Tiny Recursive Control: Iterative Reasoning for Efficient Optimal Control

TL;DR

This work proposes Tiny Recursive Control (TRC), a compact neural architecture that achieves high-quality optimal control by iteratively refining a control sequence using a shared refinement operator. A two-level latent structure processes each refinement step, enabling capacity to emerge from computation depth rather than parameter count. TRC demonstrates near-optimal performance on nonlinear problems (Van der Pol oscillator and powered descent) with millisecond-scale inference and under 10 MB of weights, highlighting the practicality of recursive reasoning for continuous control in aerospace. While offering interpretability through intermediate control solutions, the approach currently lacks formal stability guarantees and depends on demonstrations for training, pointing to fertile directions for future work.

Abstract

Neural network controllers increasingly demand millions of parameters, and language model approaches push into the billions. For embedded aerospace systems with strict power and latency constraints, this scaling is prohibitive. We present Tiny Recursive Control (TRC), a neural architecture based on a counterintuitive principle: capacity can emerge from iteration depth rather than parameter count. TRC applies compact networks (approximately 1.5M parameters) repeatedly through a two-level hierarchical latent structure, refining control sequences by simulating trajectories and correcting based on tracking error. Because the same weights process every refinement step, adding iterations increases computation without increasing memory. We evaluate TRC on nonlinear control problems including oscillator stabilization and powered descent with fuel constraints. Across these domains, TRC achieves near-optimal control costs while requiring only millisecond-scale inference on GPU and under 10~MB memory, two orders of magnitude smaller than language model baselines. These results demonstrate that recursive reasoning, previously confined to discrete tasks, transfers effectively to continuous control synthesis.

Figures (11)

• Figure 1: TRC architecture. Left: initial control generation from encoded state. Right: one refinement iteration showing trajectory simulation, error computation, and the two-level latent structure. The high-level latent $\mathbf{z}_H$ maintains strategic context and guides the low-level latent $\mathbf{z}_L$, which handles tactical adjustments through $n$ cycles before feeding back to update $\mathbf{z}_H$. Both levels share the same reasoning module $\mathcal{L}_\theta$. The iteration repeats $K$ times with $\mathbf{z}_0$ conditioning each step.
• Figure 2: Van der Pol oscillator training convergence: control loss (blue) and improvement metric (green) over 50 epochs.
• Figure 3: Van der Pol oscillator trajectory results. All trajectories converge to the origin (target state), with the phase portrait showing successful stabilization from diverse initial conditions in the nonlinear regime.
• Figure 4: Iterative refinement for Van der Pol oscillator. (a) Control evolution showing dramatically reduced variance across iterations. Initial predictions (purple) have high uncertainty; final iteration (yellow) converges to consistent damping strategy. (b) Cost reduction of approximately 90% from iteration 0 to 3.
• Figure 5: Latent space evolution for Van der Pol oscillator. (Left) All samples converge from scattered initial states to a single attractor point, indicating the model discovers a universal control strategy. (Right) Refinement paths show consistent flow toward low-cost solutions regardless of initial condition.