Adversarial training achieves optimal test error for shallow networks.
problem Achieving optimal adversarial test error for general data distributions.
method Applying new Rademacher complexity bounds and properties of optimal adversarial predictors.
result Adversarial training can achieve optimal adversarial test error for general data distributions.
Randomly sampled interpolators achieve zero generalization error with enough data.
problem Understanding the high generalization ability of machine learning models.
method Algebraic geometry tools to prove zero generalization error for random interpolators.
result Generalization error of randomly sampled interpolators becomes zero once the number of training samples exceeds a geometric threshold.
Interpolation improves performance in nearest neighbor algorithms without over-parametrization.
problem Achieving zero training error in deep learning without over-parametrization.
method Introduced a class of interpolated weighting schemes in nearest neighbor algorithms.
result Mild data interpolation strictly improves prediction performance and statistical stability.
Overparameterized deep networks have the capacity to memorize training data with zero \emph{training error}. Even after memorization, the \emph{training loss} continues to approach zero, making the model overconfident and the test performance degraded. Since existing regularizers do not directly aim to avoid zero train…
We consider general non-Euclidean distance measures between real world objects that need to be classified. It is assumed that objects are represented by distances to other objects only. Conditions for zero-error dissimilarity based classifiers are derived. Additional conditions are given under which the zero-error deci…
Renormalized pruning improves neural network accuracy.
problem Over-parameterized neural networks waste many parameters.
method Propose renormalizing sparse neural networks.
result Renormalized pruning converges to zero error.
This paper provides a mathematical foundation for deep neural networks solving PDEs.
problem Mathematical foundation for deep neural networks solving high-dimensional PDEs.
method Decomposed generalization error into approximation and training errors; derived gradient flow in the wide network limit.
result Generalization error tends to zero as the number of neurons and training time tend to infinity.
A common strategy to train deep neural networks (DNNs) is to use very large architectures and to train them until they (almost) achieve zero training error. Empirically observed good generalization performance on test data, even in the presence of lots of label noise, corroborate such a procedure. On the other hand, in…
A continuing mystery in understanding the empirical success of deep neural networks is their ability to achieve zero training error and generalize well, even when the training data is noisy and there are more parameters than data points. We investigate this overparameterized regime in linear regression, where all solut…
In principle, zero-shot learning makes it possible to train a recognition model simply by specifying the category's attributes. For example, with classifiers for generic attributes like \emph{striped} and \emph{four-legged}, one can construct a classifier for the zebra category by enumerating which properties it posses…
Bias correction needed after deep learning regression training.
problem Systematic error accumulation in deep learning regression models.
method Adjust bias of the machine learning model post-training.
result Bias correction efficiently solves error accumulation.
Estimates the generalization error of deep neural networks without relying on capacity measures.
problem Understanding how generalization error scales with training data for deep neural networks.
method Derives estimates of generalization error for deep networks based on two assumptions: zero training error and error probability proportional to distance to nearest training point.
result Estimates the generalization error of DNNs as O(1/(δN^{1/d})), matching experimental behavior.
Deep nets exhibit 'Neural Collapse' during training's final phase, simplifying decision-making.
problem Understanding and optimizing deep learning training phases.
method Direct measurements on three deepnet architectures across seven datasets.
result Deep nets exhibit 'Neural Collapse' during training's final phase, simplifying decision-making.
Artificial neural networks are most commonly trained with the back-propagation algorithm, where the gradient for learning is provided by back-propagating the error, layer by layer, from the output layer to the hidden layers. A recently discovered method called feedback-alignment shows that the weights used for propagat…
Convolutional Neural Networks (CNN) are being actively explored for safety-critical applications such as autonomous vehicles and aerospace, where it is essential to ensure the reliability of inference results in the presence of possible memory faults. Traditional methods such as error correction codes (ECC) and Triple …
This work precisely characterizes and improves the tradeoff between robustness and accuracy in linear regression.
problem Tradeoff between robustness and accuracy in adversarial training.
method Characterizes the effect of augmentation on standard error in linear regression; proves RST improves robust error without sacrificing standard error.
result RST improves both standard and robust error for neural networks under various perturbations.
We propose a simple extension to the ReLU-family of activation functions that allows them to shift the mean activation across a layer towards zero. Combined with proper weight initialization, this alleviates the need for normalization layers. We explore the training of deep vanilla recurrent neural networks (RNNs) with…
DD algorithm tracks test error from train error without validation data.
problem Systematic generalization gap between train and test errors in modern model training.
method Decoupled descent (DD) algorithm that cancels data reuse biases via approximate message passing.
result DD algorithm rigorously demonstrates zero-cost validation and 100% data utilization.
