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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,695 papers · 148 categories

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3887751,1631,550 · Jun 202019922001200920172026
48 results for Interpolation Learning

The paper proposes a method for generating uniform interpolations on data manifolds.

problem Generating high-quality interpolations between data samples on complex manifolds.
method Autoencoder network with interpolation network, regularized by a Riemannian metric.
result The method generates interpolations that remain within the manifold's distribution.

Study interpolating estimators for causal learning from observational data.

problem Learning causal models from observational data in complex model classes.
method Investigate min-norm interpolators and ridge-regularized regressors in a linearly confounded model.
result Interpolators cannot be optimal for causal learning under the principle of independent causal mechanisms, requiring stronger regularization.

New approach uses interpolation models and error bounds for verifiable scientific machine learning.

problem Challenges in verifying and validating modern scientific machine learning workflows.
method Combines multiple standard interpolation techniques with error bounds for efficient computation and comparative performance analysis.
result Error bounds for interpolation techniques can be computed or estimated efficiently, aiding in validation goals.

This paper explores how deep learning models can fit data exactly and why this is important.

problem Understanding why deep learning models can fit data exactly and generalize well.
method Interpolation and over-parameterization as key themes to understand deep learning.
result Interpolation and over-parameterization are crucial for deep learning models to fit data exactly and generalize well.

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.

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.

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.

In order to generate novel 3D shapes with machine learning, one must allow for interpolation. The typical approach for incorporating this creative process is to interpolate in a learned latent space so as to avoid the problem of generating unrealistic instances by exploiting the model's learned structure. The process o…

2019-12-08abs ↗pdf ↗

The study identifies conditions under which algorithmic stability explains generalization in interpolating learning systems.

problem Understanding when algorithmic stability explains generalization in interpolating learning systems.
method Modeling training as a function-space trajectory and measuring sensitivity to single-sample perturbations.
result There exist interpolating regimes with small risk where contractive sensitivity cannot hold, showing that stability is not a universal explanation.

New optimization method helps models generalize better after achieving near-perfect training performance.

problem Models can achieve near-perfect training performance but fail to generalize well to unseen examples.
method GROKtimizer combines rapid convergence to interpolation with post-interpolation norm minimization using Critically Damped Momentum.
result GROKtimizer provides a quadratic speedup over classical gradient descent, offering a natural solution for selecting low-norm interpolating solutions.

The paper connects flatness to generalization in learning multi-index models with neural networks.

problem Understanding the generalization of non-convex neural networks using flatness measures.
method Analyzes 2-layer non-convex homogeneous neural networks and their connection to multi-index models.
result Flattest interpolators achieve small population loss and generalize well, establishing a direct link between flatness and generalization.

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.

SoftKI combines SKI and variational methods for scalable GP regression.

problem Scalable Gaussian Process regression on high-dimensional datasets.
method SoftKI approximates kernel via softmax interpolation from a smaller number of learned points.
result SoftKI is competitive with other approximated GP methods for modest data dimensions.

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 2\ell_2-norm scaling as n\sqrt{n}, close to the minimal interpolator's complexity.

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-2\ell_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.

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.

Loose bounds found for least-norm interpolant in over-parameterized settings.

problem Failures of model-dependent generalization bounds for least-norm interpolation.
method Analysis of generalization performance of least-norm linear regressor in over-parameterized regime.
result Generalization bounds for least-norm interpolant can be very loose, even when true excess risk goes to zero.

New bounds for linear interpolators show how they generalize under covariate shifts.

problem Understanding how linear interpolators generalize under covariate shifts.
method Proved non-asymptotic excess risk bounds for benignly-overfit linear interpolators in transfer learning.
result Identified beneficial and malignant covariate shifts based on overparameterization degree.

The paper studies the minimum ℓ₁-norm interpolator's risk behavior in over-parameterized settings.

problem Understanding the risk behavior of minimum ℓ₁-norm interpolators in high-dimensional settings.
method Exact characterization of the risk behavior through a system of two non-linear equations.
result Observation of a multi-descent phenomenon in the generalization risk of the minimum ℓ₁-norm interpolator.

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.

DSoftKI scales GP regression with full derivative observations.

problem Efficiently fitting and predicting full derivative observations in Gaussian Processes.
method Extends SoftKI by using local temperature vectors for interpolation, enabling encoding of local directional sensitivity.
result DSoftKI achieves accurate predictions and scales to larger datasets with full derivative observations.

