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MADGRAV: a multilevel anomaly-detection pipeline for gravitational-wave searches applied to LIGO data

Gianluca Inguglia, Huw Haigh, Ulyana Dupletsa, Alessandro Longo

arXiv:2609.39583v1gr-qcastro-ph.IMcs.LG

TL;DR

High-mass compact-binary signals can span only a few observable cycles, motivating searches less dependent on waveform templates. MADGRAV combines anomaly detection with CNN-based glitch classification, coherence testing, and candidate ranking on LIGO data; it reports 47 binary black hole mergers at calibrated FAR below 1 yr^-1. The authors conclude that anomaly-detection searches can be an independent, calibrated channel for massive black hole binary mergers.

  • Problem

    At high detector-frame masses, signals may span only a few observable cycles, and waveform features such as higher modes, precession, and eccentricity may be incompletely represented in search template banks.

    Source: §1 · p. 1

  • Method

    MADGRAV uses a convolutional autoencoder with minimal-template-bank weak supervision, plus CNN stages for glitch suppression and detector coherence.

    Source: §1 · p. 2, §2.1 · pp. 2–3

  • Results

    47 binary black hole mergers are detected at calibrated FAR < 1 yr^-1, with source-frame total masses spanning 14–236 M⊙ and median 69 M⊙.

    Source: §4 · p. 8, §6 · p. 13

  • Takeaways & Limitations

    The authors characterize anomaly-detection searches as an independent, calibrated detection channel for massive black hole binary mergers.

    Source: §6 · p. 14

    Above 100 M⊙, ranking statistics are the main cause of missed events; lowering the candidate floor would increase the FAR by admitting more background triggers.

    Source: §6 · p. 13

Abstract

from arXiv · show

We present the results of \textbf{MADGRAV}, a deep-learning-based search for high-mass compact binary coalescences, applied to the data collected by the LIGO interferometers during the third observing run and during the first and second part of the fourth observing run. The \textbf{MADGRAV} pipeline consists of a series of sequential convolutional neural networks that perform anomaly detection, glitch classification, coherence testing, and signal ranking. Data from the Hanford and Livingston LIGO detectors are studied (both individually and in coherence) by way of 1 second Q-transform windows. Of the candidates that survive every stage of the pipeline, 48 reach the significance threshold, and we report 47 gravitational wave detections characterised by a false alarm rate below $1\,{\rm yr}^{-1}$ with a probability of astrophysical origin $p_{\rm astro}>0.9$. Of the 47 detections, 44 are shared with the minimally modelled coherent WaveBurst search. The observed total source-frame masses, extracted from official gravitational wave transient catalogues, are in the $14-236 M_{\odot}$ range with a median of $69 M_{\odot}$, and a median SNR of 16. We note that the recovered fraction of confident detections rises with mass: for LIGO detectors network SNR $>10$ the pipeline recovers $8.1\%$ of confident catalog events below $30 M_{\odot}$, $39.8\%$ between $30$ and $100 M_{\odot}$, and $53.3\%$ above $100 M_{\odot}$, corresponding to $33.3\%$, $45.5\%$ and $53.3\%$ of the events detected by coherent WaveBurst in the same bins. These results suggest that anomaly detection pipelines can serve as an independent detection channel complementary to matched filtering in the high-mass high-SNR regime.

1 Introduction

High-mass compact-binary searches motivate weakly modelled approaches because signals may span only a few observable cycles and can include features incompletely represented in template banks. MADGRAV extends anomaly detection to real LIGO network data with additional CNN stages and detector-coherence testing.

1 Introduction

  • At sufficiently high detector-frame masses, signals may shrink to a few cycles in current observatories’ sensitive band, while higher modes, precession, and eccentricity may be incompletely represented in template banks.These features motivate unmodelled or weakly modelled searches; cWB played an important role in detecting GW190521 and GW231123.Source: §1 · p. 1
  • Existing machine-learning searches include template-trained methods and unsupervised or semi-supervised alternatives, including autoencoder anomaly searches and template-free coincidence training.The passage lists examples across convolutional and recurrent autoencoders, MLy, noise-only training, and inter-detector coincidence.Source: §1 · p. 1
  • MADGRAV adapts an earlier anomaly-detection pipeline to real LIGO data and adds CNN layers for glitch suppression and detector coherence.Its convolutional autoencoder uses a minimal template bank for weak supervision to flag potential signals as anomalies relative to typical detector noise.Source: §1 · p. 2

2 The MADGRAV pipeline

MADGRAV applies a frozen convolutional-autoencoder front end to whitened LIGO time–frequency tiles, then combines anomaly, glitch, coherence, and specialist-network information to rank candidates. Its models are trained on O3a data and applied without retraining to later observing runs.

