we complement these experiments with non-asymptotic error bounds that link reconstruction accuracy to score-sequence length. Beyond methodology, the paper demonstrates a practical privacy risk: publishing granular trust scores can leak latent behavioural information about both devices and evaluation models. We therefore discuss counter-measures -- score quantisation, calibrated noise, obfuscated embedding spaces -- and situate them within wider debates on transparency versus confidentiality in networked AI systems. All datasets, reproduction scripts and extended proofs accompany the submission so that results can be verified without proprietary code.