Robust Betatron-Tune Measurement from Schottky Spectra: Complementary Classical and Deep-Learning Paradigms

Deming Li; Jian Dong; Manzhou Zhang; Peihan Sun; Renxian Yuan

REVIEW 3 major objections 5 minor 23 references

Robust Betatron-Tune Measurement from Schottky Spectra: Complementary Classical and Deep-Learning Paradigms

T0 review · 3 major / 5 minor · reviewed 2026-08-02 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A CNN likelihood map plus a discrete (q,v) Bayes tracker gives the most accurate betatron-tune readout from Schottky spectra at low SNR, with a training-free classical counterpart close behind.

desk verdict Honest, carefully built paper with two genuinely new estimators, but the headline low-SNR advantage rests entirely on a synthetic benchmark from the authors' own simulator, and real beam only shows feasibility. read the letter →

arxiv 2607.13791 v3 pith:D6AMBNDB submitted 2026-07-15 physics.acc-ph

Peihan Sun , Manzhou Zhang , Renxian Yuan , Deming Li , Jian Dong This is my paper · ORCID

classification physics.acc-ph

keywords SchottkyspectrabetatrontuneslowextractionmedicalprotonsynchrotronBayesiantrackingconvolutionalneuralnetworkmotioncompensationlow-SNRdiagnostics

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper sets out to make passive betatron-tune measurement from Schottky spectra reliable in the difficult conditions of compact medical proton synchrotrons: short acquisition windows, low signal-to-noise ratio, and residual narrow-band interference. It develops two estimators that share one spectral front-end but accumulate temporal context in different ways: a classical motion-compensated coherent moving average feeding a matched-filter bank and gated centroid, and a deep-learning pipeline in which a convolutional network converts each spectrum into a tune-likelihood map that a discrete (q,v) Bayesian filter propagates frame to frame. On a synthetic dynamic-tune benchmark the deep-learning estimator has the lowest mean absolute error (geometric mean 0.187e-3 tune units) and by far the lowest rate of catastrophic misses (0.14 percent), while the classical estimator beats a latency-compensated published baseline and needs no training data or GPU. Both run end-to-end on real beam data from the target facility without retraining, and median per-frame latency stays below 1 ms.

What carries the argument

The shared front-end is the folded PSD on a uniform 1024-bin tune grid. The classical estimator's key mechanism is the motion-compensated coherent exponential moving average, which shifts the pooled spectrum by a velocity estimate before averaging, with a velocity-adaptive decay, then detects the sideband with a multi-width Gaussian matched-filter bank and refines it with a median/MAD-gated centroid. The deep-learning estimator's key mechanism is the combination of a likelihood-map CNN — using FFT-evaluated global convolutions with an implicit damped-oscillator kernel, giving full-axis receptive field at O(L log L) cost — and a discrete (q,v) Bayes tracker that propagates a log-posterior ove

What would settle it

Acquire Schottky spectra during a real accelerating ramp or slow-extraction cycle at the target facility with an independently known tune (for instance, a kicker-excitation reference or a dedicated tune meter), then measure the geometric-mean absolute error of the deep-learning estimator versus the classical estimator and the prior CNN+Kalman baseline at effective SNR near -15 dB. If the deep-learning estimator's error advantage over the classical and Kalman baselines fails to appear, or reverses, on real data, the simulator-fidelity premise — and with it the central comparison — collapses.

Watch

Extended reading notes

Core claim

The central claim is that betatron-tune readout from low-SNR Schottky spectra is best served not by choosing between classical and learned per-frame estimators, but by pairing a fixed spectral front-end with a temporal representation matched to the estimator's strengths. The deep-learning estimator's advantage comes from feeding a full tune-grid likelihood map, not a scalar, into a discrete two-dimensional (q,v) Bayes tracker: the multi-modal map keeps a wrong per-frame peak recoverable, and the velocity-aware posterior rejects clutter and noise while reporting per-frame uncertainty. The classical estimator achieves competitive accuracy at moderate SNR with a velocity-shifted coherent EMA th

Load-bearing premise

The load-bearing premise is that the synthetic Schottky simulator used to train and benchmark both estimators faithfully represents the target facility's real spectra in exactly the regimes where the claims are made — the paper's own real-beam acquisitions are near-stationary and do not exercise the low-SNR, dynamic-tune, or narrow-band conditions that separate the estimators.

