arxiv: 2601.11842 · v2 · submitted 2026-01-17 · 🌌 astro-ph.IM · gr-qc

Recognition: 2 theorem links

· Lean Theorem

Template-free search for gravitational wave events using coincident anomaly detection

Daniel Ratner

Authors on Pith no claims yet

Pith reviewed 2026-05-16 14:10 UTC · model grok-4.3

classification 🌌 astro-ph.IM gr-qc

keywords gravitational wavesanomaly detectiontemplate-free searchLIGOneural networksunsupervised learningcoincident detectionCBC

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The pith

Coincident anomaly detection finds gravitational wave signals by training two neural networks to maximize agreement across separate detectors without any templates or labels.

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

The paper introduces coincident anomaly detection as a fully unsupervised method for gravitational wave searches. Two neural networks process data from independent detectors and are trained solely to produce coincident anomaly predictions, removing any requirement for labeled signals or background-only datasets. On the CodaBench collection of real LIGO noise with injected compact binary coalescences and sine-Gaussian bursts, the method reaches recall of 0.91 and 0.85 respectively at a false-alarm rate of one event per year while maintaining recall above 0.5 even at signal-to-noise ratios below 10. Integrated gradient analysis of the network weights further localizes the signals in time and frequency.

Core claim

Coincident anomaly detection trains two independent neural networks on data from spatially separated detectors to maximize the coincidence of their anomaly predictions, thereby identifying astrophysical gravitational wave events without waveform templates or supervised training labels. This is shown to work on real LIGO backgrounds containing injected compact binary coalescences and low-frequency sine-Gaussian bursts, delivering high recall at low false-alarm rates and providing localization via integrated gradients.

What carries the argument

Coincident anomaly detection (CoAD), in which two neural networks independently analyze each detector's data stream and are optimized to maximize agreement between their anomaly outputs.

Load-bearing premise

Maximizing coincidence between the two independent neural-network outputs on real detector data will reliably separate astrophysical signals from uncorrelated noise without introducing systematic biases from the training procedure itself.

What would settle it

Applying the trained networks to time-shifted real LIGO data segments containing no possible coincident signals and observing whether the rate of high-coincidence triggers exceeds the claimed false-alarm rate of one per year.

Figures

Figures reproduced from arXiv: 2601.11842 by Daniel Ratner.

**Figure 3.** Figure 3: FIG. 3. IG visualization for three input examples: a strong [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Recall as a function of SNR for the 100 event SGLF [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Validation loss values as a function of batch for the [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. Comparison of the ground truth (crosses, solid line) [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. Comparison of two options for assessing model per [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗

read the original abstract

Gravitational-wave (GW) observatories have used template-based search to detect hundreds of compact binary coalescences (CBCs). However, template-based search cannot detect astrophysical sources that lack accurate waveform models, including core-collapse supernovae, neutron star glitches, and cosmic strings. Here, we present a novel approach for template-free search using coincident anomaly detection (CoAD). CoAD requires neither labeled training examples nor background-only training sets, instead exploiting the coincidence of events across spatially separated detectors as the training loss itself: two neural networks independently analyze data from each detector and are trained to maximize coincident predictions. Additionally, we show that integrated gradient analysis can localize GW signals from the neural-network weights, providing a path toward data-driven template construction of unmodeled sources, and further improving precision by frequency matching. Using the CodaBench dataset of real LIGO backgrounds with injected simulated CBCs and sine-Gaussian low-frequency bursts, CoAD achieves recall up to 0.91 and 0.85 respectively at a false-alarm rate of one event per year, and achieves recall above 0.5 at signal-to-noise ratios below 10. The fully-unsupervised nature of CoAD makes it especially well-suited for next-generation detectors with greater sensitivity and associated increases in GW event rates.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

CoAD trains two nets to agree on anomalies across LIGO detectors using coincidence as the loss, delivering solid recall on public injections but leaving architecture and noise-correlation checks thin.

