Unsupervised Particle Tracking with Neuromorphic Computing

TL;DR

The paper investigates unsupervised identification of charged-particle trajectories in CMS Phase-2-like geometry using a two-layer spiking neural network with synaptic-delays learned via a modified Spike-Timing-Dependent Plasticity rule. Hits are time-encoded in a neuromorphic framework, enabling real-time, low-power pattern recognition amidst heavy detector noise. A multi-objective genetic algorithm optimizes hyperparameters to achieve high acceptance, strong selectivity, and low fake rates, demonstrating near-perfect performance for single tracks under high background and revealing challenges for multi-track separation due to refractory/inhibition effects. The work argues for the potential of neuromorphic-triggering concepts in future high-energy physics experiments and outlines a concrete pathway toward hardware implementations, including 3D extensions and enhanced encoding schemes for improved track discrimination.

Abstract

We study the application of a neural network architecture for identifying charged particle trajectories via unsupervised learning of delays and synaptic weights using a spike-time-dependent plasticity rule. In the considered model, the neurons receive time-encoded information on the position of particle hits in a tracking detector for a particle collider, modeled according to the geometry of the Compact Muon Solenoid Phase II detector. We show how a spiking neural network is capable of successfully identifying in a completely unsupervised way the signal left by charged particles in the presence of conspicuous noise from accidental or combinatorial hits. These results open the way to applications of neuromorphic computing to particle tracking, motivating further studies into its potential for real-time, low-power particle tracking in future high-energy physics experiments.

Figures (21)

• Figure 1: Spike-based encoding (a) and processing of information using a spiking neuron unit (b). Spikes are asynchronous binary events used to represent detector hits and neuron activations. By encoding information in a succession of spikes, such as their order or temporal distance, non-binary modes of information coding can be used. By leveraging physical phenomena for integration (in synapses) and processing (in dendrites and the soma of the neuron) of spike codes the energy efficiency and latency can be improved versus ordinary logic information processing mehonic2024review, in particular when the output precision is limited by noise verhelst2015analogdigital.
• Figure 2: Layout of the silicon sensors in one sector of the Phase-2 CMS tracker cms_tracker_layout.
• Figure 3: Sketch of the Network Architecture. In the final network presented in Sec. \ref{['sec:final_results']} there are 10 afferents, $N_{L_0}=6$ neurons in layer $L_0$ and $N_{L_1}=6$ neurons in layer $L_1$.
• Figure 4: Comparison of membrane potential evolution in firing and non-firing events. In the top plot, neuron 10 surpasses the firing threshold at $t \approx 143.7 \, \text{ns}$, experiencing a sharp increase in potential followed by a reset governed by the reset potential $\eta(t - t_i)$. An entire event is $25 \, \text{ns}$. The firing neuron also induces an IPSP $\mu(t - t_k)$ in the other neurons, suppressing their activation and reinforcing the competition mechanism. In the bottom plot, neurons exhibit sub-threshold oscillations but do not fire, indicating that the input signals were insufficient to reach the activation threshold.
• Figure 5: Model of spike-time-dependent plasticity of connection delays implementing a modified Hebbian learning concept. The x-axis denotes the time difference, $\Delta t =t_j - t_i+t_{\text{max}}$, and the y-axis, $\Delta d$, is the corresponding update of the delay. The parameters defining this unsupervised learning rule were found by the genetic algorithm.

Theorems & Definitions (11)

• definition thmcounterdefinition: Hebbian STDP rule for Synaptic Weights
• definition thmcounterdefinition: STDP rule for synaptic delays
• definition thmcounterdefinition: Neuron Activation Indicator Function
• definition thmcounterdefinition: Network Activation Indicator Function
• definition thmcounterdefinition: Acceptance per neuron per class
• definition thmcounterdefinition: Fake rate per neuron
• definition thmcounterdefinition: Aggregate acceptance per class
• definition thmcounterdefinition: Aggregate fake rate
• definition thmcounterdefinition: Selectivity of the network
• definition thmcounterdefinition: Detection Efficiency