Editorial extensions

If this is right

If the simulator fidelity holds, the deep-learning estimator could replace kicker-excitation tune measurement with passive low-SNR Schottky readout during slow extraction, avoiding beam disturbance.
The discrete tracker's per-frame posterior standard deviation provides a ready-made uncertainty channel for gating downstream systems such as spill-quality feedback — something the classical estimator does not provide.
The classical estimator's tune-unit parametrization and training-free operation mean it can be deployed to other synchrotrons with minimal recalibration, making it a safe default when GPU or training infrastructure is absent.
The operating-regime decision matrix gives a practical rule: use the deep-learning estimator whenever SNR is tight or unpredictable, and the classical estimator at moderate SNR on benign, slowly varying tunes.
Both estimators' sub-millisecond latency (0.12 ms on CPU, 0.40 ms on GPU) supports real-time, closed-loop tune measurement at millisecond frame cadences.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A natural next test is to collect real ramping-cycle Schottky data with an independent tune reference (e.g., a kicker-based measurement on a sacrificial cycle) and compare estimators at -10 to -20 dB; if the deep-learning advantage does not survive the real noise structure, the paper's central comparison rests on simulator fidelity.
The length-portability of the CNN suggests the same trained network could be applied to spectra with different harmonic grids, or even to other frequency-domain diagnostics such as chromaticity from Schottky spectra, provided the coordinate and weight channels are scaled accordingly.
The observed complementarity hints at a practical fusion: run both estimators and treat large disagreement as a flag for anomalous spectra (beam loss, interference, or model mismatch), rather than committing to a single estimator.
One could ablate further by training on intentionally mismatched noise models (colored, non-Gaussian) to see whether the likelihood-map tracker retains robustness, which would separate simulator-fidelity effects from architectural benefits.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Bottom line: two new estimators, both described in enough detail to be built from the paper, and the synthetic benchmark is run carefully. But the claim that matters — the deep-learning estimator's low-SNR edge — is demonstrated only on spectra from the authors' own simulator, and the real-beam data explicitly does not cover the regimes where the two estimators differ. Treat the headline numbers as provisional.

The paper does a lot well. The classical motion-compensated coherent EMA with matched-filter bank and MAD-gated centroid is a coherent, inventive design; the deep-learning pipeline (likelihood-map CNN with FFT global convolutions plus a discrete (q,v) Bayes tracker) is a sensible separation of spectral recognition from temporal inference. The ablations are illuminating: the tracker decomposition shows the (q,v) posterior is what gives the deep estimator its edge, and the classical EMA ablation shows both pooling and motion compensation matter. Cross-fold consistency, latency measurements, and the honest scope statement in Section 4 all speak for the authors.

The soft spots are real, and they are load-bearing. The dynamic-tune benchmark is generated by the same simulator family used to train the CNN and to set the classical estimator's parameters. That cannot fully separate 'recognizes Schottky sidebands' from 'recognizes this simulator's noise.' The tracker's velocity envelope and process noise are explicitly calibrated to the benchmark trajectories, which is a form of leakage into the evaluation. The real-beam section is a feasibility and cross-estimator agreement check, not a validation of the claimed operating regimes, and the authors say so. No code or data are released, so the numbers are currently not independently checkable.

None of this makes the paper incoherent. The central argument holds up as far as it goes: the proposed methods are new, the experimental design is internally consistent, and the limitations are stated. What is missing is independent evidence. If the low-SNR advantage survives on spectra from a different source, or on ramp data with a known tune reference, this becomes a solid contribution to accelerator instrumentation.

