Analysis shows BN prevents gradient vanishing/explosion in residual networks.
problem Gradient vanishing/explosion problem in residual networks.
method Mathematical analysis of BN and residual network training.
result BN confounds gradient variance, preventing vanishing/explosion.
Deep residual networks trained with gradient descent have small generalization gap.
problem Limited theoretical understanding of why residual networks generalize well.
method Analyzing overparameterized deep residual networks trained by gradient descent.
result Demonstrates that residual networks have a small generalization gap between training and test error.
Gradient descent converges globally in deep linear residual networks with ZAS initialization.
problem Optimizing deep linear residual networks for convergence.
method Zero-asymmetric (ZAS) initialization for gradient descent.
result Gradient descent converges to an ε-optimal point in O(L^3 log(1/ε)) iterations.
Residual networks maintain stability, allowing deep learning without degradation.
problem Training error increases with network depth.
method Lyapunov stability analysis and convex decomposition of functions.
result Residual networks maintain stable equilibria, preventing overfitting.
Gradient oversmoothing and expansion hinder deep GNN training, solved with normalization.
problem Gradient oversmoothing and expansion prevent deep GNN training.
method Proposed normalization method to constrain the Lipschitz bound of each layer.
result Residual GNNs with hundreds of layers can be efficiently trained with the proposed normalization.
Gradient descent efficiently finds global minima in deep neural networks.
problem Training deep neural networks efficiently and reliably.
method Gradient descent, leveraging the stability of the Gram matrix induced by the network architecture.
result Gradient descent achieves zero training loss in polynomial time for deep over-parameterized neural networks with residual connections.
Residual Networks are shown to be equivalent to boosting feature representation.
problem Improving feature representation in deep learning models.
method Proved ResNet's equivalence to Online Gradient Boosting and proposed decision tree residual modules.
result ResNet can achieve Online Gradient Boosting regret bounds through architectural changes.
Deep residual networks implicitly converge to neural ODEs.
problem Link between discrete and continuous deep learning models.
method Establishing implicit regularization for residual networks towards neural ODEs.
result Deep residual networks initialized as discretizations of neural ODEs converge to such ODEs during training.
A new method for learning gradient flows from population dynamics.
problem Reconstructing population dynamics from limited data.
method Residual approach to enforce continuity equations, combining with data-fitting divergence.
result Demonstrated state-of-the-art performance across trajectory inference benchmarks.
PRISMA uses PDE residuals for fast, robust, and accurate inference.
problem Slow gradient-based optimization and instability in PDE residual-based methods.
method Integrates PDE residuals directly into the model's architecture via attention mechanisms in the spectral domain.
result Competitive accuracy with significantly lower inference costs and faster speeds.
New method uses ResNet's feature optimization for gradient boosting.
problem Improving gradient boosting methods for classification tasks.
method Functional Gradient Boosting based on Residual Network Perception.
result ResFGB method outperforms state-of-the-art methods like LightGBM.
Fixup replaces normalization in deep networks, achieving similar stability and performance.
problem The effectiveness of normalization layers in deep neural networks.
method Fixed-update initialization (Fixup) to solve exploding and vanishing gradient problems.
result Residual networks trained with Fixup achieve state-of-the-art performance without normalization.
A new one-point feedback scheme improves ZO algorithms for black-box optimization.
problem Optimizing black-box functions without gradient information.
method Proposes a one-point feedback scheme to estimate gradients using residuals.
result Matches query complexity of two-point schemes for deterministic Lipschitz functions.
Study on profinite rigidity of direct products of free and surface groups.
problem Profinite rigidity of direct products in residually free groups.
method Rank gradients of pro-p groups, virtual homology of limit groups. result Direct products of free and surface groups are profinitely rigid.
Investigates the relationship between ResNets and Neural ODEs, quantifying their closeness and providing training methods.
problem Quantifying the distance between ResNet dynamics and Neural ODE solutions.
method Bounding the distance between hidden state trajectories and Neural ODE solutions, using gradient descent and Heun's method.
result Gradient descent and Heun's method can implicitly regularize ResNets towards Neural ODEs, especially for smooth residual functions.
Stacking improves deep neural network training efficiency.
problem Improving the efficiency of training deep neural networks.
method Proposes stacking as a form of accelerated gradient descent.
result Proves stacking provides accelerated training for certain deep linear residual networks.
AdaComp compresses gradients adaptively for efficient distributed training.
problem Communication constraints in distributed training of deep neural networks.
method Adaptive Residual Gradient Compression (AdaComp) that selects gradient residues and tunes compression rate.
result Excellent compression rates (200X-40X) without accuracy loss.
