A preprint describes a quantum-inspired model that treats freeway driving as a changing mix of possible behaviors, rather than assigning every vehicle a fixed type. It learns how much a trajectory resembles different profiles and lets those weights shift with traffic context and recent history. In an example trajectory, the mix moved smoothly from free flow to transition and then congestion as conditions changed. The design is aimed at connecting individual vehicle states with larger traffic patterns.
A model built from vehicle trajectories
The analysis used I-24 MOTION data from a 4.33-mile stretch of Interstate 24 near Nashville, Tennessee. A network of 294 cameras recorded traffic at 25 frames per second. The release contained 771,946 trajectories, including 519,665 westbound trajectories, or 67.3 percent, across 239.8 minutes of morning traffic.
For the modeled population, the researchers kept passenger vehicles in four classes and required each trajectory to last at least 10 seconds. The resulting analytic set contained 253,442 trajectories: 35.3 percent sedans, 34.9 percent midsize vehicles, 2.9 percent vans and 16.1 percent pickups. Semis and trucks, which made up 9.6 percent and 1.2 percent of the release respectively, were excluded. The analytic unit was an eligible vehicle trajectory, not an explicitly reported count of unique drivers.
The model used speed, spacing and jerk as behavioral variables. Jerk is the rate at which acceleration changes. It also used local traffic density, speed entropy and acceleration entropy as contextual variables. At its core, the system represents behavior with an evolving density matrix, a mathematical object that can hold a probability mixture of states. The unsupervised model learns interactions among the variables from data instead of fixing their form in advance.
Three regimes, with room inside one of them
The fit was assessed with penalized negative log-likelihood, or NLL, a score that falls when a model assigns greater likelihood to observed behavior. The uninformative reference state had an NLL of 4.605, a single static density matrix scored 2.230, and the full evolving, context-conditioned framework scored 0.880. The paper reports that the full framework assigned roughly 3.9 times the average likelihood of the static matrix.
The learned profiles were interpreted as three traffic regimes: free flow, congested stop-and-go driving and transitional following. Profile 1 was the fastest and had the largest average spacing, at 62.2 feet per second and 193.7 feet. Profile 2 was the slowest and most tightly spaced, at 27.4 feet per second and 117.6 feet. Profile 3 sat between them, at 53.5 feet per second and 154.5 feet.
The profiles also differed in their internal structure. A purity score was 0.999 for Profile 1 and 0.997 for Profile 3, indicating that both were effectively single-mode states. Profile 2 had a lower purity of 0.734 and retained several modes. The model also learned different relationships among the variables: Profile 1's strongest pair was spacing and jerk, with mutual information of 0.228 nats, while Profile 3's strongest pair was speed and jerk at 0.133 nats. Profile 2 showed weak coupling across all pairs.
The balance among profiles changed with the surrounding traffic. The model gave Profile 2 a greater contribution as density rose, while Profile 3's contribution fell with density but increased with acceleration entropy. Profile 1 was most active when acceleration entropy was low. These are learned associations within the model, not evidence that density or traffic variability directly causes a particular driving response.
Inside the congested profile, the largest mode represented steady following, accounting for 85.2 percent of the profile's mass and 93 percent of active frames. Other modes represented acceleration and braking events. The reported mean jerk was +1.85 feet per second cubed, with a spread of 1.71, during acceleration events, and -3.10 feet per second cubed, with a spread of 2.95, during braking events. That decomposition lets the model distinguish routine congested following from sharper changes in motion.
From a vehicle state to traffic patterns
The authors also report agreement between the learned representation and the fundamental diagram, the traffic relationship linking flow, density and speed. They report that the model reproduced hysteresis loops, in which traffic can trace different paths as conditions change.
In an illustrative integration with an IDM car-following model, a state-supported follower slowed and recovered with the vehicle ahead, tracked its leader and adopted different desired speeds and spacings as the profile composition moved from Profile 1 through Profile 3 to Profile 2.
The trained representation was also used to forecast each vehicle's speed three seconds ahead on lane 1. Reported mean absolute errors were 3.77 mph in calm conditions, 4.51 mph in busy conditions and 4.98 mph between traffic waves. The paper presents this as a short-horizon model application across three tested traffic conditions.
A narrow test with clear limits
The evidence has a narrow base. The evaluation used one freeway corridor and passenger-vehicle trajectories, while the behavioral vector was longitudinal and did not directly represent lane-changing. Behavior and context were modeled at the same time step despite driver response delays. Several settings were selected empirically for I-24 MOTION rather than learned or guaranteed to transfer, leaving the model's portability to other settings unresolved.
The manuscript identifies itself as arXiv:2608.25907v1, dated 26 August 2026. The authors report a public open-source toolkit covering data processing, model training, inference and post-analysis.
Paper data and sources
Original title: Quantum-Inspired Modeling of Driving Behavior
Authors: Mohammad Elayan, Omid Armantalab, Wissam Kontar
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
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