Multi-class Temporal Logic Neural Networks

TL;DR

This work proposes a method that combines neural networks that represent STL specifications for multi-class classification of time-series data, and introduces STL-based attributes for enhancing the interpretability of the results.

Abstract

Time-series data can represent the behaviors of autonomous systems, such as drones and self-driving cars. The task of binary and multi-class classification for time-series data has become a prominent area of research. Neural networks represent a popular approach to classifying data; However, they lack interpretability, which poses a significant challenge in extracting meaningful information from them. Signal Temporal Logic (STL) is a formalism that describes the properties of timed behaviors. We propose a method that combines all of the above: neural networks that represent STL specifications for multi-class classification of time-series data. We offer two key contributions: 1) We introduce a notion of margin for multi-class classification, and 2) we introduce STL-based attributes for enhancing the interpretability of the results. We evaluate our method on two datasets and compare it with state-of-the-art baselines.

Figures (4)

• Figure 1: Example of a three-dimensional output space.
• Figure 2: Trajectories in the naval scenario. The green trajectories are labeled as class $1$. The blue trajectories are labeled as class $2$. The yellow trajectories are labeled as class $3$.
• Figure 3: Examples of trajectories in the synthetic dataset. Region $1$, $2$, $3$, $4$ corresponds to the region specified by the predicate of $\phi_1$, $\phi_2$, $\phi_3$, $\phi_4$, respectively.
• Figure 4: The average absolute robustness value versus the epoch for positive and negative code, with and without margin, respectively.

Theorems & Definitions (3)

• Definition 1: Robustness
• Definition 2: Multi-class STL margin
• Example 1