Exploring Low Energy Excess in MINER with sapphire detectors using Convolutional Variational Autoencoder (CVAE)

Abstract: As cryogenic detectors push toward ever-lower energy thresholds, their sensitivity is increasingly constrained by a persistent low-energy background known as the low-energy excess (LEE). We report observation of LEE in the MINER experiment using a sapphire ($\mathrm{Al_2O_3}$) detector at energies around 200 eV, with the excess reproducibly reappearing after each non-operational warm-up period. To address this limiting background, we implement an unsupervised convolutional variational autoencoder (CVAE) framework that identifies anomalous events through a reconstruction-based anomaly score. For the first time in a pulse-shape driven analysis, we uncover a significant deviation in the rise-time of LEE events relative to Monte Carlo simulated ideal signals. Using this feature, we develop a discrimination pipeline based on rise-time selection. This method achieves up to 53\% rejection of LEE events, corresponding to an expected sensitivity improvement of nearly 10\% for MINER at HFIR. These findings are consistent with a scenario in which a substantial fraction of the LEE originates from bulk-related defects or microfractures within the detector crystal, while leaving room for additional detector-related contributions. Our result provides a powerful, data-driven pathway for mitigating LEE and enhancing the discovery potential of next-generation cryogenic experiments.

• The paper demonstrates the effectiveness of a convolutional variational autoencoder (CVAE) in identifying low energy excess events through pulse-shape analysis.
• It utilizes simulated and real data to reveal significant pulse-shape deviations, with real signals showing slow pre-pulse components at loss scores above 0.04.
• The CVAE approach enhances CEνNS sensitivity by around 10% and achieves up to 53% LEE rejection, highlighting its potential for rare-event searches.

Pulse-Shape-Driven Anomaly Detection and LEE Discrimination in MINER Sapphire Cryogenic Detectors via Convolutional Variational Autoencoder

Introduction and Background

Low-threshold cryogenic phonon detectors have advanced toward detecting sub-keV events, critically enhancing sensitivity in applications such as CE$\nu$NS and rare-event searches. However, these detectors confront a persistent, sharply rising low-energy excess (LEE) background near operational thresholds. LEE, first revealed in solid-state detectors like Ge and $\mathrm{CaWO_4}$ in EDELWEISS and CRESST [LEE_CRESST_2019, LEE_EDELWEISS_2019], has since been observed across multiple platforms and materials—showing reproducible behavior after each thermal cycling and resisting association with conventional particle backgrounds, including DM.

The MINER experiment, deployed at Texas A&M using a sapphire ($\mathrm{Al_2O_3}$) detector, reports LEE at energies $\sim$200 eV, with increased rates after non-operational warm-up periods (Figure 1). This temporal behavior, combined with mismatch between simulated and observed spectra in the 200–400 eV region, motivates a comprehensive analysis using unsupervised deep-learning techniques capable of capturing waveform-level anomalies without bias from model assumptions.

Figure 1: Single-scatter spectrum in the low-energy region, collected over multiple data-taking periods, demonstrating systematic LEE behavior post-warm-ups.

CVAE Architecture and Training

An unsupervised convolutional variational autoencoder (CVAE) framework is utilized to characterize and discriminate LEE events based on pulse-shape deviations. The CVAE is trained on MC-generated ideal signal events—created by injecting detector pulse templates into noise traces selected through rigorous quality criteria (Figure 2).

Figure 2: Left: Noise trace selection based on Max–Min distribution; Right: MC-generated pulses compared to ideal pulse templates across energies.

The CVAE architecture comprises encoder and decoder blocks constructed from Conv1D and Leaky ReLU layers, compressing $\mathbf{x}$ (pulse of length 1024 samples) into a 256-dimensional latent space parameterized by $\mu$ and $\log\sigma^2$, and reconstructing from sampled latent vectors (Figure 3). Training minimizes a composite loss: MSE reconstruction plus KL-divergence regularization, controlled by $\beta = 5 \times 10^{-2}$. The loss converges rapidly and generalizes well, as shown by training and validation dynamics over 50 epochs (Figure 4).

Figure 3: Schematic of CVAE architecture showing encoder, latent space sampling, and decoder for pulse waveform reconstruction.

Figure 4: Total loss over training epochs, demonstrating convergence and stability of learning.

Analysis: Loss Score Distributions and Anomaly Template Generation

Upon applying the trained CVAE to real single-scatter events (200–500 eV), the reconstruction loss score distribution for real pulses shows a significant population at higher loss, compared to MC where low loss dominates (Figure 5). This indicates pulse-shape deviation in real data characteristic of LEE.

Figure 5: Distribution of CVAE loss scores for MC and real data, highlighting anomalous structure in real pulses.

