Behavioral Heterogeneity as Quantum-Inspired Representation

Abstract

Driver heterogeneity is often reduced to labels or discrete regimes, compressing what is inherently dynamic into static categories. We introduce quantum-inspired representation that models each driver as an evolving latent state, presented as a density matrix with structured mathematical properties. Behavioral observations are embedded via non-linear Random Fourier Features, while state evolution blends temporal persistence of behavior with context-dependent profile activation. We evaluate our approach on empirical driving data, Third Generation Simulation Data (TGSIM), showing how driving profiles are extracted and analyzed.

Figures (5)

• Figure 1: Schematic of the proposed framework. Behavioral variables are mapped via RFF into a normalized feature space, where quadratic state formation yields density-matrix profiles. Context variables modulate profile weighting, and density-matrix constraints ensure valid state representation.
• Figure 2: Context activation coefficients ($\beta$) across identified behavioral profiles.
• Figure 3: Marginal activation of dominant eigenmodes across behavioral variables. Rows denote profiles and columns denote $\Delta v$, $a$, and $h$.
• Figure 4: Multimodal activation heatmaps for Profile 3. Shaded contours represent the localized activation of each mode, illustrating the structural diversity within the profile geometry.
• Figure 5: Pairwise Frobenius distances between identified behavioral profiles. Numerical values represent the magnitude of divergence in profile geometry.