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Graphical calculus is an intuitive visual notation for manipulating tensors and index contractions. Using graphical calculus leads to simple and memorable derivations, and with a bit of practice one can learn to prove complex identities…

Constructive Solid Geometry (CSG) is a geometric modeling technique that defines complex shapes by recursively applying boolean operations on primitives such as spheres and cylinders. We present CSGNe, a deep network architecture that takes…

Many applications in 3D shape design and augmentation require the ability to make specific edits to an object's semantic parameters (e.g., the pose of a person's arm or the length of an airplane's wing) while preserving as much existing…

Graphs emerge in almost every real-world application domain, ranging from online social networks all the way to health data and movie viewership patterns. Typically, such real-world graphs are big and dynamic, in the sense that they evolve…

We introduce a new OpenMath content dictionary, named tensor1, containing symbols for the expression of tensor formulas. These symbols support the expression of non-Cartesian coordinates and invariant, multilinear expressions in the context…

Segmentation of axon and myelin from microscopy images of the nervous system provides useful quantitative information about the tissue microstructure, such as axon density and myelin thickness. This could be used for instance to document…

Purpose: Semantic segmentation and landmark detection are fundamental tasks of medical image processing, facilitating further analysis of anatomical objects. Although deep learning-based pixel-wise classification has set a…

Tensors are a fundamental data structure for many scientific contexts, such as time series analysis, materials science, and physics, among many others. Improving our ability to produce and handle tensors is essential to efficiently address…

Deep learning is currently the subject of intensive study. However, fundamental concepts such as representations are not formally defined -- researchers "know them when they see them" -- and there is no common language for describing and…

We present a system for object recognition based on a semantic graph representation, which the system can learn from image examples. This graph is based on intrinsic properties of objects such as structure and geometry, so it is more robust…

Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…

Semantic types are a more powerful and detailed way of describing data than atomic types such as strings or integers. They establish connections between columns and concepts from the real world, providing more nuanced and fine-grained…

As the number of deep learning frameworks increase and certain ones gain popularity, it spurs the discussion of what methodologies are employed by these frameworks and the reasoning behind them. The goal of this survey is to study how…

In this work, the human parsing task, namely decomposing a human image into semantic fashion/body regions, is formulated as an Active Template Regression (ATR) problem, where the normalized mask of each fashion/body item is expressed as the…

Other than vector representations, the direct objects of human cognition are generally high-order tensors, such as 2D images and 3D textures. From this fact, two interesting questions naturally arise: How does the human brain represent…

Despite significant progress of deep learning in recent years, state-of-the-art semantic matching methods still rely on legacy features such as SIFT or HoG. We argue that the strong invariance properties that are key to the success of…

We propose a novel framework to understand the text by converting sentences or articles into video-like 3-dimensional tensors. Each frame, corresponding to a slice of the tensor, is a word image that is rendered by the word's shape. The…

Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…

This paper proposes a new architecture - Attentive Tensor Product Learning (ATPL) - to represent grammatical structures in deep learning models. ATPL is a new architecture to bridge this gap by exploiting Tensor Product Representations…

Neural representations have emerged as a new paradigm for applications in rendering, imaging, geometric modeling, and simulation. Compared to traditional representations such as meshes, point clouds, or volumes they can be flexibly…