Glitches: Definitions in Pulsars, GW & ML

• Glitches are abrupt departures from expected behavior, manifesting as sudden spin-up events in pulsars, transient noise in GW detectors, and local oscillations in decision-tree outputs.
• In pulsar timing, glitches are modeled as permanent steps with decaying recovery components, providing insights into neutron star interiors via quantified metrics like recovery fraction Q and timescales.
• Glitches in gravitational-wave detectors and ML systems are mitigated through CNN classification, Bayesian inference, and mixed-integer programming to preserve signal integrity and model robustness.

Across the literatures summarized here, glitch is a domain-specific technical term rather than a single phenomenon. In pulsar astronomy, it denotes a sudden spin-up event that punctuates secular spin-down and is often accompanied by changes in $\dot{\nu}$ and post-glitch recovery (Haskell et al., 2015). In gravitational-wave detector characterization, it denotes a transient, non-Gaussian burst of noise in the strain data stream, typically lasting less than a few seconds and arising from instrumental or environmental causes (Glanzer et al., 2022). In decision-tree ensembles, it denotes a small neighborhood in input space where the model output abruptly oscillates under a monotonic change in one feature (Chandra et al., 19 Jul 2025). The common vocabulary reflects abrupt departures from smooth or expected behavior, but the governing observables, models, and scientific implications differ sharply across these domains.

1. Formal definitions and representations

In pulsar timing, the standard phase model is

$$\phi(t)=\phi_{0}+\nu(t-t_{0})+\frac{1}{2}\dot{\nu}(t-t_{0})^{2}+\frac{1}{6}\ddot{\nu}(t-t_{0})^{3},$$

and a glitch is modeled as a combination of permanent steps and a decaying component. One representation is

$$\nu(t)=\nu_{0}(t)+\Delta\nu_{p}+\Delta\dot{\nu}_{p}t+\Delta\nu_{d}e^{-t/\tau_{d}},$$

with total frequency jump $\Delta\nu_g=\Delta\nu_{p}+\Delta\nu_{d}$ and recovery fraction

$Q=\Delta\nu_{d}/\Delta\nu_g.$

The instantaneous change in spin-down rate is

$$\Delta\dot{\nu}_g = \Delta\dot{\nu}_{p} - Q\Delta\nu_g/\tau_{d}.$$

This formalism distinguishes permanent changes in $\nu$ and $\dot{\nu}$ from transient relaxation, and it underlies most of the timing analyses in the pulsar literature summarized here (Yuan et al., 2010).

In gravitational-wave data analysis, a glitch is defined as a transient, non-Gaussian burst of noise in the strain channel. Gravity Spy operationalizes this by using Omicron to find transient excess-power events, converting each event into Omega scans at $0.5\ \mathrm{s}$, $1\ \mathrm{s}$, $$\phi(t)=\phi_{0}+\nu(t-t_{0})+\frac{1}{2}\dot{\nu}(t-t_{0})^{2}+\frac{1}{6}\ddot{\nu}(t-t_{0})^{3},$$0, and $$\phi(t)=\phi_{0}+\nu(t-t_{0})+\frac{1}{2}\dot{\nu}(t-t_{0})^{2}+\frac{1}{6}\ddot{\nu}(t-t_{0})^{3},$$1, and classifying the resulting time-frequency morphology with a convolutional neural network. In the O3 configuration, the model used $$\phi(t)=\phi_{0}+\nu(t-t_{0})+\frac{1}{2}\dot{\nu}(t-t_{0})^{2}+\frac{1}{6}\ddot{\nu}(t-t_{0})^{3},$$2 classes and assigned each event the class of highest confidence $$\phi(t)=\phi_{0}+\nu(t-t_{0})+\frac{1}{2}\dot{\nu}(t-t_{0})^{2}+\frac{1}{6}\ddot{\nu}(t-t_{0})^{3},$$3, with $$\phi(t)=\phi_{0}+\nu(t-t_{0})+\frac{1}{2}\dot{\nu}(t-t_{0})^{2}+\frac{1}{6}\ddot{\nu}(t-t_{0})^{3},$$4 used as the fiducial threshold (Glanzer et al., 2022).

