In this paper, we study the problem of approximately computing the product of two real matrices. In particular, we analyze a dimensionality-reduction-based approximation algorithm due to Sarlos [1], introducing the notion of nuclear rank as the ratio of the nuclear norm over the spectral norm. The presented bound has i…
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48 results for “nuclear dimension”
Abstract: Extends Drinfeld correspondence to infinite-dimensional Lie groups.
problem Establishing Drinfeld correspondence in infinite dimensions.
method Extending Drinfeld correspondence to Poisson Lie groups and Lie bialgebras in infinite-dimensional settings.
result Extended Drinfeld correspondence to regular Lie groups modeled on nuclear Fréchet and Silva spaces.
Introduces dynamic asymptotic dimension for group actions and C*-algebras.
problem Dimension theory for group actions and C*-algebras.
method Introduces dynamic asymptotic dimension and studies its properties and connections.
result Dynamic asymptotic dimension bounds nuclear dimension of C*-algebras.
The paper improves tensor completion by introducing incoherent tensor norms.
problem Higher order tensor completion with varying sample sizes.
method Introducing incoherent tensor norms to improve nuclear norm minimization.
result Higher order tensors can be recovered with fewer samples than traditional methods.
Efficient system classifies EEG signals for cognitive tasks using nuclear features.
problem Classification of raw EEG signals for cognitive tasks is challenging.
method Singular value decomposition for computing dominant variances of EEG signals, using them as nuclear features, and a simple classifier.
result Nuclear features from frontal brain region achieved 100% prediction accuracy.
Muon optimizes Transformer training with heavy-tailed data, achieving optimal sample complexity.
problem Theoretical understanding of non-Euclidean optimisation methods for heavy-tailed data in training Transformers.
method Addressing the gap in theoretical understanding, we show Muon achieves optimal sample complexity under heavy-tailed noise.
result Muon finds an ε-stationary point in nuclear norm with optimal sample complexity, absorbing heavy-tailed noise without dimension dependence.
Spectral gradient methods outperform Euclidean in certain deep learning scenarios.
problem When do spectral gradient updates outperform Euclidean in deep learning?
method Layerwise condition comparing squared nuclear-to-Frobenius ratio to stable rank of activations.
result Spectral updates can be more effective than Euclidean in deep networks and transformers.
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.
We propose an approach to multivariate nonparametric regression that generalizes reduced rank regression for linear models. An additive model is estimated for each dimension of a -dimensional response, with a shared -dimensional predictor variable. To control the complexity of the model, we employ a functional fo…
NukeBERT improves performance on nuclear domain Q&A with less training data.
problem Lack of annotated data for nuclear domain Q&A.
method Developed NQuAD dataset and NukeBERT model incorporating novel BERT vocabulary technique.
result NukeBERT outperformed BERT significantly on NQuAD.
Bayesian analysis predicts properties of proton-emitting nuclei beyond the proton drip line.
problem Predicting properties of unstable nuclei in the proton-rich region.
method Bayesian Gaussian processes and mass models corrected with statistical emulators.
result Quantified predictions for separation energies and probabilities of proton emission.
Paper refines null space conditions for nuclear norm minimization in low-rank matrix recovery.
problem Establishing conditions for successful nuclear norm minimization recovery of low-rank matrices.
method Developed new null space conditions for nuclear norm minimization, proving their necessity and sufficiency.
result Weak null space condition is sufficient but not necessary for nuclear norm minimization recovery, providing a new necessary and sufficient condition.
Quantified limits of nuclear stability beyond drip lines.
problem Predicting nuclear stability beyond known isotopes.
method Microscopic nuclear mass models, Bayesian methodology, Gaussian processes.
result Quantified predictions of one- and two-nucleon separation energies.
Study on tensor nuclear norm's decomposability and subdifferential.
problem Understanding tensor nuclear norm in higher-order tensors.
method Showed decomposability over specific subspaces, derived subdifferential inclusions, and studied subgradients.
result Established the statistical performance of tensor robust principal component analysis.
Efficiently regularizes deep learning models using Jacobian nuclear norm.
problem Regularizing deep learning models to prevent overfitting and improve generalization.
method Proposes a denoising-style approximation to penalize the Jacobian nuclear norm without computing the Jacobian matrix.
result Demonstrates that penalizing the average squared Frobenius norm of and is equivalent to penalizing the Jacobian nuclear norm for function compositions.
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.
Generative model predicts cell and nuclear structure from images.
problem Predicting subcellular structures from microscopy images.
method Conditional generative model using autoencoders.
result Photo-realistic cell images generated with probabilistic interpretation.
