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Explainability and attribution for deep neural networks remains an open area of study due to the importance of adequately interpreting the behavior of such ubiquitous learning models. The method of expected gradients [10] reduced the baseline dependence of integrated gradients [27] and allowed for improved interpretability of attributions as representative of the broader gradient landscape, however both methods are visualized using an ambiguous transformation which obscures attribution information and neglects to distinguish between color channels. While expected gradients takes an expectation over the entire dataset, this is only one possible domain in which an explanation can be contextualized. In order to generalize the larger family of attribution methods containing integrated gradients and expected gradients, we instead frame each attribution as a volume integral over a set of interest within the input space, allowing for new levels of specificity and revealing novel sources of attribution information. Additionally, we demonstrate these new unique sources of feature attribution information using a refined visualization method which allows for both signed and unsigned attributions to be visually salient for each color channel. This new formulation provides a framework for developing and explaining a much broader family of attribution measures, and for computing attributions relevant to diverse contexts such as local and non-local neighborhoods. We evaluate our novel family of attribution measures and our improved visualization method using qualitative and quantitative approaches with the CIFAR10 and ImageNet datasets and the Quantus XAI library. 

With the increasing interest in explainable attribution for deep neural networks, it is important to consider not only the importance of individual inputs, but also the model parameters themselves. Existing methods, such as Neuron Integrated Gradients [18] and Conductance [6], attempt model attribution by applying attribution methods, such as Integrated Gradients, to the inputs of each model parameter. While these methods seem to map attributions to individual parameters, these are actually aggregated feature attributions which completely ignore the parameter space and also suffer from the same underlying limitations of Integrated Gradients. In this work, we compute parameter attributions by leveraging the recent family of measures proposed by Generalized Integrated Attributions, by instead computing integrals over the product space of inputs and parameters. This usage of the product space allows us to now explain individual neurons from varying perspectives and interpret them with the same intuition as inputs. To the best of our knowledge, ours is the first method which actually utilizes the gradient landscape of the parameter space to explain each individual weight and bias. We confirm the utility of our parameter attributions by computing exploratory statistics for a wide variety of image classification datasets and by performing pruning analyses on a standard architecture, which demonstrate that our attribution measures are able to identify both important and unimportant neurons in a convolutional neural network. 

ABSTRACT As the catalogue of gravitational-wave transients grows, several entries appear ‘exceptional’ within the population. Tipping the scales with a total mass of $$\sim 150 \,{\rm M}_\odot$$, GW190521 likely contained black holes in the pair-instability mass gap. The event GW190814, meanwhile, is unusual for its extreme mass ratio and the mass of its secondary component. A growing model-building industry has emerged to provide explanations for such exceptional events, and Bayesian model selection is frequently used to determine the most informative model. However, Bayesian methods can only take us so far. They provide no answer to the question: does our model provide an adequate explanation for exceptional events in the data? If none of the models we are testing provide an adequate explanation, then it is not enough to simply rank our existing models – we need new ones. In this paper, we introduce a method to answer this question with a frequentist p-value. We apply the method to different models that have been suggested to explain the unusually massive event GW190521: hierarchical mergers in active galactic nuclei and globular clusters. We show that some (but not all) of these models provide adequate explanations for exceptionally massive events like GW190521. 

Abstract Gravitational-wave observations provide the unique opportunity of studying black hole formation channels and histories—but only if we can identify their origin. One such formation mechanism is the dynamical synthesis of black hole binaries in dense stellar systems. Given the expected isotropic distribution of component spins of binary black holes in gas-free dynamical environments, the presence of antialigned or in-plane spins with respect to the orbital angular momentum is considered a tell-tale sign of a merger’s dynamical origin. Even in the scenario where birth spins of black holes are low, hierarchical mergers attain large component spins due to the orbital angular momentum of the prior merger. However, measuring such spin configurations is difficult. Here, we quantify the efficacy of the spin parameters encoding aligned-spin (χ_eff) and in-plane spin (χ_p) at classifying such hierarchical systems. Using Monte Carlo cluster simulations to generate a realistic distribution of hierarchical merger parameters from globular clusters, we can infer mergers’χ_effandχ_p. The cluster populations are simulated using Advanced LIGO-Virgo sensitivity during the detector network’s third observing period and projections for design sensitivity. Using a “likelihood-ratio”-based statistic, we find that ∼2% of the recovered population by the current gravitational-wave detector network has a statistically significantχ_pmeasurement, whereas noχ_effmeasurement was capable of confidently determining a system to be antialigned with the orbital angular momentum at current detector sensitivities. These results indicate that measuring spin-precession throughχ_pis a more detectable signature of hierarchical mergers and dynamical formation than antialigned spins. 

It has become increasingly useful to answer questions in gravitational-wave astronomy using transdimensional models where the number of free parameters can be varied depending on the complexity required to fit the data. Given the growing interest in transdimensional inference, we introduce a new package for the Bayesian inference Library (Bilby) called tBilby. The tBilby package allows users to set up transdimensional inference calculations using the existing Bilby architecture with off-the-shelf nested samplers and/or Markov Chain Monte Carlo algorithms. Transdimensional models are particularly helpful when we seek to test theoretically uncertain predictions described by phenomenological models. For example, bursts of gravitational waves can be modelled using a superposition of N wavelets where N is itself a free parameter. Short pulses are modelled with small values of N whereas longer, more complicated signals are represented with a large number of wavelets stitched together. Other transdimensional models have found use describing instrumental noise and the population properties of gravitational-wave sources. We provide a few demonstrations of tBilby, including fitting the gravitational-wave signal GW150914 with a superposition of N sine-Gaussian wavelets. We outline our plans to further develop the tbilby code suite for a broader range of transdimensional problems. 

General relativity (GR) has proven to be a highly successful theory of gravity since its inception. The theory has thrivingly passed numerous experimental tests, predominantly in weak gravity, low relative speeds, and linear regimes, but also in the strong-field and very low-speed regimes with binary pulsars. Observable gravitational waves (GWs) originate from regions of spacetime where gravity is extremely strong, making them a unique tool for testing GR, in previously inaccessible regions of large curvature, relativistic speeds, and strong gravity. Since their first detection, GWs have been extensively used to test GR, but no deviations have been found so far. Given GR’s tremendous success in explaining current astronomical observations and laboratory experiments, accepting any deviation from it requires a very high level of statistical confidence and consistency of the deviation across GW sources. In this paper, we compile a comprehensive list of potential causes that can lead to a false identification of a GR violation in standard tests of GR on data from current and future ground-based GW detectors. These causes include detector noise, signal overlaps, gaps in the data, detector calibration, source model inaccuracy, missing physics in the source and in the underlying environment model, source misidentification, and mismodeling of the astrophysical population. We also provide a rough estimate of when each of these causes will become important for tests of GR for different detector sensitivities. We argue that each of these causes should be thoroughly investigated, quantified, and ruled out before claiming a GR violation in GW observations.