Study shows gap between uniform convergence and test error in random feature models.
problem Understanding the gap between uniform convergence and test error in random feature models.
method Analytical expressions for uniform convergence over norm balls, interpolators, and minimum norm interpolator risk derived and proved.
result Uniform convergence over interpolators still gives a non-trivial bound of test error even when classical uniform convergence is vacuous.
Transformers learn unseen tasks via prompts without fine-tuning.
problem Understanding how transformers learn unseen tasks without additional fine-tuning.
method Structured data model, gradient descent, two-phase convergence analysis.
result Transformers can learn linear function classes via in-context learning.
Curiosity-Critic improves world model training by focusing on cumulative prediction error.
problem Training world models with intrinsic rewards that consider cumulative prediction error.
method Curiosity-Critic uses a surrogate reward based on the difference between current and asymptotic prediction errors, estimated online by a co-trained critic.
result Curiosity-Critic outperforms other methods in training speed and final world model accuracy.
We analyze the loss landscape and expressiveness of practical deep convolutional neural networks (CNNs) with shared weights and max pooling layers. We show that such CNNs produce linearly independent features at a "wide" layer which has more neurons than the number of training samples. This condition holds e.g. for the…
This work finds mixed equilibria in zero-sum games using interacting particle dynamics.
problem Finding mixed equilibrium points in continuous minmax games.
method A method based on entropic regularisation of two-layer zero-sum games with interacting particle dynamics.
result The sequence of empirical measures of the particle system satisfies a large deviation principle as the number of particles grows to infinity, implying convergence of the empirical measure and the Nikaidô-Isoda error.
Study explores grokking in neural networks, revealing transition from memorization to generalization.
problem Understanding the transition from memorization to generalization in over-parameterized neural networks.
method Extensive experiments and exploration of various viewpoints on grokking mechanism.
result Sharp transition from no generalization to perfect generalization observed during prolonged training.
Overparameterized models can worsen minority group errors even when overall test error improves.
problem Overparameterization exacerbates spurious correlations, harming minority groups.
method Simulations and experiments on image datasets, theoretical analysis of linear models.
result Subsampling the majority group can achieve low minority error in overparameterized models.
Improved GAN training stability through tunable classification losses.
problem Training instabilities in GANs.
method Reformulated GAN value function using class probability estimation (CPE) losses, defined (αD,αG)-GANs. result Tuning (αD,αG) can alleviate training instabilities. We study high-dimensional asymptotic performance limits of binary supervised classification problems where the class conditional densities are Gaussian with unknown means and covariances and the number of signal dimensions scales faster than the number of labeled training samples. We show that the Bayes error, namely t…
Many modern machine learning models are trained to achieve zero or near-zero training error in order to obtain near-optimal (but non-zero) test error. This phenomenon of strong generalization performance for "overfitted" / interpolated classifiers appears to be ubiquitous in high-dimensional data, having been observed …
The paper examines how adversarial training and noise affect neural network performance.
problem Overfitting in adversarial training and data augmentation.
method Adversarial training and data augmentation with noise in the context of regularized regression in RKHS.
result Appropriate regularization can prevent overfitting and improve performance.
The paper studies the loss landscape of regularized deep matrix factorization, revealing unique and sharp minimizers.
problem Understanding the loss landscape and minimizers of regularized deep matrix factorization problems.
method Theoretical analysis of ℓ2-regularized deep matrix factorization/deep linear network training problems with squared-error loss. result The unique end-to-end minimizer exists for all target matrices except for a set of Lebesgue measure zero.
The study analyzes how machine learning classifiers' error rates decrease exponentially based on large deviations theory.
problem Understanding the convergence rate of machine learning classifiers' error probabilities.
method Large deviations theory applied to machine learning classification techniques.
result The error probability of ML classifiers converges to zero exponentially, with a rate dependent on the training set size.
We use smoothed analysis techniques to provide guarantees on the training loss of Multilayer Neural Networks (MNNs) at differentiable local minima. Specifically, we examine MNNs with piecewise linear activation functions, quadratic loss and a single output, under mild over-parametrization. We prove that for a MNN with …
This paper tackles worst-class error rate in classification tasks.
problem Minimizing worst-class error rate in classification tasks, especially in medical image classification.
method Designing a boosting approach to bound the worst-class error rate using Deep Neural Networks (DNNs).
result The proposed boosting approach lowers worst-class test error rates while avoiding overfitting.