In decision-tree ensembles, a glitch has an explicitly local and ordered definition. For a model $$\phi(t)=\phi_{0}+\nu(t-t_{0})+\frac{1}{2}\dot{\nu}(t-t_{0})^{2}+\frac{1}{6}\ddot{\nu}(t-t_{0})^{3},$$5, a triple $$\phi(t)=\phi_{0}+\nu(t-t_{0})+\frac{1}{2}\dot{\nu}(t-t_{0})^{2}+\frac{1}{6}\ddot{\nu}(t-t_{0})^{3},$$6 ordered along dimension $$\phi(t)=\phi_{0}+\nu(t-t_{0})+\frac{1}{2}\dot{\nu}(t-t_{0})^{2}+\frac{1}{6}\ddot{\nu}(t-t_{0})^{3},$$7 is an $$\phi(t)=\phi_{0}+\nu(t-t_{0})+\frac{1}{2}\dot{\nu}(t-t_{0})^{2}+\frac{1}{6}\ddot{\nu}(t-t_{0})^{3},$$8-glitch if it satisfies both a sharpness condition,

$$\phi(t)=\phi_{0}+\nu(t-t_{0})+\frac{1}{2}\dot{\nu}(t-t_{0})^{2}+\frac{1}{6}\ddot{\nu}(t-t_{0})^{3},$$9

and a non-monotonicity condition,

$$\nu(t)=\nu_{0}(t)+\Delta\nu_{p}+\Delta\dot{\nu}_{p}t+\Delta\nu_{d}e^{-t/\tau_{d}},$$0

This definition encodes both non-robustness and non-monotonicity in a tiny neighborhood, and it is specific to the geometry of the model’s decision function (Chandra et al., 19 Jul 2025).

2. Pulsar glitches as rotational irregularities

Pulsar glitches are observed through phase-connected timing as sudden, discrete positive changes in rotational frequency. Surveys reported in the literature include 29 glitches in 19 young pulsars observed at Urumqi between 2002 July and 2008 December, 31 glitches in twelve young radio pulsars from the Parkes pulsar archive, and 124 glitches in 52 pulsars from a decade of Parkes timing of 74 young pulsars (Yuan et al., 2010, Zhou et al., 2018, Lower et al., 2021). The broader review literature states that about $$\nu(t)=\nu_{0}(t)+\Delta\nu_{p}+\Delta\dot{\nu}_{p}t+\Delta\nu_{d}e^{-t/\tau_{d}},$$1 of known pulsars have glitched and that the combined catalog contains 719 glitches in 239 pulsars (Zhou et al., 2022).

The observed phenomenology is diverse. The review literature classifies events into normal glitches, slow glitches, glitches with delayed spin-ups, and anti-glitches (Zhou et al., 2022). Urumqi timing identified three slow glitches in PSR J0631+1036, PSR B1822−09, and PSR B1907+10, where the event is not an instantaneous spin-up but a relatively abrupt increase in $$\nu(t)=\nu_{0}(t)+\Delta\nu_{p}+\Delta\dot{\nu}_{p}t+\Delta\nu_{d}e^{-t/\tau_{d}},$$2 followed by a gradual increase in $$\nu(t)=\nu_{0}(t)+\Delta\nu_{p}+\Delta\dot{\nu}_{p}t+\Delta\nu_{d}e^{-t/\tau_{d}},$$3 over tens to hundreds of days (Yuan et al., 2010). Delayed spin-ups were reported repeatedly in the Crab pulsar and in magnetars including 1E 2259+586 and SGR J1935+2154, with delay timescales $$\nu(t)=\nu_{0}(t)+\Delta\nu_{p}+\Delta\dot{\nu}_{p}t+\Delta\nu_{d}e^{-t/\tau_{d}},$$4 (Zhou et al., 2022). Anti-glitches, defined by $$\nu(t)=\nu_{0}(t)+\Delta\nu_{p}+\Delta\dot{\nu}_{p}t+\Delta\nu_{d}e^{-t/\tau_{d}},$$5, are rare in the current literature and are concentrated in magnetars and special accreting systems (Zhou et al., 2022).

