Related papers: TensorRight: Automated Verification of Tensor Grap…
Recurrent neural networks (RNNs) are powerful tools for sequential modeling, but typically require significant overparameterization and regularization to achieve optimal performance. This leads to difficulties in the deployment of large…
Query rewrite systems perform graph substitutions using rewrite rules to generate optimal SQL query plans. Rewriting logical and physical relational query plans is proven to be an NP-hard sequential decision-making problem with a search…
The results of Strassen and Raz show that good enough tensor rank lower bounds have implications for algebraic circuit/formula lower bounds. We explore tensor rank lower and upper bounds, focusing on explicit tensors. For odd d, we…
Constrained counting is a fundamental problem in artificial intelligence. A promising new algebraic approach to constrained counting makes use of tensor networks, following a reduction from constrained counting to the problem of…
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…
String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. Dixon, Duncan and Kissinger introduced string graphs, which are a combinatoric…
We study the tensor-on-tensor regression, where the goal is to connect tensor responses to tensor covariates with a low Tucker rank parameter tensor/matrix without the prior knowledge of its intrinsic rank. We propose the Riemannian…
Logical query plan rewriting transforms a relational database query into an equivalent but more efficient form and is crucial to the performance of database-backed applications. In existing systems, rewrite rules are typically implemented…
Tensor networks have been an important concept and technique in many research areas, such as quantum computation and machine learning. We study the exponential complexity of contracting tensor networks on two special graph structures:…
Deep learning is widely used to uncover hidden patterns in large code corpora. To achieve this, constructing a format that captures the relevant characteristics and features of source code is essential. Graph-based representations have…
A tensor is a multi-way array that can represent, in addition to a data set, the expression of a joint law or a multivariate function. As such it contains the description of the interactions between the variables corresponding to each of…
The tensor data recovery task has thus attracted much research attention in recent years. Solving such an ill-posed problem generally requires to explore intrinsic prior structures underlying tensor data, and formulate them as certain forms…
Tensorizing a neural network involves reshaping some or all of its dense weight matrices into higher-order tensors and approximating them using low-rank tensor network decompositions. This technique has shown promise as a model compression…
Despite the widespread use of LLMs due to their superior performance in various tasks, their high computational costs often lead potential users to opt for the pretraining-finetuning pipeline. However, biases prevalent in manually…
Tensors decompositions are a class of tools for analysing datasets of high dimensionality and variety in a natural manner, with the Canonical Polyadic Decomposition (CPD) being a main pillar. While the notion of CPD is closely intertwined…
Tensors, or multidimensional arrays, are data structures that can naturally represent visual data of multiple dimensions. Inherently able to efficiently capture structured, latent semantic spaces and high-order interactions, tensors have a…
Generalizing work of K\"unnemann, Paturi, and Schneider [ICALP 2017], we study a wide class of high-dimensional dynamic programming (DP) problems in which one must find the shortest path between two points in a high-dimensional grid given a…
We introduce an efficient algorithm for reducing bond dimensions in an arbitrary tensor network without changing its geometry. The method is based on a novel, quantitative understanding of local correlations in a network. Together with a…
String diagrams provide a convenient graphical framework which may be used for equational reasoning about morphisms of monoidal categories. However, unlike term rewriting, rewriting string diagrams results in shorter equational proofs,…
In recent years, a class of dictionaries have been proposed for multidimensional (tensor) data representation that exploit the structure of tensor data by imposing a Kronecker structure on the dictionary underlying the data. In this work, a…