Research map / Learning theory and algorithms / Sample complexity
The Effect of Manifold Entanglement and Intrinsic Dimensionality on Learning
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Increase entanglement in Archimedean spiral data | Fully-connected neural network · Archimedean spirals | sample complexity: 167.87∗∗∗ | Mixed |
| Increase intrinsic dimensionality at low entanglement | Fully-connected neural network · Archimedean spirals | sample complexity: 0.07 | No clear effect |
| Increase intrinsic dimensionality at entanglement level 2.0 | Fully-connected neural network · Archimedean spirals | sample complexity: 32.79∗∗∗ | Hurt |
| Increase extrinsic dimensionality | Fully-connected neural network · Archimedean spirals | sample complexity: 0.53 | No clear effect |
| Increase entanglement in step-function data | Fully-connected neural network · Step-function datasets | sample complexity: 27.28∗∗∗ | Hurt |
| Increase intrinsic dimensionality, with a larger increase at higher entanglement | Fully-connected neural network · Step-function datasets | sample complexity: 0.95∗∗∗ | Hurt |
| Increase extrinsic dimensionality | Fully-connected neural network · Step-function datasets | sample complexity: −1.75∗∗∗; 0.58 | Mixed |
| Increase entanglement in the SVHN binary task | Convolutional neural network with batch normalization · SVHN (8, 9) | normalized sample complexity: 0.084∗∗∗ | Hurt |
| Increase intrinsic dimensionality at original entanglement | Convolutional neural network with batch normalization · SVHN (8, 9) | normalized sample complexity: 0.0003∗∗∗ | Hurt |
| Increase entanglement in the CIFAR-10 binary task | Convolutional neural network with batch normalization · CIFAR-10 (cat, dog) | normalized sample complexity: 0.112∗∗∗ | Hurt |
| Increase intrinsic dimensionality at original entanglement | Convolutional neural network with batch normalization · CIFAR-10 (cat, dog) | normalized sample complexity: 0.0003∗∗∗ | Hurt |
Closest papers by meaning
- Analyzing and Improving Representations with the Soft Nearest Neighbor Loss (ICML 2019 · similarity 0.88)
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