The size distribution is itself a diagnostic. Parkes work on twelve pulsars reported glitches from $$\nu(t)=\nu_{0}(t)+\Delta\nu_{p}+\Delta\dot{\nu}_{p}t+\Delta\nu_{d}e^{-t/\tau_{d}},$$6 to $$\nu(t)=\nu_{0}(t)+\Delta\nu_{p}+\Delta\dot{\nu}_{p}t+\Delta\nu_{d}e^{-t/\tau_{d}},$$7 in $$\nu(t)=\nu_{0}(t)+\Delta\nu_{p}+\Delta\dot{\nu}_{p}t+\Delta\nu_{d}e^{-t/\tau_{d}},$$8 and validated the bimodal distribution with peaks at $$\nu(t)=\nu_{0}(t)+\Delta\nu_{p}+\Delta\dot{\nu}_{p}t+\Delta\nu_{d}e^{-t/\tau_{d}},$$9 and $\Delta\nu_g=\Delta\nu_{p}+\Delta\nu_{d}$0 (Zhou et al., 2018). Urumqi timing found amplitudes from a few parts in $\Delta\nu_g=\Delta\nu_{p}+\Delta\nu_{d}$1 up to $\Delta\nu_g=\Delta\nu_{p}+\Delta\nu_{d}$2 (Yuan et al., 2010). A decade-long Parkes program established completeness to fractional increases in spin-frequency greater than $\Delta\nu_g=\Delta\nu_{p}+\Delta\nu_{d}$3 (Lower et al., 2021). For the Crab pulsar, a dedicated completeness analysis over 29 years of daily observations found a rapid decrease in the number of glitches below $\Delta\nu_g=\Delta\nu_{p}+\Delta\nu_{d}$4, implying a substantial minimum glitch size rather than an observationally hidden continuum to arbitrarily small events (Espinoza et al., 2014).

3. Post-glitch recovery, activity, and interior physics

Post-glitch recovery is not uniform. Many large glitches show exponential recovery, but the timescale and recovery fraction vary strongly across sources and even across glitches in the same source. Urumqi data reported exponential recoveries on 100–1000 day timescales in many large glitches, including $\Delta\nu_g=\Delta\nu_{p}+\Delta\nu_{d}$5 d with $\Delta\nu_g=\Delta\nu_{p}+\Delta\nu_{d}$6 in J0631+1036, $\Delta\nu_g=\Delta\nu_{p}+\Delta\nu_{d}$7 d with $\Delta\nu_g=\Delta\nu_{p}+\Delta\nu_{d}$8 in B1809−173, and $\Delta\nu_g=\Delta\nu_{p}+\Delta\nu_{d}$9 d with $Q=\Delta\nu_{d}/\Delta\nu_g.$0 in J1853+0545; B1758−23 showed little or no recovery with $Q=\Delta\nu_{d}/\Delta\nu_g.$1 (Yuan et al., 2010). Parkes analyses likewise reported that exponential decays were observed in large glitches and have very low $Q=\Delta\nu_{d}/\Delta\nu_g.$2, with pre-glitch pulse frequency extrapolation reached on timescales of 40 or 80 days in the observed sample (Zhou et al., 2018). In the Crab pulsar, the event at MJD 53067.1 had $Q=\Delta\nu_{d}/\Delta\nu_g.$3, $Q=\Delta\nu_{d}/\Delta\nu_g.$4, $Q=\Delta\nu_{d}/\Delta\nu_g.$5, and $Q=\Delta\nu_{d}/\Delta\nu_g.$6 (Wang et al., 2012).

Glitches also reorganize secular spin evolution. The glitch activity parameter

$Q=\Delta\nu_{d}/\Delta\nu_g.$7

is positively correlated with $Q=\Delta\nu_{d}/\Delta\nu_g.$8, and fractional glitch amplitudes correlate with characteristic age with a broad peak near $Q=\Delta\nu_{d}/\Delta\nu_g.$9 years, albeit with a spread of two to three orders of magnitude at all ages (Yuan et al., 2010). In young pulsars, large positive inter-glitch $$\Delta\dot{\nu}_g = \Delta\dot{\nu}_{p} - Q\Delta\nu_g/\tau_{d}.$$0 values can produce very large inter-glitch braking indices, while long-term evolution remains much smaller once the step changes in $$\Delta\dot{\nu}_g = \Delta\dot{\nu}_{p} - Q\Delta\nu_g/\tau_{d}.$$1 are averaged over. A Parkes study reported a near one-to-one relationship between the inter-glitch value of $$\Delta\dot{\nu}_g = \Delta\dot{\nu}_{p} - Q\Delta\nu_g/\tau_{d}.$$2 and the change in spin-down of the previous glitch divided by the inter-glitch time interval (Lower et al., 2021).

The dominant physical interpretation in the review literature is superfluid angular-momentum transfer mediated by quantized vortices, together with pinning, creep, mutual friction, and possible collective avalanche behavior. The review of pulsar-glitch models describes crust-quake models, vortex pinning and “snowplow” models, vortex creep, mutual-friction-dominated recovery, vortex avalanches and self-organized criticality, and hydrodynamical instabilities as the main theoretical frameworks (Haskell et al., 2015). The Crab minimum-size analysis strengthens threshold-based interpretations by arguing that the smallest observed Crab glitch requires the motion of at least several billion superfluid vortices and that glitches are clearly separated from timing noise (Espinoza et al., 2014). This does not yield a single accepted trigger mechanism, but it sharply constrains any successful model.