The paper improves generalization bounds using interpolation between various divergences.

problem Improving generalization bounds in machine learning.
method Derives new PAC-Bayes generalization bounds based on (f,Γ)(f, Γ)-divergence and interpolates between various divergences.
result Connects derived bounds to earlier statistical learning results and provides practical training objectives.

Paper introduces a method to explain deep learning models and identify good generalization.

problem Limited interpretability of neural networks hinders progress and real-world applications.
method Polytope interpolation method for local explainability and generalization assessment.
result Developed a method to identify deep learning models with good generalization properties.

A new image interpolation model using sparse representation and nonlocal linear regression.

problem Image interpolation without blurring and noise.
method Sparse representation, nonlocal self-similarity, nonlocal linear regression, adaptive sub-dictionary learning, weighted encoding.
result Our method outperforms state-of-the-art methods in quantitative measures and visual quality.

Paper investigates optimal interpolation methods in linear regression.

problem Understanding when interpolating methods generalize well in linear regression.
method Investigates optimal response-linear interpolators using functions linear in the response variable.
result Provides a closed-form expression for the optimal interpolator and shows it can be derived as the limit of gradient descent.

The over-parameterized models attract much attention in the era of data science and deep learning. It is empirically observed that although these models, e.g. deep neural networks, over-fit the training data, they can still achieve small testing error, and sometimes even {\em outperform} traditional algorithms which ar…

2019-09-25abs ↗pdf ↗

We introduce Interpolation Consistency Training (ICT), a simple and computation efficient algorithm for training Deep Neural Networks in the semi-supervised learning paradigm. ICT encourages the prediction at an interpolation of unlabeled points to be consistent with the interpolation of the predictions at those points…

2019-03-09abs ↗pdf ↗

In this paper, we present a new deep learning architecture for addressing the problem of supervised learning with sparse and irregularly sampled multivariate time series. The architecture is based on the use of a semi-parametric interpolation network followed by the application of a prediction network. The interpolatio…

2019-09-13abs ↗pdf ↗

Deep networks can interpolate noisy data without losing generalization.

problem Characterizing the relationship between interpolation and generalization in overparameterized deep networks.
method Analyzing the loss landscape of neural network functions over volumes around training data points, varying model parameters and training epochs.
result Loss sharpness in the input space follows a double descent, with large models predicting noisy targets over larger volumes around training data points.

Develops interpolation methods for matrix functions in statistics and machine learning.

problem Estimating matrix functions in statistics and machine learning.
method Interpolates log-determinant and trace of matrix powers using modified sharp bounds.
result Accuracy and performance demonstrated in numerical examples.

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.

Study optimizes linear regression analysis for high-dimensional settings.

problem Understanding high-dimensional linear regression with interpolation and regularization.
method Localized uniform convergence analysis of optimistic rates for linear regression.
result Recover guarantees for ridge and LASSO regression under random designs.

New framework shows ERM is optimal for both interpolation and extrapolation in domain generalization.

problem Formalizing and solving the challenges of domain generalization.
method Reformulated domain generalization as an online game between a risk-minimizing player and an adversary.
result ERM is minimax-optimal for both interpolation and extrapolation in domain generalization.

The paper explores why a specific type of predictor works well in noisy data.

problem Understanding why a specific type of predictor (minimum-norm interpolator) works well in noisy data.
method The paper uses uniform convergence and zero-error predictors in a norm ball to explain the success of the minimum-norm interpolator.
result The minimum-norm interpolator is consistent, and this can be explained by uniform convergence of zero-error predictors in a norm ball.

In modern supervised learning, many deep neural networks are able to interpolate the data: the empirical loss can be driven to near zero on all samples simultaneously. In this work, we explicitly exploit this interpolation property for the design of a new optimization algorithm for deep learning, which we term Adaptive…

2019-06-13abs ↗pdf ↗

Deep linear networks can closely approximate interpolants without improving risk.

problem Understanding the risk bounds of deep linear networks compared to minimum 2\ell_2-norm solutions.
method Bounding excess risk of interpolating deep linear networks trained using gradient flow.
result Deep linear networks can closely approximate or match minimum 2\ell_2-norm solutions in terms of risk.