Optimal rates for shallow ReLU networks in nonparametric regression.
problem Approximating smooth and non-smooth functions with shallow ReLU networks.
method Analysis of shallow ReLUk neural networks, using variation norms and deep learning theory. result Optimal approximation rates for shallow ReLU networks in nonparametric regression.
We solve the optimization of two-layer ReLU networks using convex math.
problem Optimizing two-layer ReLU neural networks.
method Exact characterization of optimal solutions via convex optimization.
result We prove that all globally optimal solutions can be found via convex optimization.
Wide deep neural networks are easy to optimize without constraints.
problem Optimizing wide deep neural networks.
method Analysis of optimization landscapes and empirical-risk minimization.
result Wide neural networks have no confined points, making optimization easier.
Optimization algorithms help overparameterized neural networks achieve high performance.
problem Understanding the convergence of optimization algorithms on overparameterized neural networks.
method Analyzing a broad class of optimization algorithms using dynamical systems and finite over-parameterized neural networks with ReLU activation.
result The Heavy Ball method converges to global minimum at a linear rate, while NAG converges sublinearly.
LiPopt uses polynomial optimization to estimate neural network Lipschitz constants efficiently.
problem Estimating the Lipschitz constant of neural networks efficiently.
method Sparse polynomial optimization, leveraging network connectivity to reduce complexity.
result Superior estimates of the ℓ∞-Lipschitz constant compared to existing methods. GAIL with neural networks converges to global optima and has a known rate.
problem Uncertainty about GAIL with neural networks achieving global optimality.
method Gradient-based alternating updates algorithm.
result Established sublinear convergence to globally optimal solution.
Braid theory optimizes neural network structures.
problem Optimizing the architecture of neural networks.
method Using braid theory to describe and construct neural network structures.
result Braid-based networks outperform other architectures in classification tasks.
We propose a new scalable method to optimize the architecture of an artificial neural network. The proposed algorithm, called Greedy Search for Neural Network Architecture, aims to determine a neural network with minimal number of layers that is at least as performant as neural networks of the same structure identified…
A novel neural network approach for optimization problems.
problem Constrained optimization problems.
method Neural Optimization Machine (NOM) using a specially designed NN architecture and training procedure.
result Solves optimization problems efficiently, especially in high-dimensional spaces.
Optimizes wireless power control using graph neural networks and counterfactual optimization.
problem Mitigating interference in wireless networks with multiple transmitter-receiver pairs.
method Graph neural network architecture combined with unsupervised primal-dual counterfactual optimization.
result Guarantees a minimum rate constraint that adapts to network size, balancing user rates.
HyCNNs improve convex function learning and optimal transport.
problem Learning and optimizing convex functions efficiently.
method Combining Maxout networks and ICNNs to create a new neural architecture.
result HyCNNs require fewer parameters and outperform existing methods in convex tasks.
Deep neural networks can solve optimal stopping problems without dimensionality issues.
problem Optimal stopping problems in high-dimensional state spaces.
method Established a general framework for deep ReLU neural networks to approximate value functions and continuation values.
result Deep neural networks can approximate value functions and continuation values with error at most ε of size κd^q ε^(-r).
Optimal stock price prediction model using recurrent neural networks with RMSprop optimizer.
problem Stock price prediction using neural networks.
method Comparison of fully connected, convolutional, and recurrent architectures; inclusion of three optimization techniques.
result Single layer recurrent neural network with RMSprop optimizer produces optimal results with validation and test MAE of 0.0150 and 0.0148 respectively.
Study on deep neural networks using concentration inequalities and optimal stopping.
problem Understanding the performance and structure of stochastic deep neural networks.
method Introduced concentration inequalities for SDNN outputs and an EC classifier. Determined the optimal number of layers via an optimal stopping procedure.
result Optimal number of layers for SDNNs determined via an optimal stopping procedure.
Optimizes graph neural networks using natural gradient descent.
problem Improving efficiency and performance of graph neural networks.
method Employing natural gradient descent to optimize graph neural networks.
result Natural gradient optimization leads to superior performance compared to existing methods.
Deep neural networks solve stochastic control problems with delay.
problem Challenges in stochastic control problems with delay due to path-dependence and high dimensions.
method Employing recurrent neural networks (RNNs) to parameterize policies and optimize objectives.
result RNNs, especially LSTMs, efficiently capture path-dependence and outperform feedforward networks in training and performance.