2 The MADGRAV pipeline

  • The pipeline scans whitened strain from Hanford and Livingston using time–frequency representations and was adapted from an earlier convolutional-autoencoder pipeline for the two-detector network.The implementation was tested on real O3a, O3b, O4a, and O4b data.Source: §2 · p. 2

2.1 Architecture and training

  • The CAE uses an overcomplete 65,536-dimensional latent space, with reconstruction error on a pixel-registered map as its detection feature.Compression by up to a factor of four leaves detections and injection efficiency unchanged at fixed FAR, while stronger compression degrades them.Source: §2.1 · p. 2
  • The frozen CAE assigns per-detector anomaly scores to 1 s Q-transform tiles after noise-only training and signal-injection fine-tuning with a margin objective.The fine-tuning objective drives signal reconstruction error upward relative to noise; the model uses m = 3 and λ = 2.Source: §2.1 · pp. 2–3
  • The glitch arm scores detector tiles individually, while two gated specialist CNNs classify coincident tiles in 20–140 Hz and 50–500 Hz bands.The specialists target different frequency-dependent glitch morphologies; the cross-detector coherence statistic tests whether excess power is consistent between sites.Source: §2.1 · pp. 3–4

2.2 Detection flow

  • Candidates trigger when network excess significance exceeds 4.0, then receive a likelihood-ratio ranking from seven features before specialist gates and false-alarm-rate estimation.The statistic of record uses arm-conditioned background counting and an empirical calibration factor; the model and thresholds were frozen after O3a training and applied without retraining to O3b, O4a, and O4b.Source: §2.2 · p. 4, Figure 1 · p. 4

3 Blind search and significance estimation

The blind search scans coincident Hanford–Livingston data across O3a, O3b, O4a, and O4b, and assigns significance using time-slide backgrounds and calibrated false-alarm rates. Of the 48 candidates passing the raw threshold, 47 meet the reported FAR requirement.

3 Blind search and significance estimation

  • The foreground scan covers 442.9 days of coincident livetime across O3a, O3b, O4a, and O4b, with thresholds fixed before catalog cross-matching.The runs contribute 106.8, 96.4, 125.6, and 114.1 days, respectively.Source: §3 · p. 5
  • Candidates are ranked against time-slide backgrounds from their own indexed subset, while the likelihood-ratio model is fitted only on the other subset.Background livetimes per subset range from 266 to 623 years; the method avoids scoring a candidate or background trigger with a model that has previously seen it.Source: §3 · p. 5
  • The injection campaigns use three waveform banks spanning detector-frame total masses from 10 to 400 M⊙ and are importance-weighted to a uniform-in-volume distance prior.Campaigns include 122,850, 70,200, 58,500, and 70,200 scored injections in O3a, O3b, O4a, and O4b, respectively.Source: §3 · p. 5
  • The glitch arm gate passes all 48 candidates and removes 37% of background families that set the FARs, equivalent to 40% of the summed louder-family counts.Source: §3 · p. 6
  • The adopted statistic has calibration K = 5.60, 4.59, 1.43, and 3.62 for O3a, O3b, O4a, and O4b, respectively.A single-channel rank gives K = 1.00 in all four runs; the larger adopted-statistic values primarily reflect arm-conditioned counting, with a further factor from taking the minimum across channels.Source: §3 · p. 6
  • 47 of the 48 candidates passing the raw threshold have calibrated FAR below 1 yr^-1.The paper reports FAR as its primary significance and also computes an astrophysical-origin probability using run-specific injection signal densities and an analytic noise density.Source: §3 · p. 6

4 Results

MADGRAV reports 47 detections at calibrated FAR < 1 yr^-1, all with p_astro > 0.90, and the recovered fraction rises with mass. Its sensitive volume–time peaks near 100–130 M⊙, while injection recovery plateaus below unity.

