International Business Machines Corporation

Ramot at Tel-aviv University Ltd.

Tufts College

Tufts University

Tel Aviv-yafo University

Haim Avron

Lior Horesh

Misha E Kilmer

Vasileios Kalantzis

Shashanka Ubaru

Oguzhan Murat Onen

Elizabeth Newman

Tayfun Gokmen

Mark Steven Squillante

David Paul Woodruff

Guy M Cohen

Wilfried Haensch

David Nahamoo

Chai Wah Wu

Raya Horesh

Tomasz J Nowicki

Kenneth Lee Clarkson

Malte Johannes Rasch

Vikas Sindhwani

Anshul Gupta

Gal Shulkind

Leo S Liberti

Osman Asif Malik

Huy Le Nguyen

Jiani Zhang

Techniques for generating and managing, including simulating and training, deep tensor neural networks are presented. A deep tensor neural network comprises a graph of nodes connected via weighted edges. A network management component (NMC) extracts features from tensor-formatted input data based on tensor-formatted parameters. NMC evolves tensor-formatted input data based on a defined tensor-tensor layer evolution rule, the network generating output data based on evolution of the tensor-formatted input data. The network is activated by non-linear activation functions, wherein the weighted edges and non-linear activation functions operate, based on tensor-tensor functions, to evolve tensor-formatted input data. NMC trains the network based on tensor-formatted training data, comparing output training data output from the network to simulated output data, based on a defined loss function, to determine an update. NMC updates the network, including weight and bias parameters, based on the update, by application of tensor-tensor operations.

Generating and managing deep tensor neural networks

A computer implemented method for speeding up execution of a convex optimization operation one or more quadratic complexity operations to be performed by an analog crossbar hardware switch, and identifying one or more linear complexity operations to be performed by a CPU. At least one of the quadratic complexity operations is performed by the analog crossbar hardware, and at least one of the linear complexity operations is performed by the CPU. An iteration of an approximation of a solution to the convex optimization operation is updated by the CPU.

Accelerated Quasi-Newton methods on analog crossbar hardware

Methods and systems for solving a linear system include setting resistances in an array of settable electrical resistances in accordance with values of an input matrix. A series of input vectors is applied to the array as voltages to generate a series of respective output vectors. Each input vector in the series of vectors is updated based on comparison of the respective output vectors to a target vector. A solution of a linear system is determined that includes the input matrix based on the updated input vectors.

Analog hardware matrix computation

A computer-implemented method is presented for performing matrix sketching by employing an analog crossbar architecture. The method includes low rank updating a first matrix for a first period of time, copying the first matrix into a dynamic correction computing device, switching to a second matrix to low rank update the second matrix for a second period of time, as the second matrix is low rank updated, feeding the first matrix with first stochastic pulses to reset the first matrix back to a first matrix symmetry point, copying the second matrix into the dynamic correction computing device, switching back to the first matrix to low rank update the first matrix for a third period of time, and as the first matrix is low rank updated, feeding the second matrix with second stochastic pulses to reset the second matrix back to a second matrix symmetry point.

Matrix sketching using analog crossbar architectures

A method of performing Principal Component Analysis is provided. The method includes receiving, by a computing device, evolving data for processing/visualization. The method further includes, by the computing device, a dimensionality for reducing of the evolving data using the PCA, wherein the PCA is performed on analog crossbar hardware. The method also includes using, by the computing device, the evolving data for visualization having the dimensionality thereof reduced by the principal component analysis for a further application.

Fast PCA of evolving data using analog crossbar array

A computer-implemented method for analyzing a time-varying graph is provided. The time-varying graph includes nodes representing elements in a network, edges representing transactions between elements, and data associated with the nodes and the edges. The computer-implemented method includes constructing, using a processor, adjacency and feature matrices describing each node and edge of each time-varying graph for stacking into an adjacency tensor and describing the data of each time-varying graph for stacking into a feature tensor, respectively. The adjacency and feature tensors are partitioned into adjacency and feature training tensors and into adjacency and feature validation tensors, respectively. An embedding model and a prediction model are created using the adjacency and feature training tensors. The embedding and prediction models are validated using the adjacency and feature validation tensors to identify an optimized embedding-prediction model pair.

Tensor-based predictions from analysis of time-varying graphs

An illustrative embodiment includes a method for solving a dynamical system. The method comprises: obtaining multidimensional snapshots representing respective discrete solutions of the dynamical system; storing the multidimensional snapshots within a snapshot tensor having an order of at least three; generating a basis for at least a subspace of a state space of the dynamical system at least in part by performing a decomposition of the snapshot tensor; deriving a reduced order model at least in part by using the basis to project the dynamical system from the state space onto the subspace; and solving the reduced order model of the dynamical system.

Multi-linear dynamical model reduction

A computer-implemented method is presented for optimal experimental design to correct a misspecified model approximating a behavior of a dynamic system. The method includes formulating an experiment, determining experimental settings for configuring controllable experimental parameters based on mutual information and submodularity, measuring informative values associated with each choice of experimental design, as prescribed by the controllable experimental parameters, and learning a correction function based on the measured informative values. The computer-implemented method further includes determining an experimental design setup for gaining information content, and combining the experimental design setup with the experimental settings to construct a corrected model of the dynamic system.

Optimal experimental design based on mutual information and submodularity

A tensor decomposition method, system, and computer program product include compressing multi-dimensional data by truncated tensor-tensor decompositions.

Optimal multi-dimensional data compression by tensor-tensor decompositions tensor

Methods and systems for model discovery include forming a mathematical program based on a set of observational data to generate an objective function and one or more constraints. The mathematical program represents a model space as an expression tree comprising operators and operands. The mathematical program is solved by optimizing the objective function subject to the one or more constraints to determine a model in the model space that best fits the set of observational data.

Globally convergent system and method for automated model discovery

A system, method and computer program product for quickly and approximately solving structured regression problems. In one aspect, the system, method and computer program product are applied to problems that arise naturally in various statistical modeling settings&#x2014;when the design matrix is a Vandermonde matrix or a sequence of such matrices. Using the Vandermonde matrix structure further accelerates the solution of the regression problem, achieving running times that are faster than 'input sparsity'. The modeling framework speedup benefits of randomized regression for solving structured regression problems.

Sketching structured matrices in nonlinear regression problems

Embodiments of the invention relate to sketching for M-estimators for performing regression. One embodiment includes providing one or more sets of input data. A matrix A and a vector b are generated using the input data. A processor device is used for processing the matrix A and the vector b based on a randomized sketching matrix S. A vector x that minimizes a normalized measure function is determined based on the matrix A and the vector b. A relationship between the input data is determined based on the vector x.

Regression using M-estimators and polynomial kernel support vector machines and principal component regression

Systems and methods to reduce I/O (input/output) with regard to out-of-core liner solvers and/or to speed up out-of-core linear solvers.

Growing community of inventors

Tel Aviv, Israel

Haim Avron