We present a framework for inferring an atmospheric transmission profile from a spectral scene. This framework leverages a lightweight, physics-based simulator that is automatically tuned – by virtue of autodifferentiation and differentiable programming – to construct a surrogate atmospheric profile to model the observed data. We demonstrate utility of the methodology by (i) performing atmospheric correction, (ii) recasting spectral data between various modalities (e.g. radiance and reflectance at the surface and at the sensor), and (iii) inferring atmospheric transmission profiles, such as absorbing bands and their relative magnitudes.

Symmetry has been a fundamental tool in the exploration of a broad range of complex systems. In machine learning, symmetry has been explored in both models and data. In this paper we seek to connect the symmetries arising from the architecture of a family of models with the symmetries of that family’s internal representation of data. We do this by calculating a set of fundamental symmetry groups, which we call the intertwiner groups of the model. Each of these arises from a particular nonlinear layer of the model and different nonlinearities result in different symmetry groups. These groups change the weights of a model in such a way that the underlying function that the model represents remains constant but the internal representations of data inside the model may change. We connect intertwiner groups to a model’s internal representations of data through a range of experiments that probe similarities between hidden states across models with the same architecture. Our work suggests that the symmetries of a network are propagated into the symmetries in that network’s representation of data, providing us with a better understanding of how architecture affects the learning and prediction process. Finally, we speculate that for ReLU networks, the intertwiner groups may provide a justification for the common practice of concentrating model interpretability exploration on the activation basis in hidden layers rather than arbitrary linear combinations thereof.

It is often said that a deep learning model is ``invariant'' to some specific type of transformation. However, what is meant by this statement strongly depends on the context in which it is made. In this paper we explore the nature of invariance and equivariance of deep learning models with the goal of better understanding the ways that they actually capture these concepts on a formal level. We introduce a family of invariance and equivariance metrics that allow us to quantify these properties in a way that disentangles them from other metrics such as loss or accuracy. We use our metrics to better understand the two most popular methods used to build invariance into networks, data augmentation and equivariant layers. We draw a range of conclusions about invariance and equivariance in deep learning models, ranging from whether initializing a model with pretrained weights has an effect on a trained model's invariance, to the extent to which invariance learned via training can generalize to out-of-distribution data.

In this paper we present a novel approach for identifying fraudulent papers from their titles and abstracts. The premise of the approach is that there are holes in the presentation of the approach and findings of fraudulent research papers. As an abstract is intended to highlight key features of the approach as well as important conclusions the authors seek to determine if the assumed existence of holes can be identified from analysis of abstracts alone. The data set considered is derived from papers sharing a single author with labels determined based on a formal linguistic analysis of the complete documents. To detect these logical and literary holes we utilize techniques from topological data analysis which summarizes data based on the presence of multi-dimensional, topological holes. We find that, in fact, topological features derived through a combination of techniques in natural language processing and time-series analysis allow for superior detection of the fraudulent papers than the natural language processing tools alone. Thus we conclude that the connections and holes present in the abstracts of research cons contributes to an ability to infer the scientific validity of the corresponding work.

With the recent addition of large, curated and labeled data sets to the remote sensing discipline, deep learning models have largely surpassed the performance of classical techniques. These deep models, typically Convolutional Neural Networks, are invariant to translation through the use of successive convolution layers which are themselves equivariant to translation. Further, the combination of multiple convolution and pooling layers means that in practice, the model is also approximately invariant to translation. However, until recently these models could only approach rotational invariance through data augmentation. Here we propose using a new model formulation which achieves rotational equaivariance without data augmentation for overhead imagery classification. We utilize the popular xView data set to compare the rotational equivariance formalization against a regular CNN and CNN with rotational data augmentation for the task of image classification.

We have previously shown that augmenting orthogonal matching pursuit (OMP) with an additional step in the identification stage of each pursuit iteration yields improved k-sparse reconstruction and denoising performance relative to baseline OMP. At each iteration a "path," or geodesic, is generated between the two dictionary atoms that are most correlated with the residual and from this path a new atom that has a greater correlation to the residual than either of the two bracketing atoms is selected. Here, we provide new computational results illustrating improvements in sparse coding and denoising on canonical datasets using both learned and structured dictionaries. Two methods of constructing a path are investigated for each dictionary type: the Euclidean geodesic formed by a linear combination of the two atoms and the 2-Wasserstein geodesic corresponding to the optimal transport map between the atoms. We prove here the existence of a higher-correlation atom in the Euclidean case under assumptions on the two bracketing atoms and introduce algorithmic modifications to improve the likelihood that the bracketing atoms meet those conditions. Although we demonstrate our augmentation on OMP alone, in general it may be applied to any reconstruction algorithm that relies on the selection and sorting of high-similarity atoms during an analysis or identification phase.

New depth sensors, like the Microsoft Kinect, produce streams of human pose data. These discrete pose streams can be viewed as noisy samples of an underlying continuous ideal curve that describes a trajectory through high-dimensional pose space. This paper introduces a technique for generalized curvature analysis (GCA) that determines features along the trajectory which can be used to characterize change and segment motion. Tools are developed for approximating generalized curvatures at mean points along a curve in terms of the singular values of local mean-centered data balls. The features of the GCA algorithm are illustrated on both synthetic and real examples, including data collected from a Kinect II sensor. We also applied GCA to the Carnegie Mellon University Motion Capture (MoCaP) database. Given that GCA scales linearly with the length of the time series we are able to analyze large data sets without down sampling. It is demonstrated that the generalized curvature approximations can be used to segment pose streams into motions and transitions between motions. The GCA algorithm can identify 94.2 percent of the transitions between motions without knowing the set of possible motions in advance, even though the subjects do not stop or pause between motions.

Many data sets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a multiscale description of the homological features within a data set. A useful representation of this homological information is a persistence diagram (PD). Efforts have been made to map PDs into spaces with additional structure valuable to machine learning tasks. We convert a PD to a finite- dimensional vector representation which we call a persistence image (PI), and prove the stability of this transformation with respect to small perturbations in the inputs. The discriminatory power of PIs is compared against existing methods, showing significant performance gains. We explore the use of PIs with vector-based machine learning tools, such as linear sparse support vector machines, which identify features containing discriminating topological information. Finally, high accuracy inference of parameter values from the dynamic output of a discrete dynamical system (the linked twist map) and a partial differential equation (the anisotropic Kuramoto-Sivashinsky equation) provide a novel application of the discriminatory power of PIs.