Who should read it: anyone working on non-invasive tune measurement in compact medical synchrotrons or similar low-SNR Schottky diagnostics. It deserves a serious referee: the method detail is enough to reproduce, and the claims, if independently confirmed, matter. I would send it to peer review, with an explicit request that the synthetic-only validation be addressed or clearly scoped.

Referee Report

3 major / 5 minor

Summary. The paper presents two betatron-tune estimators fed by a common folded-spectrum front end: a classical motion-compensated coherent-EMA estimator with a matched-filter bank and gated centroid, and a deep-learning estimator combining a convolutional likelihood-map network with a discrete (q,v) Bayes tracker. On a synthetic dynamic-tune benchmark spanning three trajectory speeds and five SNR levels, the deep-learning estimator attains the lowest aggregate MAE (geometric mean 0.187×10^-3 vs 0.243×10^-3 for CNN+KF and 0.418×10^-3 for the classical estimator) and the lowest catastrophic-miss rate; the classical estimator outperforms the latency-compensated T-PD baseline while requiring no training data or GPU. Robustness studies cover beam-loss recovery, narrow-band interference, out-of-distribution SNR, ablations, latency, input-length scaling, and acquisition resolution. A preliminary real-beam study at SAPT shows end-to-end operation and cross-estimator consistency on near-stationary coasting-beam acquisitions.

Significance. If the synthetic simulator faithfully represents the operational SAPT regimes, the contribution is significant: the likelihood-map-plus-Bayes-tracker architecture provides a large accuracy and tail-risk improvement in the low-SNR, dynamic-tune regime that is most relevant to compact medical synchrotrons, while the classical estimator offers a practical CPU-only, training-free alternative. The paper is careful in several respects: all estimators receive identical input streams; the deep-learning results are cross-validated over five folds; ablations decompose the tracker and CNN contributions; latency is measured on deployed hardware; and the authors explicitly acknowledge the synthetic-only evidence for the headline regime. The main limitation is that the central dynamic-tune and low-SNR claims are not validated against independent spectra or real ramp data with a known tune reference, and some tracker motion constants are calibrated using the benchmark trajectories themselves, which limits the strength of the claims as currently stated.

major comments (3)

[Sections 3.1, 3.3, 3.6, 4] The central accuracy claim (Tables 2-3) rests entirely on spectra from the authors' own Schottky simulator, referenced to [10] with "no new Schottky-signal generator introduced." The paper's own limitation statement (Section 4) concedes that the real-beam acquisitions "do not exercise the dynamic-tune, deep-low-SNR, or narrow-band regimes in which the two estimators are claimed to differ." As a result, the benchmark cannot distinguish recognition of betatron sidebands from recognition of this simulator's spectral statistics. The claims should either be explicitly scoped to synthetic spectra throughout, or the authors should provide independent validation (e.g., an external simulator, measured spectra with an independent tune reference, or a hardware-in-the-loop test) before the operational generalization is asserted.
[Section 2.5 (Eq. 2.20) and Section 3.1] The tracker motion constants are calibrated to the benchmark trajectories: sigma_v is set "so that 4 sigma_v covers the largest per-frame velocity change measured on the evaluated trajectories," and v_max is chosen to "cover... the fastest ramp trajectories evaluated." Evaluating the estimator on the same trajectory family used to set its motion-model constants is a circularity risk for the reported margin over baselines. Please provide a sensitivity analysis over sigma_v and v_max, and/or evaluate on held-out trajectory ensembles with velocity statistics outside the calibration range, to show that the deep-learning advantage is not an artefact of matching the benchmark's motion envelope.
[Section 3.4.2 (Tables 5-6)] The drifting-clutter robustness result, which is cited as a key differentiator, is based on a single representative 600-frame energy ramp with three interference lines; the five-cell geometric mean is over five SNR levels of that one ramp, not over independent ramp realizations. Because the frames are strongly autocorrelated, the reported per-cell statistics have very low effective sample size. The paper should report results over multiple random ramp realizations (with randomized line positions/amplitudes) or provide a statistical justification for treating the single ramp as sufficient. The same concern applies to the stationary-clutter stream.

