Fanghui Liu, Yudong Chen, Lorenzo Rosasco, Yichen Wang
We lifted 4 functions out of this paper's own repositories and ran 4 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.
| Repository | Role | Ran |
|---|---|---|
| yichenblue/norm-capacity | canonical | 4 of 4 |
| Function | Status | Where it lives |
|---|---|---|
| compute_variance_beta | Ran | yichenblue/norm-capacity/src/Gaussian_design/random_feature_ridge_regression/random_feature_ridge_regression.py pointer only (licence: NONE) · get_code("a4e46bd3edd53de7") |
| make_resnet18k | Ran | yichenblue/norm-capacity/src/Deep_NNs/deep_double_descent_ResNet18.py pointer only (licence: NONE) · get_code("9e1fb7fda2faa973") |
| solve_lambda_star | Ran | yichenblue/norm-capacity/src/Gaussian_design/random_feature_ridge_regression/random_feature_ridge_regression.py pointer only (licence: NONE) · get_code("2cd8c566c5b775b4") |
| solve_self_consistent_equations | Ran | yichenblue/norm-capacity/src/Gaussian_design/random_feature_ridge_regression/random_feature_ridge_regression.py pointer only (licence: NONE) · get_code("290aa109a9a64251") |
Some links come from the archived Papers with Code dataset (CC BY-SA 4.0): attribution and licence.
Understanding how the test risk scales with model complexity is a central question in machine learning. Classical theory is challenged by the learning curves observed for large over-parametrized deep networks. Capacity measures based on parameter count typically fail to account for these empirical observations. To tackle this challenge, we consider norm-based capacity measures and develop our study for random features based estimators, widely used as simplified theoretical models for more complex networks. In this context, we provide a precise characterization of how the estimator's norm concentrates and how it governs the associated test error. Our results show that the predicted learning curve admits a phase transition from under-to over-parameterization, but no double descent behavior. This confirms that more classical U-shaped behavior is recovered considering appropriate capacity measures based on models norms rather than size. From a technical point of view, we leverage deterministic equivalence as the key tool and further develop new deterministic quantities which are of independent interest.
The same record, over MCP at https://syntology.ai/mcp:
get_harvested_code_for_paper("2502.01585")
get_code_for_paper("2502.01585")
have("2502.01585")
Connect an agent — have() is free.