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Emergence of Physical Intelligence via Controllable Information Production

NeurIPS 2026 · Multi-agent systems and games › Human-AI and goal-conditioned · approach: Intrinsically motivated exploration · 0 citations (OpenAlex)

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Proposes Controllable Information Production (CIP), an intrinsic motivation objective defined as the open-loop Kolmogorov-Sinai entropy rate derived from the Hessian of the optimal value function, and optimizes it with MPC (iCEM) on MuJoCo-MJX pendulum and humanoid-like gibbon tasks.

Problem

Existing intrinsic motivation methods rely on mutual-information objectives with designer-chosen random variables, which are biased and lack a principled link to dynamics and optimal control; the paper seeks a dynamics-grounded IM signal that drives useful physical behavior such as self-righting.

Approach

Defines CIP as the open-loop Kolmogorov-Sinai entropy of the linearized dynamics, shown to equal the log-determinant growth rate of the optimal value Hessian (via a Riccati decomposition), and estimates it with a stable log-domain recursion that avoids QR decomposition.

Key results

• CIP achieves normalized final height of 0.9996 on Cart Pole, 0.9913 on Double Pendulum, 0.9931 on Triple Pendulum, and 0.9319 on Gibbon, outperforming empowerment, DIAYN, DADS, SMM, and ICM on all four systems.
• Only CIP and (partially) empowerment reach upright positions; the gibbon humanoid self-righting is reported as not previously demonstrated with IM alone.
• The log-domain estimator converges to known KSE values faster than the QR-based Lyapunov baseline on two chaotic parameter regimes.

Surprising findings

• Empowerment achieves the same top score as CIP on Cart Pole (0.9996), so the advantage is not uniform across systems.

Limitations

• Requires efficient access to dynamics Jacobians, restricting applicability to differentiable simulators.
• Random-shooting MPC controller is simple, limits scalability and is myopic, can get stuck in local optima.
• Experiments are limited to simulated MuJoCo-MJX systems with a theoretically-motivated but linearized derivation.

Experimental setup

Benchmarks: URLB Cart Pole Double Pendulum Triple Pendulum Gibbon

Metrics: normalized mean extremity height over final 10% of episode estimated CIP (nats/s) over time convergence of KSE estimator

Baselines: Empowerment DIAYN DADS SMM ICM

Builds on: URLB iCEM Pesin's theorem DIAYN DADS

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