Gravity Prior and Temporal Horizon Shape Interceptive Behavior under Active Inference

Accurate interception of moving objects, such as catching a ball, requires the nervous system to overcome sensory delays, noise, and environmental dynamics. One key challenge is predicting future object motion in the presence of sensory uncertainty and inherent neural processing latencies. Theoretical frameworks such as internal models and optimal control have emphasized the role of predictive mechanisms in motor behavior. Active Inference extends these ideas by positing that perception and action arise from minimizing variational free energy under a generative model of the world. In this study, we investigate how different predictive strategies and the inclusion of environmental dynamics, specifically an internal model of gravity, influence interceptive control within an Active Inference agent. We simulate a simplified ball-catching task in which the agent moves a cursor horizontally to intercept a parabolically falling object. Four strategies are compared: short temporal horizon prediction of the next position or long horizon estimation of the interception point, each with or without a gravity prior. Performance is evaluated across diverse initial conditions using spatial and temporal error, action magnitude, and movement corrections. All strategies produce successful interception behavior, but those that incorporate gravity and longer temporal horizons outperform others. Including a gravity prior significantly improves spatial and temporal accuracy. Predicting the future interception point yields lower action values and smoother trajectories compared to short-horizon prediction. These findings suggest that internal models of physical dynamics and extended predictive horizons can enhance interceptive control, providing a unified computational account of how the brain may integrate sensory uncertainty, physical expectations, and motor planning.

💡 Research Summary

The paper investigates how internal models of gravity and the temporal horizon of prediction shape interceptive behavior within an Active Inference framework. Using a simplified two‑dimensional ball‑catching task, an agent controls a horizontal cursor to intercept a ball that follows a parabolic trajectory under gravity. Four control strategies are compared, defined by two binary factors: (1) prediction horizon – a short‑term “Next Location” strategy that predicts the ball’s position 100 ms ahead, versus a long‑term “Interceptive Location” strategy that computes the future point where the ball will cross the interception line; (2) inclusion of a gravity prior – “With Gravity” incorporates the known acceleration g = 9.81 m/s² into the generative model, while “No Gravity” assumes constant velocity.

The generative process describes the true dynamics of the ball and cursor using linear state‑space equations, with the cursor modeled as a critically damped mass‑spring‑damper system. Sensory input consists solely of noisy visual measurements of position and velocity; proprioceptive feedback is omitted to focus on visual prediction. The agent’s internal generative model mirrors the process but can optionally omit the gravity term.

Active Inference is implemented by minimizing variational free energy (VFE) at each time step. The VFE consists of a sensory prediction error term and a state prediction error term, both weighted by precision parameters. Action updates follow a gradient descent rule Δu = ‑α∂F/∂u ‑ βu, where α (learning rate) and β (damping) are tuned for each strategy using constrained optimization (fmincon with SQP). The cursor’s attractor point a(t) is recomputed every step according to the chosen strategy’s equations, effectively turning the problem into a continuous optimal control task driven by VFE minimization.

To evaluate performance, the authors sweep initial agent positions (x₀) and initial ball horizontal velocities (v₀) across wide ranges, generating 10,000 distinct trial conditions. Four metrics are recorded: (i) spatial error (absolute distance between ball and cursor at interception), (ii) temporal error (difference between ball arrival time and the time the cursor reaches minimal distance), (iii) action magnitude (peak force applied at the moment the ball first reaches the interception line), and (iv) movement corrections (number of velocity sign reversals, i.e., trajectory adjustments). Additionally, 3‑D error manifolds are visualized by varying x₀ and v₀ jointly.

Key findings:

1. Strategies that include a gravity prior consistently outperform those without it, reducing both spatial and temporal errors by roughly 15‑25 % across the parameter space. The gravity prior enables accurate extrapolation of the ball’s parabolic path, compensating for the 100 ms sensory‑motor delay.
2. The long‑horizon “Interceptive Location” strategy yields smoother trajectories and lower action magnitudes (≈30 % reduction) compared with the short‑horizon “Next Location” strategy. By targeting the eventual interception point, the agent avoids continuous fine‑grained corrections.
3. Adding gravity to the short‑horizon strategy improves temporal precision relative to the no‑gravity version, but action costs remain higher than the long‑horizon counterpart.
4. Robustness analyses show that moderate increases in sensory noise (standard deviation up to 0.05 m) have minimal impact on the gravity‑augmented, long‑horizon strategy, indicating that the combined prior and extended prediction horizon confer resilience to noisy observations.

The authors interpret these results as computational support for the hypothesis that the brain maintains an internal model of invariant physical dynamics (gravity) and flexibly adjusts its predictive horizon to achieve efficient interception. Within the Active Inference paradigm, perception and action emerge from a single free‑energy minimization process, unifying state estimation and motor control. The study demonstrates that this unified approach can match or exceed traditional Bayesian filtering plus optimal control pipelines, especially when physical priors and longer predictive windows are incorporated. The paper concludes by suggesting that future work should test these predictions in neurophysiological experiments and extend the framework to robotic platforms requiring real‑time interception under uncertainty.