4 Results

  • 47 detections pass calibrated FAR < 1 yr^-1, with 46.5 ± 4.1 predicted and all 47 having p_astro > 0.90.Counts by run are 9, 4, 15, and 19 in O3a, O3b, O4a, and O4b, respectively.Source: §4 · pp. 6, 8
  • Injection recovery reaches 50% near ρnet ≃15–20 and plateaus at 0.86–0.97, so even the loudest injections are not all recovered.Table 1 reports run-average recovery fractions over the injected mass mix.Source: §4 · p. 6, Table 1 · p. 8
  • Table 2 compares detections found with detections predicted, evaluating each event at its own (Mtot, ρnet) cell; uncertainties are Poisson-binomial.Source: Table 2 · p. 8
  • Across the catalog, recovered fractions rise from 5.6% below 30 M⊙ to 33.3% above 100 M⊙; detected source-frame masses span 14–236 M⊙, with median 69 M⊙.The recovery denominators are the 232 confident events observed by H1 and L1 simultaneously.Source: §4 · p. 8
  • For H1+L1 network SNR > 10, recovery is 8.1% below 30 M⊙, 39.8% at 30–100 M⊙, and 53.3% above 100 M⊙.These correspond to 33.3%, 45.5%, and 53.3% of cWB detections in the same mass bins.Source: §4 · p. 10

4.1 Sensitive volume–time

  • Sensitive volume–time peaks near Mtot ≈100–130 M⊙; predicted O4 detections are 63% of the total versus an observed 34/47 = 72%.The estimates weight injection recovery under the adopted detection criterion for a population uniform in comoving volume.Source: §4.1 · pp. 10–11, Figure 4 · p. 11
  • The 400 M⊙ detector-frame bank ceiling starves source-frame 330–400 M⊙ bins at the horizons, so those points are omitted and 260–330 M⊙ values are lower bounds.The stated horizon redshifts are approximately 0.3–0.5.Source: §4.1 · p. 11

5 Comparison with existing searches

MADGRAV’s injection-based sensitive volume-time approaches existing searches at the upper end of its target mass range, while its catalog detections are mostly shared with cWB. Catalog-count and sensitive-volume comparisons differ because they measure populations with different SNR distributions.

5 Comparison with existing searches

  • Of 47 MADGRAV detections, 44 are shared with cWB; the MADGRAV set is a subset of cWB’s, with three exceptions.The 47 detections equal 17% of the full catalog population and 39% of cWB’s count; these full-catalog fractions are conservative lower bounds because some events fall outside scanned coincident segments or lack H1+L1 coincidence.Source: §5 · p. 12
  • In O3a, MADGRAV’s sensitive-volume-time ratio is 0.54–1.28 of matched-filter pipelines and 0.63–1.05 of cWB at 100–160 M⊙; at 160–200 M⊙, it is 2.9–4.4 versus all except PyCBC-BBH.The comparison uses matched FAR and reweighted LVK sensitivity-injection releases; external O3 IMBH benchmarks retain their own conventions.Source: Figure 5 · p. 12, §5 · pp. 12–13
  • The comparison drops injections that limit ratios below 20 and above 230 M⊙; 260–330 M⊙ estimates are lower bounds under the bank ceiling.The high-mass lower-bound caveat applies to Fig. 5 and the corresponding sensitive-volume-time results.Source: §5 · pp. 12–13
  • In O3b, MADGRAV’s sensitive-volume-time ratio is 0.16–0.45 below 100 M⊙ and 0.45–1.12 at 100–160 M⊙, closing most of the gap at the top.The reported ratios compare MADGRAV with matched-filter pipelines and cWB at matched FAR.Source: §5 · p. 13
  • Below 100 M⊙, catalog-count ratios exceed sensitive-volume-time ratios in O4 because catalogs condition on detected events (median network SNR 9.9–10.6), unlike volume-weighted injections (median SNR 7.0).For Mtot ≥20 M⊙, reported efficiency ranges from 0.05–0.09 at network SNR 10 to 0.68–0.76 at 20.Source: §5 · p. 13
  • In O4, sensitive-volume-time ratios are 0.07–0.20 below 100 M⊙, peak at 0.20–0.30 at 100–160 M⊙, and fall to 0.13–0.22 by 200–260 M⊙.With corrected reference spectra, the paper attributes the deficit to the search itself rather than solely to its spectra.Source: §5 · p. 13
  • For comparable catalog events, summed per-cell recovery probabilities broadly agreed across O3a–O4b: predictions of 7.8, 4.0, 11.6, and 23.2 versus 9, 4, 15, and 18 found yielded ratios 0.86, 1.00, 0.77, and 1.29.Source: §5 · p. 13

