Proposes a new regularization method for deep learning models.
problem Lack of leverage from neighboring sample relationships in existing regularization techniques.
method Patch-level Neighborhood Interpolation (Pani) that constructs patch-level graphs and linearly interpolates neighborhood patch features.
result Demonstrates effectiveness of Pani in both supervised and semi-supervised settings.
t-distributed Stochastic Neighborhood Embedding (t-SNE) is a method for dimensionality reduction and visualization that has become widely popular in recent years. Efficient implementations of t-SNE are available, but they scale poorly to datasets with hundreds of thousands to millions of high dimensional data-points. W…
DELIMIT is a framework extension for deep learning in diffusion imaging, which extends the basic framework PyTorch towards spherical signals. Based on several novel layers, deep learning can be applied to spherical diffusion imaging data in a very convenient way. First, two spherical harmonic interpolation layers are a…
Hybrid controller combines model-based and policy-based reinforcement learning.
problem Combining model-based and policy-based reinforcement learning for stability and robustness.
method Designs a hybrid controller that interpolates a model-based linear controller and a differentiable policy.
result Proven to maintain stability and universal approximation properties.
New step-size methods improve SHB convergence for stochastic optimization.
problem Tuning step-size and momentum parameters in SHB is challenging.
method Proposed MomSPSmax, MomDecSPS, and MomAdaSPS for SHB. result Convergence guarantees for SHB to solution neighborhoods and exact minimizers.
New study shows mean estimation algorithms can't beat sub-Gaussian rate in general.
problem Improving mean estimation beyond worst-case scenarios.
method Constructing counterexamples and introducing neighborhood optimality.
result No reasonable estimator can achieve better than sub-Gaussian error rate for any distribution.
New algorithms improve SGD convergence and reduce variance for over-parameterized models.
problem Slower convergence in non-interpolation settings for SGD variants.
method Proposed AdaSPS and AdaSLS with variance reduction for robust convergence.
result Achieves faster convergence rates and robustness in non-interpolation settings.
Study shows harmful overfitting in Sobolev spaces even as training data grows.
problem Harmful overfitting in Sobolev spaces under noisy conditions.
method Geometric argument using Sobolev inequalities.
result Approximately norm-minimizing interpolators exhibit harmful overfitting.
We derive spectral sequences for the intersection homology of stratified fibrations and approximate tubular neighborhoods in manifold stratified spaces. These neighborhoods include regular neighborhoods in PL stratified spaces.
Sharp bounds on ERM's minimal error in regression.
problem Understanding ERM's performance in regression tasks.
method Sharp lower bounds for ERM in random and fixed design settings.
result ERM's performance depends on the global or local complexity of the model.
Making an adaptive prediction based on one's input is an important ability for general artificial intelligence. In this work, we step forward in this direction and propose a semi-parametric method, Meta-Neighborhoods, where predictions are made adaptively to the neighborhood of the input. We show that Meta-Neighborhood…
Improved SEG method converges to Nash equilibrium in bilinear games.
problem Stochastic bilinear minimax optimization problem
method Stochastic ExtraGradient (SEG) method with constant step size, iteration averaging, and scheduled restarting.
result Provable convergence to Nash equilibrium under standard settings, optimal convergence rate in interpolation setting.
This paper shows how forward rate interpolations are equivalent to discount factor interpolations in yield curve construction.
problem The challenge of choosing between different interpolation methods for yield curve construction.
method Demonstrates the equivalence between forward rate interpolations and discount factor interpolations.
result Some popular interpolation methods on forward rates are equivalent to classical interpolation methods on discount factors.
Data-driven neighborhood definitions and graph constructions are often used in machine learning and signal processing applications. k-nearest neighbor~(kNN) and ε-neighborhood methods are among the most common methods used for neighborhood selection, due to their computational simplicity. However, the choice of param…
Study geodesics entering a fixed cusp neighborhood multiple times.
problem Understanding geodesics entering a specific cusp neighborhood multiple times.
method Investigate reciprocal geodesics entering a fixed cusp neighborhood a fixed number of times.
result Characterized the class of reciprocal geodesics entering a fixed cusp neighborhood a fixed number of times.
