Related papers: TensorRight: Automated Verification of Tensor Grap…
We provide a novel analysis of low-rank tensor completion based on hypergraph expanders. As a proxy for rank, we minimize the max-quasinorm of the tensor, which generalizes the max-norm for matrices. Our analysis is deterministic and shows…
We introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates…
One of the major optimizations employed in deep learning frameworks is graph rewriting. Production frameworks rely on heuristics to decide if rewrite rules should be applied and in which order. Prior research has shown that one can discover…
Tensor processing infrastructures such as deep learning frameworks and specialized hardware accelerators have revolutionized how computationally intensive code from domains such as deep learning and image processing is executed and…
High-dimensional data arise naturally in many areas of science and engineering, including machine learning, signal processing, computational physics, and statistics. Such data are often represented as tensors, multi-dimensional…
We consider the problem of tensor completion with graphs serving as side information to represent interrelationships among variables. Existing approaches suffer from several limitations: (1) they are often task-specific and lack generality…
We provide a graphical treatment of SAT and #SAT on equal footing. Instances of #SAT can be represented as tensor networks in a standard way. These tensor networks are interpreted by diagrams of the ZH-calculus: a system to reason about…
Axon is a language that enables shape and rank inference for tensors in a Deep Learning graphs. It aims to make shapes implicit and inferred, in a similar manner to how types are implicit and inferred in many functional programming…
We study the recovery of the underlying graphs or permutations for tensors in the tensor ring or tensor train format. Our proposed algorithms compare the matricization ranks after down-sampling, whose complexity is $O(d\log d)$ for $d$-th…
The real-world effectiveness of deep neural networks often depends on their latency, thereby necessitating optimization techniques that can reduce a model's inference time while preserving its performance. One popular approach is to…
This paper conducts a rigorous analysis for provable estimation of multidimensional arrays, in particular third-order tensors, from a random subset of its corrupted entries. Our study rests heavily on a recently proposed tensor algebraic…
Many compilers, synthesizers, and theorem provers rely on rewrite rules to simplify expressions or prove equivalences. Developing rewrite rules can be difficult: rules may be subtly incorrect, profitable rules are easy to miss, and rulesets…
We study the rank one completion problem for tensors of arbitrary orders. The notion of rank one determinable tensors is introduced. We explore its properties and propose a recursive algorithm for computing rank one tensor completion. This…
Domain-specific languages (DSLs) for machine learning are revolutionizing the speed and efficiency of machine learning workloads as they enable users easy access to high-performance compiler optimizations and accelerators. However, to take…
Tensor graph superoptimisation systems perform a sequence of subgraph substitution to neural networks, to find the optimal computation graph structure. Such a graph transformation process naturally falls into the framework of sequential…
The unification of symbolic reasoning and neural networks remains a central challenge in artificial intelligence. Symbolic systems offer reliability and interpretability but lack scalability, while neural networks provide learning…
This study aims to solve the over-reliance on the rank estimation strategy in the standard tensor factorization-based tensor recovery and the problem of a large computational cost in the standard t-SVD-based tensor recovery. To this end, we…
Recent efforts to unravel the mystery of implicit regularization in deep learning have led to a theoretical focus on matrix factorization -- matrix completion via linear neural network. As a step further towards practical deep learning, we…
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…
We give reconstruction algorithms for subclasses of depth-3 arithmetic circuits. In particular, we obtain the first efficient algorithm for finding tensor rank, and an optimal tensor decomposition as a sum of rank-one tensors, when given…