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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. 

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. 

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.