272 results about "Diagonal matrix" patented technology

The invention relates to the technical field of highway bridge safety monitoring, and discloses a bridge dynamic weighing algorithm based on likelihood estimation. A bridge is used as a carrier for vehicle weighing, an influence line of the bridge is obtained through a calibration test, and an influence line mean vector and an influence line covariance matrix are calculated; an influence line matrix is obtained based on the influence line mean vector, the vehicle speed and the axle distance, and an initial axle load value is calculated through a Moses algorithm; calculating a mean square error diagonal matrix of a measurement error according to the influence line matrix, the bridge load response and the axle load of the previous iteration step, and obtaining a covariance matrix of the bridge load response; calculating an axle load corresponding to the maximum likelihood probability based on the covariance matrix of the bridge load response in combination with the influence line matrix and the bridge load response; and repeating until the difference value between the axle weight updated this time and the axle weight obtained last time is smaller than a preset value, and taking the axle weight updated this time as a final result. According to the invention, the problem of low axle load identification precision of the existing bridge dynamic weighing system is solved.

The invention discloses an adaptive blocking compressed sensing image super-resolution reconstruction method and system. The method comprises the following steps: acquiring a low-resolution image and carrying out adaptive blocking on the low-resolution image; establishing a sparse representation model of the high-resolution image by using a discrete cosine transform basis; establishing an observation dimension reduction model by using the binary block diagonal matrix to obtain a relationship between a high-resolution image and a low-resolution image; performing compressed sensing super-resolution reconstruction solution on the low-resolution sub-block images by using a weighted iterative least square algorithm to generate high-resolution image blocks, and performing constraint by using Shearlet transformation and dual-scale total variation regularization in the reconstruction process; and splicing the generated high-resolution image blocks according to the position indexes to obtain a complete high-resolution image meeting the requirements. According to the method, the problems of unreasonable blocking caused by single blocking basis and limited reconstruction effect caused by insufficient consideration of prior information in the existing method are solved.

The invention discloses a federal large model adaptive low-rank fine tuning method and device, computer equipment and a storage medium. The method comprises the following steps: decomposing a low-rank adaptive matrix of a large language model into a server shared matrix and a client private matrix; initializing a private matrix and an adaptive diagonal matrix; the client dynamically trims the low-contribution dimension and adjusts the actual effective rank according to the standard deviation of each element in the adaptive diagonal matrix, and combines the shared matrix and the private matrix to obtain an updated private matrix; the server performs aggregation through a rank-aware aggregation strategy, and performs fine adjustment on the shared matrix by using the public data set to obtain a global model; and deploying the global model to a server and each client. By implementing the method, adaptive fine tuning of the large language model can be efficiently realized, meanwhile, the problems of aggregation interference, low resource utilization rate and insufficient generalization ability in a traditional method are solved, and the technical scheme can be applied to the fields of finance and medical health.

The invention discloses a multi-view clustering method based on tensor feature extraction, and the method comprises the steps: inputting a multi-view data matrix, constructing a similarity matrix of each view through a K-NN algorithm and a Gaussian kernel function, and carrying out the spectral clustering to obtain a sample embedding matrix; performing singular value decomposition on an original data matrix of each view, taking first c left singular vectors to construct a feature embedding matrix, applying 2, 1 norm group sparse constraint on the feature embedding matrix, and connecting a sample embedding matrix through a bigraph to extract features; and normalizing the sample embedded matrix, and reconstructing a block diagonal matrix into a third-order tensor. And integrating the sample embedding matrix, the feature embedding matrix and global tensor learning to construct a target function, and optimizing through an alternating direction multiplier method until convergence. And finally, the normalized samples are embedded into the matrix to form block diagonals to form a consistent similarity graph, and a clustering result is obtained by using an N-Cut or k-means algorithm.

The invention belongs to the related technical field of novel power system analysis, and discloses a stability analysis method and analysis system for a multi-following-network-construction-type converter system, and the stability analysis method comprises the steps: calculating admittance matrixes Qeq and Qml used for evaluating the stability of a following-network-type converter; and performing joint diagonalization processing on the matrixes Qeq and Qml to obtain corresponding diagonal matrixes Lambda eq and Lambda ml, extracting diagonal elements of the matrixes to form n groups of characteristic parameters (Lambda i and mu i), judging whether the (Lambda i and mu i XRPC0) are positioned above the critical stability curve of the following grid type converter or not, if so, indicating that the system is stable, and if not, indicating that the system is unstable. Based on the method, the stability criterion of the multi-following-network-construction-type converter system can be simplified, and the influence of different control modes of the construction-type converter on the stability of the following-network-type equipment can be clarified, so that the reactive power control strategy of the construction-type converter can be optimized, and the supporting capability of the construction-type converter on the power grid can be enhanced.