6 Discussion and outlook

MADGRAV, trained on O3a and frozen for testing through O4b, detects 47 binary black hole mergers at calibrated FAR < 1 yr^-1, with no detections lacking catalog counterparts. Misses arise at both triggering and ranking stages, motivating targeted pipeline changes.

6 Discussion and outlook

  • 47 binary black hole mergers were detected at calibrated FAR < 1 yr^-1, with zero detections lacking a catalog counterpart.The pipeline was trained on O3a data and frozen before tests spanning O3a to O4b.Source: §6 · p. 13
  • Of 139 confident catalog events with Mtot > 10 M⊙ and ρH1+L1 > 10, MADGRAV recovered 47 and missed 92 despite scanning every event segment.Sixty-two misses never triggered; 24 triggered but fell below the ln Λ = 4.0 candidate floor; of the remaining six, two were rejected as glitches or had FAR above threshold.Source: §6 · p. 13
  • Miss mechanisms vary by mass: below 30 M⊙, 29/32 misses never trigger; above 100 M⊙, ranking is the main cause.Between 30 and 100 M⊙, 31 misses never trigger and 20 are lost to ranking; above 100 M⊙, 2 of 7 fail at trigger level.Source: §6 · p. 13
  • Lowering the ln Λ candidate floor would not necessarily recover ranking-limited events and would increase background triggers, raising FAR.At ln Λ ≥3, the background would have 2–3 times more triggers, requiring the time-slide background to be regenerated at the lowered threshold.Source: §6 · p. 13
  • Combining detector scores before thresholding targets the two-thirds of misses that never trigger; improved CNN training and mass-specific optimization are also proposed.The proposed CNN stage would use real data and simulated glitches; latent-space optimization per mass region may particularly help lower-mass recovery.Source: §6 · p. 14
  • Pipeline features contributing to ln Λ could be combined in a gradient algorithm to seek a hyperplane separating signals from glitches or noise [47].The authors conclude that anomaly-detection searches are an independent, calibrated channel for massive black hole binary mergers.Source: §6 · p. 14

A Different latent space compressions

The compression tests compare bottleneck widths at matched false-alarm rate against the frozen model. Compression up to a factor of four preserves detections and overall injection efficiency, while stronger compression can reduce efficiency or dynamic range.

A Different latent space compressions

  • The comparison retrains on an independent draw of 32 O3a blocks and evaluates all models at matched FAR after common noise-window re-standardization.Bottlenecks k = 32, 20, 13, and 1 correspond to compression factors 4, 6.4, 9.8, and 128.Source: A Different latent space compressions · p. 14
  • At matched threshold, margin-trained models down to k = 13 trigger on all 47 detections and the same 83 catalog events as the frozen model.The k = 32 model adds one below-floor event, GW230609 064958; the unsupervised stage alone triggers on at most 3 of 136 catalog events at any width.Source: A Different latent space compressions · p. 14, Table 4 · p. 15
  • For k = 32, recovered fraction stays within one percentage point of the frozen model overall and within two points in every mass range, matching it from ρnet = 60.The only deficit is 4 points at ρnet = 10–12 for Mtot ≥100 M⊙; Figure 6 presents trigger-level injection recovery versus network SNR by mass stratum and bottleneck width.Source: A Different latent space compressions · p. 14, Figure 6 · p. 15
  • At k = 13, overall recovery matches but a 10^-4 noise-pair tail requires σnet = 9.6, versus 6.1 for the frozen model and 5.4 for k = 32.At k = 1, nothing is recovered below ρnet = 20 for Mtot > 22 M⊙, while recovery exceeds the frozen model below 22 M⊙.Source: A Different latent space compressions · p. 15
  • Compression up to a factor of four does not affect detection counts or overall efficiency; beyond factor 6 efficiency falls, and beyond factor 10 dynamic range is affected.The separation of signals and noise comes from the margin objective, not latent-space size; the same architecture trained jointly from the first epoch or with only the unsupervised stage does not recover catalog events.Source: A Different latent space compressions · p. 15

B Validation and calibration checks

The validation checks assess reference-spectrum consistency, efficiency systematics, empirical null calibration, and background construction. They find calibrated zero-lag counts after the consistency veto and generally small changes when foreground windows are excised.

