2024/09/07 by M. Ziad Saghir, N. Raghavendra, Saghir, Moosa +5
Medicine · #Diet and metabolism studies #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML)
paper · pdf · doi:10.48550/arxiv.2409.04913
openalex publication_date 2024/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The number of free parameters, or dimension, of a model is a straightforward way to measure its complexity: a model with more parameters can encode more information. However, this is not an accurate measure of complexity: models capable of memorizing their training data often generalize well despite their high dimension. Effective dimension aims to more directly capture the complexity of a model by counting only the number of parameters required to represent the functionality of the model. Singular learning theory (SLT) proposes the learning coefficient λ as a more accurate measure of effective dimension. By describing the rate of increase of the volume of the region of parameter space around a local minimum with respect to loss, λ incorporates information from higher-order terms. We compare λ of models trained using natural gradient descent (NGD) and stochastic gradient descent (SGD), and find that those trained with NGD consistently have a higher effective dimension for both of our methods: the Hessian trace Tr(H) , and the estimate of the local learning coefficient (LLC) λ(w^*) .