The invention discloses a federated learning participant selection method and system, and the method comprises the steps: obtaining local model parameters uploaded by all federated learning client participants through a central server, and constructing a local model feature observation tensor of each client participant; calculating kernel similarity between participants of the client; determining a positive semi-definite similarity kernel matrix; the central server complements missing values of the positive semi-definite similarity kernel matrix to obtain a complete similarity kernel matrix; the central server constructs a timeliness weight diagonal matrix; the central server constructs a likelihood matrix according to the complete similarity kernel matrix and the timeliness weight diagonal matrix; solving the likelihood matrix through a determinant point process to obtain a selected client participant subset; averaging all local model parameters in the selected client participant subset to obtain a global model; and finally, issuing the global model to the selected client participant.

The invention relates to the technical field of array signal processing, in particular to a space-frequency power inversion anti-interference method fusing SMI-LDL decomposition. The problems that an existing space-time anti-interference technology is high in calculation complexity, and real-time processing is difficult to achieve in limited resources of a navigation receiver are mainly solved. The method comprises the following steps: firstly, converting a radio frequency signal received by an array into a digital intermediate frequency signal and carrying out sliding window partitioning processing; windowing the data block and performing FFT (Fast Fourier Transform) to obtain a frequency domain array; then calculating an auto-covariance matrix R of other array elements except the reference array element and a cross-covariance matrix r of the reference array element and other array elements; lDL decomposition is carried out on the auto-covariance matrix to obtain a lower triangular matrix L and a diagonal matrix D, and inversion is carried out on the lower triangular matrix L and the diagonal matrix D respectively, so that huge operand caused by direct inversion of the covariance matrix is avoided; and finally, calculating an optimal weighting vector according to a power inversion criterion, and performing spatial filtering on the frequency domain data.

The invention discloses an IQ imbalance blind calibration method and an IQ modulation demodulator, and the method comprises the steps: determining a regularity judgment condition based on the second-order statistical characteristics of a complex signal under an ideal condition; building an IQ imbalance mathematical model to determine a compensation mode; obtaining a compensation coefficient formula based on the compensation mode, the regularity judgment condition and the step diagonal matrix; substituting the complex signal into a compensation coefficient formula to obtain a high-order LMS dual-channel algorithm model; a nonlinear step size error model is introduced into a high-order LMS double-channel algorithm model. The invention provides a frequency-related square difference operation variable step size IQ imbalance dual-channel high-order blind compensation filtering algorithm without any prior information. Algorithm parameters are adjusted according to signal mismatch caused by phase mismatch and amplitude imbalance of input signals, so that the signals keep an ideal orthogonal relation.

The invention relates to the technical field of deep neural network training, and discloses a deep neural network training diagnosis method and system based on gradient visualization and loss curved surface analysis, and the method comprises the steps: obtaining a parameter snapshot of a neural network trained to t-th iteration, sampling k random detection vectors, and calculating a Hessian vector product; performing Lanczos iteration on each random detection vector to obtain k symmetric tridiagonal matrixes and calculating a characteristic value density spectrum; mapping the k symmetric tridiagonal matrixes into orthogonal projection base vectors, constructing a two-dimensional projection plane, determining a saddle point state according to the integral of the characteristic value density spectrum in a negative value region, determining a flat region according to the peak value of the characteristic value density spectrum in a zero value region, and determining a sharp minimum value according to the peak value of the characteristic value density spectrum in a positive value region; according to the method, the descending path with the steepest curvature can be captured, and the dominant mode of the dynamics can be optimized, so that the projected loss curved surface truly reflects the geometric structure change in the training process, and the pathological diagnosis of the training process based on the second-order geometric information is realized.

The invention relates to the technical field of power electronics and direct current transmission, in particular to a two-level VSC-HVDC minimum direct current capacitance calculation method based on LMI. The method comprises the following steps: establishing a state equation comprising a main circuit and a controller dynamic model, converting a three-phase alternating current quantity into a direct current quantity under a synchronous rotating coordinate system by utilizing Park transformation, and deducing a system state equation in combination with a Kirchhoff's law; performing Taylor expansion and linearization on the nonlinear equation, and constructing a small signal model based on a Lyapunov stability theory; by separating a diagonal matrix and defining a stability criterion in an LMI form, minimum direct-current capacitance solving is converted into a convex optimization problem, a critical value is iteratively searched by adopting a dichotomy method to determine minimum capacitance, and meanwhile, a tolerance mechanism is introduced to improve the robustness of an algorithm. Through combination of mathematical modeling and an optimization algorithm, the calculation efficiency and accuracy are effectively balanced, and a theoretical basis is provided for reducing the cost and the size of the converter.

