From Raw Data to Structural Semantics: Trade-offs among Distortion, Rate, and Inference Accuracy

TL;DR

This paper investigates the use of topological signatures called persistence diagrams for efficient data transmission and inference, demonstrating significant advantages over raw data and autoencoder representations in terms of rate and robustness.

Contribution

It introduces novel definitions for distortion and rate of persistence diagram semantics and quantitatively analyzes their trade-offs, showing improved transmission efficiency and robustness.

Findings

PD semantics require significantly lower transmission rates for high inference accuracy.

PD semantics outperform raw data and autoencoder representations in noisy channels.

Simulations confirm robustness and efficiency of PD-based communication.

Abstract

This work explores the advantages of using persistence diagrams (PDs), topological signatures of raw point cloud data, in a point-to-point communication setting. PD is a structural semantics in the sense that it carries information about the shape and structure of the data. Instead of transmitting raw data, the transmitter communicates its PD semantics, and the receiver carries out inference using the received semantics. We propose novel qualitative definitions for distortion and rate of PD semantics while quantitatively characterizing the trade-offs among the distortion, rate, and inference accuracy. Simulations demonstrate that unlike raw data or autoencoder (AE)-based latent representations, PD semantics leads to more effective use of transmission channels, enhanced degrees of freedom for incorporating error detection/correction capabilities, and improved robustness to channel imperfections. For instance, in a binary symmetric channel with nonzero crossover probability settings, the minimum rate required for Bose, Chaudhuri, and Hocquenghem (BCH)-coded PD semantics to achieve an inference accuracy over 80% is approximately 15 times lower than the rate required for the coded AE-latent representations. Moreover, results suggest that the gains of PD semantics are even more pronounced when compared with the rate requirements of raw data.