Research map / Learning theory and algorithms / Prediction and decision losses
Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topology
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply 50% dropout during training | Two-layer [650,650] network · MNIST | mean normalized neural persistence | Helped |
| Apply batch normalization | Two-layer [650,650] network · MNIST | mean normalized neural persistence | Helped |
| Use neural-persistence stopping instead of validation-loss stopping | Fully connected networks · Fashion-MNIST | test accuracy: -0.08% | No clear effect |
| Use neural-persistence stopping instead of validation-loss stopping | Fully connected networks · Fashion-MNIST, b ≤ 8 | stopping epoch: -0.62 epochs on average | Helped |
| Use neural-persistence stopping instead of validation-loss stopping | Fully connected networks · Fashion-MNIST, b ≤ 8 | test accuracy: -0.06% | No clear effect |
| Apply neural-persistence stopping in a convolutional network | LeNet-like CNN · Fashion-MNIST | test accuracy: up to 4% | Hurt |
| Replace exact unrolling with the closed-form convolutional approximation (ablation) | Convolutional neural persistence · Convolutional filter evaluation | runtime: 8.77 seconds -> 0.00038 seconds | Helped |
| Use the p-norm of all network weights as a proxy for neural persistence (ablation) | Neural-persistence early stopping · Early stopping experiments | stopping criterion activation | Hurt |
| Initialize weights for high neural persistence rather than with Xavier initialization (ablation) | [20,20,20] network · Fashion-MNIST | validation accuracy after training: 0.098 to 0.863 | No clear effect |
| Use the approximate convolutional persistence calculation rather than the exact calculation (ablation) | First convolutional layer · Fashion-MNIST | early-stopping result | No clear effect |
| Use the second convolutional layer or both convolutional layers for persistence stopping (ablation) | LeNet-like CNN · Fashion-MNIST | test accuracy | No clear effect |
| Use neural-persistence stopping rather than validation-loss stopping with reduced training data | [500,500,200] fully connected network · MNIST and Fashion-MNIST, reduced training data | test accuracy | Helped |
Closest papers by meaning
- Topological Generalization Bounds for Discrete-Time Stochastic Optimization Algorithms (NeurIPS 2024 · similarity 0.87)
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- Towards Scalable Topological Regularizers (ICLR 2025 · similarity 0.84)
- On the Limitations of Fractal Dimension as a Measure of Generalization (NeurIPS 2024 · similarity 0.84)
- On the Hardness of Training Deep Neural Networks Discretely (AAAI 2025 · similarity 0.84)
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