Templates constructed as averages within loss-score bins reveal that increased loss corresponds to a slow pre-pulse component (Figure 6), raising rise-time relative to MC, especially for loss $>0.04$. Residual analysis confirms that only real data exhibits these deviations in the specified index range, while MC remains baselined.

Figure 6: Comparison of real and MC templates across loss score intervals; residuals highlight pronounced LEE-induced deviations.

Rise-Time Estimation via Pulse Filtering

To robustly quantify the rise-time as a discriminant, pulses are processed through four filtering techniques: Savitzky–Golay, Gaussian, Butterworth, and wavelet denoising (Figure 7). Across all filters, rise-time for MC templates remains tightly in 20–40 μs, while real data with high CVAE loss yields rise-times up to three times longer (Figure 8).

Figure 7: Example of real and MC pulses through various filters, illustrating waveform preservation and noise reduction.

Figure 8: Rise-time distributions and ratios (real/MC) across CVAE loss scores and filter types.

LEE Event Discrimination Pipeline and Spectral Impact

A pipeline is constructed leveraging rise-time as a threshold for LEE discrimination, with receiver operating characteristic (ROC) analysis performed on datasets combining MC and high-loss-score real events ($>0.04$). The optimal threshold—maximizing the $\mathrm{CaWO_4}$0 score—provides AUC $\mathrm{CaWO_4}$10.7 across all filters (Figure 9), indicating moderate discrimination efficacy. The wavelet filter achieves $\mathrm{CaWO_4}$253\% LEE rejection at high $\mathrm{CaWO_4}$3.

Figure 9: ROC curves for rise-time-based LEE discrimination, showing optimal threshold selection for multiple filters.

Applying the rise-time thresholds to the real dataset yields pronounced suppression of LEE in the energy spectrum, especially in the lowest bins (Figure 10).

Figure 10: Energy spectra before and after rise-time-based filtering, evidencing LEE suppression effectiveness.

Signal Sensitivity Enhancement

Implementing the rise-time selection (optimally via wavelet filter) reduces background in the critical 200–500 eV ROI, providing a $\mathrm{CaWO_4}$410\% improvement in CE$\mathrm{CaWO_4}$5NS significance for MINER at HFIR (Figure 11). Significance in the lowest bin is increased by a factor of $\mathrm{CaWO_4}$61.4, demonstrating the practical benefit in rare-event searches.

Figure 11: Left: Background and signal models before and after LEE rejection; Right: Bin-wise significance enhancement and corresponding ratios.

Theoretical Implications and Future Prospects

The observed pulse-shape anomalies are consistent with bulk defect or microfracture mechanisms, releasing energy via delayed phonon emission following crystal relaxation post-cooldown [microfracture_LEE, fracture_process]. This scenario explains the temporal regeneration and decay of LEE after thermal cycling. However, a residual LEE remains even after rise-time-based filtering—implying possible surface or sensor-proximal processes, which are not efficiently captured by the slow-component criterion. A dedicated bulk-surface analysis is necessary for comprehensive background understanding.

The CVAE-based approach provides a model-independent, data-driven method for anomaly detection and waveform discrimination, transferable to other cryogenic detector platforms (SuperCDMS, EDELWEISS, NUCLEUS, CRESST) facing similar LEE challenges. This technique augments traditional pulse-shape cuts with robust, unsupervised neural network evaluations, advancing the toolkit for next-generation rare-event searches.

Conclusion

The MINER study demonstrates the utility of unsupervised CVAE pulse-shape analysis in identifying and discriminating LEE events, achieving up to 53\% rejection and enhancing CE$\mathrm{CaWO_4}$7NS sensitivity by $\mathrm{CaWO_4}$810\%. The presence of slow pre-pulse components in LEE traces, and their temporal behavior, align with bulk defect/microfracture models. The proposed method is broadly applicable across cryogenic detectors, offering improved background mitigation and enhanced discovery potential. Future directions include refined bulk/surface discrimination, integration with likelihood-based analyses, and extension to new materials and readout technologies.

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References:

• "Exploring Low Energy Excess in MINER with sapphire detectors using Convolutional Variational Autoencoder (CVAE)" (2605.31190)
• "Spontaneous generation of athermal phonon bursts within bulk silicon causing excess noise, low energy background events, and quasiparticle poisoning in superconducting sensors" (Chang et al., 22 May 2025)
• "Low-Energy Backgrounds in Solid-State Phonon and Charge Detectors" (Baxter et al., 11 Mar 2025)
• "A semi-supervised approach to dark matter searches in direct detection data with machine learning" (Herrero-Garcia et al., 2021)