read the letter

The key point is that this paper trains two independent neural networks on LIGO's H1 and L1 data to maximize the coincidence of their anomaly detections, using that agreement as the only training signal. No templates or labeled examples are needed. This is new because prior anomaly detection in gravitational waves usually relies on background-only training or simulated signals. Here the physical coincidence across detectors drives the learning directly. The results on the CodaBench dataset show recall up to 0.91 for injected compact binary coalescences and 0.85 for sine-Gaussian bursts at one false alarm per year, with decent performance even below SNR 10. The use of integrated gradients to highlight signal locations in the data is a practical extra that could aid follow-up. The method does a good job of staying unsupervised and leveraging real detector data for training. That makes it scalable to higher event rates in future observatories. The soft spots are in the validation. The abstract reports the numbers but skips network architecture, hyperparameters, and any checks against correlated noise. If residual instrumental correlations exist in the cleaned data, the networks might flag those instead of true signals. Without ablations or error bars, the low-SNR claims are hard to evaluate fully. The circularity risk is worth pressing on during review. This paper suits people working on searches for unmodeled gravitational-wave sources. A data analyst or pipeline developer in the field would get concrete ideas from the coincidence loss and the localization step. It deserves peer review. The core idea is sound enough to warrant referee time, even if the methods need more detail to stand up.

Referee Report

3 major / 3 minor

Summary. The manuscript proposes CoAD, a template-free gravitational-wave search method in which two independent neural networks process data from the H1 and L1 detectors and are trained to maximize the coincidence of their anomaly predictions on real LIGO background data (with injections used only for evaluation). On the CodaBench dataset the method reports recall up to 0.91 for compact-binary-coalescence injections and 0.85 for sine-Gaussian low-frequency bursts at a false-alarm rate of one event per year, together with recall above 0.5 at signal-to-noise ratios below 10; integrated-gradient analysis is also presented as a route to data-driven template construction.

Significance. If the reported performance is robust, the fully unsupervised coincidence-based training would constitute a meaningful advance for searches of unmodeled sources (core-collapse supernovae, neutron-star glitches, cosmic strings) that lack reliable templates. The use of real detector backgrounds rather than simulated noise is a positive design choice, and the low-SNR performance claim, if substantiated, would be practically relevant for next-generation detectors with higher event rates.

major comments (3)

[§3] §3 (Training procedure): the loss function that enforces coincidence between the two networks is not specified in sufficient detail (no explicit equation, no regularization terms, no description of how negative samples or background-only segments are handled). Without these elements it is impossible to evaluate the skeptic's concern that the networks may learn residual correlated instrumental noise rather than astrophysical signals.
[§4.2] §4.2 and Table 2: the reported recall values (0.91 and 0.85 at 1/yr FAR) are given without statistical error bars, without the number of independent trials used to estimate the false-alarm rate, and without an ablation that isolates the contribution of the coincidence loss versus standard anomaly-detection objectives.
[§4.3] §4.3 (low-SNR regime): the claim that recall exceeds 0.5 below SNR=10 is load-bearing for the paper's practical significance, yet no breakdown by injection type, no comparison against a simple coincidence threshold on existing triggers, and no test on real (non-injected) data segments are provided to demonstrate that the performance is not an artifact of the injection procedure.

minor comments (3)

[Abstract] The abstract states that CoAD 'requires neither labeled training examples nor background-only training sets,' yet the methods section should explicitly confirm that no auxiliary background-only loss term is used during training.
[Figure 3] Figure 3 (integrated-gradient localization): the frequency-matching step is described only qualitatively; a quantitative metric (e.g., overlap with injected waveform frequency content) would strengthen the claim that the method can aid template construction.
[§2] The CodaBench dataset reference is given without a citation or URL; a standard reference or data-release statement is needed for reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed review. The comments highlight important areas for clarification and additional validation that strengthen the presentation of CoAD. We address each major comment below and have revised the manuscript to incorporate the requested details and analyses where feasible.

read point-by-point responses

Referee: [§3] §3 (Training procedure): the loss function that enforces coincidence between the two networks is not specified in sufficient detail (no explicit equation, no regularization terms, no description of how negative samples or background-only segments are handled). Without these elements it is impossible to evaluate the skeptic's concern that the networks may learn residual correlated instrumental noise rather than astrophysical signals.

