Behavioral Heterogeneity as Quantum-Inspired Representation

Mohammad Elayan; Wissam Kontar

cs.LGMar 24, 2026

Behavioral Heterogeneity as Quantum-Inspired Representation

Authors: Mohammad Elayan, Wissam Kontar

Organizations: University of Nebraska–Lincoln, Lincoln, NE, USA

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 & tables

Fig. 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.

Profile	$\lambda_{1}$	$\lambda_{2}$	$\lambda_{3}$	$\lambda_{4}$
1	0.9999	0.0000	0.0000	0.0000
2	0.9999	0.0001	0.0000	0.0000
3	0.7151	0.2783	0.0062	0.0003
4	0.9999	0.0001	0.0000	0.0000

TABLE I : Leading eigenvalues of learned behavioral profiles (

K{=}4

Fig. 2 : Context activation coefficients ( $\beta$ ) across identified behavioral profiles.

Fig. 3 : Marginal activation of dominant eigenmodes across behavioral variables. Rows denote profiles and columns denote $\Delta v$ , $a$ , and $h$ .

Fig. 4 : Multimodal activation heatmaps for Profile 3. Shaded contours represent the localized activation of each mode, illustrating the structural diversity within the profile geometry.

Fig. 5 : Pairwise Frobenius distances between identified behavioral profiles. Numerical values represent the magnitude of divergence in profile geometry.

State Representation Learning

State representation learning develops compact, task-relevant descriptions of observations and histories for prediction, control, and decision-making.

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Aug 26, 2026J/K move · Enter open · S save

Quantum-Inspired Modeling of Driving Behavior

Mohammad Elayan, Omid Armantalab, Wissam Kontar

Civil & Environmental Engineering, University of Nebraska–Lincoln, Lincoln, NE, USA

Traffic Flow Theory Intelligent Transportation Systems Quantum-Inspired ML

Open paper AskPDF arXiv

Driver behavior is heterogeneous, context-dependent, and changes over time, and these properties shape the traffic phenomena we observe. Most models, however, fix in advance which behavioral variables interact and how. Behavior outside that form is absorbed as noise, while models flexible enough to capture it tend to lose interpretability. We introduce a quantum-inspired representation of driver behavior that combines properties usually treated separately or in part: it is continuous, probabilistic, context-dependent, history-dependent, and represents interactions among behavioral variables as learned from data. Each driver is encoded as an evolving density matrix, providing a unified representation of behavioral uncertainty, temporal evolution, and context-dependent behavioral variation. Trained without supervision on the I-24 MOTION dataset, the framework recovers three interpretable driving profiles representing three regimes: free flow, transition, and congestion. The profiles capture the behavioral range of the data and the smooth transitions drivers make between regimes as conditions change. The same representation also reproduces known macroscopic phenomena, aligning with the fundamental diagram and reproducing hysteresis loops. We also show how the representation supports practical use: it supplies context-dependent parameters to classical car-following models, and gives an autonomous vehicle a live behavioral read of the surrounding drivers with a short-horizon forecast of their motion. The framework points toward models of traffic that are interpretable and trustworthy by construction. We release an open-source toolkit on GitHub (https://github.com/mselayan/quantum-driver-representation) spanning data processing, training, inference, and analysis.

Abstract

State Representation Learning

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