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Neural network-based timewalk correction for the Timepix4 ASIC

This paper introduces a compact feed-forward neural network for correcting timewalk in Timepix4 hybrid pixel detectors that outperforms traditional heuristic fits by achieving comparable time resolutions with only 20% of the calibration data while eliminating the need for explicit functional ansatzes or binning schemes.

Original authors: David Bacher, Kazu Akiba, Martin van Beuzekom, Victor Coco, Raphael Dumps, Tim Evans, Kevin Heijhoff, Malcolm John, Edgar Lemos Cid, Tommaso Pajero

Published 2026-10-08

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CC BY 4.0

Original authors: David Bacher, Kazu Akiba, Martin van Beuzekom, Victor Coco, Raphael Dumps, Tim Evans, Kevin Heijhoff, Malcolm John, Edgar Lemos Cid, Tommaso Pajero

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the high-energy world of particle physics, scientists build massive machines to smash atoms together and study the debris. To make sense of the billions of collisions happening every second, they rely on detectors that act like ultra-fast cameras, snapping pictures of charged particles as they fly by. For decades, these cameras have been excellent at recording where a particle passed through, but they have struggled to record exactly when. Adding precise timing to these detectors is the next great frontier, allowing researchers to sort through the chaotic pile of overlapping collisions and see the true sequence of events. However, getting a perfect timestamp is difficult because the electronics that read the signal are not perfectly uniform. When a particle hits a sensor, it creates an electrical charge. The larger the charge, the faster the electronics register the hit. This means a strong signal arrives slightly earlier than a weak one, even if the particles hit at the exact same moment. This delay, known as "timewalk," is a nuisance that must be corrected to achieve the precision needed for future experiments.

To fix this, researchers at the University of Oxford, Nikhef, and CERN have developed a new way to calibrate these detectors using artificial intelligence. They tested their method on a specific chip called Timepix4, which is a tiny grid of sensors designed to track particles with incredible speed. The team compared their new approach against the standard method used in the field. The traditional way to correct for the timing delay involves creating a complex map. Scientists take a huge amount of data, divide the sensor surface into tiny squares, and fit a specific mathematical curve to the data in each square. This works well if there is plenty of data, but it becomes a slow and fragile process if the data is sparse or unevenly distributed. If a square on the map doesn't have enough hits, the correction fails, leaving gaps in the data.

The researchers proposed replacing this rigid, map-based system with a compact neural network, a type of computer program designed to learn patterns from data. Instead of forcing the data into pre-defined boxes and fitting curves, the neural network looks at the raw information—the size of the electrical charge and the exact spot where the particle hit the sensor—and learns the relationship directly. It is like teaching a student to recognize a face by showing them thousands of examples, rather than giving them a checklist of features to measure. The team trained this network using data collected from a beam of particles at CERN's SPS accelerator in 2025. They tested the system on sensors of two different thicknesses, one measuring 100 micrometers and the other 300 micrometers, to see how well the network could adapt to different physical conditions.

The results showed that the neural network was not only accurate but also far more efficient than the traditional method. When the researchers had a large amount of calibration data, both methods performed equally well, reaching a timing precision of 180 picoseconds for the thinner sensors and 300 picoseconds for the thicker ones. A picosecond is one trillionth of a second, a timescale so fast that light travels only a fraction of a millimeter in that duration. However, the true advantage of the neural network appeared when the amount of available data was limited. In the real world, collecting massive amounts of calibration data can be difficult if the particle beam is weak or small. The traditional method struggled in these conditions, requiring hundreds of hits per sensor pixel to produce a reliable correction. In contrast, the neural network achieved the same high level of precision with only about 20 percent of the data.

Furthermore, the neural network never failed to provide an answer. The traditional method, which relies on filling specific bins of data, would simply stop working if a particular area of the sensor did not have enough hits, leaving those measurements uncorrected. The neural network, having learned a continuous pattern, could provide a correction for every single hit, regardless of how little data was available. This means that for experiments where data is scarce, the new method can achieve the same performance five times faster than the old way. The study confirms that machine learning can replace complex, manual calibration procedures with a more robust and flexible system, paving the way for more precise timing in the next generation of particle detectors without the need for massive data collection campaigns.

