A Spiking Sequence Generator for Polar Trajectories on Neuromorphic Hardware

Technical Summary: A Spiking Sequence Generator for Polar Trajectories on Neuromorphic Hardware

Problem Statement
Neuromorphic controllers for size, weight, and power (SWaP) constrained robotic systems require neural architectures that balance energy efficiency with interpretability at the level of system dynamics. Current approaches typically fall into two extremes: end-to-end trained spiking neural networks (SNNs), which often lack interpretability and safety guarantees, or converted classical controllers, which fail to fully exploit neuromorphic dynamics and offer minimal advantage over modern low-power processors. Furthermore, while neural manifolds (low-dimensional dynamical systems observed in neuroscience) offer a promising framework for generating behaviors like locomotion and orientation, implementing them on neuromorphic hardware is challenging. Randomly connected recurrent networks (e.g., reservoir computing) often require prohibitively large reservoirs to be space-efficient, and existing attractor network implementations (e.g., ring attractors) often prioritize continuous representation over hardware efficiency and explicit controllability.

Methodology
The authors propose a spiking neural network (SNN) architecture designed to generate controllable polar trajectories using a Winner-Take-All (WTA) framework. The system is implemented on the SpiNNaker2 neuromorphic processor. The architecture consists of three primary components:

1. Core WTA Dynamics: A recurrent population of Leaky-Integrate-and-Fire (LIF) neurons with self-excitation and global inhibition. This ensures that only one neuron is active at any given time, creating a stable, discrete state representation. The authors derive tuning rules for self-excitation weights and synaptic decay factors to maintain a constant inter-spike interval (ISI) once a neuron is stimulated.
2. Controlled Rotation (Speed and Direction): To induce rotation within the WTA population, the authors introduce two accessory populations (ascending and descending) that provide controlled perturbations. These populations utilize multiplicative exponential synapses (shunting inhibition) to modulate the effective gain of the rotation neurons. By adjusting the inter-spike interval of external modulatory inputs to these accessory populations, the system can independently control the speed of rotation and the direction (clockwise or counter-clockwise) without altering the underlying connectivity matrix.
3. Trajectory Radius Control: A readout population decouples the trajectory's amplitude (radius) from its phase (direction). Each readout neuron receives excitatory input from a specific WTA neuron and modulatory input from external signals. By varying the modulation rate, the firing rate of the readout neurons—and thus the radius of the polar trajectory—can be controlled independently for each angle, allowing for arbitrary polar shapes.

The network was first developed and tuned in a PyTorch simulation environment to ensure zero discrepancy between software and hardware behavior before deployment. The authors also describe a brute-force optimization method using the simulation model to determine the specific stimulation ISIs required to generate user-defined polar curves (e.g., rose curves) in a single-shot manner.

Key Results
The system was deployed on a single-chip SpiNNaker2 development board. The authors conducted benchmarking experiments comparing the neuromorphic implementation against a consumer-grade CPU (Intel Core i5) and GPU (NVIDIA RTX 4070).

• Performance: The SpiNNaker2 system demonstrated a two to three orders of magnitude reduction in wall-clock step time compared to the CPU and GPU. Simulation steps on SpiNNaker2 ranged from 5 to 12 microseconds, whereas the GPU required approximately 2.4 milliseconds per step.
• Energy Efficiency: The neuromorphic system consumed three to four orders of magnitude less energy (0.3 to 0.8 millijoules) for the simulation phase compared to the GPU (15–18 joules) and CPU (2.1–2.6 joules).
• Scalability: The maximum network size is currently limited by the memory required to store precomputed input spike trains. For short simulations (150 steps), the system could support up to 524 WTA nodes, decreasing to 35 nodes for longer simulations (5000 steps).
• Functionality: The network successfully generated complex, user-defined polar trajectories (including harmonic modulations and rose curves) by optimizing the external stimulation parameters.

Significance and Claims
The paper claims to provide a concrete methodology for implementing controllable, low-dimensional dynamical systems on neuromorphic hardware that preserves interpretability and explicit control. Unlike end-to-end trained networks, this approach allows for the independent manipulation of trajectory parameters (speed, direction, radius) through human-interpretable mechanisms.

The authors emphasize that while the WTA approach introduces discretized angular resolution (a trade-off compared to continuous ring attractors), it offers superior hardware efficiency and minimal coupling between control inputs. The work demonstrates that neuromorphic hardware can significantly outperform conventional computing platforms in both latency and energy consumption for this specific class of dynamical systems, provided the initialization overhead is amortized over sustained operation. The authors position this architecture as a foundational design pattern for rhythmic controllers in embedded robotics, such as those required for locomotion, scanning behaviors, and sensorimotor coordination.

Limitations and Future Work
The authors acknowledge that the current implementation is constrained by memory limits related to storing precomputed spike trains and the lack of iterative, closed-loop evaluation support for exponential synapses in the current SpiNNaker2 API. They note that the initialization overhead (loading data and interfacing) currently dominates energy consumption for short simulations, though this is expected to diminish in sustained, embedded deployments. Future work includes exploring toroidal architectures for spherical coordinates, mapping the dynamics to Stable Heteroclinic Channels (SHCs) for more complex control algorithms, and applying the system to robotic sensory integration and locomotion tasks.