Study shows how neural networks learn eigenfunctions of the NTK in underparameterized settings.
problem Understanding the dynamics of MSE optimization in underparameterized neural networks.
method Analysis of gradient flow dynamics, focusing on eigenfunctions of the NTK.
result Eigenfunctions of the NTK determine the learning dynamics in underparameterized networks.
The study examines deep convolutional neural networks and their learning ability.
problem Understanding the learning ability of deep convolutional neural networks (DCNNs).
method Examines DCNNs under both underparameterized and overparameterized settings, using a novel network deepening scheme.
result Establishes the first learning rates of underparameterized DCNNs and shows how adding layers can create interpolating DCNNs with good learning rates.
Overparameterized ensembles don't offer generalization benefits over single large models.
problem Theoretical limitations of ensembles in overparameterized settings.
method Using ensembles of random feature (RF) regressors, the paper clarifies how modern ensembles differ from underparameterized counterparts.
result Infinite ensembles of overparameterized RF regressors become pointwise equivalent to single infinite-width RF regressors, and finite width ensembles converge to single models with the same parameter budget.
The study uncovers the conditions under which diffusion models memorize or generalize.
problem Understanding the balance between memorization and generalization in diffusion models.
method Theoretical and mathematical framework to investigate memorization and generalization in diffusion models.
result Theoretical crossover point predicts a phase transition in diffusion models, validating the hypothesis.
The paper explores how gradient descent trains associative memories, revealing oscillations and convergence issues.
problem Training dynamics of associative memories in overparameterized and underparameterized settings.
method Reduction to particle system dynamics, theory, and experiments.
result Oscillatory transitory regimes and benign loss spikes in overparameterized settings, suboptimal memorization in underparameterized settings.
Model shows loss curve with two distinct exponents due to sparse activations.
problem Sparse activations impact neural network scaling laws.
method Introduced a model for neural scaling laws under sparse activations, derived asymptotic population loss, and analyzed gradient-descent dynamics.
result Loss curve exhibits double-descent peak near interpolation threshold with two distinct scaling exponents.
The Gauss-Newton method is analyzed for neural networks using Riemannian optimization techniques.
problem Training neural networks with smooth activations and convergence rates.
method Riemannian optimization perspective, analyzing the Gauss-Newton method in both underparameterized and overparameterized regimes.
result Geometric convergence rates independent of conditioning and eigenvalues, demonstrating accelerated convergence.
Tilting loss functions improves machine learning performance.
problem Improving machine learning models, especially in under- and over-parameterized networks.
method Using evolving loss functions that emphasize different classes cyclically.
result Dynamical loss functions lead to better generalization and stability in training.
Neural networks fit fewer samples than their parameters suggest in practice.
problem Understanding the practical limitations of neural network flexibility.
method Examination of neural network optimization, parameter efficiency, and loss surfaces.
result Neural networks can only fit training sets with significantly fewer samples than their parameters suggest.
New framework explains diverse impacts of data augmentation.
problem Understanding the varied effects of data augmentation on model performance.
method Developed a theoretical framework to characterize DA's impact on linear models.
result Data augmentation induces implicit spectral regularization through two effects.
Deep neural networks, in particular convolutional neural networks, have become highly effective tools for compressing images and solving inverse problems including denoising, inpainting, and reconstruction from few and noisy measurements. This success can be attributed in part to their ability to represent and generate…
New method for selecting data points in deep learning models.
problem Selecting data points for overparameterized deep learning models.
method Proposes a new experimental design strategy for overparameterized regression and interpolation.
result Demonstrates the effectiveness of the new method in single shot deep active learning.
Ensembles of random-feature models can't outperform a single large model.
problem Finding the optimal balance between model size and ensemble size.
method Deterministic equivalent risk estimates and scaling laws analysis.
result Ensembles of random-feature models achieve near-optimal performance only under specific conditions.
