Low-rank approach to metric learning from data.
problem Learning a Mahalanobis metric from data.
method Low-rank geometric mean metric learning (GMML) approach.
result Competes effectively with GMML at lower ranks.
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48 results for “low rank effects”
This work examines how low-rank weights improve adversarial robustness in neural networks.
problem Improving adversarial robustness in neural networks.
method The study investigates the impact of low-rank structure on adversarial robustness through compression measures.
result Promoting low-rank structure in weight matrices enhances adversarial robustness in neural networks.
Research reveals deep networks often learn low-rank structures, leading to more efficient training and fine-tuning.
problem Efficient training and deployment of large-scale deep learning models.
method Complementary theoretical perspectives on low-rank structures during training and convergence, and practical applications of LoRA and masked training.
result Understanding and exploiting low-rank structures can improve efficiency and effectiveness of training and fine-tuning.
Paper proposes a method for estimating complex low-rank matrices from phase-only measurements.
problem Estimating complex low-rank matrices from magnitude-only measurements.
method A hierarchical prior model with a Gaussian-Wishart distribution is used to promote low-rankness. A variational EM algorithm is developed to solve the problem.
result The proposed method is less sensitive to initialization and performs well with random initialization.
LORIS model estimates main and interaction effects in large data frames.
problem Handling large data frames with missing values and explicit modeling of main effects.
method Low-rank interaction and sparse additive effects (LORIS) model with mixed coordinate gradient descent (MCGD).
result LORIS method provides statistical guarantees and converges efficiently for large data sets.
Proposes a low-rank PGD attack for more efficient adversarial training.
problem Efficiency and effectiveness of adversarial training methods.
method Variation of PGD to compute low-rank perturbations.
result Low-rank PGD attacks are more efficient and comparable to traditional attacks.
Paper proposes a new technique to compress CNNs while maintaining accuracy.
problem CNNs struggle with traditional low-rank approximation methods, leading to degraded accuracy.
method Introduces a training technique that finds a flat minimum in low-rank approximation without a decomposed structure.
result CNN models can be compressed with higher accuracy and lower computation than conventional methods.
Recovery of low-rank matrices has recently seen significant activity in many areas of science and engineering, motivated by recent theoretical results for exact reconstruction guarantees and interesting practical applications. A number of methods have been developed for this recovery problem. However, a principled meth…
Optimizes wide low-rank neural networks for reduced parameters and cost.
problem Reducing the number of learnable parameters in wide neural networks.
method Analyzed edge-of-chaos dynamics and derived formulae for optimal weight and bias variances.
result Optimal weight and bias variances for low-rank networks follow from multiplicative scaling.
Low-rank matrices explain data science patterns.
problem Why do data matrices often have low rank?
method A generative model with latent variables and piecewise functions.
result Approximating large matrices with low rank is feasible.
New methods recover best rank-r approximations from few entries.
problem Recovering best rank-r approximations from limited data entries.
method Two agnostic approaches: spectral truncation and projected gradient descent.
result Projected gradient descent yields superior performance.
FedLoRU improves FL efficiency by using low-rank updates.
problem Communication inefficiency and performance reduction in Federated Learning.
method Proposes FedLoRU, a low-rank update framework for FL, which reduces communication costs while maintaining performance.
result FedLoRU achieves convergence rates similar to FedAvg and is robust to heterogeneous and large numbers of clients.
Proposes tensor Q-rank for better tensor rank recovery in complex data.
problem Improving tensor rank recovery for complex data with low sampling rate.
method Introduces tensor Q-rank and two selection methods for , proposing VMTQN and MOTQN models.
result Demonstrates superior performance in tensor completion problems compared to TNN-based methods.
Paper introduces G-LowTESTR for efficient tensor bandits.
problem Efficient decision-making in multi-dimensional data with non-linear reward functions.
method Generalized low-rank tensor contextual bandits model and G-LowTESTR algorithm.
result G-LowTESTR achieves superior regret bound compared to vectorization and matricization methods.
New tensor completion method reduces impact of outliers.
problem Recover tensors from incomplete data with outliers.
method Proposes a new correntropy-based objective function and half-quadratic minimization.
result Demonstrates robust performance with real and synthetic data.
The study assesses low-rank approximations in Gaussian Process regression.
problem Improving Gaussian Process regression efficiency with low-rank approximations.
method Analyzes two low-rank approximations: random Fourier features and Mercer expansion truncation.
result Bounds on the divergence and error between exact and approximate GP models.
