spiking-dynamic-neural-manifolds-implementation

name	spiking-dynamic-neural-manifolds-implementation
description	Concrete implementation recipe for dynamic neural manifold control on neuromorphic hardware (SpiNNaker 2), derived from arXiv 2607.07373. Covers rate→spike conversion, sparse circulant weight memory, three control knobs (gain/speed, additive current/shape, subspace inhibition/selection), PCA-based manifold validation, and closed-loop maze navigation with linear readout training. Use when porting ring-attractor sequential SNNs to spike-based neuromorphic chips or building explainable low-dimensional control substrates.
version	1.0.0
date	2026-07-14T00:00:00.000Z
arxiv_id	2607.07373
source_skill	dynamic-neural-manifolds-neuromorphic-control
tags	["spiking neural network","ring attractor","neural manifold","subspace rotation","SpiNNaker 2","closed-loop control","low-dimensional dynamics","explainable neuromorphic","PCA validation"]
activation_keywords	["dynamic neural manifold implementation","ring attractor spiking","rate to spike conversion","sparse circulant weights","subspace inhibition","SpiNNaker 2 ring network","closed-loop SNN control","neural trajectory PCA","manifold control knobs"]

Spiking Dynamic Neural Manifolds — Implementation Recipe (arXiv 2607.07373)

Companion to dynamic-neural-manifolds-neuromorphic-control. This skill is the how-to: the exact transformations and validation steps to deploy a rate-based ring-attractor manifold model on a spike-based neuromorphic chip. The conceptual overview lives in the sibling skill; here we give the engineering primitives.

When to use this skill

• Porting a rate-based sequential neural model to SpiNNaker 2 / Loihi / BrainScaleS (spike-based hardware).
• Building an explainable low-dimensional control substrate where geometry = behavior.
• Validating that a sparse/spiking implementation matches the rate-based baseline.

Architecture (always start here)

1. Ring network of N neurons (paper uses N=500) with asymmetric recurrent weights → stable bump of activity travels around the ring → oscillatory sequence.
2. Connectivity: circulant weight matrix, 20–50% sparsity (paper uses 50% in core figures, 20% in comparison sweeps). Scale kept weights by ×2 to compensate for lost synapses.
3. Three control inputs (the "control knobs"):
   • S multiplicative gain → trajectory SPEED (rotations/sec around ring).
   • I(t) additive (Gaussian) current → trajectory SHAPE / bump RADIUS (number of co-active neurons).
   • p_inh ∈ [0,1] subspace inhibition fraction → subspace SELECTION / ROTATION (switch behavioral state).
4. Readout: linear decoder trained from ring spikes → motor/control outputs.

Step 1 — Rate → Spike conversion (critical for performance)

The original model (Lehr et al. 2024,2025) is rate-based. SpiNNaker 2 is spike-optimized, so:

• Add a probabilistic rate→spike layer: treat each neuron's rate r_i as the probability of spiking in the current timestep. spike_i ~ Bernoulli(r_i).
• This drastically cuts inter-neuron communication (spikes only when active) vs. broadcasting continuous rates.
• Timestep: dt = 1 ms (real-time threshold on SpiNNaker 2).

Step 2 — Sparse circulant weight memory trick

On-chip SRAM is tiny (128 KB/core). Recording 32 neurons' rates fills 128 KB in ~1000 steps (1 s). Mitigations: