Generalised matrix-matrix multiplication forms the kernel of many mathematical algorithms. A faster matrix-matrix multiply immediately benefits these algorithms. In this paper we implement efficient matrix multiplication for large matrices using the floating point Intel Pentium SIMD (Single Instruction Multiple Data) a…
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48 results for “matrix multiplication”
Matrix multiplication is a fundamental building block for large scale computations arising in various applications, including machine learning. There has been significant recent interest in using coding to speed up distributed matrix multiplication, that are robust to stragglers (i.e., machines that may perform slower …
Localized sketching improves matrix multiplication and ridge regression complexity.
problem Efficiently approximate matrix multiplication and ridge regression with limited data availability.
method Localized sketching matrices for block diagonal structure, reducing sample complexity.
result Localized sketching achieves sample complexity matching global sketching methods.
Paper proposes new costs for learning multiple centers in MDNs.
problem Learning multiple centers for density approximation in MDNs.
method Combines MDNs with contrastive costs using four types of kernelized matrix costs.
result New costs improve data density approximation in MDNs.
Improves matrix multiplication throughput for asymmetric bit-width operands.
problem Matrix multiplications between asymmetric bit-width operands, especially 8- and 4-bit, are not efficiently handled by existing SIMD instructions.
method Proposes a new SIMD matrix multiplication instruction that uses mixed precision on inputs (8- and 4-bit) and accumulates into 16-bit output, improving throughput.
result Offers 2x improvement in throughput compared to existing symmetric-operand-size instructions, with negligible overflow.
Weyl Tensors, Strongly Regular Graphs, Multiplicative Characters, and a Quadratic Matrix Equationmath.GR
Solutions to a quadratic matrix equation are linked to strongly regular graphs and multiplicative characters.
problem Solving a specific quadratic matrix equation in Riemannian geometry.
method Constructing nonzero solutions using group rings and multiplicative characters of finite fields.
result Solutions relate to strongly regular graphs and multiplicative characters of finite fields.
JAMPI improves matrix multiplication in Spark, boosting performance by up to 24%.
problem Efficiently performing matrix multiplication in Spark.
method Combining asynchronous network IO, auto-vectorization, and barrier execution mode.
result Up to 24% performance increase in distributed matrix multiplication.
This note gives a simple analysis of a randomized approximation scheme for matrix multiplication proposed by Sarlos (2006) based on a random rotation followed by uniform column sampling. The result follows from a matrix version of Bernstein's inequality and a tail inequality for quadratic forms in subgaussian random ve…
Stella Nera accelerates matrix multiplications with a hash-based approach, achieving high energy efficiency and accuracy.
problem High computational and energy demands due to matrix multiplications in AI models.
method Stella Nera uses Maddness, a hash-based product quantization, to eliminate multipliers and achieve lookups and additions.
result Achieved an energy efficiency of 161 TOp/s/W@0.55V, 25x better than conventional MatMul accelerators.
Multiple clustering aims at exploring alternative clusterings to organize the data into meaningful groups from different perspectives. Existing multiple clustering algorithms are designed for single-view data. We assume that the individuality and commonality of multi-view data can be leveraged to generate high-quality …
Study proposes memory-efficient backpropagation for linear layers in neural networks.
problem Significant memory usage in backpropagation through linear layers in neural networks.
method Randomized matrix multiplications to reduce memory usage with a moderate decrease in test accuracy.
result Demonstrated benefits of the proposed method on fine-tuning pre-trained models.
Paper defines multiplicities for quaternion eigenvalues without complex matrix concepts.
problem Defining multiplicities for quaternion eigenvalues without traditional matrix concepts.
method Introduces two definitions for algebraic and geometric multiplicities equivalent to classical definitions.
result Definitions are equivalent to classical ones and prove all properties easily.
New algorithms estimate matrix norms without matrix multiplication.
problem Estimating matrix norms efficiently in a matrix-free setting.
method Randomized algorithms based on Hutchinson's estimator modifications.
result Oracle complexity bounds for two-to-infinity and one-to-two norms.
A new algorithm speeds up matrix multiplication without actual multiplication.
problem Efficiently multiplying matrices in machine learning.
method Learning-based algorithm that uses hashing, averaging, and byte shuffling.
result Often runs 100x faster than exact matrix products and 10x faster than current approximate methods.
Paper introduces SMM for forecasting multiple time series with missing values.
problem Forecasting multiple time series with missing and noisy values.
method Sliding Mask Method (SMM) using Non-negative Matrix Factorization (NMF).
result The method outperforms state-of-the-art methods in time series forecasting.
A new method combines multiple cancer datasets to improve analysis.
problem Combining multiple cancer datasets for comprehensive analysis.
method Multiple Augmented Reduced Rank Regression (maRRR) method.
result Improved power and insights from combining multiple cancer datasets.
New algorithm for active learning in multiple matrix completion problems.
problem Simultaneous matrix completion with unknown ranks and varying sizes.
method MAlocate algorithm that adapts to unknown ranks and sizes.
result Minimax-optimal performance demonstrated with lower-bound analysis.
Improved covariance matrix estimation for multiple classes with limited data.
problem Estimating covariance matrices for multiple classes with scarce data.
method Coupled regularized sample covariance matrix estimator (RSCM) that combines pooled SCM and scaled identity matrix for regularization.
result The coupled RSCM estimators outperform cross-validation in classification tasks with comparable accuracy but faster computation.
Federated multi-view matrix factorization learns from multiple data sources without centralizing user data.
problem Cold-start federated recommendations and multi-view data structure.
method Federated learning framework extended to multi-view matrix factorization.
result Federated multi-view matrix factorization outperforms simpler methods in cold-start federated recommendations.
Transfer knowledge from multiple sources to improve matrix completion.
problem Matrix completion with noisy data.
method Aggregating singular subspaces information from multiple sources to solve a two-way PCA problem and transform into a low-dimensional linear regression.
result Guaranteed statistical efficiency in transforming the high-dimensional target matrix completion problem.
We extend Kyle's model to include stochastic liquidity and multiple assets.
problem Modeling informed trading with stochastic liquidity and multiple assets.
method Developed a variational formulation and derived a matrix-valued martingale depth process.
result A linear-Gaussian equilibrium with stochastic matrix-valued price impact.
We extend kernelized matrix factorization with a fully Bayesian treatment and with an ability to work with multiple side information sources expressed as different kernels. Kernel functions have been introduced to matrix factorization to integrate side information about the rows and columns (e.g., objects and users in …
Motivated by electricity consumption metering, we extend existing nonnegative matrix factorization (NMF) algorithms to use linear measurements as observations, instead of matrix entries. The objective is to estimate multiple time series at a fine temporal scale from temporal aggregates measured on each individual serie…
Collective Matrix Completionstat.ML
Matrix completion aims to reconstruct a data matrix based on observations of a small number of its entries. Usually in matrix completion a single matrix is considered, which can be, for example, a rating matrix in recommendation system. However, in practical situations, data is often obtained from multiple sources whic…
The matrix-based Renyi's α-order entropy functional was recently introduced using the normalized eigenspectrum of a Hermitian matrix of the projected data in a reproducing kernel Hilbert space (RKHS). However, the current theory in the matrix-based Renyi's α-order entropy functional only defines the entropy of a single…
BiQGEMM efficiently multiplies quantized DNN weights using lookup tables.
problem Efficiently multiplying quantized DNN weights on CPUs/GPUs with limited memory.
method BiQGEMM pre-computes and stores redundant intermediate results in lookup tables.
result BiQGEMM achieves lower overall computations and higher performance.
Despite advances in scalable models, the inference tools used for Gaussian processes (GPs) have yet to fully capitalize on developments in computing hardware. We present an efficient and general approach to GP inference based on Blackbox Matrix-Matrix multiplication (BBMM). BBMM inference uses a modified batched versio…
Recent studies utilize multiple kernel learning to deal with incomplete-data problem. In this study, we introduce new methods that do not only complete multiple incomplete kernel matrices simultaneously, but also allow control of the flexibility of the model by parameterizing the model matrix. By imposing restrictions …
Proposes a Bayesian approach for integrating multiple linked matrices.
problem Integrating multiple linked matrices for diverse applications.
method Empirical Bayes Linked Matrix Decomposition (EB-LMD).
result Efficient estimation algorithm with no tuning parameters.
Efficiently computes matrix square roots and their inverses for large matrices.
problem Computing matrix square roots and inverses for large matrices efficiently.
method Combines Krylov subspace methods with rational approximation for quadratic-time computation.
result Achieves 4 decimal places of accuracy with fewer than 100 matrix-vector multiplications.
Paper recovers multi-subspace matrices from permuted data.
problem Recovering a multi-subspace matrix from permuted data with corrupted columns.
method Four-stage algorithm pipeline: outlier identification, subspace reconstruction, outlier classification, unsupervised sensing.
result The pipeline provides theoretical guarantees for reliable multi-subspace matrix recovery.
A Diagrammatic Approach to Improve Computational Efficiency in Group Equivariant Neural Networkscs.LG
New algorithm speeds up group equivariant neural networks computations.
problem Challenging computations in group equivariant neural networks.
method Diagrammatic framework based on category theory for matrix multiplication.
result Exponential improvement in time complexity for matrix multiplication.
Multi-view clustering aims at integrating complementary information from multiple heterogeneous views to improve clustering results. Existing multi-view clustering solutions can only output a single clustering of the data. Due to their multiplicity, multi-view data, can have different groupings that are reasonable and …
New method tackles high-dimensional SBL without covariance matrices.
problem Sparse coding problem in high-dimensional settings.
method Parallel solution of multiple linear systems using conjugate gradient algorithm.
result Our method scales better in computation time and memory.
Linear algebra algorithms are used widely in a variety of domains, e.g machine learning, numerical physics and video games graphics. For all these applications, loop-level parallelism is required to achieve high performance. However, finding the optimal way to schedule the workload between threads is a non-trivial prob…
We present the multiplicative recurrent neural network as a general model for compositional meaning in language, and evaluate it on the task of fine-grained sentiment analysis. We establish a connection to the previously investigated matrix-space models for compositionality, and show they are special cases of the multi…
New method proves Jones Polynomial's connect sum property.
problem Jones Polynomial's behavior under connect sums.
method Trip matrix method for calculating Jones Polynomial.
result Jones Polynomial is multiplicative under connect sums.
This paper identifies and estimates the label noise transition matrix without ground truth labels.
problem Learning with noisy labels and identifying the noise transition matrix.
method Building on Kruskal's identifiability results, the paper characterizes the identifiability of the label noise transition matrix for the generic case at the instance level.
result The necessity of multiple noisy labels in identifying the noise transition matrix for the generic case at the instance level.
We derive exponential tail inequalities for sums of random matrices with no dependence on the explicit matrix dimensions. These are similar to the matrix versions of the Chernoff bound and Bernstein inequality except with the explicit matrix dimensions replaced by a trace quantity that can be small even when the dimens…
Improved MMWU algorithm achieves instance-optimal regret bound for matrix LEA.
problem Matrix Learning from Expert Advice problem.
method Developed a general potential-based framework for matrix LEA, using a new Jensen's trace inequality.
result Achieved instance-optimal regret bound of .
The paper infers multiple graphs from stationary signals on them.
problem Inferring multiple graphs from signals observed on their nodes.
method Convex optimization method leveraging matrix polynomial commutation.
result High-probability bounds on recovery error provided.
A new algorithm speeds up matrix operations in Neural Networks.
problem Time-consuming matrix operations in Neural Networks.
method An algorithm that increases the degree of parallelism of matrix multiplication.
result The algorithm speeds up several matrix operations in Neural Networks.
Advances in molecular "omics'" technologies have motivated new methodology for the integration of multiple sources of high-content biomedical data. However, most statistical methods for integrating multiple data matrices only consider data shared vertically (one cohort on multiple platforms) or horizontally (different …
NMF with specific constraints is equivalent to LDA.
problem Dimensionality reduction of non-negative data.
method NMF with normalization constraints and Dirichlet prior.
result NMF with these constraints is equivalent to LDA.
Fast Convolutive Nonnegative Matrix Factorization Through Coordinate and Block Coordinate Updatescs.LG
Identifying recurring patterns in high-dimensional time series data is an important problem in many scientific domains. A popular model to achieve this is convolutive nonnegative matrix factorization (CNMF), which extends classic nonnegative matrix factorization (NMF) to extract short-lived temporal motifs from a long …
Optimal Subspace Embeddings: Resolving Nelson-Nguyen Conjecture Up to Sub-Polylogarithmic Factorscs.DS
We prove optimal subspace embedding conjecture up to sub-polylogarithmic factors.
problem Optimal dimension and sparsity of subspace embeddings.
method Iterative decoupling technique to analyze higher-order trace moment bounds.
result Sub-polylogarithmic factors in dimension and sparsity of subspace embeddings.
Nonnegative matrix factorization (NMF), a dimensionality reduction and factor analysis method, is a special case in which factor matrices have low-rank nonnegative constraints. Considering the stochastic learning in NMF, we specifically address the multiplicative update (MU) rule, which is the most popular, but which h…
Algorithm counts intersections of normal curves efficiently.
problem Efficiently solving word problems in mapping class groups of punctured surfaces.
method Fast algorithm for counting intersections of normal curves on triangulated surfaces.
result Efficient solution of the word problem for mapping class groups of punctured surfaces.