This study presents a rapid multiple incremental and decremental mechanism based on Weight-Error Curves (WECs) for support-vector analysis. Recursion-free computation is proposed for predicting the Lagrangian multipliers of new samples. This study examines Ridge Support Vector Models, subsequently devising a recursion-…
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48 results for “Lagrangian multiplier”
The paper proves transversality for special Lagrangian submanifolds in a 6D manifold.
problem Counting special Lagrangian submanifolds in higher dimensions.
method Proving transversality for the moduli space of perturbed special Lagrangian submanifolds using a Lagrange multipliers problem.
result The moduli space is generically a set of isolated points.
Simplifies neural network models by explicitly enforcing constraints in Cartesian coordinates.
problem Learning dynamics of complex systems efficiently and accurately.
method Embedding systems into Cartesian coordinates and using Lagrange multipliers to enforce constraints.
result Explicitly enforcing constraints leads to a 100x improvement in accuracy and data efficiency.
The Information Autoencoding Family: A Lagrangian Perspective on Latent Variable Generative Modelsstat.ML
A large number of objectives have been proposed to train latent variable generative models. We show that many of them are Lagrangian dual functions of the same primal optimization problem. The primal problem optimizes the mutual information between latent and visible variables, subject to the constraints of accurately …
We discuss two generalizations of the inverse problem of the calculus of variations, one in which a given mechanical system can be brought into the form of Lagrangian equations with non-conservative forces of a generalized Rayleigh dissipation type, the other leading to Lagrangian equations with so-called gyroscopic fo…
This work analyzes machine learning for Lagrangian Relaxation in MILP.
problem Improving efficiency in solving large-scale MILP problems.
method Data-driven Algorithm Design approach to learn Lagrangian multipliers.
result Stochastic Gradient Ascent achieves the minimax optimal rate for learning multipliers.
The multiplier spectral curve of a conformal torus in the 4-sphere is essentially, see arXiv:0712.2311, given by all Darboux transforms of the conformal torus. In the particular case when the conformal immersion is a Hamiltonian stationary torus in Euclidean 4-space, the left normal of the immersion is harmonic, hence …
Minimizing a function over an intersection of convex sets is an important task in optimization that is often much more challenging than minimizing it over each individual constraint set. While traditional methods such as Frank-Wolfe (FW) or proximal gradient descent assume access to a linear or quadratic oracle on the …
The information bottleneck (IB) problem tackles the issue of obtaining relevant compressed representations of some random variable for the task of predicting . It is defined as a constrained optimization problem which maximizes the information the representation has about the task, , while ensuring t…
It is shown that the Euler-Lagrange equations for a Lagrangian system on a Lie algebroid are obtained as the equations for the critical points of the action functional defined on a Banach manifold of curves. The theory of reduction and the relation with Lagrange multiplier method are also studied.
Training neural networks under physical constraints using a stochastic augmented Lagrangian approachphysics.comp-ph
Stochastic approach improves neural network training for kinetic simulations.
problem Training neural networks under physical constraints in kinetic fusion simulations.
method Stochastic augmented Lagrangian approach using pyTorch.
result Higher model prediction accuracy achieved compared to fixed penalty method.
Method solves nonconvex constrained optimization problems with a new augmented Lagrangian approach.
problem Nonconvex composite functional constraints with inequality constraints.
method First-order augmented Lagrangian method with smoothed prox-linear reformulation.
result Explicit convergence rates for the proposed method in terms of KKT residual.
In recent years, constrained optimization has become increasingly relevant to the machine learning community, with applications including Neyman-Pearson classification, robust optimization, and fair machine learning. A natural approach to constrained optimization is to optimize the Lagrangian, but this is not guarantee…
A new algorithm for faster model selection in twin multi-class SVM.
problem Challenges in effective solution of multi-classification and fast model selection in twin multi-class SVM.
method Sample data set partition strategy, Lagrangian multipliers, piecewise linear update, initialization algorithm, and event-based iteration.
result Comparable classification performance achieved without solving quadratic programming problems.
We address the problem of solving convex optimization problems with many convex constraints in a distributed setting. Our approach is based on an extension of the alternating direction method of multipliers (ADMM) that recently gained a lot of attention in the Big Data context. Although it has been invented decades ago…
In this paper we provide generalized Helmholtz conditions, in terms of a semi-basic 1-form, which characterize when a given system of second order ordinary differential equations is equivalent to the Lagrange equations, for some given arbitrary non-conservative forces. For the particular cases of dissipative or gyrosco…
New knot homology theory from symplectic geometry.
problem Developing a symplectic counterpart to instanton knot homology.
method Using symplectic character varieties and Floer homology, a new invariant for knots in 3-manifolds is constructed.
result Symplectic instanton knot homology (SIK) is a new invariant of knots and links in 3-manifolds.