minor comments (5)

[Sections 3.2 and 3.5.4] The no-tracker deep-learning readout is described inconsistently: Section 3.2 uses a "peak-local soft-argmax," while Table 12 labels the row "DL, no tracker" as a "whole-map soft-argmax." Please clarify which readout is actually used in each table and ensure the metric is defined consistently.
[Figure 7 caption] Panel (b) is captioned "fast, 15 dB" but the text and the surrounding discussion refer to the -15 dB condition. Please correct the sign or the label.
[Section 2.5] Minor typos: "kernel-size-71D convolution" should read "kernel-size-7 1D convolution" (two typos in one phrase), and τ=0.5 is described as "bin" where the temperature is dimensionless. These should be cleaned up before publication.
[Section 3.3 / T-PD baseline] The latency-compensated T-PD comparison selects N* per trajectory shape to minimize MAE on the same benchmark used for the headline comparison. This is a permissive treatment of the baseline; the paper should state whether the reported N*=3 also transfers to the robustness studies, or whether it was re-selected there.
[Table 14] For the CNN+KF baseline, the reported mean posterior sigma (0.264×10^-3) is far below the realized within-acquisition std (6.132×10^-3), indicating severe miscalibration. The text notes this only implicitly. It would be helpful to add an explicit caution that the CNN+KF uncertainty is not calibrated on this real-beam set, especially since the proposed deep-learning estimator is compared against it.

Circularity Check

2 steps flagged · score 4.0 of 10

Dynamic-tune advantage is partly in-sample: motion-model constants are calibrated to the benchmark trajectories, and the central accuracy comparison relies on the authors' own Schottky simulator.

fitted input called prediction [Section 2.5, Prediction; Section 2.4, Local-window argmax; evaluated in Section 3.3]
"The process-noise scale is a physical, facility-level calibration, σv = 5×10−4 tune units per frame (approximately one bin per frame at L=1024), set so that 4σ_v covers the largest per-frame velocity change measured on the evaluated trajectories... The window restricts the readout to a tune-velocity envelope compatible with the trajectories considered in Section 3."

The Bayesian tracker's process-noise scale and velocity envelope, and the classical estimator's local search window, are explicitly calibrated to the same synthetic dynamic-tune trajectories on which both estimators are then benchmarked. Eq. (2.20) and the vmax/Vmax envelope therefore contain the test dynamics by construction; the reported ability to track those fast trajectories is partly a check that the motion model covers its own calibration set, not an independent out-of-sample prediction. This reduces part of the claimed dynamic-tune advantage to a fitted prior rather than to measured recognition quality.
self citation load bearing [Section 3.1, Evaluation setup; Section 4, Conclusions]
"no new Schottky-signal generator is introduced for this work [10] ... The accuracy, robustness, and complementarity results rest on synthetic Schottky spectra with known ground truth; the near-stationary SAPT real-beam acquisitions of Section 3.6 do not exercise the dynamic-tune, deep-low-SNR, or narrow-band regimes in which the two estimators are claimed to differ."

The central benchmark that supports the headline accuracy comparison is generated by the authors' own prior simulator [10], and the only operational data are conceded not to cover the regimes where the estimators are claimed to differ. The claim that the two estimators separate in dynamic-tune, deep-low-SNR, and narrow-band conditions is therefore grounded in the same authors' generator, with no external or operational data breaking the self-referential validation loop. The real-beam section supports feasibility and cross-estimator consistency, but not the regime-dependent comparison itself.

full rationale

The estimator outputs are not mathematically equal to fitted inputs: Tables 2 through 13 report genuine measurements on bit-identical streams, the deep-learning/classical estimators have structurally different mechanisms, and the real-beam run is an independent feasibility check. However, two load-bearing choices reduce the force of the headline comparison. First, the motion-model constants (σ_v, v_max, and the classical search window) are calibrated to the very benchmark trajectories on which the dynamic-tune advantage is measured, so part of that advantage is guaranteed by construction rather than demonstrated. Second, the synthetic benchmark itself originates from the authors' prior simulator [10], while the paper explicitly concedes that the real-beam acquisitions do not exercise the distinguishing regimes. These issues make the dynamic-tune claim partly in-sample and self-referential, but they do not make the whole derivation an identity, and the paper is transparent about the limitation. Score 4 reflects partial circularity with independent content remaining.