Flora uses random projections to achieve high-rank updates with low memory usage.
problem Excessive memory usage in large neural networks during training.
method Flora approximates LoRA using random projections to enable high-rank updates with sublinear space complexity.
result Flora achieves high-rank updates with significantly reduced memory usage compared to LoRA.
The study assesses low-rank approximations in Gaussian Process regression.
problem Improving the efficiency of Gaussian Process regression while maintaining accuracy.
method Analyzes two low-rank approximations: random Fourier features and Mercer expansion truncation, and bounds the divergence and error between exact and approximate models.
result Theoretical bounds on the divergence and error between exact and approximate Gaussian Process models are provided.
Efficient algorithm for Hadamard decomposition of matrices.
problem Decomposing matrices into low-rank factors efficiently.
method Alternating optimization with SVD-inspired initialization and momentum.
result Significantly improved performance compared to existing methods.
Matrix completion works well for smooth non-linear structures, even without low-rank assumptions.
problem Matrix completion for smooth non-linear structures.
method Nuclear-norm penalization for matrices lying in a low-dimensional non-linear manifold.
result Nuclear-norm penalization is minimax rate optimal for recovering smooth non-linear matrices with missing data.
New method estimates heterogeneous treatment effects with improved guarantees.
problem Estimating treatment effects in panel data with heterogeneous assignments.
method Matrix completion approach with row-wise error analysis.
result Achieves a row-wise error bound.
PSI-LinUCB improves scalability for large recommender systems.
problem Efficiently training and inferring for large action spaces in recommender systems.
method Represent inverse design matrix as diagonal + low-rank correction, derive stable rank-1 and batched updates, use projector-splitting integrator.
result Demonstrated effectiveness on recommender system datasets, achieving scalable training and inference.
Develops PRPCA for smooth image recovery combining low-rank and smoothness.
problem Image matrix recovery under low-rank and smoothness assumptions.
method Projected Robust PCA (PRPCA) framework combining low-rank and smoothness.
result Explicit statistical guarantees for PRPCA, reducing matrix dimensionality.
DM2L tackles missing labels in multi-label learning by modeling local and global rank structures.
problem Missing labels in multi-label learning.
method DM2L imposes local low-rank structures and global high-rank structures on predictions of instances from the same and different labels, respectively.
result DM2L outperforms state-of-the-art methods in multi-label learning with missing labels.
Study on core consistency preservation in compressed tensors.
problem Ensuring low-rank structure is maintained during tensor compression.
method Theoretical analysis and experimental validation of compression schemes.
result Identified sufficient conditions for preserving core consistency.
Estimates low-rank distributional matrices from incomplete samples.
problem Matrix completion for distributional entries with limited observed data.
method Kernel mean embeddings, Tucker rank, functional unfolding operators.
result Effective estimator for distributional matrix completion established.
LR-EDNN reduces PDE solver complexity by limiting network weights to low-rank subspace.
problem Efficiently solving time-dependent PDEs with deep neural networks.
method Low-rank constraint on network weights using SVD for efficient parameter updates.
result LR-EDNN achieves comparable accuracy to full EDNN with fewer parameters and lower cost.
Boosting framework improves Factorization Machines for recommendation systems.
problem Finding informative interactions between features in recommendation systems.
method Adaptive Boosting framework of Factorization Machines (AdaFM) that adaptively searches for proper ranks.
result AdaFM outperforms state-of-the-art Factorization Machines on real-world datasets.
A new method for efficient neural network fine-tuning using queryable low-rank update atoms.
problem Rigidity of static low-rank adaptation methods when input and depth-wise computation vary.
method A shared queryable memory of low-rank update atoms, allowing dynamic and context-sensitive adaptation.
result Improves final test performance and training stability compared to standard low-rank adaptation.
New nonconvex regularizers improve low-rank matrix recovery efficiency and accuracy.
problem Efficiently recover low-rank matrices from incomplete data.
method Factor group-sparse regularization, related to Schatten-p norms.
result Improved generalization error bounds for Schatten-p norms as p decreases.
BoostNE learns multiple network embeddings from coarse to fine.
problem Complex node interactions cannot be fully captured by a single low-rank embedding matrix.
method BoostNE proposes a multi-level network embedding framework using gradient boosting.
result BoostNE outperforms existing network embedding methods on various datasets.
New approach uses compressible dynamics to train deep models efficiently.
problem Efficient training of deep overparameterized models with low-rank structures.
method Leveraging low-dimensional structures and compressible dynamics within model parameters.
result Improved training efficiency and reduced overfitting in language models.