TEAM generates more powerful adversarial examples for DNNs.
problem Vulnerability of DNNs to imperceptible adversarial examples.
method TEAM uses Taylor expansion and Lagrangian multiplier method to craft adversarial examples.
result TEAM generates adversarial examples with 100% attack success rate using smaller perturbations.
A new Lagrangian method for graph neural networks accelerates state computation.
problem Efficiently computing states in graph neural networks for complex data.
method Lagrangian optimization for state convergence in graph neural networks.
result The proposed method accelerates state computation without iterative phases.
By and large, Backpropagation (BP) is regarded as one of the most important neural computation algorithms at the basis of the progress in machine learning, including the recent advances in deep learning. However, its computational structure has been the source of many debates on its arguable biological plausibility. In…
Study on relativistic nonholonomic mechanics with time-dependent constraints.
problem Formulating classical time-dependent nonholonomic mechanics.
method Invariant formulation using moving frames and Chaplygin systems.
result Hamiltonization of time-dependent constraints achieved.
New variational approach for privacy and fairness in data representations.
problem Learning private and fair representations while preserving relevant information.
method Variational formulation of privacy and fairness optimization problems using Lagrangians.
result Control over the trade-off between utility and privacy/fairness through a Lagrange multiplier parameter.
A new algorithm finds optimal solutions for constrained decision processes.
problem Optimizing state-value functions with constraints in CMDPs.
method Gradient-Aware Search (GAS) exploiting PWLC structure.
result GAS converges faster and more reliably than existing methods.
Paper solves optimization problems with convex expectation constraints using a new algorithm.
problem Minimizing convex expectation functions with inequality convex expectation constraints.
method Stochastic Augmented Lagrangian-Type Algorithm (Stochastic Linearized Proximal Method of Multipliers).
result Algorithm achieves convergence rates for objective reduction and constraint violation.
A new method solves variational inequality problems with multiple constraints without needing optimal Lagrange multipliers.
problem Solving variational inequality problems with multiple functional constraints efficiently.
method Constrained Gradient Method (CGM) for Minty variational inequality problems.
result The Constrained Gradient Method achieves complexity similar to projection-based methods but with cheaper oracles.
We study the space of holomorphic discs with boundary on a surface in a real 2-dimensional vector bundle over a compact 2-manifold. We prove that, if the ambient 4-manifold admits a fibre-preserving transitive holomorphic action, then a section with a single complex point has -close sections such that any (non…
Semi-basic 1-forms and Helmholtz conditions for the inverse problem of the calculus of variationsmath.DG
We use Frölicher-Nijenhuis theory to obtain global Helmholtz conditions, expressed in terms of a semi-basic 1-form, that characterize when a semispray is locally Lagrangian. We also discuss the relation between these Helmholtz conditions and their classic formulation written using a multiplier matrix. When the semi-bas…
Bayesian Entropy Neural Networks enforce constraints on deep learning predictions.
problem Deep learning models lack well-defined constraints in their outputs.
method Bayesian Entropy Neural Networks (BENN) using Maximum Entropy principles and the method of multipliers.
result BENN improves model robustness and reliability across various applications.
Bayesian optimization tackles mixed discrete-continuous problems with Gaussian processes.
problem Optimizing problems with both discrete and continuous variables using costly simulations.
method Relaxing discrete variables into continuous latent variables, using Bayesian optimization, and incorporating compatibility constraints with Lagrangians.
result Comparative analysis of different mixed Bayesian optimization approaches.
We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our main analysis technique provides a fresh perspective on Nesterov's excessive gap te…
Proposes a new method for GNNs that avoids iterative node state convergence.
problem Iterative computation of node states in GNNs is inefficient and requires many epochs.
method Constrained optimization in the Lagrangian framework to learn transition function and node states simultaneously.
result The proposed method compares favorably with existing models on various benchmarks.
New unoriented versions of Schur and Bogomolov multipliers for finite groups.
problem Defining and analyzing unoriented versions of Schur and Bogomolov multipliers.
method Using cohomology groups and quotient groups to define unoriented multipliers.
result Triviality of unoriented Bogomolov multiplier for certain groups, nontriviality for others.
