TY - CONF
T1 - GROKKING IN LINEAR ESTIMATORS - A SOLVABLE MODEL THAT GROKS WITHOUT UNDERSTANDING
AU - Levi, Noam
AU - Beck, Alon
AU - Bar Sinai, Yohai
N1 - Publisher Copyright:
© 2024 12th International Conference on Learning Representations, ICLR 2024. All rights reserved.
PY - 2024
Y1 - 2024
N2 - Grokking is the intriguing phenomenon where a model learns to generalize long after it has fit the training data. We show both analytically and numerically that grokking can surprisingly occur in linear networks performing linear tasks in a simple teacher-student setup with Gaussian inputs. In this setting, the full training dynamics is derived in terms of the training and generalization data covariance matrix. We present exact predictions on how the grokking time depends on input and output dimensionality, train sample size, regularization, and network initialization. We demonstrate that the sharp increase in generalization accuracy may not imply a transition from "memorization" to "understanding", but can simply be an artifact of the accuracy measure. We provide empirical verification for our calculations, along with preliminary results indicating that some predictions also hold for deeper networks, with non-linear activations.
AB - Grokking is the intriguing phenomenon where a model learns to generalize long after it has fit the training data. We show both analytically and numerically that grokking can surprisingly occur in linear networks performing linear tasks in a simple teacher-student setup with Gaussian inputs. In this setting, the full training dynamics is derived in terms of the training and generalization data covariance matrix. We present exact predictions on how the grokking time depends on input and output dimensionality, train sample size, regularization, and network initialization. We demonstrate that the sharp increase in generalization accuracy may not imply a transition from "memorization" to "understanding", but can simply be an artifact of the accuracy measure. We provide empirical verification for our calculations, along with preliminary results indicating that some predictions also hold for deeper networks, with non-linear activations.
UR - http://www.scopus.com/inward/record.url?scp=85210114858&partnerID=8YFLogxK
M3 - ???researchoutput.researchoutputtypes.contributiontoconference.paper???
AN - SCOPUS:85210114858
T2 - 12th International Conference on Learning Representations, ICLR 2024
Y2 - 7 May 2024 through 11 May 2024
ER -