Interpolated-MLPs control inductive bias for better performance in low-compute tasks.
problem Low-compute performance gap between MLPs and CNNs.
method Introduced Interpolated MLP (I-MLP) approach to control inductive bias incrementally.
result Continuous logarithmic relationship between inductive bias and performance in low-compute tasks.
Study shows how networks converge to minimum norm solutions with regularization.
problem Interpolating between known regions in shallow ReLU networks.
method Investigates empirical risk minimizers and weight decay regularizers.
result Empirical risk minimizers converge to minimum norm interpolants under specific conditions.
Noise affects the effectiveness of interpolating models, especially those with strong inductive biases.
problem The impact of noise on interpolating models with strong inductive biases.
method Analyzing linear and classification models with sparse ground truths, proving fast rates for interpolators.
result Strong inductive biases can lead to faster but noisier interpolators, contrary to intuition.
Strong inductive biases prevent harmless interpolation in overparameterized models.
problem Understanding the conditions under which overparameterized models can interpolate noise without overfitting.
method Theoretical analysis of high-dimensional kernel regression and deep neural networks, focusing on the role of inductive biases.
result The strength of an estimator's inductive bias determines whether interpolation is harmless or requires fitting noise for good generalization.
A new tradeoff between regularization and sharpness improves model performance in overparameterized settings.
problem Improving model performance in overparameterized settings with minimum-norm interpolators.
method Proposes a regularization-sharpness tradeoff for overparameterized linear regression with an ℓ^p penalty.
result Empirical validation shows the tradeoff terms can distinguish performant linear interpolators.
Characterizes kernel interpolation in large dimensions, revealing optimal and sub-optimal regions.
problem Understanding the phase diagram of kernel interpolation in large dimensions.
method Characterization of variance and bias under various source conditions.
result Determined the ( s , γ ) (s,γ) ( s , γ ) -phase diagram of large-dimensional kernel interpolation. Matrix SMD converges to unique solution minimizing Bregman divergence.
problem High-dimensional multi-output classification and matrix completion problems.
method Stochastic Mirror Descent with matrix parameters and matrix mirror functions.
result Matrix SMD converges exponentially to the unique solution minimizing Bregman divergence.
Neural networks learn incrementally from orthogonal data, interpolating with minimal complexity.
problem Understanding the learning dynamics and implicit bias in ReLU networks with orthogonal data.
method Gradient flow analysis of two-layer ReLU networks from small initialization with orthogonal training data.
result The learned interpolator has a squared ℓ 2 \ell_2 ℓ 2 -norm scaling as n \sqrt{n} n , close to the minimal interpolator's complexity. Deep networks generalize well even when they fit training data perfectly, thanks to overparametrization.
problem Understanding generalization in overparametrized deep networks.
method Random features regression, asymptotic analysis, ensemble averaging.
result Bias remains constant beyond the interpolation threshold, while variance components decay with overparametrization.
The paper analyzes optimal implicit bias in linear regression for over-parameterized models.
problem Finding the best generalization performance in over-parameterized linear regression.
method Asymptotic analysis of generalization performance for convex functions/potentials.
result Optimal implicit bias that achieves the best generalization error under certain conditions.
Two-layer ReLU networks often converge to simpler solutions, improving generalization.
problem Understanding generalization in overparametrized neural networks, especially for complex tasks.
method Theoretical analysis of two-layer ReLU networks, focusing on the early alignment phase.
result Two-layer ReLU networks often converge to simpler solutions rather than interpolating the training data, leading to better generalization.
Regression models can interpolate noisy data and still perform well, contrary to the bias-variance tradeoff.
problem Understanding why overparametrized models can generalize well despite the bias-variance tradeoff.
method Analysis of minimum norm solutions and ridge regression, focusing on the smallest singular value of the regression matrix.
result Testing error exhibits double descent behavior as model order increases, contrary to the classical bias-variance tradeoff.
Unified framework approximates gradient descent's implicit bias in high dimensions.
problem Understanding gradient descent's behavior in overparameterized settings with convex losses.
method Unified framework for convex losses, including sensitivity analysis.
result Approximation of minimum-norm interpolation in high dimensions.
The paper analyzes the generalization error of min-norm interpolators in transfer learning with limited test samples.
problem Characterizing the generalization error of min-norm interpolators in transfer learning with limited test samples.
method Characterizes the bias and variance of pooled min- ℓ 2 \ell_2 ℓ 2 -norm interpolation under covariate shift and model shift. result Shows that adding data can hurt when SNR is low and is beneficial at higher SNR levels under certain conditions.