Assumptions & free parameters 8 free parameters · 5 assumptions · 0 invented entities

No new physical entity is introduced. The cost is paid in fitted constants: several classical readout windows and both tracker motion parameters are hand-set or calibrated to the benchmark trajectories. The simulator and preprocessing chain are inherited from the authors' prior works [9,10], so the performance claims partly depend on assumptions in those papers.

free parameters (8)

classical EMA pool cap beta_max = 0.50 (N=2 frames equivalent)
Set as a hand-chosen trade-off between noise averaging and lag; the stationary-limit pool depth is not derived from first principles.
classical local search window w_q = 1e-2 tune units (20 bins at L=1024)
Deployment-fixed envelope for the local argmax; chosen to admit per-frame deflections up to one fiftieth of the folded-tune range.
classical centroid window q_c = 0.05 tune units
Called 'the single deployment-tuned parameter of the readout' in Section 2.4.
matched-filter kernel widths = {0.5,1,2,4} x 1e-3 tune units
Dyadic bank chosen to cover sideband widths encountered at SAPT; not derived from data or theory.
tracker velocity envelope vmax = 2e-2 tune units/frame (41 bins at L=1024)
Set to cover the fastest ramp trajectories evaluated in Section 3; calibrated to the benchmark envelope.
tracker velocity process noise sigma_v = 5e-4 tune units/frame
The text states it is set so that 4 sigma_v covers the largest per-frame velocity change measured on the evaluated trajectories; this is a fitted value targeted at the benchmark.
map-loss support sigma_max = 0.025 tune units
Upper bound on bunched-beam sideband width used to define the windowed map loss; fixed by physics assumption, not measured.
softmax readout temperature tau = 0.5 bin
Sharpening temperature for map readout and training; fixed by design choice.

assumptions (5)

domain assumption Additive PSD model: S_t(f) = S_sig_t(f) + S_noise_t(f), Eq. (2.4)
The whole estimation problem is framed as recovering a sideband in additive noise; in reality the noise may be signal-dependent or non-stationary.
domain assumption The synthetic Schottky simulator from the authors' prior work [10] faithfully represents SAPT operational conditions
Training and dynamic-tune evaluation both use this simulator; Section 4 concedes real-beam data do not exercise the claimed dynamic/deep-SNR regimes.
domain assumption Gaussian sideband shape for matched filters and Gaussian motion/observation model in the tracker
Matched-filter bank uses Gaussian kernels; tracker uses Gaussian velocity transition and quantisation blur. Real sidebands may be non-Gaussian.
domain assumption Narrow-band interference can be modeled by randomized Gaussian lines not drawn from measured spectra
Section 2.1 states injected lines act as synthetic surrogates rather than features from measured spectra; this may not cover real clock/RF contamination.
domain assumption Eigendecoupling on the 3x3 cross-spectral density matrix isolates the transverse tune channel in real beam data
Section 3.6 relies on per-frequency eigendecoupling of X,Y,Z channels; residual cross-talk assumptions are plausible but not independently verified.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Robust Betatron-Tune Measurement from Schottky Spectra: Complementary Classical and Deep-Learning Paradigms." pith.science (2026). https://pith.science/paper/D6AMBNDB