New method for tensor recovery with fewer samples.
problem Recovering low-TT-rank tensors from few samples.
method Minimizing a weighted sum of nuclear norms of unfoldings.
result Significantly fewer samples required for recovery.
NPMR uses nuclear norm penalty for multinomial regression, predicting baseball outcomes.
problem Predicting at bat outcomes in baseball with improved accuracy.
method Nuclear penalized multinomial regression (NPMR) applied to MLB data.
result NPMR provides better prediction probabilities for batter-pitcher matchups.
Study estimates risks of nuclear waste storage projects.
problem Cost and schedule risks in nuclear waste storage projects.
method Reference class of 216 past projects for cost risk, 200 for schedule risk.
result Cost and schedule risks are substantial for nuclear waste storage projects.
Machine learning predicts nuclear physics parameters with high accuracy.
problem Predicting nuclear physics parameters for superheavy elements.
method Gradient boosted trees algorithm trained on nuclear data.
result Predictions have standard deviation from 0.00035 to 0.73.
Paper tackles robust prediction of nuclear reactor materials under scarce data.
problem Challenges of data scarcity and uncertainty in nuclear reactor design.
method Meta-learning approach informed by uncertainty and prior knowledge.
result Achieves superior performance in rupture life prediction.
A deep learning framework separates overlapping nuclei in histology images.
problem Challenges in nuclear segmentation due to overlapping nuclei.
method Proposal-free spatially-aware deep learning framework with multi-scale spatial information.
result State-of-the-art performance in nuclear segmentation on a multi-organ data set.
Classifying the Equation of State from Rotating Core Collapse Gravitational Waves with Deep Learningastro-ph.IM
Deep learning predicts nuclear equation of state from rotating core collapse GW signals.
problem Classifying the nuclear equation of state from rotating core collapse gravitational wave signals.
method Employed deep convolutional neural networks to classify visual and temporal patterns in GW signals.
result Up to 97% correct classifications of nuclear equation of state in the test set.
Neural surrogates speed up 5D gyrokinetic simulations of plasma turbulence.
problem Expensive numerical simulations of plasma turbulence hinder fusion reactor design.
method Trained a hierarchical vision transformer in 5D to predict plasma quantities faster.
result Neural surrogates predict plasma quantities two orders of magnitude faster than numerical codes.
Deep Neural Operator Driven Real Time Inference for Nuclear Systems to Enable Digital Twin Solutionsstat.ML
DeepONet accelerates nuclear DT inference with high accuracy and efficiency.
problem Real-time prediction and model evaluation in nuclear systems.
method Deep Neural Operator (DeepONet) for surrogate modeling.
result DeepONet outperforms traditional ML methods in accuracy and speed.
A new tensor p-shrinkage nuclear norm improves low-rank tensor completion.
problem Estimating tensors from partial observations with low rank.
method Proposed tensor p-shrinkage nuclear norm (p-TNN) and an efficient algorithm.
result Upper bound of recovery error provided for the LRTC model.
Deep learning detects corrosion in nuclear fuel canisters.
problem Ensuring safety and integrity of used nuclear fuel dry storage canisters.
method Residual neural networks (ResNets) for real-time corrosion detection of canister images.
result Deep learning approach accurately detects corrosion and classifies canisters as corroded or intact.
Paper solves TRPCA problem for tensor data with new tensor nuclear norm.
problem Exact recovery of tensor low-rank and sparse components.
method Introduces tensor-tensor product and new tensor nuclear norm to solve TRPCA.
result The new tensor nuclear norm guarantees exact recovery of tensor data.
Bayesian optimization helps find best nuclear interaction parameters.
problem Finding best coupling constants in complex nuclear interaction models.
method Bayesian optimization applied to chiral effective field theory.
result Bayesian optimization performs well in low-dimensional parameter domains.
Study optimizes nuclear power plant decommissioning risk management.
problem Optimizing risk management for decommissioning nuclear power plants.
method Numerical stochastic optimization approach linking risk aversion to an optimization problem.
result Optimal strategy involves de-risking similar to a concave strategy.
The study uses statistical methods to analyze nuclear mass models.
problem Understanding the information content of nuclear masses from models.
method Bayesian calibration, Bayesian model averaging, chi-square correlation analysis, principal component analysis.
result A dramatic parameter reduction can be achieved in both 4-parameter and 14-parameter models.