Study robust recovery of low-rank matrices from corrupted measurements without rank prior.
problem Robust recovery of low-rank matrices from corrupted Gaussian measurements with unknown rank.
method Subgradient method with diminishing stepsizes for nonconvex nonsmooth problem.
result Subgradient method converges to exact low-rank solution at sublinear rate under RDPP condition.
Develops efficient method for updating models with small data changes.
problem Efficiently updating models when data changes (e.g., adding/removing instances/features).
method Generalized Low-Rank Update (GLRU) for non-linear estimators.
result Provides updated solutions with computational complexity proportional to dataset changes.
PILNO uses neural operators to solve PDEs efficiently on point clouds.
problem Solving partial differential equations (PDEs) on point cloud data efficiently.
method Physics-informed low-rank neural operator framework combining low-rank kernel approximations and an encoder-decoder architecture.
result PILNO efficiently approximates solution operators of PDEs on point cloud data, satisfying PDE constraints and boundary conditions.
On the Partial Convexification for Low-Rank Spectral Optimization: Rank Bounds and Algorithmsmath.OC
Partial convexification improves tractability of low-rank spectral optimization problems.
problem Minimizing linear objectives subject to matrix inequalities and low-rank constraints.
method Partial convexification of the domain set, deriving rank bounds, and developing a column generation algorithm.
result The partial convexification LSOP-R is equivalent to the original LSOP under certain conditions and yields high-quality solutions.
Novel Fréchet regression method handles errors-in-variables with low-rank covariates.
problem Regression with noisy and limited covariate data.
method Combines global Fréchet regression and principal component regression for low-rank structure.
result Improved efficiency and accuracy in high-dimensional and noisy data settings.
Determinantal point processes (DPPs) are an elegant model for encoding probabilities over subsets, such as shopping baskets, of a ground set, such as an item catalog. They are useful for a number of machine learning tasks, including product recommendation. DPPs are parametrized by a positive semi-definite kernel matrix…
Bilateral Random Projectionsstat.ML
Low-rank structure have been profoundly studied in data mining and machine learning. In this paper, we show a dense matrix 's low-rank approximation can be rapidly built from its left and right random projections and , or bilateral random projection (BRP). We then show power scheme can further…
Unified approach tackles high-dimensional tensor bandits with convex optimization and weakly decomposable regularizers.
problem Challenges in high-dimensional generalized tensor bandits where existing algorithms fail.
method Proposes a generalized linear tensor bandits algorithm with a unified analytical framework using convex optimization and weakly decomposable regularizers.
result Unified analytical framework provides better bounds and broader applicability compared to existing methods.
Recovery of Low-Rank Plus Compressed Sparse Matrices with Application to Unveiling Traffic Anomaliescs.IT
Given the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, the goal of this paper is to establish deterministic conditions under which exact recovery of the low-rank and sparse components becomes possible. This fundamental identifiability issue arises with tra…
Low rank tensor learning, such as tensor completion and multilinear multitask learning, has received much attention in recent years. In this paper, we propose higher order matching pursuit for low rank tensor learning problems with a convex or a nonconvex cost function, which is a generalization of the matching pursuit…
GCL-LRR improves node classification in noisy graphs.
problem Noise in real-world graph data impairs GNNs' effectiveness.
method Two-stage transductive learning with low-rank regularization and attention.
result Improved node classification performance in noisy graphs.
Paper detects communities from graph signals using low-rank excitation modeling.
problem Detect communities in graphs from noisy signals.
method Model signals as graph filter outputs, apply spectral method to covariance matrix.
result Community structure can be retrieved directly from graph signals.
AIR-Net adapts low-rank regularization dynamically for better image completion.
problem Fixed low-rank regularization limits adaptability to different images.
method AIR-Net uses adaptive and implicit regularization parameterized by a dynamic Laplacian matrix.
result AIR-Net enhances implicit regularization and outperforms fixed methods in non-uniform missing data scenarios.
Low-rank regularizer improves DNN robustness.
problem Improving DNN robustness to input perturbations.
method Low-rank regularizer applied to DNN intermediate layers.
result LR-trained models are more robust to Gaussian and adversarial noise.
Proposes a model to clean and analyze network data.
problem Noisy and missing connections in network data.
method Generalized linear model with low rank effects.
result Efficient algorithm for fitting the model and demonstrating its effectiveness.
Tensor regression networks improve neural network compression and regularization.
problem Improving neural network compression and regularization with low-rank tensor approximations.
method Investigating various low-rank tensor approximations in tensor regression networks.
result Tensor regression networks with Global Average Pooling layer outperformed in deep CNNs, while shallow CNNs with tensor regression and dropout achieved lower test error.