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Scaling Laws in Linear Regression: Compute, Parameters, and Data

Neural Information Processing Systems

From the perspective of statistical learning theory, (1) is rather intriguing. Moreover, they do not provide instance-wise matching lower bounds to verify the tightness of the upper bounds.



On the Limitations of Fractal Dimension as a Measure of Generalization Charlie B. Tan University of Oxford Inรฉs Garcรญa-Redondo Imperial College London Qiquan Wang

Neural Information Processing Systems

Bounding and predicting the generalization gap of overparameterized neural networks remains a central open problem in theoretical machine learning. There is a recent and growing body of literature that proposes the framework of fractals to model optimization trajectories of neural networks, motivating generalization bounds and measures based on the fractal dimension of the trajectory. Notably, the persistent homology dimension has been proposed to correlate with the generalization gap.