This paper analyzes how normalization layers improve neural network training.
problem Improving generalization performance and training speed of neural networks.
method Global convergence analysis of two-layer neural networks with ReLU activations and Weight Normalization.
result Introduction of normalization layers changes the optimization landscape, enabling faster convergence.
Theory proposes neural networks can be initialized for optimal information transmission.
problem Optimizing neural networks for optimal information transmission and representation.
method Developed a corrected mean-field framework to study neural networks as information channels, proving mutual information maximization at dynamic isometry.
result Mutual information maximization is realized between inputs and propagated signals when neural networks are initialized at dynamic isometry.
Paper develops exact convex optimization for neural networks with polynomial activations.
problem Training two-layer neural networks with nonlinear polynomial activations.
method Exact convex optimization using semidefinite programming.
result Global optimization of neural networks is polynomial-time computable.
This paper presents a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it to a finite dimensional one which corresponds to optimizing a neural network wi…
Neural networks have been used prominently in several machine learning and statistics applications. In general, the underlying optimization of neural networks is non-convex which makes their performance analysis challenging. In this paper, we take a novel approach to this problem by asking whether one can constrain neu…
Deep neural networks solve optimal risk sharing problems.
problem Optimally sharing financial positions among agents with different risk measures.
method Neural network-based framework to compute inf-convolution and optimal allocations.
result Convergence of neural network approximations to theoretical values.
This paper improves deep neural network approximation for fully connected networks, achieving optimal convergence rates.
problem Improving approximation of fully connected deep neural networks for optimal convergence rates.
method Deriving approximation bounds specifically for a narrower fully connected deep neural network.
result Achieves an optimal rate (up to a logarithmic factor) for fully connected deep neural networks.
SMGD trains low-bit neural networks with memory constraints.
problem Training large neural networks with limited memory.
method Stochastic Markov Gradient Descent (SMGD).
result Encouraging numerical results and theoretical guarantees.
Paper analyzes NAC with neural networks for efficient policy optimization.
problem Improving sample and iteration complexity in policy optimization.
method Entropy regularization, averaging, neural network approximation, and optimization techniques.
result Entropy regularization and averaging ensure stability and sharp sample complexity bounds.
Gradient descent methods for deep ReLU networks achieve optimal generalization rates.
problem Generalization of gradient descent methods for deep neural networks
method Establishing minimax-optimal rates for GD and SGD with deep ReLU networks
result Gradient descent methods for deep ReLU networks achieve optimal generalization rates
Novel analysis of neural networks using geometric algebra and convex optimization.
problem Understanding the inner workings of deep neural networks.
method Geometric (Clifford) algebra and convex optimization.
result Optimal weights are given by the wedge product of training samples.
Deep neural networks can learn smooth functions without parameters.
problem Learning smooth functions from shallow ReLU neural networks.
method Using over-parameterized shallow ReLU neural networks with norm constraints.
result Least squares estimators based on shallow neural networks are minimax optimal.
Paper introduces multitask neural networks for efficient stochastic control problems.
problem Infeasibility of simulating state variables in some stochastic control problems.
method Multitask neural networks with dynamic task balancing.
result Multitask neural networks outperform state-of-the-art approaches in derivatives pricing problems.
AskewSGD optimizes quantized neural networks with interval-constrained optimization.
problem Training deep neural networks with quantized weights.
method Formulates QNN training as smoothed interval-constrained optimization, proposes AskewSGD for solving each subproblem.
result AskewSGD avoids projections and allows infeasible iterates, performs better than state-of-the-art methods.
NAS helps find best neural network designs.
problem Designing optimal neural network architectures.
method Optimization algorithms and search spaces.
result Introduction to major advances in NAS for CNNs.
The paper explores how splitting data samples influences optimal neural network hyperparameters.
problem Understanding the effectiveness of neural networks and their hyperparameters.
method Investigates the role of sample splitting in neural network hyperparameter selection.
result Optimal hyperparameters derived from sample splitting lead to a neural network model that minimizes prediction risk asymptotically.
Convex dual network improves neural network reconstruction for medical imaging.
problem Non-convex nature of neural networks hinders their use in sensitive applications.
method Introduces a convex duality framework for a two-layer fully-convolutional ReLU denoising network.
result Training neural networks with weight decay regularization induces path sparsity and piecewise linear filtering.