Urban2Vec combines street view imagery and POIs for better urban neighborhood embeddings.
problem Lack of comprehensive representation of urban neighborhoods using heterogeneous data.
method Unsupervised multi-modal framework using CNN for visual features and bag-of-words for POI data.
result Urban2Vec achieves better performance than baseline models and comparable to fully-supervised methods.
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.
Skeleta and other pure subsets of manifold stratified spaces are shown to have neighborhoods which are teardrops of stratified approximate fibrations (under dimension and compactness assumptions). In general, the stratified approximate fibrations cannot be replaced by bundles, and the teardrops cannot be replaced by ma…
New FX option interpolations impact implied volatilities.
problem Different interpolations of FX option quotes lead to varying implied volatilities.
method Analysis of various exact interpolations of broker quotes.
result Different interpolations result in different implied volatilities.
New framework distinguishes knots via neighborhood invariants.
problem Distinguishing knots and knotoids.
method Study of knotoid spectra and neighborhood invariants.
result Neighborhood invariants can distinguish knots of higher Gordian distance.
Kernel interpolation is inconsistent for norms with smoothness above a constant.
problem Inconsistency of kernel interpolation in reproducing kernel Hilbert spaces.
method Lower bounds for generalization error in Sobolev norms.
result Kernel interpolation is always inconsistent for norms with smoothness above a constant.
This paper tackles selection bias in recommender systems by considering the neighborhood effect.
problem Selection bias in recommender systems due to filtering and user selection.
method Formalizes neighborhood effect as interference problem, introduces treatment representation, and proposes ideal loss.
result Proposed methods achieve unbiased learning when both selection bias and neighborhood effect are present.
Maximally hyperbolic solutions contain future neighborhoods of intersecting hypersurfaces.
problem Maximally globally hyperbolic solutions of higher-dimensional vacuum Einstein equations.
method Analyzing intersections of characteristic hypersurfaces.
result Contains a future neighborhood of intersecting hypersurfaces.
Many prediction problems can be phrased as inferences over local neighborhoods of graphs. The graph represents the interaction between entities, and the neighborhood of each entity contains information that allows the inferences or predictions. We present an approach for applying machine learning directly to such graph…
Bayesian interpolants explain neural network inferences concisely.
problem Understanding neural network inferences.
method Adapting Craig interpolants for neural networks.
result Produces precise, understandable explanations.
Near-interpolating models grow norms quickly, affecting generalization.
problem Understanding the trade-off between interpolation and generalization in near-interpolating models.
method Random matrix theory and eigendecay analysis of data covariance matrix.
result Near-interpolating models exhibit rapid norm growth and worse generalization trade-offs.
The paper improves interpolation in generative models by using specific base distributions.
problem Unexpected side effects in linear interpolations of normalizing flows.
method Enforces a specific manifold using Dirichlet and von Mises-Fisher base distributions.
result Superior performance in terms of bits per dimension, FID, and KID scores for interpolation.
Proposes a new NMF method incorporating neighborhood structure for better anomaly detection.
problem NMF's inability to incorporate neighborhood structure information limits its performance in nonlinear manifold structures.
method Integrates neighborhood structure information using Minimum Spanning Tree (MST) within NMF framework.
result Empirical results show superior performance in anomaly detection using the proposed method.
Study on transverse knots and their neighborhoods, proving unique standard neighborhoods and destabilization results.
problem Understanding the structure and properties of transverse knots and their neighborhoods.
method Proves unique standard neighborhoods and structure theorems for non-loose Legendrian knots through destabilization results.
result Finds a manifold with infinite tight contact structures, up to contactomorphism, without Giroux torsion.
