Does data interpolation contradict statistical optimality?
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Mikhail Belkin
cs.LGstat.MLcs.AImath.OCcs.CVmath.STstat.THcs.CLcs.DSneural networks
On Valency
published · living versionsPreprints & journals
72 papers in the corpus · 2009–2026A Theoretical Analysis of Generalization Dynamics in Neural Networks under Gradient Descent with Weight Decay
0 citations
Convergent Evolution: How Different Language Models Learn Similar Number Representations
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Breaking Data Symmetry is Needed For Generalization in Feature Learning Kernels
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Catching rationalization in the act: detecting motivated reasoning before and after CoT via activation probing
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Toward universal steering and monitoring of AI models.
3 citations
General and Efficient Steering of Diffusion Models
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SynEL: A synthetic benchmark for entity linking.
1 citation
The Features at Convergence Theorem: a first-principles alternative to the Neural Feature Ansatz for how networks learn representations
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Linear Recursive Feature Machines provably recover low-rank matrices.
3 citations
A Gap Between the Gaussian RKHS and Neural Networks: An Infinite-Center Asymptotic Analysis
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Task Generalization With AutoRegressive Compositional Structure: Can Learning From Tasks Generalize to Tasks?
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Fast training of large kernel models with delayed projections
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Mirror Descent on Reproducing Kernel Banach Spaces
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Context-Scaling versus Task-Scaling in In-Context Learning
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Eigenvectors of the De Bruijn Graph Laplacian: A Natural Basis for the Cut and Cycle Space
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Emergence in non-neural models: grokking modular arithmetic via average gradient outer product
1 citation
Mechanism for feature learning in neural networks and backpropagation-free machine learning models.
76 citations
Average gradient outer product as a mechanism for deep neural collapse
2 citations
UNDIAL: Self-Distillation with Adjusted Logits for Robust Unlearning in Large Language Models
7 citations
On the Nystrom Approximation for Preconditioning in Kernel Machines
1 citation
More is Better in Modern Machine Learning: when Infinite Overparameterization is Optimal and Overfitting is Obligatory
6 citations
Mechanism of feature learning in convolutional neural networks
3 citations
Catapults in SGD: spikes in the training loss and their impact on generalization through feature learning
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On Emergence of Clean-Priority Learning in Early Stopped Neural Networks
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Wide and deep neural networks achieve consistency for classification.
20 citations
Cut your Losses with Squentropy
1 citation
Toward Large Kernel Models
2 citations
Mechanism of feature learning in deep fully connected networks and kernel machines that recursively learn features
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Restricted Strong Convexity of Deep Learning Models with Smooth Activations
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A Universal Trade-off Between the Model Size, Test Loss, and Training Loss of Linear Predictors
1 citation
Benign, Tempered, or Catastrophic: A Taxonomy of Overfitting
3 citations
A note on Linear Bottleneck networks and their Transition to Multilinearity
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On the Inconsistency of Kernel Ridgeless Regression in Fixed Dimensions
5 citations
Quadratic models for understanding catapult dynamics of neural networks
2 citations
Simple, fast, and flexible framework for matrix completion with infinite width neural networks.
23 citations
Limitations of Neural Collapse for Understanding Generalization in Deep Learning
9 citations
Local Quadratic Convergence of Stochastic Gradient Descent with Adaptive Step Size
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Fit without fear: remarkable mathematical phenomena of deep learning through the prism of interpolation
153 citations
Risk Bounds for Over-parameterized Maximum Margin Classification on Sub-Gaussian Mixtures
13 citations
Overparameterized neural networks implement associative memory.
59 citations
On the linearity of large non-linear models: when and why the tangent kernel is constant
51 citations
Linear Convergence of Generalized Mirror Descent with Time-Dependent Mirrors
2 citations
Multiple Descent: Design Your Own Generalization Curve
29 citations
Evaluation of Neural Architectures Trained with Square Loss vs Cross-Entropy in Classification Tasks
50 citations
Classification vs regression in overparameterized regimes: Does the loss function matter?
69 citations
Reply to Loog et al.: Looking beyond the peaking phenomenon.
6 citations
Loss landscapes and optimization in over-parameterized non-linear systems and neural networks
113 citations
Reconciling modern machine-learning practice and the classical bias-variance trade-off.
1,594 citations
Back to the Future: Radial Basis Function Network Revisited.
53 citations
Kernel Machines Beat Deep Neural Networks on Mask-based Single-channel Speech Enhancement
7 citations
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