Proposes log density gradient to improve reinforcement learning sample complexity.
problem Residual error in gradient estimation in policy gradient methods.
method Log density gradient method to correct residual error, using state-action discounted distributional formulation.
result Min-max optimization method to approximate log density gradient with on-policy samples, achieving sample complexity of m−1/2. New method improves matrix completion accuracy, especially in noisy data.
problem Noisy matrix completion in recommendation systems and signal processing.
method Residual Spectral Matching criterion and pseudo-gradient algorithms.
result Improved numerical performance in noisy data environments.
Deep linear ResNets converge globally with certain transformations.
problem Global convergence of training deep linear ResNets.
method Gradient descent and stochastic gradient descent for training L-hidden-layer linear ResNets. result GD and SGD can converge to global minimum for deep linear ResNets with specific transformations.
Wrapped loss function improves convergence and accuracy in multi-output models.
problem Nonconforming residual distributions in multi-output models.
method Proposes a 'Wrapped Loss Function' to regularize nonconforming residual distributions.
result Advanced properties of faster convergence, better accuracy, and improved handling of imbalanced data.
Wasserstein gradient boosting predicts probability distributions for supervised learning.
problem Distribution-valued supervised learning where outputs are probability distributions.
method Fits a new weak learner to Wasserstein gradients of loss functionals of probability distributions.
result Superior performance in probabilistic prediction compared to existing methods.
Gradient descent converges to global minima for ResNets with linearly scaled width.
problem Understanding the convergence of deep residual networks with varying network width and dataset size.
method Analyzing the Jacobian of ResNets and applying gradient descent for quadratic loss.
result Gradient descent converges to global minima for ResNets with linearly scaled width and independent of depth.
Deep linear networks minimize sharpness, avoiding large eigenvalues.
problem Understanding optimization dynamics in deep linear networks for regression.
method Analyzing sharpness (largest eigenvalue of Hessian) of minimizers and gradient flow solutions.
result Gradient flow implicitly regularizes towards flat minima, with sharpness bounded by a constant.
Residual Flows improve flow-based models for density estimation.
problem Density estimation using flow-based models with biased log-density estimates.
method Proposed a Russian roulette estimator for unbiased log-density estimation and used an alternative infinite series for gradient calculation. Improved invertible residual blocks with activation functions avoiding derivative saturation and generalized Lipschitz condition to induced mixed norms.
result Residual Flows achieve state-of-the-art performance on density estimation and outperform coupling block networks in joint generative and discriminative modeling.
Effective Gram matrix predicts deep network generalization.
problem Understanding and predicting deep network generalization.
method Derived a differential equation governing generalization gap, analyzed with effective Gram matrix.
result Effective Gram matrix accurately predicts test loss during training.
DORE reduces communication costs in distributed learning by 95%.
problem High communication costs in distributed learning for large-scale models.
method DORE: Double Residual Compression Algorithm for stochastic gradient descent.
result DORE reduces communication costs by over 95%.
Deep networks can approximate smooth functions by compositions of nearly identity functions.
problem Optimizing deep networks for smooth function approximation.
method Representing smooth functions as compositions of near-identity functions with decreasing Lipschitz constants.
result Functional gradient methods for residual networks avoid suboptimal critical points in the near-identity region.
The study shows how to find specific transformations of gradient vector fields.
problem Finding transformations of gradient vector fields with specific symmetries.
method Analyzes residual subsets of Riemannian metrics and their flows.
result Residual subsets of metrics allow for specific transformations of gradient vector fields.
Study shows how deep residual networks can be analyzed as shallow network ensembles for optimization.
problem Understanding why deep neural networks can be trained to zero loss despite non-convex optimization landscapes.
method Mean-field analysis of deep residual networks, focusing on their continuum limit as a two-layer network.
result Derives the first global convergence result for multilayer neural networks in the mean-field regime.
PGD-trained models have a preferential direction in their gradients, which improves robustness.
problem Mathematical lack of clarity in the direction of preferential gradient alignment after adversarial training.
method Proposed a novel definition of preferential direction and evaluated it using a metric based on GANs.
result PGD-trained models have higher alignment with the proposed preferential direction than baseline models.
Deep learning for HJB PDEs using synthetic data and residual minimization.
problem Solving Hamilton-Jacobi-Bellman PDEs for optimal control problems.
method Gradient-augmented synthetic dataset for supervised learning, residual minimization.
result Improves accuracy and efficiency of deep learning for HJB PDEs.