B Validation and calibration checks

  • Reference spectra rebuilt from full-run GWOSC strain reproduce published BNS inspiral ranges for all four runs to 0.94–1.06.They set injection amplitudes and horizons and use a 4 s transform with 0.25 Hz resolution.Source: B Validation and calibration checks · p. 15
  • Efficiency ratios on 25 event-free segments range from 1.50 at 20–40 M⊙ to 1.00 above 200 M⊙ in O3a, so no correction is applied.O3b ratios are 0.88–0.99 and O4 ratios 1.00–1.13; the relative ⟨VT⟩ systematic falls from 0.62 to 0.04 across the stated O3a mass ranges and from 0.21 to 0.01 in O3b.Source: B Validation and calibration checks · p. 15
  • The pseudo-foreground calibration factor K is 5.60, 4.59, 1.43, and 3.62 in O3a, O3b, O4a, and O4b, respectively.The glitch-arm gate removes glitch pairs dominating the O4 pseudo-foreground, reducing K in glitch-dominated runs; the single-channel unconditioned rank gives K = 1.00 in all four runs.Source: B Validation and calibration checks · p. 15
  • After the consistency veto, two unmatched triggers remain at 2.4 and 4.7 yr^-1, and none remain below 1 yr^-1, consistent with a calibrated statistic.Before the veto, four unmatched zero-lag triggers had FAR < 1 yr^-1; the post-veto counts are consistent with approximately three expected below 5 yr^-1 and 0.6 below 1 yr^-1 in 0.61 years.Source: B Validation and calibration checks · p. 15
  • Inclusive and foreground-excluded background FARs agree to 5 × 10^-5 yr^-1 for all but eight events, while K shifts by less than 0.61 in every run.One O4b detection, GW240406 062847, rises above 1 yr^-1 under the inclusive background; the largest K shift is in O4a, where the gate leaves few glitch families in the pseudo-foreground.Source: B Validation and calibration checks · p. 16

C Construction of pastro

The paper estimates astrophysical-origin probabilities with a per-run two-component Poisson mixture fitted to foreground-excluded FARs. Signal densities come from injections passing the same detection chain, while noise counts are pinned to their time-slide null expectation.

C Construction of pastro

  • The two-component Poisson mixture fits only Λs, pinning Λn to its null expectation because 4–19 candidates per run cannot constrain a free noise count.The fit uses per-arm foreground-excluded FAR x = FARexcl before calibration factor K on x ∈ [0, 1 yr^-1]; K enters only the admission rule for candidates and injections.Source: C Construction of pastro · p. 16
  • Signal density ps is the histogram of candidate FARs from per-run injections that pass the identical chain, gate, veto, and per-arm counting.Injections are weighted uniformly in comoving volume and reweighted to the published catalog total-mass distribution; intervals use 5–95% ranges over 200 bootstrap replicates.Source: C Construction of pastro · p. 16
  • Pinned noise counts Λn are 0.146, 0.132, 0.172, and 0.156 across O3a–O4b, versus fitted Λs of 8.98, 3.99, 14.91, and 18.89.The resulting mixture is signal-dominated by two orders of magnitude.Source: C Construction of pastro · p. 16
  • Under the mixture, pastro decreases monotonically with FAR and cannot reorder candidates or add detections beyond the FAR threshold.Floating Λn changes the lowest probability among the 47 detections from 0.913 to 0.970; multiplying Λn by K leaves 42 detections above 0.95, while two named detections fall to 0.83 and 0.88.Source: C Construction of pastro · p. 16
  • When signal density reaches the injection campaign floor, the reported probability is an upper bound; GW190521 030229 has pastro < 10^-3.The probability for each event is computed from the fitted signal and noise components as a two-component mixture.Source: C Construction of pastro · p. 16

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