- Numerical inverse scattering transform for the coupled modified Korteweg-de Vries equation
2026/04/30 by Wen-Xin Zhang, Yong Chen · 1 voice
Mathematics · Physics and Astronomy · #Gradient descent #Inverse scattering problem #Inverse scattering transform #Matrix (chemical analysis) #NIST #Nonlinear Waves and Solitons #Numerical analysis #Numerical methods for differential equations #Numerical methods in inverse problems #Quantum inverse scattering method #Scalar (mathematics) #Scattering #math.NA #nlin.SI
- Learning in the Recurrent State: Gradient Descent with Linear Recurrent Networks
2024/10/15 by Yudou Tian, Y. Tian, Sushma, Neeraj Mohan +11 · 3 voices
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Algorithm #Artificial intelligence #Artificial neural network #Computer science #Context (archaeology) #Descent (aeronautics) #Fault Detection and Control Systems #Geography #Gradient descent #Mathematical economics #Mathematics #Model Reduction and Neural Networks #Neural Networks and Applications #Space (punctuation) #State (computer science) #State space #Statistics
- Transformers as Support Vector Machines
2023/08/31 by Davoud Ataee Tarzanagh, Yingcong Li, Tarzanagh, Davoud Ataee +5 · 5 voices · 13 citations
Computer Science · Mathematics · #Algorithm #Applied mathematics #Artificial intelligence #Artificial neural network #Computer science #Deep learning #Discrete mathematics #Domain Adaptation and Few-Shot Learning #Equivalence (formal languages) #Gradient descent #Machine Learning and Data Classification #Mathematical optimization #Mathematics #Nonlinear system #Pairwise comparison #Parameterized complexity #Softmax function #Support vector machine #Topic Modeling #Transformer #Voltage
- Exact Mean Square Linear Stability Analysis for SGD
2023/06/13 by Rotem Mulayoff, Mulayoff, Rotem, Tomer Michaeli +1 · 2 citations
Computer Science · Decision Sciences · Mathematics · #Advanced Bandit Algorithms Research #Applied mathematics #Artificial neural network #Computer science #Convergence (economics) #Covariance #Gradient descent #Machine Learning and ELM #Mathematical analysis #Mathematics #Maxima and minima #Monotonic function #Stability (learning theory) #Statistics #Stochastic Gradient Optimization Techniques
- Sobolev Acceleration and Statistical Optimality for Learning Elliptic Equations via Gradient Descent
2022/05/15 by Yiping Lu, José Blanchet, Lu, Yiping +3 · 3 citations
Mathematics · Medicine · Physics and Astronomy · #Acceleration #Applied mathematics #Artificial intelligence #Artificial neural network #Computational Physics (physics.comp-ph) #Computer science #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Gradient descent #Hilbert space #Kernel (algebra) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Mathematical analysis #Mathematical optimization #Mathematics #Model Reduction and Neural Networks #Norm (philosophy) #Numerical Analysis (math.NA) #Partial differential equation #Pure mathematics #Radiomics and Machine Learning in Medical Imaging #Sobolev space #Statistical Methods and Inference #Statistics Theory (math.ST)
- When and why PINNs fail to train: A neural tangent kernel perspective
2021/10/12 by Sifan Wang, Xinling Yu, Paris Perdikaris · 214 citations
Decision Sciences · Engineering · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Artificial intelligence #Artificial neural network #Computer science #Convergence (economics) #Discrete mathematics #Geometry #Gradient descent #Kernel (algebra) #Limit (mathematics) #Mathematical analysis #Mathematical optimization #Mathematics #Model Reduction and Neural Networks #Nuclear reactor physics and engineering #Probabilistic and Robust Engineering Design #Tangent
- Learning Linearized Assignment Flows for Image Labeling
2021/08/02 by Alexander Zeilmann, Stefania Petra, Zeilmann, Alexander +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #34C40 #62H35 #68T05 #68U10 #91A22 #Algorithm #Applied mathematics #Artificial intelligence #Artificial neural network #Automatic differentiation #Balanced flow #Cell Image Analysis Techniques #Computer science #FOS: Computer and information sciences #FOS: Mathematics #Flow (mathematics) #Function (biology) #Geometry #Gradient descent #Image (mathematics) #Iterative method #Krylov subspace #Machine Learning (cs.LG) #Mathematical analysis #Mathematical optimization #Mathematics #Medical Image Segmentation Techniques #Optimization and Control (math.OC) #Parameter space #Rank (graph theory) #Representation (politics) #Subspace topology #Topological and Geometric Data Analysis
- On the Implicit Bias of Initialization Shape: Beyond Infinitesimal Mirror Descent
2021/02/19 by Shahar Azulay, Azulay, Shahar, Edward Moroshko +11 · 5 citations
Computer Science · Mathematics · Physics and Astronomy · #68T07 (Primary) #Algorithm #Applied mathematics #Artificial intelligence #Artificial neural network #Computer science #FOS: Computer and information sciences #Flow (mathematics) #G.1.6 #Geometry #Gradient descent #I.2.6 #Inductive bias #Infinitesimal #Initialization #Kernel (algebra) #Machine Learning (cs.LG) #Machine Learning and ELM #Mathematical analysis #Mathematics #Model Reduction and Neural Networks #Physics #Pure mathematics #Scale (ratio) #Stochastic Gradient Optimization Techniques #Tangent #acm:68T07 #cs.LG #msc:68T07
- Homeomorphic-Invariance of EM: Non-Asymptotic Convergence in KL Divergence for Exponential Families via Mirror Descent
2020/11/02 by Frederik Künstner, Frederik Kunstner, Raunak Kumar +4 · 4 citations
Computer Science · Mathematics · #Applied mathematics #Artificial intelligence #Artificial neural network #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #Bregman divergence #Computer science #Convergence (economics) #Divergence (linguistics) #Expectation–maximization algorithm #Exponential family #Exponential function #FOS: Computer and information sciences #Gaussian #Gaussian Processes and Bayesian Inference #Gradient descent #Invariant (physics) #Kullback–Leibler divergence #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Mathematical analysis #Mathematical optimization #Mathematics #Maximum likelihood #Parametrization (atmospheric modeling) #Physics #Probabilistic logic #Statistical Methods and Inference #Statistics #cs.LG #stat.ML
- Global convergence of a modified Fletcher–Reeves conjugate gradient method with Armijo-type line search
2006/09/04 by Li Zhang, Weijun Zhou, Donghui Li · 3 citations
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Applied mathematics #Computer science #Conjugate gradient method #Conjugate residual method #Convergence (economics) #Convexity #Derivation of the conjugate gradient method #Descent (aeronautics) #Descent direction #Function (biology) #Geometry #Gradient descent #Gradient method #Iterative Methods for Nonlinear Equations #Line (geometry) #Line search #Mathematical optimization #Mathematics #Nonlinear conjugate gradient method #Optimization and Variational Analysis
- Greedy function approximation: A gradient boosting machine.
2001/10/01 by Jerome H. Friedman · 587 citations
Computer Science · Mathematics · Physics and Astronomy · #Applied mathematics #Artificial intelligence #Artificial neural network #Boosting (machine learning) #Computer science #Gradient boosting #Gradient descent #Logistic regression #Machine Learning and Algorithms #Mathematical optimization #Mathematics #Minification #Model Reduction and Neural Networks #Neural Networks and Applications #Random forest #Regression #Statistics