Technical Summary: Neural Network-Based Timewalk Correction for the Timepix4 ASIC

Problem Statement
Hybrid pixel detectors are essential for charged-particle tracking in high-luminosity collider environments, where adding picosecond-level timing is critical for four-dimensional tracking. Achieving this performance requires correcting "timewalk," a charge-dependent bias in the Time-of-Arrival (ToA) measurement caused by fixed-threshold discriminators. Additionally, non-uniform weighting fields in sensors introduce a dependence on the intrapixel impact position.

The conventional solution involves heuristic fits performed independently in bins of input variables (charge and position). This approach has significant limitations:

It requires an explicit functional ansatz and a specific binning scheme.
It demands densely populated calibration data; as the number of input variables increases, the required data volume grows rapidly.
It fails or produces poor results in regions with sparse data, leading to uncorrected hits and reduced tracking efficiency.

Methodology
This paper proposes replacing the bin-by-bin heuristic fits with a compact feed-forward neural network (NN) to learn the timewalk correction directly from data.

Inputs and Architecture: The NN is a fully connected, feed-forward multi-layer perceptron. It takes the measured charge ( $q$ ) and the reconstructed intrapixel impact position ( $x, y$ ) as inputs. These inputs match those used by the conventional fit-based method to ensure a fair comparison. The network outputs a predicted time correction ( $\Delta t_{NN}$ ).
Training: The network is trained using the Adam optimizer with a mean squared error (MSE) loss. Outliers (time residuals > 10 $\times$ median absolute deviation) are rejected. The study explores various network complexities (depth and width) to find a robust architecture.
Comparison Baseline: The NN is compared against a standard fit-based correction using data from the Timepix4 beam telescope at the CERN SPS (2025). The telescope utilized 180 GeV/c mixed hadron beams and sensors of two thicknesses: 100 $\mu$ m (perpendicular incidence) and 300 $\mu$ m (tilted by 9 $^\circ$ ).
Evaluation Metrics: Performance is measured by time resolution (RMS of the central 99th percentile of time residuals) and correction efficiency (fraction of hits with a valid correction).

Key Results
The study evaluated the methods across varying calibration sample sizes (1 to 5000 hits per pixel) and model complexities.

Model Complexity: A scan of network width and depth identified a two-layer, sixteen-neuron architecture (2L16N) as the optimal compromise. Smaller networks lacked capacity to capture the dependence, while larger networks (e.g., 3L64N) suffered from overfitting and unstable training when data was scarce.
Data Efficiency: The NN-based correction significantly outperforms the fit-based method in data-scarce regimes.
- 100 $\mu$ m Sensors: At 1 hit per pixel, the NN achieves a time resolution of ~~350 ps, compared to ~700 ps for the fit-based method. The NN reaches its asymptotic resolution (~~180 ps) with only ~100 hits per pixel, whereas the fit-based method requires ~500 hits.
- 300 $\mu$ m Sensors: Similarly, the NN reaches its asymptotic resolution (~300 ps) with ~100 hits per pixel, while the fit-based method requires ~500 hits.
- Overall Efficiency: The NN requires only 20% of the calibration data to achieve the same asymptotic time resolution as the fit-based baseline for both sensor thicknesses.
Correction Efficiency: The fit-based method suffers from low efficiency at low data volumes because bin-by-bin fits fail to converge in sparsely populated bins (dropping to ~20% efficiency for 100 $\mu$ m sensors at 1 hit/pixel). In contrast, the NN is defined everywhere and maintains 100% correction efficiency regardless of the calibration sample size.
Intrapixel Dependence: For the 300 $\mu$ m tilted sensors, the timewalk dependence on intrapixel position is complex, involving different charge-sharing scenarios. The NN successfully learns these multidimensional correlations without explicit binning, whereas the fit-based method requires complex binning strategies to capture similar effects.

Significance and Claims
The paper claims that the neural network approach offers a methodological advantage by learning the multidimensional dependence of timewalk directly from data, eliminating the need for explicit functional forms or arbitrary binning choices.

The primary significance is the fivefold reduction in the required calibration data volume to reach asymptotic timing performance. This is particularly valuable in scenarios where acquiring large calibration datasets is difficult due to limited beam intensity or beam size. The authors emphasize that while the current study uses only charge and position inputs to match the baseline, the NN framework allows for the straightforward inclusion of additional observables (e.g., track angles, neighbor pixel information) as inputs without the combinatorial explosion of binning dimensions required by the fit-based approach. Future work is planned to investigate these extensions.

Technical Summary: Neural Network-Based Timewalk Correction for the Timepix4 ASIC

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