@misc{pith2026260713791,
  author       = {Pith},
  title        = {Pith review of: Robust Betatron-Tune Measurement from Schottky Spectra: Complementary Classical and Deep-Learning Paradigms},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/D6AMBNDB}},
  note         = {Machine review of arXiv:2607.13791}
}

read the original abstract

Schottky spectra provide key beam diagnostics, with betatron sidebands encoding the fractional tune. Reliable tune measurement is particularly important for third-order resonance slow extraction in compact medical proton synchrotrons, where low signal-to-noise ratios and limited frequency resolution can compromise conventional peak-detection and curve-fitting methods. This work develops two complementary tune estimators with a shared spectral front-end but different temporal representations. The classical estimator coherently pools motion-compensated spectra, detects the sideband using a multi-width matched-filter bank, and performs sub-bin estimation through local argmax and an adaptive MAD-gated centroid. The deep-learning estimator converts each spectrum into a tune-likelihood map using a convolutional neural network with FFT-based global convolutions, then propagates the posterior with a discrete two-dimensional (q,v) Bayesian tracker under a Gaussian motion model while also reporting posterior uncertainty. On a synthetic dynamic-tune benchmark, the deep-learning estimator outperforms published baselines across the operating range, while the classical estimator exceeds the latency-compensated baseline and requires neither training data nor GPU acceleration. On near-stationary SAPT beam data, both methods operate end-to-end, with the deep-learning model requiring no retraining. Median per-frame latency remains below 1 ms on commodity hardware, supporting real-time-capable tune measurement in compact medical synchrotrons.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

23 extracted references · 2 linked inside Pith

[10]

P. Sun, M. Zhang, R. Yuan, D. Li, J. Dong and Y. Shi,Real-time-capable betatron tune measurement from schottky spectra using deep learning and uncertainty-aware kalman filtering,Journal of Instrumentation21(2026) P02049

2026
[1]

Zhang, D.-M

M.-Z. Zhang, D.-M. Li, L.-R. Shen, H.-R. Zhang, Z.-L. Chen, H.-W. Du et al.,Sapt: a synchrotron-based proton therapy facility in shanghai,Nuclear Science and Techniques34(2023) 148

2023
[2]

K.Łasocha, C.Lannoy, T.Levens, N.Mounet, O.MarqversenandD.Alves,Onlineanalysisofproton and lead ion lhc schottky spectra,
[3]

Łasocha, T

K. Łasocha, T. Pieloni, N. Mounet, D. Alves and C. Lannoy,Jacow: Extraction of lhc beam parameters from schottky signals,JACoW HB2023(2024) 382

2024
[4]

van der Meer,Stochastic damping of betatron oscillations in the isr, Tech

S. van der Meer,Stochastic damping of betatron oscillations in the isr, Tech. Rep. (1972)

1972
[5]

S. van der Meer,Diagnostics with schottky noise, inFrontiers of Particle Beams; Observation, Diagnosis and Correction: Proceedings of a Topical Course Held by the Joint US-CERN School on Particle Accelerators at Anacapri, Isola di Capri, Italy, October 20–26, 1988, pp. 423–433, Springer (2005)

1988
[6]

Caspers,Schottky signals for longitudinal and transverse bunched-beam diagnostics,

F. Caspers,Schottky signals for longitudinal and transverse bunched-beam diagnostics,
[7]

M. Betz, O. Jones, T. Lefevre and M. Wendt,Bunched-beam schottky monitoring in the lhc,Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment874(2017) 113

2017

Show all 23 references

[8]

Lasocha and D

K. Lasocha and D. Alves,Estimation of transverse bunch characteristics in the lhc using schottky-based diagnostics,Physical Review Accelerators and Beams25(2022) 062801. – 43 –

2022
[9]

P. Sun, M. Zhang, R. Yuan, D. Li, J. Dong and Y. Shi,High-accuracy schottky diagnostics for low-snr betatron tune measurement in ramping synchrotrons,Journal of Instrumentation20(2025) P06058

2025
[11]

Boussard,Schottky noise and beam transfer function diagnostics, Tech

D. Boussard,Schottky noise and beam transfer function diagnostics, Tech. Rep. CERN (1986)

1986
[12]

Chanon,Schottky signal analysis: tune and chromaticity computation, Tech

O. Chanon,Schottky signal analysis: tune and chromaticity computation, Tech. Rep. (2016)

2016
[13]

