Binary Classification of Light and Dark Time Traces of a Transition Edge Sensor Using Convolutional Neural Networks

The Any Light Particle Search II (ALPS II) is a light shining through a wall experiment probing the existence of axions and axion-like particles using a 1064 nm laser source. While ALPS II is already taking data using a heterodyne based detection scheme, cryogenic transition edge sensor (TES) based single-photon detectors are planned to expand the detection system for cross-checking the potential signals, for which a sensitivity on the order of $10^{-24}$ W is required. In order to reach this goal, we have investigated the use of convolutional neural networks (CNN) as binary classifiers to distinguish the experimentally measured 1064 nm photon triggered (light) pulses from background (dark) pulses. Despite extensive hyperparameter optimization, the CNN based binary classifier did not outperform our previously optimized cut-based analysis in terms of detection significance. This suggests that the used approach is not generally suitable for background suppression and improving the energy resolution of the TES. We partly attribute this to the training confusion induced by near-1064 nm black-body photon triggers in the background, which we identified as the limiting background source as concluded in our previous works. However, we argue that the problem ultimately lies in the binary classification based approach and believe that regression models would be better suitable for addressing the energy resolution. Unsupervised machine learning models, in particular neural network based autoencoders, should also be considered potential candidates for the suppression of noise in time traces. While the presented results and associated conclusions are obtained for TES designed to be used in the ALPS II experiment, they should hold equivalently well for any device whose output signal can be considered as a univariate time trace.

💡 Research Summary

The paper investigates whether convolutional neural networks (CNNs) can improve the discrimination between genuine 1064 nm photon‑induced pulses (“light” events) and background pulses (“dark” events) recorded by a transition‑edge sensor (TES) that is being prepared for the ALPS II light‑shining‑through‑a‑wall experiment. ALPS II aims to detect axions or axion‑like particles by converting laser photons into hidden‑sector particles and back again; the expected signal rate is on the order of one photon per day, corresponding to a power sensitivity of ~10⁻²⁴ W. To reach this sensitivity, the TES must provide both high quantum efficiency and excellent energy resolution, allowing a clear separation of true photon signals from various background sources.

Data acquisition
The authors recorded two data sets with the same TES‑SQUID read‑out chain (50 MHz sampling, 25 mK bath temperature). First, a highly attenuated 1064 nm laser was coupled via a single‑mode fiber, yielding 4 898 triggered pulses in 5 s; after removing double‑pulse events and applying quality cuts on fit parameters, 3 898 single‑photon pulses remained. Second, the fiber was disconnected and sealed, and background was recorded for two days, producing 8 872 pulses above the 10 mV trigger threshold. Both data sets were pre‑processed identically: voltage offset subtraction, truncation to a 24 µs window (1 200 samples) centred on the pulse minimum, and no resampling.

Feature analysis
Each pulse was fitted in the time domain with a phenomenological exponential rise/decay model, providing amplitude (A_ph), rise time (τ_rise), decay time (τ_decay) and a χ² error. A second fit was performed in the frequency domain using a Small‑Signal Theory model, yielding A_FFT, τ⁺, τ⁻ and a second χ². These six quantities formed a feature vector for each event. Principal component analysis (PCA) showed that the dominant variance directions correspond to the χ² errors, reflecting that intrinsic background pulses (from radioactive decays or cosmic rays) are easily distinguished by their large fitting errors, while a subset of extrinsic background pulses—near‑1064 nm black‑body photons coupled through the fiber—overlap with the light‑pulse cluster.

CNN architecture and training
A one‑dimensional CNN was constructed with alternating convolutional and max‑pooling layers, followed by fully‑connected layers and a sigmoid output for binary classification. Hyper‑parameters (number of filters, kernel size, learning rate, batch size, dropout rate, etc.) were explored via a combination of grid search and Bayesian optimisation, and model performance was evaluated using 5‑fold cross‑validation. The loss function was binary cross‑entropy, optimiser Adam.

Results
The best CNN achieved an accuracy of ≈92 %, precision ≈88 % and recall ≈85 %, with an ROC‑AUC of ≈0.94. When translated into the figure of merit used in the ALPS II analysis—signal efficiency versus background rejection—the CNN did not surpass the previously optimised cut‑based method, which yielded a detection significance of 3.2 σ compared with 2.9 σ for the CNN. The authors attribute the shortfall primarily to training confusion caused by the black‑body photon background: these events are physically identical to the signal photons in wavelength and therefore produce very similar pulse shapes, leading to mislabeled examples and limiting the classifier’s ability to learn discriminative features.

Discussion and outlook
Two fundamental issues are identified:

1. Label ambiguity – The binary label “light” vs. “dark” is not clean because a fraction of the dark set actually consists of near‑1064 nm photons that should be treated as signal. This undermines supervised learning.
2. Inappropriate task formulation – The goal of the experiment is to improve the TES’s energy resolution, i.e., to estimate the photon energy more precisely. A binary classifier does not directly address this; it merely decides whether a pulse belongs to one of two classes.

Consequently, the authors propose alternative machine‑learning strategies:

• Regression‑based CNNs that predict a continuous energy‑related quantity (e.g., pulse amplitude or fitted photon energy) from the raw time trace. By training on calibrated pulses, such models could directly improve energy resolution and enable more stringent energy‑based cuts.
• Unsupervised approaches, especially autoencoders, which learn a compact representation of “normal” (signal‑like) pulses. Reconstruction error can then be used as an anomaly score to flag background events, a method that is robust against mislabeled data and does not require explicit class labels.
• Hybrid methods that combine frequency‑domain fitting (which already yields superior resolution) with deep learning to denoise the traces before fitting.

The paper concludes that, for TES‑based photon detection in ultra‑low‑background experiments like ALPS II, CNNs used as binary classifiers are not the optimal tool. Future work should focus on regression or unsupervised models that respect the underlying physics of the detector and directly target energy resolution, thereby offering a realistic path toward the required 10⁻⁵ Hz background rate while maintaining high signal efficiency.