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Continuous deep learning models, referred to as Neural Ordinary Differential Equations (Neural ODEs), have received considerable attention over the last several years. Despite their burgeoning impact, there is a lack of formal analysis techniques for these systems. In this paper, we consider a general class of neural ODEs with varying architectures and layers, and introduce a novel reachability framework that allows for the formal analysis of their behavior. The methods developed for the reachability analysis of neural ODEs are implemented in a new tool called NNVODE. Specifically, our work extends an existing neural network verification tool to support neural ODEs. We demonstrate the capabilities and efficacy of our methods through the analysis of a set of benchmarks that include neural ODEs used for classification, and in control and dynamical systems, including an evaluation of the efficacy and capabilities of our approach with respect to existing software tools within the continuous-time systems reachability literature, when it is possible to do so. 

This paper introduces robustness verification for semantic segmentation neural networks (in short, semantic segmentation networks [SSNs]), building on and extending recent approaches for robustness verification of image classification neural networks. Despite recent progress in developing verification methods for specifications such as local adversarial robustness in deep neural networks (DNNs) in terms of scalability, precision, and applicability to different network architectures, layers, and activation functions, robustness verification of semantic segmentation has not yet been considered. We address this limitation by developing and applying new robustness analysis methods for several segmentation neural network architectures, specifically by addressing reachability analysis of up-sampling layers, such as transposed convolution and dilated convolution. We consider several definitions of robustness for segmentation, such as the percentage of pixels in the output that can be proven robust under different adversarial perturbations, and a robust variant of intersection-over-union (IoU), the typical performance evaluation measure for segmentation tasks. Our approach is based on a new relaxed reachability method, allowing users to select the percentage of a number of linear programming problems (LPs) to solve when constructing the reachable set, through a relaxation factor percentage. The approach is implemented within NNV, then applied and evaluated on segmentation datasets, such as a multi-digit variant of MNIST known as M2NIST. Thorough experiments show that by using transposed convolution for up-sampling and average-pooling for down-sampling, combined with minimizing the number of ReLU layers in the SSNs, we can obtain SSNs with not only high accuracy (IoU), but also that are more robust to adversarial attacks and amenable to verification. Additionally, using our new relaxed reachability method, we can significantly reduce the verification time for neural networks whose ReLU layers dominate the total analysis time, even in classification tasks. 

Abstract As the Advanced LIGO and Advanced Virgo interferometers, soon to be joined by the KAGRA interferometer, increase their sensitivity, they detect an ever-larger number of gravitational waves with a significant presence of higher multipoles (HMs) in addition to the dominant (2, 2) multipole. These HMs can be detected with different approaches, such as the minimally-modeled burst search methods, and here we discuss one such approach based on the coherent WaveBurst (cWB) pipeline. During the inspiral phase the HMs produce chirps whose instantaneous frequency is a multiple of the dominant (2, 2) multipole, and here we describe how cWB can be used to detect these spectral features. The search is performed within suitable regions of the time-frequency representation; their shape is determined by optimizing the receiver operating characteristics. This novel method has already been used in the GW190814 discovery paper (Abbott et al 2020 Astrophys. J. Lett. 896 L44) and is very fast and flexible. Here we describe in full detail the procedure used to detect the (3, 3) multipole in GW190814 as well as searches for other HMs during the inspiral phase, and apply it to another event that displays HMs, GW190412, replicating the results obtained with different methods. The procedure described here can be used for the fast analysis of HMs and to support the findings obtained with the model-based Bayesian parameter estimates. 

Abstract The coherent WaveBurst (cWB) pipeline implements a minimally-modelled search to find a coherent response in the network of gravitational wave detectors of the LIGO-Virgo Col-laboration in the time-frequency domain. In this manuscript, we provide a timely introduction to an extension of the cWB analysis to detect spectral features beyond the main quadrupolar emission of gravitational waves during the inspiral phase of compact binary coalescences; more detailed discussion will be provided in a forthcoming paper [1]. The search is performed by defining specific regions in the time-frequency map to extract the energy of harmonics of main quadrupole mode in the inspiral phase. This method has already been used in the GW190814 discovery paper (Astrophys. J. Lett. 896 L44). Here we show the procedure to detect the (3, 3) multipole in GW190814 within the cWB framework. 

Abstract Rotating nonaxisymmetric neutron stars (NSs) are promising sources for continuous gravitational waves (CWs). CWs may, if detected, inform us about the internal structure and equation of state of NSs. Here, we present a narrowband search for CWs from known pulsars, for which a matched-filter search can be applied. Narrowband searches are robust to mismatches between electromagnetic (EM) and gravitational emissions, in contrast to fully targeted searches where they are assumed to be phase-locked. In this work, we search for the CW counterparts emitted by 34 pulsars using data from the first and second parts of the fourth LIGO–Virgo–KAGRA observing run. We use the 5n-vector narrowband pipeline, which applies frequency-domain matched filtering. In previous searches, it covered a narrow range in the frequency—frequency time derivative (f— $\dot{f}$ ) space. Here, we also explore a range in the second time derivative of the frequency $\ddot{f}$ around the EM observations. Additionally, for the first time, we target sources in a binary system with this kind of search. We find no evidence for CWs and therefore set upper limits on the strain amplitude emitted by each pulsar. For 20 analyses, we report an upper limit below the theoretical spin-down limit. The tightest constraint is for pulsar PSR J0534+2200 (the Crab pulsar), for which our strain upper limit on the CW amplitude corresponds to ≤0.04% of the spin-down power being radiated in the CW channel. 

