Fly-CfC: Connectome-Constrained Closed-Form Continuous-Time Neural Networks for Sub-Millisecond Autonomous Flight

Continuous-time recurrent neural networks, particularly Liquid Time-Constant (LTC) and Closed-Form Continuous-Time (CfC) models, provide expressive temporal dynamics and adaptive time-scale modeling. However, their bio-constrained manifestations (e.g., Neural Circuit Policies) have predominantly remained confined to the 19–28 neuron circuits of Caenorhabditis elegans, while whole-brain connectome models suffer from prohibitive computational overheads that preclude real-time closed-loop robotic control. Here, we present Fly-CfC, the first functional, connectome-constrained continuous-time neural network directly derived from the whole-brain connectome of Drosophila melanogaster (male-cns v1.0). By isolating the sensorimotor visual-to-motor pathway, we extracted an ultra-sparse subcircuit comprising 1,683 Visual Projection Neurons (VPNs), 1,961 Recurrent Units, and 1,300 Descending Neurons (DNs). The architecture enforces an extreme biological sparsity of 99.5119% (34,882 active biological synapses out of 7.15 million potential pairs) embedded within an analytical continuous-time ODE formulation. We mathematically establish and empirically verify a strict Zero Gradient Leakage Theorem (∂L/∂W_masked ≡ 0.0000000), ensuring absolute preservation of synaptic topologies during gradient updates. Across high-fidelity simulations, Fly-CfC achieves a sub-millisecond inference latency of 0.45 ms/step (>1,900 FPS) on consumer-grade hardware—2.6× faster than dense CfC baselines. In dynamic 2D environments and 6-DOF closed-loop 3D PyBullet quadcopter slalom regimes, Fly-CfC demonstrated a 100% survival rate (zero collisions) across all evaluation episodes with omnidirectional looming detection. Our results bridge the decades-long divide between large-scale biological connectomics and ultra-low-power, agile robotic navigation.