ResNets are effective due to their insensitivity to weight initialization.
problem Training deep neural networks with vanishing/exploding gradients.
method Simplified analysis of ResNet models, demonstrating the effect of batch normalization.
result ResNets are insensitive to weight initialization, improving training stability.
SA-PEF improves federated learning efficiency by correcting gradient mismatches.
problem Slow decay of residual error in federated learning under non-IID data.
method Integrates step-ahead correction with partial error feedback.
result Achieves faster convergence and target accuracy compared to standard EF.
D2SRM solves complex PDEs using deep learning.
problem High-dimensional, Hessian-dependent fully nonlinear parabolic PDEs.
method Single scalar space-time network generating derivative-consistent approximations trained through residuals and penalties.
result Well-posedness and convergence theory established for globally Lipschitz equations.
JKO-iFlow uses neural ODEs to improve generative models with reduced memory and training complexity.
problem Efficiently training deep generative models in high dimensions with reduced memory and training complexity.
method JKO scheme inspired neural ODE flow network with adaptive time reparameterization.
result JKO-iFlow achieves competitive performance compared to existing models at reduced computational and memory cost.
A new ensemble learning method called Residual Likelihood Forests improves performance and reduces model size.
problem Improving machine learning classification performance with compact models.
method Sequential optimization of conditional likelihoods in a boosting-like framework, combining multiplicatively.
result Significant performance improvements and reduced model size compared to other ensemble methods.
RDL-Net improves speech enhancement with fewer parameters and better performance.
problem Improving speech enhancement with fewer parameters and better performance.
method Proposes RDL-Net, a CNN combining residual and dense aggregations without over-allocating parameters.
result RDL-Net achieves higher speech enhancement performance with fewer parameters and lower computational requirements.
Paper studies ResNet dynamics using NTH, reducing width requirement.
problem Understanding ResNet dynamics and improving training efficiency.
method Uses Neural Tangent Hierarchy (NTH) to analyze ResNet dynamics.
result Reduces width requirement from quartic to cubic for ResNet.
AGBM accelerates GBM with theoretical guarantees.
problem Accumulation of errors in GBM's momentum term.
method Incorporates Nesterov's acceleration techniques and a corrected pseudo residual.
result First GBM type with theoretically-justified accelerated convergence rate.
New method improves deep policy gradient algorithms by learning relative state values.
problem High sample complexity and instability in policy gradient methods.
method Uses a new state-value function approximation based on residual variance.
result Empirical improvement across diverse continuous control tasks and algorithms.
SCORE improves tree-based predictions with boosted residual extraTrees.
problem Improving tree-based prediction models with reduced errors.
method Inspired by representation learning, SCORE uses boosting, regularized regression, and variable selection.
result SCORE provides comparable or superior performance compared to other models.
Framework calculates positional influence in causal residual Transformers.
problem Understanding positional influence in causal residual Transformers.
method Adjoint-sensitivity framework for positional influence in causal residual Transformers.
result Exact evolution of adjoint-energy influence density and decomposition into residual transmission, nonlocal Volterra, and local channels.
LoBoost improves local conformal prediction for gradient-boosted trees without extra data splits.
problem Quantifying uncertainty in gradient-boosted tree predictions.
method Model-native local conformal prediction using leaf structure.
result Competitive interval quality and improved test MSE with large calibration speedups.
A simple gating mechanism improves deep learning convergence.
problem Vanishing or exploding gradients in deep networks.
method Introducing a zero-initialized parameter to each residual connection.
result Training deep networks (up to 120 layers) with fast convergence and better performance.
ResNets promote smoother interpolations than MLPs, enhancing generalization.
problem Understanding the difference in smoothness between ResNets and MLPs.
method Neural Tangent Kernel (NTK) analysis during gradient descent training.
result ResNet's NTK results in smoother interpolations than MLPs.
This paper improves speech recognition models using deep neural networks.
problem Improving automatic speech recognition models.
method Deployment of residual, densely-connected, and highway networks into speech recognition.
result Significant improvements in speech recognition models.
RFRBoost uses random features to boost deep residual neural networks, improving performance and computational efficiency.
problem Improving performance of deep residual neural networks (RFNNs) while preserving convex optimization benefits.
method Random Feature Representation Boosting (RFRBoost) using boosting theory and random features at each layer.
result RFRBoost significantly outperforms RFNNs and end-to-end trained MLP ResNets in small- to medium-scale tabular datasets.