Stochastic Interpolants

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3 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

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Grokking through the Lens of Minimum-Norm Interpolation
Sep 29, 2026Gil Kur, Ileana Rugina, Clémentine Carla Juliette Dominé +1Stochastic Interpolants Interpolation
ETH Zürich · Institute of Science and Technology Austria · Harvard University
Minimal-Norm Univariate Two-Layer ReLU Classification: Exact Solutions and Global Optimality with Skip Connections
Sep 23, 2026Karolina Drabik, Ben Lewis, Antoni Puch +4Rectified Linear Unit Networks Regularization
Department of Mathematics, Informatics and Mechanics, University of Warsaw, Poland · Department of Computer Science, University of Warwick, UK · INRIA & LMO, Université Paris-Saclay, France
FlowSGS: Improving Flow Matching Priors for Inverse Imaging with Stochastic Interpolants
Sep 17, 2026Tianao Li, Xinhui Qian, Emma AlexanderBayesian Inverse Problems Posterior Sampling
Department of Computer Science, Northwestern University · NSF-Simons AI Institute for the Sky (SkAI) · Department of Statistics and Data Science, Northwestern University
A Weighted Kernel Method for Approximation that Adapts to Learned Multivariable Structure
Sep 15, 2026John E. Darges, Laura WeidensagerKernel Method Approximation
Department of Mathematics, Emory University · Department of Mathematics, Simon Fraser University
Limit Points of Reflow with Minibatch Optimal Transport
Aug 7, 2026Antonin Chambolle, Johannes HertrichRectified Flow Stochastic Interpolants
Université Paris Dauphine - PSL & Inria · ENS Paris
Benign interpolation and Occam's razor
Aug 4, 2026Tom F. Sterkenburg, Daniel A. Herrmann, Jan-Willem RomeijnStochastic Interpolants Interpretability
Semi-Supervised Conditional Generative Learning through Stochastic Interpolation and Sufficient Representations
Jul 18, 2026Changyu Liu, Yuling Jiao, Jian HuangSemi-Supervised Learning Generative Architectures
Institute for Mathematics and Artificial Intelligence, Wuhan University, Wuhan, China. · School of Artificial Intelligence, Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan, China. · Departments of Data Science and Artificial Intelligence, and Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China.
A Theoretical Analysis of Memory and Overfitting Phenomena in Stochastic Interpolation Models
Jun 7, 2026Yunchen Li, Shaohui Lin, Zhou YuStochastic Interpolants Overfitting
East China Normal University
Second-Order Path Kernel Interpolation Formulas in Machine Learning
Jun 5, 2026Jin Guo, Roy Y. He, Jean-Michel MorelStochastic Interpolants Stochastic Gradient Descent
Department of Mathematics, City University of Hong Kong, Hong Kong · Division of Industrial Data Science, Lingnan University, Hong Kong
Covariance Shrinkage via Stochastic Interpolation
Jun 5, 2026Mathieu Chalvidal, Florentin Coeurdoux, Eric Vanden-EijndenCovariance Stochastic Interpolants
Capital Fund Management 23 Rue de l’Universit´e, 75007 Paris
How abundant are good interpolators?
Jun 4, 2026August Y. Chen, Ahmed El AlaouiStochastic Interpolants Overparameterization
Cornell University, Department of Computer Science. Ithaca, NY, USA. · Cornell University, Department of Statistics and Data Science. Ithaca, NY, USA.
Nonlocal Mean Field Schrödinger Bridge with Learned Interactions
Jun 2, 2026Daisuke Inoue, Dante Kalise, Mathieu LaurièreSchrödinger Bridges Mean-Field Limit
Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom. · Shanghai Frontiers Science Center of Artificial Intelligence and Deep Learning, NYU-ECNU Institute of Mathematical Sciences, NYU Shanghai, Shanghai 200126, People’s Republic of China.
Fast Generalization after Interpolation via Critically Damped Momentum Optimization
Jun 1, 2026Luca Muscarnera, Silas Ruhrberg Estévez, Yuanzhang Xiao +1Stochastic Interpolants Gradient Descent
Midpoint Generative Models
May 28, 2026Daniil Shlenskii, Nikita Gushchin, Lev Novitskiy +2Generative Models Stochastic Interpolants
1AXXX, Russia · 2Applied AI Institute, Russia · 3Kandinsky Lab, Russia
The Interplay Between Interpolation and Aggregation in Regression: Optimal Sample Complexity
May 28, 2026Mikael Møller Høgsgaard, Kasper Green Larsen, Liang-Yu ZouStochastic Interpolants Learnability
Department of Computer Science, Aarhus University, Aarhus, Denmark · Department of Statistics, University of Oxford, Oxford, United Kingdom
Mildly Overparameterized ReLU Networks on Orthogonal Data: Incremental Learning and Implicit Bias
May 26, 2026James Town, Etienne Boursier, Ben Lewis +2Rectified Linear Unit Networks Stochastic Interpolants
University of Warwick · INRIA LMO, Université Paris-Saclay
Learning Energy-Based Models from Stochastic Interpolants using Spatiotemporal Differences
May 26, 2026Hanlin Yu, RuiKang OuYang, Partha Kaushik +3Diffusion Models Contrastive Learning
University of Helsinki · University of Cambridge · Carnegie Mellon University +1
Disentangling Generation and Regression in Stochastic Interpolants for Controllable Image Restoration
May 20, 2026Yi Liu, Jia Ma, Wengen Li +3Image Restoration Stochastic Interpolants
Tongji University · Fudan University
Supersampling Stable Diffusion and Beyond: A Seamless, Training-Free Approach for Scaling Neural Networks Using Common Interpolation Methods
May 9, 2026Md Abu Obaida Zishan, Jannatun Noor, Annajiat Alim RaselDenoising Diffusion Probabilistic Model Stochastic Interpolants
School of Data and Sciences BRAC University, Dhaka · Computing for Sustainability and Social Good (C2SG) Research Group Department of Computer Science and Engineering United Internation University, Dhaka
Neural Operators as Efficient Function Interpolators
May 8, 2026Vasilis Niarchos, Angelos Sirbu, Sokratis TrifinopoulosFourier Neural Operators Neural Operators
Department of Physics, CCTP and ITCP, University of Crete, 71303, Greece · Theoretical Physics Department, CERN, Geneva, Switzerland · Physik-Institut, Universität Zürich, 8057 Zürich, Switzerland
Predictive-Generative Drift Decomposition for Speech Enhancement and Separation
May 7, 2026Julius Richter, Yoshiki Masuyama, Christoph Boeddeker +3Speech Enhancement Speech Separation
MERL Cambridge, MA, USA
Adversarial Robustness of NTK Neural Networks
Apr 28, 2026Yuxuan HouNeural Tangent Kernel Neural Network
1Qiuzhen College, Tsinghua University
Generative Modeling via Kernelized Stochastic Interpolants
Feb 23, 2026Florentin Coeurdoux, Etienne Lempereur, Nathanaël Cuvelle-Magar +2Stochastic Interpolants Stochastic Differential Equations
Capital Fund Management, Paris, France · Département d’informatique, ENS, Université PSL, Paris, France · Collège de France, Paris, France +2
Multi-Marginal Flow Matching with Adversarially Learnt Interpolants
Oct 1, 2025Oskar Kviman, Kirill Tamogashev, Nicola Branchini +3Conditional Flow Matching Interpolation
KTH · University of Edinburgh
Generalization error of min-norm interpolators in transfer learning
Jun 20, 2024Yanke Song, Kenneth Gu, Sohom Bhattacharya +1Stochastic Interpolants Empirical Risk Minimization
Department of Statistics, Harvard University · Department of Statistics, Stanford University · Department of Statistics, University of Florida