Neural networks optimize stopping boundaries in financial instruments.
problem Optimizing stopping boundaries in financial instruments.
method Deep neural networks and empirical risk minimization for parameterizing stopping boundaries.
result Proved existence of stopping boundary under natural assumptions.
BraidNet uses braid theory to optimize neural networks for image classification.
problem Image classification problems
method Procedural optimization of neural networks combining information theory and braid theory
result BraidNet outperforms other networks in learning speed and accuracy
Improved hypernetwork for efficient neural network hyperparameter tuning.
problem Efficiently optimizing hyperparameters in neural networks.
method Proposed Δ-STN architecture focusing on accurate best-response Jacobian approximation. result Significantly improved hyperparameter tuning accuracy and stability.
New method trains quantized neural networks to global optimality.
problem Training optimal quantized neural networks is intractable due to combinatorial non-convex optimization.
method Convex optimization strategy using hidden convexity, semidefinite lifting, and Grothendieck's identity.
result Quantized NN problems can be solved to global optimality in polynomial-time.
A neural network approach unifies Lasso for variable selection.
problem Combining statistical and machine learning techniques for variable selection.
method Representing Lasso through a neural network and developing a new optimization algorithm.
result The new optimization algorithm achieves better performance than previous methods.
A graph VAE framework optimizes neural architectures in a continuous space.
problem Discovering efficient neural architectures in a discrete space.
method Graph VAE framework with VAE and GNN components, joint learning of predictors and decoders.
result The framework discovers powerful neural architectures with both excellent performance and high computational efficiency.
UNOT solves optimal transport problems efficiently using neural networks.
problem Computational expense in solving optimal transport problems.
method UNOT (Universal Neural Optimal Transport) uses Fourier Neural Operators to predict OT distances and plans accurately and efficiently.
result UNOT achieves up to 7.4x speedup over the Sinkhorn algorithm while maintaining accuracy.
This paper proposes a deep Convolutional Neural Network(CNN) with strong generalization ability for structural topology optimization. The architecture of the neural network is made up of encoding and decoding parts, which provide down- and up-sampling operations. In addition, a popular technique, namely U-Net, was adop…
The paper proves neural networks' consistency and optimal convergence rates for various function classes.
problem Proving neural networks' consistency and optimal convergence rates for diverse function classes.
method Analyzes wide and deep ReLU neural networks trained on logistic loss and Kolmogorov-Donoho optimal function classes.
result Proves universal consistency and minimax optimal convergence rates for neural networks.
Neural network predicts optimal pension investments based on preferences.
problem Optimal pension investment problem with varying preferences.
method Used a neural network to identify optimal solutions to a family of investment problems.
result Validated network accuracy using classical numerical methods.
Muon optimizer outperforms GD in neural networks.
problem Optimizing matrix-structured parameters in neural networks.
method Muon optimizer specifically designed for matrix parameters, analyzing convergence rate and low-rank Hessian structure.
result Muon can outperform Gradient Descent due to its ability to leverage the low-rank structure of Hessian matrices.
PDA method optimizes neural networks with global convergence rate analysis.
problem Quantitative convergence rate for neural network optimization in mean field regime.
method Particle dual averaging (PDA) method, combining Langevin algorithm and outer loop optimization.
result Established quantitative global convergence for two-layer mean field neural networks.
This paper compares deeper and wider neural networks for optimal generalization error in Sobolev losses.
problem The dilemma of choosing between deeper or wider neural networks for optimal generalization error.
method Analytical investigations into the influence of sample points, parameters, and loss function regularity on neural network architecture.
result A higher number of parameters favors wider neural networks, while more sample points and greater loss function regularity favor deeper neural networks.
GT-DDP optimizer trains residual networks using game theory.
problem Applying DDP to residual networks.
method Game-theoretic DDP optimizer for residual networks.
result Improved training convergence and variance reduction.
Study assesses neural nets for optimization problems, highlighting SiLU's effectiveness.
problem Using neural nets for optimization problems, especially for accurate approximations.
method Determined best activation function (SiLU) for nonlinear optimization problems. Analyzed function approximations using neural networks and interpolation/regression models.
result Neural nets can deliver competitive zero- and first-order approximations but underperform on second-order approximations.