Nolden,Instrumentation and diagnostics using schottky signals,Proc

F. Nolden,Instrumentation and diagnostics using schottky signals,Proc. DIPAC 01(2001) 6

2001
[14]

Lasocha and D

K. Lasocha and D. Alves,Estimation of longitudinal bunch characteristics in the lhc using schottky-based diagnostics,Physical Review Accelerators and Beams23(2020) 062803

2020
[15]

Schafer,What is a savitzky-golay filter?[lecture notes],IEEE Signal processing magazine28 (2011) 111

R.W. Schafer,What is a savitzky-golay filter?[lecture notes],IEEE Signal processing magazine28 (2011) 111

2011
[16]

Shewhart,Economic control of quality of manufactured product, Barakaldo Books (2022)

W.A. Shewhart,Economic control of quality of manufactured product, Barakaldo Books (2022)

2022
[17]

Rousseeuw and C

P.J. Rousseeuw and C. Croux,Alternatives to the median absolute deviation,Journal of the American Statistical association88(1993) 1273

1993
[18]

Vaswani, N

A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A.N. Gomez et al.,Attention is all you need,Advances in neural information processing systems30(2017)

2017
[19]

Gu and T

A. Gu and T. Dao,Mamba: Linear-time sequence modeling with selective state spaces,arXiv preprint arXiv:2312.00752(2023)

2023 arXiv
[20]

A. Gu, K. Goel, A. Gupta and C. Ré,On the parameterization and initialization of diagonal state space models,Advances in neural information processing systems35(2022) 35971

2022
[21]

M. Poli, S. Massaroli, E. Nguyen, D.Y. Fu, T. Dao, S. Baccus et al.,Hyena hierarchy: Towards larger convolutional language models, inInternational Conference on Machine Learning, pp. 28043–28078, PMLR, 2023

2023
[22]

Hendrycks and K

D. Hendrycks and K. Gimpel,Gaussian error linear units (gelus),arXiv preprint arXiv:1606.08415 (2016)

2016 arXiv
[23]

Loshchilov and F

I. Loshchilov and F. Hutter,Decoupled weight decay regularization, 2019. – 44 –

2019

Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.

[1] [10]

P. Sun, M. Zhang, R. Yuan, D. Li, J. Dong and Y. Shi,Real-time-capable betatron tune measurement from schottky spectra using deep learning and uncertainty-aware kalman filtering,Journal of Instrumentation21(2026) P02049

2026

[2] [1]

Zhang, D.-M

M.-Z. Zhang, D.-M. Li, L.-R. Shen, H.-R. Zhang, Z.-L. Chen, H.-W. Du et al.,Sapt: a synchrotron-based proton therapy facility in shanghai,Nuclear Science and Techniques34(2023) 148

2023

[3] [2]

K.Łasocha, C.Lannoy, T.Levens, N.Mounet, O.MarqversenandD.Alves,Onlineanalysisofproton and lead ion lhc schottky spectra,

[4] [3]

Łasocha, T

K. Łasocha, T. Pieloni, N. Mounet, D. Alves and C. Lannoy,Jacow: Extraction of lhc beam parameters from schottky signals,JACoW HB2023(2024) 382

2024

[5] [4]

van der Meer,Stochastic damping of betatron oscillations in the isr, Tech

S. van der Meer,Stochastic damping of betatron oscillations in the isr, Tech. Rep. (1972)

1972

[6] [5]

S. van der Meer,Diagnostics with schottky noise, inFrontiers of Particle Beams; Observation, Diagnosis and Correction: Proceedings of a Topical Course Held by the Joint US-CERN School on Particle Accelerators at Anacapri, Isola di Capri, Italy, October 20–26, 1988, pp. 423–433, Springer (2005)

1988

[7] [6]

Caspers,Schottky signals for longitudinal and transverse bunched-beam diagnostics,

F. Caspers,Schottky signals for longitudinal and transverse bunched-beam diagnostics,

[8] [7]

M. Betz, O. Jones, T. Lefevre and M. Wendt,Bunched-beam schottky monitoring in the lhc,Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment874(2017) 113

2017