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In high-dimensional classification problems, a commonly used approach is to first project the high-dimensional features into a lower dimensional space, and base the classification on the resulting lower dimensional projections. In this…

The topology of the large-scale structure of the universe contains valuable information on the underlying cosmological parameters. While persistent homology can extract this topological information, the optimal method for parameter…

We present a framework for simulating signal propagation in geometric networks (i.e. networks that can be mapped to geometric graphs in some space) and for developing algorithms that estimate (i.e. map) the state and functional topology of…

Overparameterized shallow neural networks admit substantial parameter redundancy: distinct parameter vectors may represent the same predictor due to hidden-unit permutations, rescalings, and related symmetries. As a result, geometric…

Over the past decade, deep learning has proven to be a highly effective tool for learning meaningful features from raw data. However, it remains an open question how deep networks perform hierarchical feature learning across layers. In this…

The topological analysis of four-dimensional (4D) image-type data is challenged by the immense size that these datasets can reach. This can render the direct application of methods, like persistent homology and convolutional neural networks…

The dominant approach in probing neural networks for linguistic properties is to train a new shallow multi-layer perceptron (MLP) on top of the model's internal representations. This approach can detect properties encoded in the model, but…

We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…

To better understand complexity in neural networks, we theoretically investigate the idealised phenomenon of lossless network compressibility, whereby an identical function can be implemented with fewer hidden units. In the setting of…

Decomposing tensors into orthogonal factors is a well-known task in statistics, machine learning, and signal processing. We study orthogonal outer product decompositions where the factors in the summands in the decomposition are required to…

Human experts cannot efficiently access the physical information of quantum many-body states by simply "reading" the coefficients, but have to reply on the previous knowledge such as order parameters and quantum measurements. In this work,…

Neural networks are widely used for image-related tasks but typically demand considerable computing power. Once a network has been trained, however, its memory- and compute-footprint can be reduced by compression. In this work, we focus on…

We present a learning-based approach for virtual try-on applications based on a fully convolutional graph neural network. In contrast to existing data-driven models, which are trained for a specific garment or mesh topology, our fully…

A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear…

Neural networks in many varieties are touted as very powerful machine learning tools because of their ability to distill large amounts of information from different forms of data, extracting complex features and enabling powerful…

This paper presents a novel generative model to synthesize fluid simulations from a set of reduced parameters. A convolutional neural network is trained on a collection of discrete, parameterizable fluid simulation velocity fields. Due to…

In order to utilize identification to the best extent, we need robust and fast algorithms and systems to process the data. Having palmprint as a reliable and unique characteristic of every person, we extract and use its features based on…

Nonparametric feature selection in high-dimensional data is an important and challenging problem in statistics and machine learning fields. Most of the existing methods for feature selection focus on parametric or additive models which may…

We give a partonic interpretation for the deeply virtual Compton scattering (DVCS) measurements of the H1 and ZEUS collaborations in the small-x_B region in terms of generalized parton distributions. Thereby we have a closer look at the…

Deep networks for image classification often rely more on texture information than object shape. While efforts have been made to make deep-models shape-aware, it is often difficult to make such models simple, interpretable, or rooted in…