# Parallelized Hierarchical Connectome: A Spatiotemporal Recurrent Framework for Spiking State-Space Models

arXiv: https://arxiv.org/abs/2604.01295 · HTML: https://mlsanity.com/paper/2604.01295/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Apr 2026.

## Built on by (most cited first, 2 of 2)

- [VGPT-RSI for RH-Adjacent Formal Progress: Boundary Certificates, Verified Finite Lagarias Inequalities, and Explicit Failure Localization](https://mlsanity.com/paper/2606.15096/) (2026)
- [URCHIN: A Horizontal Spiking Language Model for Data-Constrained Pretraining](https://mlsanity.com/paper/2609.13899/) (2026)

## Abstract (arXiv)

This work presents the Parallelized Hierarchical Connectome (PHC), a general architectural framework that upgrades temporal-only State-Space Models (SSMs) into spatiotemporal recurrent networks. Conventional SSMs achieve parallel-scan training but are limited to temporal recurrence, lacking lateral or feedback interactions within a single timestep. PHC maps the diagonal SSM core to a shared Neuron Layer and inter-neuronal communication to a shared Synapse Layer of hierarchical regions, reconnected by a Multi-Transmission Loop iterating spatial recurrence within each temporal window, at parameter complexity Theta(D^2) versus Theta(D^2 L) of stacked SSMs. This spatiotemporal framework enables the seamless integration of neuro-physical priors typically intractable for standard SSMs, including adaptive LIF, synaptic delay, STP, Dale's Law with E/I-asymmetric topology, and STDP. The framework is instantiated as PHCSSM, the first spiking SSM that integrates all five biological priors and is evaluated on long-sequence data, achieving test accuracy competitive with state-of-the-art SSM baselines at 1,312 to 4,891 trainable parameters (1 to 4 orders of magnitude smaller than every baseline). PHCSSM further admits a sequential recurrent spiking neural network (RSNN) deployment mode that converges asymptotically to the parallel-scan training mode without artificial-neural-network-to-spiking-neural-network (ANN-to-SNN) conversion, with cross-backend reproducibility verified across four hardware backends (x86 CPU, H100 GPU, Cortex-A76, Cortex-M4F) including end-to-end deployment on the Cortex-M4F microcontroller (40 KB SRAM, 128 KB Flash). PHCSSM thereby bridges parallel-scan SSM and biologically grounded RSNN, two paradigms with previously incompatible training regimes, into a single architecture and trained weights.