New approach uses distributed persistence for stable, parallelizable topological analysis of large point clouds.
problem Estimating the full persistence diagram of large point clouds is expensive, unstable, and not a sufficient statistic.
method Proposes distributed persistence as a new invariant, which is perfectly parallelizable, more stable, and has a rich inverse theory.
result The map from point clouds to distributed persistence invariants is a global quasi-isometry, interpolating between purely geometric and topological invariants.
Deep neural networks can interpolate any dataset in the overparametrized regime.
problem Interpolating any dataset with deep neural networks in the overparametrized regime.
method Proving universal approximations and interpolating any dataset with deep neural networks, considering specific conditions on activation functions.
result Interpolation of any dataset is possible in the overparametrized regime with deep neural networks.
Interpolation hurts robust generalization even without noise.
problem The challenge of robust generalization in the absence of noise.
method Avoiding interpolation through ridge regularization.
result Ridge regularization improves robust generalization.
Uniform convergence of interpolators proven for Gaussian data.
problem Interpolation learning in high-dimensional linear regression with Gaussian data.
method Generic uniform convergence guarantee in terms of Gaussian width.
result Consistency of interpolators for minimum-norm and near-minimal-norm cases.
The paper characterizes vector fields as interpolating sesqui-harmonic maps on Riemannian manifolds.
problem Characterizing vector fields as interpolating sesqui-harmonic maps on Riemannian manifolds.
method Characterization theorem and critical point condition for interpolating sesqui-harmonic vector fields.
result Conditions for vector fields to be interpolating sesqui-harmonic maps on compact manifolds.
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.
Revises GNN neighborhood aggregation for more accurate node classification.
problem Flaws in benchmark GNN models for node classification.
method Statistical signal processing approach to neighborhood aggregation.
result Novel insights for designing more efficient GNN models.
Proves a new law of robustness for interpolating arbitrary data distributions.
problem Understanding robust interpolation for arbitrary data distributions.
method Proves a Lipschitzness lower bound for robust interpolation.
result Demonstrates a two-fold law of robustness for interpolating functions.
Interpolating between points is a problem connected simultaneously with finding geodesics and study of generative models. In the case of geodesics, we search for the curves with the shortest length, while in the case of generative models we typically apply linear interpolation in the latent space. However, this interpo…
The study proves a neighborhood theorem for mean curvature flow in higher dimensions.
problem Proving a canonical neighborhood theorem for mean curvature flow in higher dimensions.
method Proved a canonical neighborhood theorem for mean curvature flow of compact submanifolds in RN with a pinching condition. result Proved a canonical neighborhood theorem for mean curvature flow in dimensions n≥5. A neighborhood homotopy is an equivalence relation on spatial graphs which is generated by crossing changes on the same component and neighborhood equivalence. We give a complete classification of all 2-component spatial graphs up to neighborhood homotopy by the elementary divisor of a linking matrix with respect to th…
We consider interpolating sesqui-harmonic Legendre curves in Sasakian space forms. We find the necessary and sufficient conditions for Legendre curves in Sasakian space forms to be interpolating sesqui-harmonic. Finally, we obtain an example for an interpolating sesqui-harmonic Legendre curve in a Sasakian space form.
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. GraphAIR improves graph representation learning by capturing non-linear interactions.
problem Challenges in capturing non-linear interactions in graph data.
method Integrates neighborhood aggregation and interaction modeling.
result Demonstrates improved performance on node classification and link prediction tasks.
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.
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
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)-phase diagram of large-dimensional kernel interpolation. Study on biharmonic and interpolating sesqui-harmonic vector fields on para-Kähler--Norden manifolds.
problem Investigating higher-order harmonicity in pseudo-Riemannian geometry.
method Deriving first variations of bienergy and interpolating sesqui-energy functionals, characterizing biharmonic and interpolating sesqui-harmonic vector fields.
result Explicit characterizations and examples of vector fields satisfying biharmonic and interpolating sesqui-harmonic conditions.
In sparse-view Computed Tomography (CT), only a small number of projection images are taken around the object, and sinogram interpolation method has a significant impact on final image quality. When the amount of sparsity (the amount of missing views in sinogram data) is not high, conventional interpolation methods hav…