Bayesian imputation optimizes bias-variance tradeoff in time-series data.
problem Look-ahead bias in imputation of missing time-series data.
method Wasserstein interpolation for Bayesian posterior consensus distribution.
result Optimal control of look-ahead bias and variance in imputation.
A new method interpolates between sampling and variational inference using stochastic mixtures.
problem Combining the strengths of sampling and variational inference methods.
method Develops a framework using stochastic mixtures of simple component distributions to interpolate between sampling and variational inference.
result Improves on both sampling and variational inference methods by reducing bias and variance.
New algorithms optimize spectral risk measures, improving interpolation between average and worst-case performance.
problem Optimizing spectral risk measures for learning systems.
method Developed stochastic algorithms to optimize spectral risk measures by characterizing their subdifferential and addressing challenges like biasedness of subgradient estimates and non-smoothness.
result Our approach outperforms out-of-the-box stochastic subgradient and dual averaging methods in optimizing spectral risk measures.
Adversarial training leads to large generalization gap, decomposed into bias and variance.
problem Understanding the large generalization gap in adversarially trained models.
method Bias-Variance decomposition of test risk as a function of adversarial perturbation radius.
result Bias increases monotonically with adversarial perturbation radius and is dominant in test risk.
Randomly trained neural networks can generalize well if there's a simpler underlying teacher model.
problem Why randomly trained neural networks generalize well despite interpolating training data.
method Examined a random neural network that interpolates training data and showed it generalizes well if there's a simpler underlying teacher model.
result Randomly trained neural networks can generalize well if there's a simpler underlying teacher model.
Our paper characterizes how ReLU affects GD's implicit bias in high-dimensional neural networks.
problem Understanding the implicit bias of gradient descent on neural networks.
method Novel primal-dual analysis tracking predictions and coefficients.
result The implicit bias approximates the minimum- ℓ 2 \ell_2 ℓ 2 -norm solution with high probability. 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.
Two-layer neural networks can overfit without increasing risk when data is noisy.
problem Understanding why neural networks can overfit without increasing risk in noisy data.
method Combining bias and variance analysis in a high-dimensional setting.
result The excess learning risk of the interpolator decays under mild conditions.
This work studies finite-sample properties of the risk of the minimum-norm interpolating predictor in high-dimensional regression models. If the effective rank of the covariance matrix Σ Σ Σ of the p p p regression features is much larger than the sample size n n n , we show that the min-norm interpolating predictor is not de…
Covariance shrinkage via stochastic interpolation
problem High-dimensional covariance estimation
method Recasting shrinkage as empirical risk minimization
result Reduces statistical risk through scheduling, flow maps, and early stopping
Deep reinforcement learning (DRL) on Markov decision processes (MDPs) with continuous action spaces is often approached by directly training parametric policies along the direction of estimated policy gradients (PGs). Previous research revealed that the performance of these PG algorithms depends heavily on the bias-var…
Deep learning models can have low bias and variance, contrary to classical theory.
problem Understanding the performance of deep learning models at high complexity.
method Developed a fine-grained bias-variance decomposition for random feature kernel regression, analyzing the effects of sampling, initialization, and labels.
result The variance terms exhibit non-monotonic behavior and can diverge at the interpolation boundary, even in the absence of label noise.
Local Gradient Descent with local steps converges to the centralized model in the interpolation regime.
problem Understanding the implicit bias of Local Gradient Descent in the interpolation regime.
method Analyzing the implicit bias of Local Gradient Descent for classification tasks with linearly separable data.
result The aggregated global model from Local-GD converges exactly to the centralized model in the interpolation regime.
A new method for computing Greeks without bias, improving stability.
problem Inaccurate and unstable computation of second order Greeks (like Gamma) in financial instruments.
method Apply Chebyshev interpolation techniques to finite differences for improved stability.
result Improved stability and accuracy in computing spot Greeks without bias.
Study investigates overparametrization in survival models, revealing complex loss behavior.
problem Understanding overparametrization in survival models through interpolation.
method Defined interpolation and finite-norm interpolation, rigorously analyzed four survival models.
result Overparametrization can lead to improved performance in survival models, contrary to classical learning theory.
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.
Unified framework explains why overfitting is benign in interpolating learning.
problem Understanding why overfitting is benign in highly overparameterized models.
method Spectral-transport stability framework.
result Sharp benign-overfitting criterion and explicit phase-transition rates.