Optimal ridge regularization computed iteratively from generative parameters.
problem Finding the optimal ridge regularization strength for linear regression.
method Iterative procedure to compute optimal regularization strength numerically.
result The proposed procedure attains near-optimal generalization across various conditions.
Active learning introduces bias; this paper fixes it.
problem Bias in active learning due to non-representative training data.
method Formalized bias, identified situations where it's harmful/helpful, introduced corrective weights.
result Corrective weights can improve active learning, especially with overparameterized models.
Study shows overparameterization helps in generalizing from smooth interpolants.
problem Understanding generalization in overparameterized linear models.
method Analysis of random Fourier series model with weighted trigonometric interpolation.
result Weighted trigonometric interpolation leads to lower generalization error in overparameterized scenarios.
This research shows loss weighting remains effective in last layer retraining despite model overparameterization.
problem Overcoming biases in machine learning models at scale.
method Theoretical and practical exploration of last layer retraining in an overparameterized setting.
result Loss weighting is still effective in last layer retraining, but weights must account for model overparameterization.
A new criterion selects models in overparameterized settings.
problem Model selection for overparameterized models with more parameters than data.
method Establishes Bayesian duality and introduces the Interpolating Information Criterion.
result The Interpolating Information Criterion selects models in overparameterized settings.
This study explains how different training methods affect the minimizer of neural networks.
problem How training methods influence the minimizer of neural networks.
method Explains how initialization size, adaptive optimization (AdaGrad), and stochastic mini-batch training affect the minimizer.
result Different training methods lead to different minimizers, even in overparameterized networks.
Deep convolutional neural networks trained on large datsets have emerged as an intriguing alternative for compressing images and solving inverse problems such as denoising and compressive sensing. However, it has only recently been realized that even without training, convolutional networks can function as concise imag…
Study optimal ridge regularization for out-of-distribution prediction.
problem Optimal ridge regularization for predicting out-of-distribution data.
method Established conditions for optimal regularization under covariate and regression shifts, proving monotonic risk in data aspect ratio.
result Negative regularization can be optimal under shifts, even with isotropic or underparameterized training features.
Generative models, such as GANs, learn an explicit low-dimensional representation of a particular class of images, and so they may be used as natural image priors for solving inverse problems such as image restoration and compressive sensing. GAN priors have demonstrated impressive performance on these tasks, but they …
We analyze the condition number of random feature matrices and prove their well-conditioned nature.
problem Understanding the condition number of random feature matrices and its impact on generalization error.
method Established concentration bounds and derived risk bounds for regression problems using random feature matrices.
result The risk associated with random feature matrices exhibits the double descent phenomenon, improving even with noise.
SGD implicitly regularizes linear regression problems better than ridge regression for many cases.
problem Understanding implicit regularization in linear regression problems.
method Comparing SGD and ridge regression on a broad class of least squares problems.
result SGD generalizes no worse than ridge regression for many problem instances, sometimes better.
Paper addresses adversarial robustness in deep learning.
problem Fragility of deep learning to adversarial perturbations.
method Semi-infinite constrained learning and non-convex duality theory.
result Adversarial training is equivalent to a statistical problem over perturbation distributions.
Study shows label noise impacts neural representations' information content, revealing double descent behavior.
problem Impact of label noise on neural network hidden representations.
method Information Imbalance proxy of conditional mutual information to compare hidden representations.
result Representations learned with noisy labels are more informative than those with clean labels in the underparameterized regime, and equally informative in the overparameterized regime.
Overparameterized models generalize well despite fitting noisy data.
problem Understanding why overparameterized models generalize well despite fitting noisy data.
method Statistical signal processing perspective.
result Overparameterized models often outperform underparameterized models in test performance.
Under-parameterized networks can either copy or average teacher weights, leading to universal optimal solutions.
problem Approximating a teacher network with an under-parameterized student network.
method Analyzing shallow neural networks with erf activation function and unitary teacher weights, proving copy-average configurations are critical points and finding the optimal solution.
result The optimal solution for under-parameterized networks has a universal structure, whether copying or averaging teacher neurons.