This paper presents by simulation how approximate multipliers can be utilized to enhance the training performance of convolutional neural networks (CNNs). Approximate multipliers have significantly better performance in terms of speed, power, and area compared to exact multipliers. However, approximate multipliers have…
LP algorithm optimizes neural networks with architectural constraints.
problem Training neural networks with specific architectural constraints.
method Lagrangian optimization and saddle point search in adjoint space.
result LP algorithm is fully parallelizable and feasible for training deep networks.
Effective features can improve the performance of a model, which can thus help us understand the characteristics and underlying structure of complex data. Previous feature selection methods usually cannot keep more local structure information. To address the defects previously mentioned, we propose a novel supervised o…
Multiply twisted productsmath.DG
In this paper, we compute the index form of the multiply twisted products. We study the Killing vector fields on the multiply twisted product manifolds and determine the Killing vector fields in some cases. We compute the curvature of the multiply twisted products with a semi-symmetric metric connection and show that t…
The statistical properties of the multipliers of the absolute returns are investigated using one-minute high-frequency data of financial time series. The multiplier distribution is found to be independent of the box size when is larger than some crossover scale, providing direct evidence of the existence of sca…
Derives formula for present value of future consumer goods multiplier.
problem Evaluating the present value of future consumer goods investments.
method Derives a formula based on geometric sequence and investigates macroeconomic implications.
result The present value of the future consumer goods multiplier is close to one.
Unified framework for clustering and learning causal graphs across subjects.
problem Bias and obscured subpopulation-specific dependencies in multivariate systems.
method Directed Acyclic Graph-based Dependency Clustering via Alternating Direction Method of Multipliers (DAG-DC-ADMM) integrated with Structural Equation Modeling (SEM).
result Unified framework recovers cluster-specific causal dependency structures with high true positive rate and low false discovery rate.
The present article is devoted to the construction of a unified formalism for Palatini and unimodular gravity. The basic idea is to employ a relationship between unified formalism for a Griffiths variational problem and its classical Lepage-equivalent variational problem. As a way to understand from an intuitive viewpo…
Article establishes criteria for multiplier Hermitian-Einstein metrics on KSM-manifolds.
problem Existence of multiplier Hermitian-Einstein metrics on Fano manifolds.
method Criterion based on KSM-data and continuous paths connecting solitons.
result Explicit example of a KSM-manifold with a family of multiplier Hermitian-Einstein metrics.
Proposes a method for multi-view clustering that integrates consistent and complementary graph regularizers.
problem Multi-view clustering where views have both consistent and complementary information.
method Consistent and complementary graph-regularized multi-view subspace clustering (GRMSC).
result The proposed method outperforms state-of-the-art methods on benchmark datasets.
We show that many machine learning goals, such as improved fairness metrics, can be expressed as constraints on the model's predictions, which we call rate constraints. We study the problem of training non-convex models subject to these rate constraints (or any non-convex and non-differentiable constraints). In the non…
Properties of data are frequently seen to vary depending on the sampled situations, which usually changes along a time evolution or owing to environmental effects. One way to analyze such data is to find invariances, or representative features kept constant over changes. The aim of this paper is to identify one such fe…
Paper tackles multivariate shape-constrained convex regression problems.
problem Fitting a convex function to data with component-wise monotonicity and uniform Lipschitz continuity.
method Least squares estimator via solving a constrained convex quadratic programming problem. Efficient algorithms designed: sGS-ADMM and pALM.
result Both proposed algorithms outperform state-of-the-art methods in numerical experiments.
Develops regularity theory for Beckmann's optimal transport problem.
problem Minimizing total squared flux in continuous transport from source to target.
method Unconstrained Lagrangian formulation, variational first order optimality conditions, Schauder estimates.
result Exact Hölder regularity of potential, flux, and flow generating on bounded, regular domains.
Einstein multiply warped products and generalized Kasner manifolds with multidimensional basemath.DG
The paper examines conditions for Einstein multiply warped products and estimates their parameters.
problem Existence and non-existence of non-trivial Einstein multiply warped products.
method Analyzes conditions for the existence or non-existence of Einstein multiply warped products, especially generalized Kasner type.
result Estimates the Einstein parameter that conditions the existence of such metrics.
Historically, the banking multiplier has been in a range of 4 to 100, with 25% to 1% reserve ratios at most layers of the banking system encompassing the majority of its range in recent centuries. Here it is shown that multipliers over 1 000 can occur from a new mechanism in banking. This new multiplier uses a default …