Related papers: Upgrading Subgroup Triple Product Property Triples

Multiple hypothesis testing is widely used to evaluate scientific studies involving statistical tests. However, for many of these tests, p-values are not available and are thus often approximated using Monte Carlo tests such as permutation…

In this short note, we compute higher extension groups for all irreducible representations and deduce the multiplicity formula for finite length representations in triple product case.

In a paper published in 1981, Sch\"onhage showed that large total matrix multiplications can be reduced to powers of partial matrix multiplication tensors, which correspond to the bilinear computation task of multiplying matrices with some…

Sum-product networks (SPNs) are probabilistic models characterized by exact and fast evaluation of fundamental probabilistic operations. Its superior computational tractability has led to applications in many fields, such as machine…

We present new algorithms to detect and correct errors in the product of two matrices, or the inverse of a matrix, over an arbitrary field. Our algorithms do not require any additional information or encoding other than the original inputs…

We present algorithms for real and complex dot product and matrix multiplication in arbitrary-precision floating-point and ball arithmetic. A low-overhead dot product is implemented on the level of GMP limb arrays; it is about twice as fast…

Recommendation systems, social network analysis, medical imaging, and data mining often involve processing sparse high-dimensional data. Such high-dimensional data are naturally represented as tensors, and they cannot be efficiently…

Existing pre-trained language models (PLMs) are often computationally expensive in inference, making them impractical in various resource-limited real-world applications. To address this issue, we propose a dynamic token reduction approach…

It is known since the 1970s that no more than 23 multiplications are required for computing the product of two 3 x 3-matrices. It is not known whether this can also be done with fewer multiplications. However, there are several mutually…

The quantum PCP conjecture asks whether it is QMA-hard to distinguish between high- and low-energy Hamiltonians even when the gap between "high" and "low" energy is large (constant). A natural proof strategy is gap amplification: start from…

This paper introduces matrix product state (MPS) decomposition as a computational tool for extracting features of multidimensional data represented by higher-order tensors. Regardless of tensor order, MPS extracts its relevant features to…

Temporal point process (TPP) models combined with recurrent neural networks provide a powerful framework for modeling continuous-time event data. While such models are flexible, they are inherently sequential and therefore cannot benefit…

Compound matrices play an important role in many fields of mathematics and have recently found new applications in systems and control theory. However, the explicit formulas for these compounds are non-trivial and not always easy to use.…

Even when aggregate accuracy is high, state-of-the-art NLP models often fail systematically on specific subgroups of data, resulting in unfair outcomes and eroding user trust. Additional data collection may not help in addressing these…

We introduce a relaxation of the notion of tensor rank, called s-rank, and show that upper bounds on the s-rank of the matrix multiplication tensor imply upper bounds on the ordinary rank. In particular, if the "s-rank exponent of matrix…

Group equivariant neural networks are growing in importance owing to their ability to generalise well in applications where the data has known underlying symmetries. Recent characterisations of a class of these networks that use high-order…

In this work faster unsigned multiplication has been achieved by using a combination of High Performance Multiplication [HPM] column reduction technique and implementing a N-bit multiplier using 4 N/2-bit multipliers (recursive…

The objective of this paper is to define an effective strategy for building an ensemble of Genetic Programming (GP) models. Ensemble methods are widely used in machine learning due to their features: they average out biases, they reduce the…

As neural networks are increasingly employed in machine learning practice, how to efficiently share limited training resources among a diverse set of model training tasks becomes a crucial issue. To achieve better utilization of the shared…

Dynamic diversification---finding a set of data points with maximum diversity from a time-dependent sample pool---is an important task in recommender systems, web search, database search, and notification services, to avoid showing users…