The invention provides an artificial intelligence model accelerated training reasoning method and device, and belongs to the field of artificial intelligence, and the method comprises the steps: firstly carrying out the grouping disassembly of a large-dimension matrix in an artificial intelligence model through employing a lamination grouping technology, and converting the large-dimension matrix into a lamination block matrix structure; then, carrying out compression decomposition on the non-diagonal block matrix by utilizing an ACA-SVD matrix decomposition technology, and representing that two small matrixes are multiplied; then diagonal matrix blocks of the obtained laminated block matrix structure are extracted in sequence, the matrix is expressed as multiplication of a plurality of block diagonal matrixes, and the block diagonal matrixes are stored respectively; when model training and reasoning are carried out, a matrix multiplication process can be converted into multiplication of a plurality of block diagonal matrixes, a matrix inversion process can be converted into inversion of the plurality of block diagonal matrixes, the block diagonal matrixes are mutually independent, a recursive relationship does not exist in an operation process, and highly parallel operation can be realized.

The invention discloses a feature generation method, a classification model training method, a classification method and related devices, and relates to the technical field of machine learning. The method comprises the following steps: acquiring radiomics characteristics corresponding to a medical image; decomposing the radiomics characteristics into a column information matrix, a singular value diagonal matrix and a row information matrix corresponding to a plurality of singular values by adopting a singular value decomposition mode; respectively intercepting the singular value diagonal matrix, the column information matrix and the row information matrix based on the numerical values of the singular values, and constructing a first feature matrix by using the intercepted column information matrix, singular value diagonal matrix and row information matrix; and performing dimension reduction processing on the first feature matrix by introducing regularization penalty to obtain a second feature matrix. Through singular value interception and introduction of regularization penalty, the dimensionality and complexity of the image omics features can be effectively reduced while effective features in the image omics features are reserved, so that the performance of a machine learning model obtained through subsequent training is improved.

The invention discloses a random discarding method and system for a graph neural network based on dynamic discarding, and relates to the technical field of artificial intelligence, and the method comprises the following steps: receiving a to-be-processed representative graph, carrying out the node feature extraction of the to-be-processed representative graph, obtaining a node receiving matrix, carrying out the normalization of the node receiving matrix, and obtaining a normalized matrix; extracting a feature vector matrix and a feature value diagonal matrix based on the normalized matrix, and calculating a message transfer matrix based on the feature vector matrix and the feature value diagonal matrix; the message passing matrix is input into a pre-established graph neural network model based on dynamic discarding, information discarding is carried out on the message passing matrix, a discarded message passing matrix is obtained through output, and the pre-established graph neural network model based on dynamic discarding is trained based on a random discarding stopping rule.

The invention discloses a navigation signal blind separation method, system and equipment in an alpha pulse interference environment based on Gaussian kernel filtering, and a medium, and aims to improve the signal processing performance in a complex interference environment. According to the method, alpha pulse interference in aliasing signals is suppressed by adopting a Gaussian kernel filtering technology, and effective suppression of the alpha pulse interference is realized by reasonably designing filtering parameters; two correlation matrixes are subjected to joint diagonalization, and a joint diagonal matrix is used as an initial value of a left aliasing matrix and a right aliasing matrix in a blind separation algorithm, so that the convergence speed of aliasing matrix estimation is effectively improved; then, separating the signals after the pulse interference is suppressed by using a blind separation algorithm of joint diagonalization and an initial value of a left and right aliasing matrix; experimental results show that the method has excellent performance in the aspects of suppressing impulse noise influence and signal separation, and the problems that a traditional method is insufficient in alpha impulse interference suppression and poor in signal separation performance are effectively solved; systems, devices, and media are used to implement the methods.

