标题： 从原始数据到结构语义：失真、速率和推理准确率之间的权衡 显示英文标题

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

摘要： 这项工作探讨了在点对点通信设置中使用持久性图（PDs）的优势，PDs 是原始点云数据的拓扑签名。PD 在结构语义上意味着它包含有关数据形状和结构的信息。而不是传输原始数据，发送方传递其 PD 语义，接收方使用接收到的语义进行推理。我们提出了 PD 语义失真和速率的新定性定义，同时定量地描述了失真、速率和推理准确性之间的权衡。模拟结果表明，与原始数据或基于自编码器（AE）的潜在表示相比，PD 语义能更有效地利用传输信道，增加纳入错误检测/纠正能力的自由度，并提高对信道缺陷的鲁棒性。例如，在具有非零交叉概率设置的二进制对称信道中，为了使 Bose、Chaudhuri 和 Hocquenghem（BCH）编码的 PD 语义实现超过 80% 的推理准确性，所需的最低速率大约是编码 AE 潜在表示所需速率的 15 倍。此外，结果表明，与原始数据的速率要求相比，PD 语义的优势更加明显。 显示英文摘要

摘要： 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.