Related papers: Differentiating a Tensor Language
Tensor methods have emerged as a powerful paradigm for consistent learning of many latent variable models such as topic models, independent component analysis and dictionary learning. Model parameters are estimated via CP decomposition of…
We show how to develop sampling-based alternating least squares (ALS) algorithms for decomposition of tensors into any tensor network (TN) format. Provided the TN format satisfies certain mild assumptions, resulting algorithms will have…
The popular Alternating Least Squares (ALS) algorithm for tensor decomposition is efficient and easy to implement, but often converges to poor local optima---particularly when the weights of the factors are non-uniform. We propose a…
Originating from condensed matter physics, tensor networks are compact representations of high-dimensional tensors. In this paper, the prowess of tensor networks is demonstrated on the particular task of one-class anomaly detection. We…
Regression analysis is a key area of interest in the field of data analysis and machine learning which is devoted to exploring the dependencies between variables, often using vectors. The emergence of high dimensional data in technologies…
Tensors, which provide a powerful and flexible model for representing multi-attribute data and multi-way interactions, play an indispensable role in modern data science across various fields in science and engineering. A fundamental task is…
Deep learning has seen tremendous success over the past decade in computer vision, machine translation, and gameplay. This success rests in crucial ways on gradient-descent optimization and the ability to learn parameters of a neural…
Tensor factorization has proven useful in a wide range of applications, from sensor array processing to communications, speech and audio signal processing, and machine learning. With few recent exceptions, all tensor factorization…
We calculate denotations under the Sweedler semantics of the Ehrhard-Regnier derivatives of various encodings of Turing machines into linear logic. We show that these derivatives calculate the rate of change of probabilities naturally…
Tensors, which give a faithful and effective representation to deliver the intrinsic structure of multi-dimensional data, play a crucial role in an increasing number of signal processing and machine learning problems. However, tensor data…
We show how to define forward- and reverse-mode automatic differentiation source-code transformations or on a standard higher-order functional language. The transformations generate purely functional code, and they are principled in the…
We theoretically and experimentally investigate tensor-based regression and classification. Our focus is regularization with various tensor norms, including the overlapped trace norm, the latent trace norm, and the scaled latent trace norm.…
Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient…
Tensor accelerators now represent a growing share of compute resources in modern CPUs and GPUs. However, they are hard to program, leading developers to use vendor-provided kernel libraries that support tensor accelerators. As a result, the…
In Computational Science, Engineering and Finance (CSEF) scripts typically serve as the "glue" between potentially highly complex and computationally expensive external subprograms. Differentiability of the resulting programs turns out to…
Differentiation lies at the core of many machine-learning algorithms, and is well-supported by popular autodiff systems, such as TensorFlow and PyTorch. Originally, these systems have been developed to compute derivatives of differentiable…
Nonnegative Tucker decomposition (NTD) is a powerful tool for the extraction of nonnegative parts-based and physically meaningful latent components from high-dimensional tensor data while preserving the natural multilinear structure of…
We develop an algorithm for minimizing a function using $n$ batched function value measurements at each of $T$ rounds by using classifiers to identify a function's sublevel set. We show that sufficiently accurate classifiers can achieve…
Deep neural networks have achieved impressive supervised classification performance in many tasks including image recognition, speech recognition, and sequence to sequence learning. However, this success has not been translated to…
The paper presents a REDUCE program for the simplification of tensor expressions that are considered as formal indexed objects. The proposed algorithm is based on the consideration of tensor expressions as vectors in some linear space. This…