Sharp analysis of out-of-distribution error in overparameterized models with importance weights.
problem Understanding and quantifying the degradation of performance in overparameterized models when faced with underrepresented data.
method Sharp analysis of an overparameterized Gaussian mixture model with spurious features and cost-sensitive interpolating solutions incorporating importance weights.
result Characterization of a novel tradeoff between worst-case robustness and average accuracy as a function of importance weight magnitude.
Neural networks can interpolate noisy data and still generalize well.
problem Generalization of neural networks trained on noisy data.
method Two-layer neural networks trained to interpolation by gradient descent on corrupted labels.
result Neural networks can achieve zero training error and optimal test error.
Boosting algorithms produce a classifier by iteratively combining base hypotheses. It has been observed experimentally that the generalization error keeps improving even after achieving zero training error. One popular explanation attributes this to improvements in margins. A common goal in a long line of research, is …
Paper establishes a universal growth rate for smooth surrogate losses in classification.
problem Analyzing growth rates of consistency bounds for various surrogate losses.
method Proves square-root growth rate for smooth margin-based losses; extends to multi-class classification.
result Demonstrates a universal square-root growth rate for smooth comp-sum and constrained losses.
Extends neural network training framework to handle noise and uncertainty.
problem Handling noise and uncertainty in neural network training.
method Integrates non-zero aleatoric noise and derives posterior covariance for epistemic uncertainty.
result Derives an estimator for posterior covariance, providing a handle on epistemic uncertainty.
Deep learning has transformed computer vision, natural language processing, and speech recognition\cite{badrinarayanan2017segnet, dong2016image, ren2017faster, ji20133d}. However, two critical questions remain obscure: (1) why do deep neural networks generalize better than shallow networks; and (2) does it always hold …
FLOPART solves peak detection by creating accurate train and test set predictions.
problem Correctly detecting peaks in sequential data.
method Dynamic programming changepoint algorithm with zero train label errors.
result FLOPART provides highly accurate predictions on both train and test sets.
Visual Speech Recognition (VSR) is the process of recognizing or interpreting speech by watching the lip movements of the speaker. Recent machine learning based approaches model VSR as a classification problem; however, the scarcity of training data leads to error-prone systems with very low accuracies in predicting un…
Noise makes data unlearnable by tricking models.
problem Unauthorized exploitation of personal data by deep learning models.
method Error-minimizing noise to reduce training examples' learnability.
result Error-minimizing noise can make training examples unlearnable by deep learning models.
More features and data lead to better model performance in random feature regression.
problem Improving model performance in random feature regression.
method Theoretical analysis of random feature regression, demonstrating the benefits of overparameterization, overfitting, and more data.
result Infinite width RF architectures are preferable to those of any finite width, and training to near-zero training loss is obligatory for near-optimal performance.
Interpolating estimators in nonparametric regression become suboptimal under adversarial attacks.
problem Adversarial robustness of interpolating estimators in nonparametric regression.
method Investigation of adversarial robustness of interpolating estimators in a nonparametric regression framework.
result Interpolating estimators must be suboptimal even under a subtle future X-attack. Deep ReLU networks generalize well with few parameters.
problem Generalization of overparametrized deep neural networks.
method Explicit bounds on test error independent of overparametrization and VC dimension.
result Generalization error is independent of network architecture and overparametrization.
Analyzes bias-variance in overparameterized linear models using random features.
problem Understanding bias-variance trade-off in overparameterized models.
method Zero-temperature cavity method and random matrix theory.
result Three phase transitions in the linear random features model.
The paper diagnoses factor models using characteristic axes and zero-curve restrictions.
problem Tackles systematic sign reversals and overcorrections in factor model pricing errors.
method Extends cap-axis integral diagnostic to general characteristic axes, measuring pricing errors as bridge-alpha curves.
result Axis-level pricing errors are nearly orthogonal to maximum-Sharpe gains, showing systematic sign reversals and overcorrections.
The paper explores the information-theoretic nature of excess risk in machine learning.
problem Understanding the excess risk in machine learning models.
method Formulates the minimax excess risk as a zero-sum game and modifies it to allow swapping of the order of play.
result Proves that under certain conditions, the duality gap is zero, allowing for the application of Bayesian results to provide bounds on minimax excess risk.