Interpolating label noise makes models vulnerable to adversarial attacks.
problem Adversarial vulnerability of models trained on noisy labels.
method Theoretical analysis of label noise and adversarial risk relationship.
result Uniform label noise induces adversarial risk similar to worst-case poisoning.
IIC provides a PAC-Bayes bound for interpolating models, revealing factors affecting generalization.
problem Theoretical challenges in understanding overparameterized models and their performance.
method PAC-Bayesian perspective applied to the Interpolating Information Criterion (IIC).
result Test error for overparameterized models achieving zero training error depends on various factors.
SKI speeds up Toeplitz Neural Networks by avoiding explicit decay bias and using frequency response.
problem Efficiently compute and update Toeplitz matrices in neural networks.
method Sparse plus low-rank decomposition, asymmetric SKI, frequency response modeling.
result Achieved significant speedup with minimal performance loss.
Interpolating models can have heavy-tailed risk, leading to rare but severe errors.
problem Interpolating models' tail risk is poorly understood, affecting rare but impactful errors.
method Large-deviation methods to study the fragility of high-dimensional linear interpolators.
result Ridgeless regression exhibits heavy-tailed risk, while ridge-regularized estimators have better tail behavior.
In the era of deep learning, understanding over-fitting phenomenon becomes increasingly important. It is observed that carefully designed deep neural networks achieve small testing error even when the training error is close to zero. One possible explanation is that for many modern machine learning algorithms, over-fit…
Breakthroughs in machine learning are rapidly changing science and society, yet our fundamental understanding of this technology has lagged far behind. Indeed, one of the central tenets of the field, the bias-variance trade-off, appears to be at odds with the observed behavior of methods used in the modern machine lear…
We introduce several techniques for sampling and visualizing the latent spaces of generative models. Replacing linear interpolation with spherical linear interpolation prevents diverging from a model's prior distribution and produces sharper samples. J-Diagrams and MINE grids are introduced as visualizations of manifol…
This work shows how penalising bias terms in norm regularisation leads to sparse solutions.
problem Understanding the relation between parameter norm regularization and the sparsity of neural network solutions.
method Analyzes one hidden ReLU layer networks with unidimensional data, showing the norm required for function representation and the importance of the bias term's norm.
result Penalising the bias terms in regularisation leads to sparse solutions, enforcing the uniqueness and sparsity of the minimal norm interpolator.
New method uses deep neural networks to interpolate spatiotemporal data.
problem Scalable interpolation of spatiotemporal data from growing earth observation systems.
method Bayesian deep learning with random feature expansions.
result Competitive or superior results compared to existing methods.
New analysis shows bias term affects conditions for benign overfitting in linear classifiers.
problem Understanding conditions for good generalization in linear classifiers with bias terms.
method Extending Hashimoto et al.'s results to include bias terms, analyzing covariance structure and label noise.
result Benign overfitting persists in linear classifiers with bias terms, with new constraints on data's covariance structure.
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.
Wide neural networks' last hidden layers split into groups of redundant neurons.
problem Understanding why wide neural networks generalize well despite overfitting.
method Analyzed the last hidden layer representations of various convolutional neural networks.
result Wide hidden layers split into groups of redundant neurons, which help generalize.
Synthetic control method improves policy evaluation in high-dimensional settings.
problem Evaluating the impact of new policies in large-scale applications.
method Two-phase approach: nearest neighbor matching followed by supervised learning.
result The method successfully improves estimate accuracy in large-scale experiments.
Adaptive data analysis is frequently criticized for its pessimistic generalization guarantees. The source of these pessimistic bounds is a model that permits arbitrary, possibly adversarial analysts that optimally use information to bias results. While being a central issue in the field, still lacking are notions of na…
New findings show GD converges to a linear interpolator even with quadratic loss function under certain conditions.
problem Understanding convergence of Gradient Descent with quadratic loss functions.
method Parameterized linear regression with quadratic loss function, empirical and theoretical analysis.
result Gradient Descent converges to a linear interpolator even with quadratic loss function under the Edge of Stability regime.
RNGI model bridges two probability densities on Riemannian manifolds efficiently.
problem Limited applicability of Euclidean stochastic interpolants to Riemannian manifolds.
method Introduces RNGI model interpolating between Riemannian manifold probability densities along geodesics.
result Proves temporal marginal density solves transport equation on Riemannian manifold.
A semi-supervised framework using stochastic interpolation and latent representations.
problem Challenges in conditional generative modeling with scarce labeled data.
method Combines conditional stochastic interpolation with low-dimensional latent representations.
result Significantly improves sample complexity and achieves faster convergence rate.