Breaking the Memory Horizon of Spiking Neural Networks via Autonomous Phase-Space Distillation and Hierarchical Sleep

Spiking Neural Networks (SNNs) offer order-of-magnitude energy efficiency improvements over dense Transformers through event-driven, sparse computation. However, recurrent SNNs suffer from a fundamental physical limitation: the fading memory horizon. Due to passive membrane dissipation (beta < 1.0) and non-linear reset dynamics, temporal trajectories exponentially decay, rendering vanilla SNNs incapable of long-horizon sequential reasoning. In this work, we propose Spiking DreamCoder, a neurosymbolic framework that eliminates the memory horizon ceiling without quadratic attention. Our architecture integrates an unsupervised Minimum Description Length (MDL) miner that monitors token sequences and triggers an offline Sleep Phase. During sleep, multi-step dynamical trajectories in a frozen resonator are distilled into rank-4 low-rank synaptic adaptations (LoRA), modulated by time-local presynaptic eligibility traces. On an 8x8 GridWorld path-integration benchmark (T=360 simulation ticks), standard recurrent SNNs fail catastrophically, stagnating at 6.00% accuracy. In contrast, Spiking DreamCoder autonomously compresses temporal sequences by 4x, achieving 94.62% accuracy with provable zero catastrophic forgetting.