Abstract We detail the population properties of binary neutron star, neutron star–black hole binary, and binary black hole mergers using 158 events from the cumulative Gravitational-Wave Transient Catalog 4.0. The black hole primary mass distribution consists of a power-law-like continuum that steepens above 35M_⊙with overdensities at 10M_⊙and 35M_⊙. Binary black holes with primary masses near 10M_⊙are more likely to have less massive secondaries, with a mass ratio distribution peaking at $q=0.71_{-0.11}^{+0.12}$ , potentially a signature of stable mass transfer during binary evolution. Black hole spins are inferred to be nonextremal, with 90% of black holes havingχ < 0.6, and preferentially aligned with binary orbits, implying many merging binaries form in isolation. However, we find that a significant fraction, 0.23–0.41, of binaries have negative effective inspiral spins, suggesting many could be formed dynamically in gas-free environments. We find evidence for correlation between effective inspiral spin and mass ratio, driven either by variation in the mode of the distribution or the width. The binary black hole merger rate increases with redshift, consistent with the cosmic star formation density. While there is no evidence of the mass spectrum evolving with redshift, the distribution of effective inspiral spin is found to broaden as redshift increases out toz ≈ 1. We infer the local merger rates (atz= 0) to be 8.8–250 Gpc⁻³yr⁻¹for binary neutron stars, 9.3–86 Gpc⁻³yr⁻¹for neutron star–black hole binaries, and 13–26 Gpc⁻³yr⁻¹for binary black holes; all values reflect central 90% credible intervals. 

We present a search for gravitational waves from inspiraling, planetary-mass ultracompact binaries using data from the first part of the fourth observing run of LIGO, Virgo, and KAGRA. Finding no evidence of such systems, we determine the maximum distance reach for such objects and their merger rate densities. Then, we identify classes of primordial black hole mass distributions for which these rate limits can be translated into relevant constraints on the mass distribution of primordial black holes, assuming that they are all composed of dark matter, in the mass range $[{10}^{-6},{10}^{-3}]M_{\odot }$ . Our constraints for the class of primordial black hole mass distribution functions $f\left(m\right)$ we consider reach down to $f\left(m\right)\sim 0.1$ . They are consistent with existing microlensing results in the planetary-mass range, provide a complementary probe to subsolar mass objects, and are publicly available [1]. 

The angular distribution of gravitational-wave power from persistent sources may exhibit anisotropies arising from the large-scale structure of the Universe. This motivates directional searches for astrophysical and cosmological gravitational-wave backgrounds, as well as continuous-wave emitters. We present results of such a search using data from the first observing run through the first portion of the fourth observing run of the LIGO-Virgo-KAGRA Collaborations. We apply gravitational-wave radiometer techniques to generate skymaps and search for both narrowband and broadband persistent gravitational-wave sources. Additionally, we use spherical harmonic decomposition to probe spatially extended sources. No evidence of persistent gravitational-wave signals is found, and we set the most stringent constraints to date on such emissions. For narrowband point sources, our sensitivity estimate to effective strain amplitude lies in the range $\left(0.03–8.4\right)\times {10}^{-24}$ across all-sky and frequency range ( $20-160$ ) Hz. For targeted sources—Scorpius X-1, SN 1987A, the Galactic Center, Terzan 5, and NGC 6397—we constrain the strain amplitude with best limits ranging from $\sim 1.1\times {10}^{-25}$ to $6.5\times {10}^{-24}$ . For persistent broadband sources, we constrain the gravitational-wave flux $F_{\alpha ,\hat{n}}^{95\%,\mathrm{UL}}\left(25\mathrm{Hz}\right)<\left(0.008–5.5\right)\times {10}^{-8}\mathrm{erg}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}{\mathrm{Hz}}^{-1}$ , depending on the sky direction $\hat{n}$ and spectral index $\alpha =0,2/3$ , 3. Finally, for extended sources, we place upper limits on the angular power spectrum $C_{\ell }^{1/2}<\left(0.63–17\right)\times {10}^{-10}{\mathrm{sr}}^{-1}$ . 

Abstract Among known neutron stars, the Vela pulsar is one of the best targets for gravitational-wave searches. It is also one of the most prolific in terms of glitches, which are sudden frequency changes in a pulsar’s rotation. Such glitches could cause a variety of transient gravitational-wave signals. Here, we search for signals associated with a Vela glitch on 2024 April 29 in data of the two LIGO detectors from the fourth LIGO–Virgo–KAGRA observing run. We search both for seconds-scale burst-like emission, primarily from fundamental (f-)mode oscillations, and for longer quasi-monochromatic transients up to 4 months in duration, primarily from quasi-static quadrupolar deformations. We find no significant detection candidates, but for the first time we set direct observational upper limits on gravitational strain amplitude that are stricter than what can be indirectly inferred from the overall glitch energy scale. We discuss the short- and long-duration observational constraints in the context of specific emission models. These results demonstrate the potential of gravitational-wave probes of glitching pulsars as detector sensitivity continues to improve.