Research map / Learning theory and algorithms / Kernels and regression theory
To Understand Deep Learning We Need to Understand Kernel Learning
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Fit the training labels exactly with a Gaussian kernel interpolant | Kernel classifier · MNIST | test classification error (%) | Helped |
| Use early stopping rather than an interpolated solution (ablation) | EigenPro kernel classifier · MNIST and other evaluated datasets | test classification error | No clear effect |
| Use a Laplacian rather than Gaussian kernel (ablation) | Interpolated kernel classifier · CIFAR-10 | test classification error (%): 51.56 -> 48.75 | Helped |
| Use a Laplacian rather than Gaussian kernel (ablation) | Interpolated kernel classifier · TIMIT | test classification error (%): 36.61 -> 36.51 | No clear effect |
| Fit random labels instead of original labels (ablation) | Laplacian kernel SGD · MNIST, SVHN, and TIMIT | epochs to overfit: MNIST: 4 -> 7; SVHN: 8 -> 21; TIMIT: 3 -> 4 | Hurt |
| Fit random labels instead of original labels (ablation) | Gaussian kernel SGD · MNIST, SVHN, and TIMIT | epochs to overfit: MNIST: 20 -> 873; SVHN: 46 -> 1066; TIMIT: 7 -> 22 | Hurt |
| Use a non-smooth Laplacian rather than smooth Gaussian kernel (ablation) | Kernel SGD fitting random labels · MNIST, SVHN, and TIMIT | epochs to overfit: MNIST random: 873 -> 7; SVHN random: 1066 -> 21; TIMIT random: 22 -> 4 | Helped |
| Add random label corruption (ablation) | Gaussian interpolated kernel classifier · MNIST and synthetic datasets | test classification error | Mixed |
Closest papers by meaning
- Generalization in Kernel Regression Under Realistic Assumptions (ICML 2024 · similarity 0.90)
- Overfitting or perfect fitting? Risk bounds for classification and regression rules that interpolate (NeurIPS 2018 · similarity 0.89)
- Stochastic Kernel Regularisation Improves Generalisation in Deep Kernel Machines (NeurIPS 2024 · similarity 0.88)
- The optimality of kernel classifiers in Sobolev space (ICLR 2024 · similarity 0.87)
- Generalization error of spectral algorithms (ICLR 2024 · similarity 0.87)
- Convolutional Deep Kernel Machines (ICLR 2024 · similarity 0.86)
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