dynamic-neural-manifolds-snn-control

name	dynamic-neural-manifolds-snn-control
description	Dynamic neural manifolds methodology for flexible closed-loop control on neuromorphic hardware. Spiking ring networks with control knobs (gain, inhibition, transient currents) that steer low-dimensional manifold geometry for explainable autonomous behavior. Implemented on SpiNNaker 2 chip. Activation: neural manifolds, neuromorphic control, SpiNNaker, ring network, subspace rotation, explainable SNN, closed-loop control, dynamic manifolds.
tags	["neuroscience","neuromorphic","SNN","control","manifolds","SpiNNaker","explainable-AI"]
version	1.0.0
author	agent
date	2026-07-12T00:00:00.000Z

Dynamic Neural Manifolds for Flexible Closed-Loop Control on Neuromorphic Hardware

arXiv: 2607.07373 | cs.NE | von Seeler, Tetzlaff, Lehr (Göttingen)

Overview

Biological circuits evolve sequential neural activity along dynamic, low-dimensional manifolds to enable flexible behavior. This paper presents a framework for implementing dynamic neural manifolds on the SpiNNaker 2 neuromorphic chip for real-time, closed-loop control, establishing an explainable approach to neuromorphic engineering.

Core Methodology

Ring Network Architecture

• Canonical oscillatory sequences modeled as a bump of activity moving along a ring of neurons
• Asymmetric recurrent connectivity leads to stable bump progression → oscillatory sequences
• Circulant weight matrix with configurable sparsity (e.g., 50%) for efficiency
• Maps to observed oscillatory sequences across brain regions (spinal cord, MEC, motor cortex)

Three Control Knobs

1. Trajectory Shape (Additive current I): Controls bump size → trajectory radius in state space

   • Excitatory current (I>0) increases bump size and radius
   • Maps to spatial extent of neural representation

2. Trajectory Speed (Multiplicative gain S): Controls how fast bump travels around ring

   • Gain amplifies inputs → faster sequence progression
   • Maps to velocity/timing of neural trajectories

3. Subspace Rotation (Heterogeneous inhibition p_inh): Selective silencing of neuron subsets

   • Inhibitory ensembles silence random subsets of neurons
   • Switching ensembles rotates neural subspace → enables behavior switching
   • Angle between orientations: arccos(1 - p_inh)
   • Each subspace encodes a different behavior/motor output

SpiNNaker 2 Implementation

• Spike-based communication: Rates → probabilistic spikes for neuron-to-neuron communication
• Sparse connectivity: Reduces computation (e.g., 20-50% sparsity with weight scaling 1/p)
• Circulant structure: Store single row + bitmask → saves memory
• Streaming control: Control parameters streamed in during runtime (no pre-specified sequences)
• Closed-loop latency: As low as 3 time steps (~3ms) from spike to control update

Key Equations

x_i(t+1) = Σ_j W_ji * r_j(t) + I(t)
r_i(t+1) = F(r_i(t) + 1/τ * (-r_i(t) + p_i(t) * S(t) * x_i(t+1)))

where W is circulant, p_i indicates active (non-inhibited) neurons, S is speed control, I is shape control.

Motor Readout

• Linear readout weights learned from ring network spike activity
• Spike smoothing via exponential moving average: s̄_i(t) = (1-α)s_i(t) + α·s̄_i(t-1)
• Motor speeds and actions decoded as: y_x = (s̄_1, ..., s̄_n, 1) · w_x

Applications

Robotic Navigation

• 2-wheeled robot navigating maze with sensory feedback
• Three subspaces: move forward, turn in place, jump
• Sensory inputs modulate control parameters → dynamic manifold reconfiguration
• High-level plan + local adaptation → integrated manifold representation

Biological Research

• Computational testbed for investigating biological neural dynamics
• Validates theoretical predictions from Lehr et al. (2024, 2025) on subspace rotations
• Bridge between circuit mechanisms and geometric manifold properties

Key Findings

1. Dynamic manifold control works robustly on neuromorphic hardware
2. Runtime scales linearly with spike count → efficient for sparse activity
3. All three control mechanisms (shape, speed, rotation) reproduce theoretical predictions
4. Subspace rotations enable behavioral switching with predictable geometry
5. Framework provides mathematically interpretable internal states → explainable AI

Pitfalls

• SRAM memory constraint: Recording rates fills 128KB SRAM quickly; use streaming instead
• Memory limits simulation time: Streaming control parameters avoids pre-specified sequences
• Weight precision: 8-bit integers with shared exponent; precision loss for large networks
• Latency budget: Must complete all updates within 1ms time step on each PE

Related Skills

• snn-learning-survey - SNN learning rules
• spiking-neural-network-analysis - SNN paper analysis
• spiking-oscillation-mapping - Oscillatory states in balanced SNNs