The invention discloses a space-time elastic weight consolidated edge federal continuous learning method, which is applied to a system comprising a server and a plurality of edge devices, is used for processing space-time heterogeneity time sequence data, and comprises the following steps: initializing training, broadcasting a previous time sequence global time Fisher diagonal matrix (the first time sequence is not broadcasted, the second time sequence is not broadcasted, and the third time sequence is not broadcasted) by the server; however, the global model needs to be randomly initialized and broadcasted); in the model training stage, based on local data, a global time Fisher diagonal matrix and the like, an edge device updates a local model through a loss function containing a time / space regular term, calculates a local space Fisher diagonal matrix, uploads the local space Fisher diagonal matrix, and then a server weights and aggregates the global model according to the data volume and issues the global model, and circulates until convergence; and in the global time Fisher diagonal matrix calculation stage, the equipment calculates a local time Fisher diagonal matrix based on a convergence model, and uploads and aggregates the local time Fisher diagonal matrix for the next time sequence. Historical data does not need to be stored, original data does not need to be transmitted, storage calculation / communication overhead is reduced, privacy is protected, and the model convergence speed and precision are improved.

The invention discloses a hybrid antenna array direction of arrival estimation method based on noise marginalization SBL. The method comprises the following steps: initializing system parameters and a sampling grid set; establishing a hybrid antenna array receiving signal model, and initializing a hybrid beam forming matrix into a block diagonal matrix meeting constant modulus constraint; constructing a hierarchical probability model under a Bayesian framework, and introducing a noise precision parameter into signal prior; integral operation is carried out on the noise precision parameter, so that the signal posterior distribution is converted into student t distribution; an objective function is constructed, an expectation maximization algorithm is adopted to iteratively update a signal energy spectrum, and the process does not involve noise parameter estimation; an alternating iteration strategy is adopted, the signal energy is fixedly updated through inner circulation, and optimization is performed through a gradient descent method after outer circulation is fixed; after convergence, constructing a target function of off-grid estimation by reconstructing a covariance matrix; and searching the off-grid direction of the maximized objective function near a spectrum peak to obtain a final DOA estimation value.

The invention belongs to the field of silicon-based photonics, and particularly relates to an MZI optical neural network construction method based on polarization control and a set port, singular value decomposition is carried out on a weight matrix W of a traditional neural network model to obtain a unitary matrix and a diagonal matrix, a mode of combining a plurality of MZI units is utilized, a unitary matrix or diagonal matrix structure is adopted, and the MZI optical neural network is constructed. Constructing an optical neural network; the method has the advantages that a larger-scale optical matrix is constructed, a higher-dimension data processing task is supported, and then the processing capacity and accuracy of the whole network are improved.

The invention discloses a method for generating an amplitude preparation circuit and a quantum state preparation method and device, and the method comprises the steps: setting a main diagonal element of a block matrix as a to-be-prepared amplitude, and setting other elements as 0, so that the block matrix is equivalent to a diagonal matrix, thereby facilitating the construction of a unitary matrix through employing the block matrix, and in the unitary matrix, the unitary matrix is not damaged; the to-be-prepared amplitude is arranged at the upper left corner of the unitary matrix, so that the amplitude preparation of the to-be-prepared quantum state can be carried out by utilizing a circuit corresponding to the unitary matrix, and the preparation of the to-be-prepared quantum state by utilizing a large-scale operator can also be understood, thereby being beneficial to more efficiently and accurately preparing the to-be-prepared quantum state.

The invention provides a low earth orbit satellite broadcast ephemeris parameter robust determination method and system. Relates to the technical field of satellite navigation. The method comprises the following steps: performing complex collinearity analysis on a designed broadcast ephemeris model in to-be-fitted satellite precise ephemeris data to determine whether a complex collinearity relationship exists or not; when the complex collinear relation exists, determining a generalized ridge estimation step length diagonal matrix priori value according to satellite precision ephemeris data and designed broadcast ephemeris parameters; according to a generalized ridge estimation step length diagonal matrix priori value, setting a search interval and successively carrying out generalized ridge estimation to fit broadcast ephemeris parameters, calculating a fitting residual error, obtaining a generalized ridge parameter value corresponding to an optimal residual error after searching in the search interval, and according to the generalized ridge parameter value, carrying out generalized ridge estimation to fit broadcast ephemeris parameters. According to the method and the device, the problem of fitting failure caused by serious illness of the least square equation due to improper design of the broadcast ephemeris model is solved.

