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

2025-08-02

AI Summary

This paper investigates the privacy risk of reconstructing high-dimensional trust embeddings from one-dimensional Siamese trust scores in distributed secure systems. To address the threat that fine-grained scores may leak device behavioral and model information, we propose a direct summation estimator grounded in Banach contraction mapping theory—first rigorously proving the existence and uniqueness of a fixed point for the reconstruction mapping, thereby ensuring faithful recovery of inter-device geometric structure under noise. Our method integrates timestamp-based similarity sequence modeling, fourth-order moment feature extraction, concatenative reconstruction, and non-asymptotic error analysis, all theoretically supported by fixed-point semantics. Empirical evaluation on synthetic data (20 devices × 10 time steps) demonstrates high-fidelity reconstruction, as measured by both Euclidean and cosine distances. The code and datasets are publicly released to facilitate reproducibility.

Technology Category

• Data Mining & Knowledge Management: Representing, Reasoning, and Using Provenance, Trust
• Machine Learning: Privacy
• Search and Optimization: Distributed Search

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

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.

Problem

• Reconstruct high-dimensional trust embeddings from one-dimensional scores
• Prove fixed-point uniqueness in reconstruction using Banach theory
• Address privacy risks from granular trust score leakage

Innovation

• Direct-sum estimator with moment features
• Fixed-point reconstruction via Banach theory
• Privacy countermeasures like score quantisation