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

TL;DR

The paper investigates using persistence diagram (PD) based topological signatures as semantic representations for point-cloud data in a point-to-point communication setting. It defines qualitative and quantitative notions of semantic distortion and rate for PD semantics, and characterizes the trade-offs between distortion, rate, and downstream inference accuracy. Empirical results on a MNIST-derived point-cloud dataset show that PD semantics achieve far lower communication rates for a given inference accuracy compared with raw data or autoencoder latent representations, and remain robust under channel impairments, especially when combined with error-correcting codes. These findings indicate that structure-based, topological semantics can markedly improve efficiency and reliability in goal-oriented communications, with practical benefits for error detection and robust inference.

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.

Figures (8)

• Figure 1: System model highlighting different stages.
• Figure 2: Uniform vector quantization.
• Figure 3: Empirical trade-off between $\hat{D}_{\textrm{MSE}}$ and $\hat{R}$.
• Figure 4: Empirical probability distributions $\hat{f}_{\boldsymbol{s}}$ [(a) and (d)], $\hat{f}^{27}_{\boldsymbol{a}}$ [(b) and (e)], and $\hat{f}_{\boldsymbol{g}}$ [(c) and (f)] for different $m$.
• Figure 5: Empirical trade-off between $\hat{A}$ and $\hat{D}_{\textrm{MSE}}$.