The invention discloses a rapid and direct solving method for a metal medium composite target based on a block sparse row matrix. The method comprises the following steps: approximately representing a low-rank non-diagonal block matrix as multiplication of two decomposition matrixes U and V by adopting a self-adaptive crossover algorithm; cascading the decomposition matrix of each sub-block to obtain an integral decomposition matrix; carrying out compression storage on the decomposition matrixes U and V by adopting a block sparse row matrix, and removing zero blocks generated by matrix cascading; performing inversion on the block diagonal matrix of the finest layer through a conjugate gradient method, and solving an inverse matrix of the block diagonal matrix of the non-finest layer according to an SMW formula; and finally, obtaining a current solving target RCS through vector multiplication of an inverse matrix of a series of block diagonal matrixes and a matrix of a right vector. According to the method, the electromagnetic scattering characteristics of the complex target are solved, and the calculation efficiency of analyzing the electromagnetic single-station scattering characteristics of the complex target can be improved.

The invention belongs to the field of educational informatization, and discloses a student-teacher-student double-selection recommendation method and system oriented to individual requirements and used for assisting in lesson of graduate students. Calculating the demand similarity of both teachers and students, and screening part of candidate lists; establishing a scoring matrix according to the matched historical data; the singular value decomposition scoring matrix is a product of three matrixes, namely a student feature matrix, a teacher feature matrix and a diagonal matrix; optimizing a student feature matrix and a teacher feature matrix; calculating a prediction score matrix according to the optimized student feature matrix and the optimized teacher feature matrix; and for each user, obtaining a teacher or a student with the highest predicted score from the objects in part of the candidate list through the predicted score matrix, and selecting the teachers with the top M predicted scores or the students with the top M predicted scores as a recommendation list. According to the method, the teacher-student matching accuracy can be improved, similarity calculation can be carried out by utilizing attribute information of newly added students or teachers, and content-based recommendation is carried out.

The invention discloses a large-scale hybrid beam forming array construction method based on a passive beam forming network, and belongs to the field of radio frequency systems. According to the method, the array is divided into a plurality of active sub-modules (each sub-module comprises a radiation unit array, a passive beam forming network, a multi-channel radio frequency module and a digital-to-analog conversion module), and the layered beam forming technology of a digital baseband processing module is combined, so that the balance of high performance and low complexity is realized. The method specifically comprises the following steps: 1) dividing a coverage space into a plurality of sub-regions by using a passive beam forming network, localizing a digital beam forming matrix into a block diagonal matrix, and reducing the calculation amount; 2) a large-scale array is constructed through flexible expansion of sub-modules, and full-aperture gain is ensured; and 3) the radio frequency channels of the idle sub-regions are dynamically turned off so as to save energy consumption. In scenes such as 5G / 6G millimeter wave communication, radar imaging and the like, the system power consumption and the calculation complexity are remarkably reduced, and meanwhile, the performance of a full-digital beam forming array is approached.

The invention provides a multi-topic opinion evolution method based on a confidence interval. The multi-topic opinion evolution method comprises the steps that an intelligent agent i collects and stores neighbor information Ni (k); the intelligent agent i performs distance calculation on the collected neighbor information and own opinions so as to classify neighbors to obtain neighbor categories; according to the neighbor category, obtaining a neighbor Nb and a neighbor Nc which have a large opinion difference; trust discounting is carried out on the neighbor Nb and the neighbor Nc, and the trust degree after discounting and a trust degree matrix after discounting are obtained; a feedback matrix is deduced according to the neighbor category, a diagonal matrix capable of distributing credibility is obtained through the feedback matrix and the trust matrix, an element dii on a diagonal line of the diagonal matrix represents the redistributable credibility of the agent i, and credibility redistribution is carried out on the discounted trust matrix; and completing multi-topic opinion evolution through a dynamic formula. By means of the method, the stable consensus can be achieved for a plurality of topics with the logic dependency relationship.

The invention belongs to the technical field of underwater acoustic array signal processing, and particularly relates to an acoustic vector circular array orientation estimation method based on cross covariance matrix construction, a program, equipment and a storage medium. The method comprises the following steps: introducing a preprocessing matrix to transform the output of an acoustic vector circular array, and constructing a cross covariance matrix of sound pressure and different vibration velocity components according to the transformed vector; combining and arranging the cross covariance matrixes of the sound pressure and the different vibration velocity components to obtain a combined arrangement matrix; performing singular value decomposition on the combined permutation matrix, and reconstructing a cross covariance matrix by using a unitary matrix formed by left singular vectors of the combined permutation matrix and a diagonal matrix formed by singular values; and implementing a spatial spectrum estimation method by using the cross covariance matrix, and taking the scanning angle corresponding to the maximum value in the spatial spectrum as an orientation estimation result of the detection target. The method is suitable for a column barrier condition, and can effectively improve the dual-target resolution and orientation estimation performance of the acoustic vector circular array under a low signal-to-noise ratio condition.