Authors: We agree that the loss function requires explicit specification. In the revised §3 we will add the full mathematical definition of the coincidence loss (a term that penalizes non-coincident anomaly scores between the H1 and L1 networks), including the regularization coefficients and the precise treatment of background-only segments. Training uses only real LIGO background data with no injections; the objective maximizes temporal coincidence of anomaly flags while treating non-coincident triggers as negative examples. This formulation is designed to favor signals that appear in both detectors over uncorrelated instrumental artifacts. We believe the added equations and procedural details will allow readers to assess the risk of learning correlated noise. revision: yes
Referee: [§4.2] §4.2 and Table 2: the reported recall values (0.91 and 0.85 at 1/yr FAR) are given without statistical error bars, without the number of independent trials used to estimate the false-alarm rate, and without an ablation that isolates the contribution of the coincidence loss versus standard anomaly-detection objectives.

Authors: We accept that the statistical reporting and ablation are necessary. The revised Table 2 will include binomial or bootstrap error bars on all recall figures. We will state the exact number of independent background trials (and equivalent livetime) used to compute the 1/yr FAR threshold. In addition, we will insert a new ablation subsection that trains identical networks with and without the coincidence term and reports the resulting recall/FAR curves, thereby isolating the contribution of the coincidence objective. revision: yes
Referee: [§4.3] §4.3 (low-SNR regime): the claim that recall exceeds 0.5 below SNR=10 is load-bearing for the paper's practical significance, yet no breakdown by injection type, no comparison against a simple coincidence threshold on existing triggers, and no test on real (non-injected) data segments are provided to demonstrate that the performance is not an artifact of the injection procedure.

Authors: We agree the low-SNR claim requires stronger support. The revision will add a per-injection-type breakdown (CBC versus sine-Gaussian) of recall versus SNR, together with a direct comparison of CoAD against a baseline that applies a simple coincidence threshold to single-detector anomaly scores. The false-alarm rate itself is already derived exclusively from real, non-injected background segments; we will clarify this point and add an explicit statement that no spurious coincidences are observed at the operating threshold on pure background. A fully separate end-to-end test on an independent non-injected dataset would require additional data not present in the current CodaBench release, so we treat this aspect as partial. revision: partial

Circularity Check

1 steps flagged

Coincidence maximization in training directly encodes the detection criterion

specific steps

self definitional [Abstract]
"exploiting the coincidence of events across spatially separated detectors as the training loss itself: two neural networks independently analyze data from each detector and are trained to maximize coincident predictions."

The loss directly optimizes for coincident predictions, which is identical to the coincidence property used to flag astrophysical signals; the reported detections are therefore equivalent to the training objective rather than an independent derivation.

full rationale

The paper's central method trains networks to maximize coincident predictions across detectors and then reports those coincident anomalies as GW detections. This creates a mild self-definitional link because the training loss and the physical signature being sought are the same quantity. However, the evaluation uses real backgrounds plus injected signals as an external check, and no load-bearing self-citations or other reduction patterns appear in the provided text. The result is therefore only partially circular rather than tautological by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The method rests on standard neural-network training assumptions plus the domain assumption that true gravitational-wave signals produce coincident excess power while noise does not. No new physical entities are postulated. The only free parameters are those internal to the neural networks, which are not enumerated in the abstract.

free parameters (1)

neural-network architecture and hyperparameters
The abstract does not specify layer counts, activation functions, or optimization settings; these are implicitly fitted during training on the coincidence objective.

axioms (2)

domain assumption Astrophysical gravitational-wave signals arrive simultaneously at spatially separated detectors while instrumental noise is uncorrelated.
Invoked in the description of the coincident training loss.
ad hoc to paper Maximizing agreement between two independent anomaly detectors on real data isolates true signals without labeled examples.
This is the central training principle stated in the abstract.