Laboratory analogs have been proposed through dipolar supersolids. Numerical work on rotating supersolids treats the angular momentum as

$$\Delta\dot{\nu}_g = \Delta\dot{\nu}_{p} - Q\Delta\nu_g/\tau_{d}.$$3

with evolution

$$\Delta\dot{\nu}_g = \Delta\dot{\nu}_{p} - Q\Delta\nu_g/\tau_{d}.$$4

In these simulations, vortices are trapped between density-modulated droplets, and stronger interdroplet superfluidity produces larger glitches; for $$\Delta\dot{\nu}_g = \Delta\dot{\nu}_{p} - Q\Delta\nu_g/\tau_{d}.$$5 no glitch was seen, whereas for $$\Delta\dot{\nu}_g = \Delta\dot{\nu}_{p} - Q\Delta\nu_g/\tau_{d}.$$6, $$\Delta\dot{\nu}_g = \Delta\dot{\nu}_{p} - Q\Delta\nu_g/\tau_{d}.$$7, and $$\Delta\dot{\nu}_g = \Delta\dot{\nu}_{p} - Q\Delta\nu_g/\tau_{d}.$$8 clear glitches appeared (Bland et al., 2024). Related work argued that rotating dipolar supersolids can reproduce glitch-like spin-up events through collective vortex unpinning and can serve as a quantum simulator of neutron-star inner-crust dynamics (Poli et al., 2023).

4. Glitches in gravitational-wave detectors

In gravitational-wave observatories, glitches are instrumental or environmental transients rather than astrophysical spin irregularities. They obscure or mimic signals, interfere with search sensitivity, and complicate parameter estimation. Gravity Spy classified 233,981 glitches from LIGO Hanford and 379,805 from LIGO Livingston in data up to the end of O3, revealing strong site-to-site differences in the glitch population (Glanzer et al., 2022).

Morphology is central to the current detector-characterization framework. In O3, Gravity Spy’s $$\Delta\dot{\nu}_g = \Delta\dot{\nu}_{p} - Q\Delta\nu_g/\tau_{d}.$$9 classes included Blip, Tomte, Fast Scattering, Scattered Light, Extremely Loud, Chirp, and No Glitch. The distributions differed sharply between sites: Livingston was dominated by Fast Scattering, Scattered Light, and Tomte, with approximate $\nu$0 fractions of about 27%, 23%, and 19% respectively; Hanford was dominated by Scattered Light, Low-frequency Bursts, and Extremely Loud, with approximate fractions of about 47%, 16%, and 9% (Glanzer et al., 2022). These differences were tied to local environment, commissioning history, and low-frequency sensitivity.

Search pipelines are sensitive to these class-dependent morphologies. In PyCBC analyses of O1/O2 data, blip, koi fish, scattered light, and scratchy glitches were shown to overlap different regions of the compact-binary template bank. Blips most strongly resembled very high-mass, strongly anti-aligned-spin templates and occurred at about 1–2 per hour; scattered-light glitches most closely matched short-duration, highly aligned-spin templates; scratchy glitches overlapped a broad range of templates, including regions below $\nu$1 (Davis et al., 2020). This made glitch classification relevant not only for data quality but also for candidate validation and glitch-conditioned significance estimates.

For long-duration burst searches, the operational problem is similar but the representation differs. A convolutional neural network trained on cross-correlated time-frequency maps of LIGO data reported more than 95% glitch retrieval while being trained only on a subset of existing glitch classes, with a validation accuracy of 95.5% and a background false-alarm rate of about 0.33% (Boudart, 2022). This indicates that glitch recognition can generalize beyond a fixed class inventory, although the same study found confusion between some steep burst morphologies and glitches.

5. Mitigation, inference, and synthesis in gravitational-wave astronomy

Because gravitational-wave inference ordinarily assumes stationary Gaussian noise, overlapping glitches can generate biased source parameters and even false deviations from general relativity. In parameterized tests of general relativity, simulated blip and tomte glitches produced false violations, whereas the scattered-light cases studied did not. Inpainting and BayesWave subtraction consistently eliminated such false violations without introducing additional effects, while aggressive bandpass filtering could remove too much signal power and itself bias the test (Kwok et al., 2021).