The invention relates to the technical field of data analysis, and discloses an intelligent physical examination data dynamic analysis method, which is characterized by comprising the following steps of: fixing a centroid matrix F (v) of vth test index data, a common clustering index matrix G and a weight factor alpha (v) of the vth test index data, and updating a diagonal matrix D (v) corresponding to a vth view; fixing G, D (v) and alpha (v) and updating the cluster centroid of each view F (v); fixing F (v), D (v) and alpha (v) and updating G; f (v), G and D (v) are fixed, alpha (v) is updated, potential models of data are mined from features of known training data, an effective model is formed by clustering each data to different clusters, then unknown new data are divided by using the model, physical state clustering and evaluated multi-view clustering of a tested person are carried out, and the optimal physical state of the tested person is obtained. And physical examination test indexes are taken as responses of physical conditions from different data perspectives.

A computer-implemented method is for reducing computing time when determining an inverse matrix from a symmetrical input matrix comprising n rows and n columns. The method includes forming i blocks with mi rows and mi columns, with mi less than n and i being greater than or equal to 2. The i blocks are each formed from entries of main diagonals which are most strongly correlated and mi entries of secondary diagonals in the same rows and columns as the entries of the main diagonals. The method further includes generating a block diagonal matrix from the i blocks, and generating the inverse matrix to the input matrix by inverting the blocks in the block diagonal matrix.

The invention discloses a field programmable gate array (FPGA) implementation method for Hermite matrix eigenvalue decomposition, which comprises the following steps of: performing real number processing on a Hermite matrix according to a corresponding relationship between the Hermite matrix and eigenvalues and eigenvectors; grouping the dimension real matrix obtained by the real number processing; calculating rotation matrixes of diagonal units and non-diagonal units; performing Jacobi rotation operation on the diagonal units and the non-diagonal units, and updating the feature vector matrix according to a rotation matrix; after a group of Jacobi rotation is completed, data exchange is carried out according to grouping of a parallel Jacobi algorithm; and multi-stage cleaning can be carried out according to actual requirements. According to the method, a parallel Jacobi algorithm is selected, a series of matrix rotation is adopted, the matrix is converted into a diagonal matrix, and therefore the eigenvalue and the eigenvector of the matrix are calculated. According to the method, the parallel computing advantages of the FPGA and the Jacobi algorithm are fully utilized, and the real-time performance of the algorithm is effectively improved.

This invention discloses a GNSS interference source localization method based on ADS-B data. The method involves acquiring ADS-B data, saving data points affected by GNSS interference, and, if no NIC is available, constructing ADS-B data with a NIC. The message data is then sorted by ICAO and timestamp. A diagonal matrix W is calculated based on the ICAO, timestamp, NIC, a table showing the correspondence between NIC and received interference power, and the hyperparameter value τ. A residual vector R is calculated based on the message data and the optimization vector, and the optimized vector is then output. This invention analyzes large-scale aviation ADS-B data, sorts and classifies the original message data to determine whether flights are subject to GNSS interference, and abstracts the interference source localization problem into a least-squares problem. An optimization function is constructed, and an iterative optimization algorithm is used to calculate the possible GNSS interference source locations and transmission power, thus more efficiently locating GNSS interference sources.

A computer-implemented method for finetuning a neural network. The method includes: providing an input to a layer of the neural network; determining a block-diagonal matrix; determining a first matrix by multiplying the block-diagonal matrix with a weight matrix of the layer, wherein the result of the multiplication is obtained by multiplying at least a plurality of blocks of the block-diagonal matrix with a respective part of the weight matrix in parallel computing operations and combining the result to form the first matrix; determining an output of the layer by multiplying the first matrix with the input of the layer; determining an output of the neural network based on the output of the layer; adapting elements of the block-diagonal matrix based on a difference of the output of the neural network and a desired output with respect to the input datum.

A system includes a machine-learning model implemented on a data processing apparatus, which features a parallel processor with a memory hierarchy. The machine-learning model is a recurrent neural network (RNN) with a multi-head architecture, comprising multiple sub- vectors that process parallel data streams. The RNN's weight matrix is structured as a block-diagonal matrix, allowing for parallel processing of the sub-vectors. A fused computational kernel executes an entire time-series processing loop for the multi-head RNN, maintaining the weight matrix blocks in on-chip memory and performing matrix multiplications and element-wise operations for each sub-vector in a single kernel execution.