Recently theoretical guarantees have been obtained for matrix completion in the non-uniform sampling regime. In particular, if the sampling distribution aligns with the underlying matrix's leverage scores, then with high probability nuclear norm minimization will exactly recover the low rank matrix. In this article, we…
Gradient descent on matrix factorization leads to minimum nuclear norm solution.
problem Optimizing underdetermined quadratic objectives over matrices.
method Gradient descent on a full dimensional factorization of the matrix.
result Gradient descent converges to the minimum nuclear norm solution.
New methods for estimating panel regression models with interactive fixed effects.
problem Estimating panel regression models with interactive fixed effects.
method Nuclear norm regularization and minimization of convex objective functions.
result Consistent estimators with computational advantages over least squares.
New method speeds up nuclear-norm constrained learning over multiple machines.
problem Synchronization slowdown and high communication costs in large-scale learning.
method Asynchronous Stochastic Frank-Wolfe (SFW-asyn) method.
result SFW-asyn achieves the same convergence rate as vanilla SFW but with speed-ups almost linear to the number of machines.
This research assesses uncertainty quantification and sensitivity analysis for DTs in nuclear fuel performance.
problem Understanding the reliability and performance of advanced nuclear fuels using DTs.
method Introduces ML-based uncertainty quantification and sensitivity analysis methods applied to BISON fuel performance code.
result Demonstrates the effectiveness of DTs in multi-criteria decision-making for nuclear fuel performance.
Recovering a large matrix from limited measurements is a challenging task arising in many real applications, such as image inpainting, compressive sensing and medical imaging, and this kind of problems are mostly formulated as low-rank matrix approximation problems. Due to the rank operator being non-convex and discont…
New Nuclear Discrepancy bound improves active learning performance.
problem Improving active learning algorithms to minimize generalization bounds.
method Proposed a new Nuclear Discrepancy bound and compared it with existing bounds.
result The Nuclear Discrepancy bound outperforms other bounds in active learning.
Paper improves Frank-Wolfe algorithm's efficiency bounds.
problem Establishing efficient iteration complexity for Frank-Wolfe algorithm.
method Using metric entropy to provide lower bounds.
result Frank-Wolfe requires many iterations for certain problems.
Paper introduces new norms for rank-constrained optimization problems.
problem Rank-constrained optimization problems in various fields.
method Introduces a family of low-rank inducing norms and regularizers.
result Other low-rank inducing norms outperform nuclear norm in matrix completion problems.
Characterizes dropout's regularizer in deep linear networks.
problem Understanding dropout's regularization effect in deep learning.
method Formal characterization of dropout's regularizer, showing it is composed of an -path regularizer and the squared nuclear norm.
result For large dropout rates, the global optima of the dropout objective can be characterized.
NuClick uses clicks inside nuclei to improve nuclear segmentation.
problem Lack of efficient tools for nuclear segmentation due to labor-intensive annotation.
method Convolutional neural network framework that uses single point clicks for nuclei segmentation.
result NuClick generates superior segmentation results and facilitates more annotations.
A new method reduces rank in Frank-Wolfe steps for nuclear norm problems.
problem High rank intermediate iterates in Frank-Wolfe algorithm for nuclear norm problems.
method Rank-drop steps to ensure rank decreases and feasibility.
result Reduced rank of solutions compared to Frank-Wolfe and variants.
Rank minimization has attracted a lot of attention due to its robustness in data recovery. To overcome the computational difficulty, rank is often replaced with nuclear norm. For several rank minimization problems, such a replacement has been theoretically proven to be valid, i.e., the solution to nuclear norm minimiza…
Exact nuclear norm, completion and decomposition for random overcomplete tensors via degree-4 SOScs.DS
New algorithms solve tensor problems with random components using SDP.
problem Exact tensor nuclear norm, decomposition, and completion for random tensors.
method Degree-4 Sum of Squares (SOS) semidefinite programs.
result Exact solutions for tensor nuclear norm, decomposition, and completion with random asymmetric components.
Paper presents a deep learning framework for faster, more accurate nuclear reactor power prediction.
problem Inaccurate and inefficient modeling of nuclear reactor transients.
method Hybrid digital twin-focused multi-stage deep learning framework using feed-forward neural networks.
result Achieved remarkable accuracy (96% classification, 2.3% MAPE) with noise-enhanced simulated data.
Joint Nuclear and Regularization for Logistic Matrix Regression with Applications to Brain Imagingstat.ME
New method uses nuclear and ℓ1 penalties for matrix regression, improving brain disorder detection.
problem Modeling high-dimensional matrix predictors with binary responses.
method Convex optimization with ADMM for low-rank and sparse structures.
result Effective in identifying brain disorder-related connectivity patterns.