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Grokking through the Lens of Minimum-Norm Interpolation

Gil Kur, Ileana Rugina, Clémentine Carla Juliette Dominé, Marco Mondelli

ETH Zürich · Institute of Science and Technology Austria · Harvard University

Stochastic Interpolants Interpolation Grokking Exact Lens

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Grokking shows that fitting the training data and learning the underlying signal can occur at very different stages. However, existing theories offer limited quantitative insight into how this delayed generalization depends on inductive bias and signal structure. Our work addresses the gap by developing a statistical theory that characterizes how regularization geometry and signal sparsity govern generalization near interpolation. In particular, we focus on the prototypical setting of high-dimensional regression and identify regimes in which sparsity-promoting regularization makes exact interpolation much more accurate than approximate fitting. In strongly overparameterized noiseless problems, we prove a zero--one generalization law and construct a family of convex norms whose interpolators transition from the trivial risk of the all-zero predictor to exact recovery, while keeping the training error equal to

0

. Furthermore, when feature dimension and sample size are proportional, we provide a precise characterization of training and generalization errors along

\ell_r

-regularization paths. This in turn allows us to quantify the generalization gain that remains near interpolation: we show that this gain increases as the norm becomes more sparsity-promoting and as the target becomes sparser, with a sharp drop in generalization reached for noiseless data and

\ell_1

regularization. Experiments on diagonal linear networks and transformers trained on modular arithmetic demonstrate the generality of our theoretical predictions. Finally, beyond grokking, our work reveals a statistical instability in minimum-norm interpolation: small perturbations in the regularization strength can lead to drastically different generalization, while preserving small training error.

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