A central methodological trend is to move from ad hoc subtraction toward explicit signal-plus-glitch inference. One Bayesian formulation writes

$\nu$2

with $\nu$3 the astrophysical signal, $\nu$4 Gaussian detector noise, and $\nu$5 the glitch. A 2025 study introduced a data-informed glitch prior by training a normalizing flow on Blip glitches from the Gravity Spy catalogue and inserting the resulting model directly into Bilby with Nessai nested sampling. In glitch-only tests, the method reported essentially $\nu$6 false-dismissal in O1 and $\nu$7 in O3, with false-alarm rates around $\nu$8–$\nu$9, and in glitch-contaminated injections it reduced bias in mass ratio, chirp mass, inclination, distance, right ascension, and declination (Malz et al., 1 May 2025).

Other approaches emphasize robustness rather than explicit glitch training. AWaRe, an encoder–decoder model with a CNN, attention mechanism, and LSTM layers trained only on gravitational-wave signals, was applied directly to real O3 glitches and to simulated injections into real glitchy data. The reported result was reliable waveform reconstruction in most scenarios, with residuals closely aligned with the background noise that the waveforms were injected in, although high-SNR glitches such as some Koi Fish cases remained challenging (Chatterjee et al., 2024). For third-generation detectors, a null-stream-based method for the Einstein Telescope used the triangular geometry to form a signal-free null stream. In simulations with a blip glitch of SNR $\dot{\nu}$0, null-stream mitigation yielded mismatch $\dot{\nu}$1, compared with $\dot{\nu}$2 without the null stream, and achieved an order of magnitude computational speed-up (Narola et al., 2024).

The necessity of mitigation is itself conditional. A 2025 study of simulated compact-binary signals and Morlet-Gabor glitches found that glitches located outside the time-frequency space spanned by the gravitational-wave model prior and with signal-to-noise ratio, conservatively, below 50 do not impact estimation of the signal parameters (Hourihane et al., 27 Jun 2025). This criterion narrows the class of transients that require expensive mitigation.

Realistic synthetic populations are also now part of the workflow. GlitchGAN, a class-conditional derivative GAN trained on DeepExtractor reconstructions of seven common O3 glitch classes, generated 1000 glitches in under 22 seconds on a CPU and was validated by both Gravity Spy and UMAP overlap between real and synthetic samples (Dooney et al., 25 Jun 2026). A key methodological conclusion of that work was that magnitude-only $\dot{\nu}$3-transform validation can be misleading, because classifiers operating on magnitude spectrograms can confidently misclassify physically unrealistic glitches from less robust models. This established phase-preserving, time-domain validation as a distinct requirement for synthetic glitch realism.

6. Glitches in machine-learned decision systems

In decision-tree ensemble models, the term describes neither astrophysical timing irregularities nor detector noise transients but a local pathology of the learned decision function. The defining pattern is a small monotonic change in one feature that causes the model output to drop and then rise again, or rise and then drop again, within a tiny neighborhood. The formalism uses ordered triples differing in only one feature and quantifies both the oscillation and its sharpness through the $\dot{\nu}$4-glitch condition (Chandra et al., 19 Jul 2025).

This notion refines, rather than replaces, broader ideas of robustness and monotonicity. The same study relates glitches to Lipschitz continuity by noting that if $\dot{\nu}$5 is globally Lipschitz with constant $\dot{\nu}$6, then the magnitude of every glitch is at most $\dot{\nu}$7; at the same time, a model can be monotone and thus glitch-free even if it is not Lipschitz (Chandra et al., 19 Jul 2025). The focus on gradient-boosted decision trees is natural because such models are piecewise linear or piecewise constant, exhibit sharp discontinuities at split thresholds, and can become globally non-robust and non-monotonic through interactions among many shallow trees.

The computational theory is stringent. Detecting whether a tree ensemble has a glitch is NP-complete, and the hardness already holds for trees of fixed depth $\dot{\nu}$8 (Chandra et al., 19 Jul 2025). The proposed practical solution is a mixed-integer linear programming encoding that uses three copies of the input variables, ordering constraints, oscillation constraints, and a sharpness constraint, with Gurobi reported as faster than Z3 on the benchmarks studied. Experiments on benchmark models including breast cancer, diabetes, IJCNN, webspam, bankruptcy, heart failure, machine failure, and steel plate defect found glitches in many real models. In the breast-cancer model, a glitch in the feature mean concave points (MCP) produced a high–low–high malignancy pattern across three nearby inputs; the study states that this pattern was independently confirmed as anomalous by three oncologists (Chandra et al., 19 Jul 2025).

The AI use of the term therefore marks a mathematically precise local inconsistency in model behavior. This is distinct from the pulsar and gravitational-wave usages, but it serves an analogous diagnostic role: a glitch is not merely an outlier, but a structured deviation whose form constrains the underlying mechanism or architecture (Chandra et al., 19 Jul 2025).