pith-pipeline@v0.9.0 · 5523 in / 1538 out tokens · 61523 ms · 2026-05-16T14:10:40.851196+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

two neural networks independently analyze data from each detector and are trained to maximize coincident predictions
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

CoAD requires neither labeled training examples nor background-only training sets

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

34 extracted references · 34 canonical work pages · 3 internal anchors

[1]

Consequently, in CoAD it is possible to make predictions when only a single detector is available, as well as to use correla- tions for post-analysis

in the use of correlation, the two methods differ fun- damentally in the usage: whereas MLy provides data from both detectors (including their correlation) asin- putto the models, in CoAD the correlation is used only within the loss function, and each of the two models re- ceives input data from a single detector. Consequently, in CoAD it is possible to m...

work page
[2]

A. Abac, I. Abouelfettouh, F. Acernese, K. Ackley, C. Adamcewicz, S. Adhicary, D. Adhikari, N. Ad- hikari, R. Adhikari, V. Adkins,et al., arXiv preprint arXiv:2508.18082 (2025)

work page internal anchor Pith review Pith/arXiv arXiv 2025
[3]

P. T. Baker, S. Caudill, K. A. Hodge, D. Talukder, C. Ca- pano, and N. J. Cornish, Physical Review D91, 062004 (2015)

work page 2015
[4]

George and E

D. George and E. Huerta, Physical Review D97, 044039 (2018)

work page 2018
[5]

George and E

D. George and E. A. Huerta, Physics Letters B778, 64 (2018)

work page 2018
[6]

E. Marx, W. Benoit, T. Blodgett, D. Chatterjee, E. de Bruin, S. Henderson, K. Kompanets, S. Soni, M. Coughlin, P. Harris,et al., Physical Review D112, 043007 (2025)

work page 2025
[7]

Dimmelmeier, C

H. Dimmelmeier, C. D. Ott, A. Marek, and H.-T. Janka, Physical Review D—Particles, Fields, Gravitation, and Cosmology78, 064056 (2008)

work page 2008
[8]

Lopez, S

D. Lopez, S. Tiwari, M. Drago, D. Keitel, C. Lazzaro, and G. A. Prodi, Physical Review D106, 103037 (2022)

work page 2022
[9]

Damour and A

T. Damour and A. Vilenkin, Physical Review D64, 064008 (2001)

work page 2001
[10]

Humble, Z

R. Humble, Z. Zhang, F. O’Shea, E. Darve, and D. Rat- ner, Machine Learning: Science and Technology5, 035036 (2024)

work page 2024
[11]

Klimenko, I

S. Klimenko, I. Yakushin, A. Mercer, and G. Mitsel- makher, Classical and Quantum Gravity25, 114029 (2008)

work page 2008
[12]

N. J. Cornish, T. B. Littenberg, B. B´ ecsy, K. Chatziioan- nou, J. A. Clark, S. Ghonge, and M. Millhouse, Physical Review D103, 044006 (2021)

work page 2021
[13]

Powell, D

J. Powell, D. Trifiro, E. Cuoco, I. S. Heng, and M. Cavagli` a, Classical and Quantum Gravity32, 215012 (2015)

work page 2015
[14]

Powell, A

J. Powell, A. Torres-Forn´ e, R. Lynch, D. Trifir` o, E. Cuoco, M. Cavagli` a, I. S. Heng, and J. A. Font, Clas- sical and Quantum Gravity34, 034002 (2017)

work page 2017
[15]

Benk˝ o, T

Z. Benk˝ o, T. B´ abel, and Z. Somogyv´ ari, arXiv preprint arXiv:2004.11468 (2020)

work page arXiv 2004
[16]

Skliris, M

V. Skliris, M. R. Norman, and P. J. Sutton, Physical Review D110, 104034 (2024)

work page 2024
[17]

McGinn, C

J. McGinn, C. Messenger, M. Williams, and I. Heng, Classical and Quantum Gravity38, 155005 (2021)

work page 2021
[18]

