Research map / Learning theory and algorithms / Kernels and regression theory
Intrinsic Dimension, Persistent Homology and Generalization in Neural Networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add topological PH-dimension regularizer (lambda=1) to training | LeNet-5 on CIFAR-10 · CIFAR-10 test accuracy across learning rates | test accuracy | Helped |
| use PH dimension of training trajectory as predictor of generalization gap | AlexNet SGD on CIFAR100 · CIFAR100 | Kendall correlation: 0.933, 0.357, 0.733 for batch 64, 100, 128 | Helped |
| swap least squares line fit for RANSAC/Huber/Tukey robust fits in dimension estimator (ablation) | PH dimension estimator · synthetic diffusion data | dimension estimation | No clear effect |
| vary alpha from 0.5 to 2.5 in PH dimension estimator (vs alpha=1) (ablation) | PH dimension estimator · synthetic Levy process data | dimension estimation accuracy | Mixed |
Closest papers by meaning
- On the Limitations of Fractal Dimension as a Measure of Generalization (NeurIPS 2024 · similarity 0.95)
- Topological Generalization Bounds for Discrete-Time Stochastic Optimization Algorithms (NeurIPS 2024 · similarity 0.92)
- Generalization at the Edge of Stability (NeurIPS 2026 · similarity 0.88)
- Towards Scalable Topological Regularizers (ICLR 2025 · similarity 0.87)
- The Effect of Intrinsic Dataset Properties on Generalization: Unraveling Learning Differences Between Natural and Medical Images (ICLR 2024 · similarity 0.87)
- Compositional PAC-Bayes: Generalization of GNNs with persistence and beyond (NeurIPS 2024 · similarity 0.87)
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