Research map / Learning theory and algorithms / Kernels and regression theory
Deep learning generalizes because the parameter-function map is biased towards simple functions
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a Gaussian-process approximation to the function prior to estimate PAC-Bayes bounds | 4-layer CNN and 1-layer fully connected network · Binarized MNIST, Fashion-MNIST, and CIFAR10 | generalization error trend across label corruption | Helped |
| Increase label corruption | DNNs trained on binarized image datasets · MNIST, Fashion-MNIST, and CIFAR10 | generalization error | Hurt |
| Use lower Gaussian-process variance hyperparameters (σw=1.0, σb=1.0) instead of the higher-variance setting (ablation) | SGD-like methods compared with approximate Bayesian inference · Boolean function learning | Pearson correlation of function-finding probabilities: advSGD: ρ=0.99 -> ρ=0.72; Adam: ρ=0.99 -> ρ=0.66 | Hurt |
| Use lower Gaussian-process variance hyperparameters (σw=1.0, σb=1.0) instead of the higher-variance setting (ablation) | SGD-like methods compared with approximate Bayesian inference · Boolean function learning | correlation p value: advSGD: p=expnumber{3}{-31} -> p=expnumber{1}{-6}; Adam: p=expnumber{8}{-42} -> p=expnumber{2}{-7} | Mixed |
| Choose weight and bias variances substantially smaller, using values measured after SGD training (ablation) | Gaussian-process PAC-Bayes bound · MNIST, Fashion-MNIST, and CIFAR10 | PAC-Bayes bound: above 50% | Hurt |
| Increase target-function Lempel-Ziv complexity | Boolean-function DNN · Boolean function learning | generalization error | Hurt |
Closest papers by meaning
- Position: Deep Learning is Not So Mysterious or Different (ICML 2025 · similarity 0.90)
- Exploring Generalization in Deep Learning (NeurIPS 2017 · similarity 0.90)
- Simplicity Bias in Overparameterized Machine Learning (AAAI 2024 · similarity 0.90)
- Understanding deep learning requires rethinking generalization (ICLR 2017 · similarity 0.90)
- Do Neural Networks Need Gradient Descent to Generalize? A Theoretical Study (NeurIPS 2025 · similarity 0.88)
- To Grok or not to Grok: Disentangling Generalization and Memorization on Corrupted Algorithmic Datasets (ICLR 2024 · similarity 0.88)
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