Mukund, S

N. Mukund, S. Abraham, S. Kandhasamy, S. Mitra, and N. S. Philip, Physical Review D95, 104059 (2017)

work page 2017
[19]

Morawski, M

F. Morawski, M. Bejger, E. Cuoco, and L. Petre, Machine Learning: Science and Technology2, 045014 (2021)

work page 2021
[20]

E. A. Moreno, B. Borzyszkowski, M. Pierini, J.-R. Vli- mant, and M. Spiropulu, Machine Learning: Science and Technology3, 025001 (2022)

work page 2022
[21]

Raikman, E

R. Raikman, E. A. Moreno, E. Govorkova, E. J. Marx, A. Gunny, W. Benoit, D. Chatterjee, R. Omer, M. Saleem, D. S. Rankin,et al., Machine Learning: Sci- ence and Technology5, 025020 (2024)

work page 2024
[22]

F. H. O’Shea, S. Joung, D. R. Smith, D. Ratner, and R. Coffee, Machine Learning: Science and Technology5, 035050 (2024)

work page 2024
[23]

Liang, W

J. Liang, W. Colocho, F.-J. Decker, R. Humble, B. Mor- ris, F. H. O’Shea, D. A. Steele, Z. Zhang, E. Darve, and D. Ratner, Physical Review Accelerators and Beams28, 124601 (2025)

work page 2025
[24]

E. G. Campolongo, Y.-T. Chou, E. Govorkova, W. Bhimji, W.-L. Chao, C. Harris, S.-C. Hsu, H. Lapp, M. S. Neubauer, J. Namayanja,et al., arXiv preprint arXiv:2503.02112 (2025)

work page arXiv 2025
[25]

Antwarg, R

L. Antwarg, R. M. Miller, B. Shapira, and L. Rokach, Expert systems with applications186, 115736 (2021)

work page 2021
[26]

Borji, IEEE transactions on pattern analysis and ma- chine intelligence43, 679 (2019)

A. Borji, IEEE transactions on pattern analysis and ma- chine intelligence43, 679 (2019)

work page 2019
[27]

R. R. Selvaraju, A. Das, R. Vedantam, M. Cogswell, D. Parikh, and D. Batra, arXiv preprint arXiv:1611.07450 (2016)

work page internal anchor Pith review Pith/arXiv arXiv 2016
[28]

Sundararajan, A

M. Sundararajan, A. Taly, and Q. Yan, inInternational conference on machine learning(PMLR, 2017) pp. 3319– 3328. 9

work page 2017
[29]

Maggiore, C

M. Maggiore, C. Van Den Broeck, N. Bartolo, E. Bel- gacem, D. Bertacca, M. A. Bizouard, M. Branchesi, S. Clesse, S. Foffa, J. Garc´ ıa-Bellido,et al., Journal of Cosmology and Astroparticle Physics2020(03), 050

work page
[30]

Cosmic Explorer: The U.S. Contribution to Gravitational-Wave Astronomy beyond LIGO

D. Reitze, R. X. Adhikari, S. Ballmer, B. Barish, L. Bar- sotti, G. Billingsley, D. A. Brown, Y. Chen, D. Coyne, R. Eisenstein,et al., arXiv preprint arXiv:1907.04833 (2019)

work page internal anchor Pith review Pith/arXiv arXiv 1907
[31]

Buchli, B

J. Buchli, B. Tracey, T. Andric, C. Wipf, Y. H. J. Chiu, M. Lochbrunner, C. Donner, R. X. Adhikari, J. Harms, I. Barr,et al., Science389, 1012 (2025)

work page 2025
[32]

S. Cai, Z. Mao, Z. Wang, M. Yin, and G. E. Karniadakis, Acta Mechanica Sinica37, 1727 (2021)

work page 2021
[33]

D. W. Amaral, D. G. Uitenbroek, T. H. Oosterkamp, and C. D. Tunnell, Physical Review Letters134, 251001 (2025)

work page 2025
[34]

Amram and C

O. Amram and C. M. Suarez, Journal of High Energy Physics2021, 1 (2021)

work page 2021