Grokking at the Edge of Linear Separability

Authors: Alon Beck, Noam Itzhak Levi, Yohai Bar-Sinai

ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental In Fig. 1, we show numerical results depicting the gradient-descent dynamics of the model across three values of λ d/N. Notably, we observe a significant grokking effect, both in the non-monotonicity of the test loss, and a delayed rise in test accuracy, only when λ λc = 1/2. (...) In Fig. 4 we present numerical simulations supporting this behavior.
Researcher Affiliation Academia 1Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel 2École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland. Correspondence to: Alon Beck <EMAIL>, Noam Levi <EMAIL>.
Pseudocode No The paper describes methods using mathematical equations and text, but it does not contain any explicitly labeled pseudocode or algorithm blocks.
Open Source Code No The paper does not include any explicit statements about releasing code or provide links to a code repository.
Open Datasets No The paper describes generating a synthetic dataset: "We study a typical logistic binary classification problem, with the goal of finding a linear separator between two Gaussians with distinct labels." and "xi N(0, σ2Id)". It does not use or provide access to any pre-existing public datasets.
Dataset Splits Yes The parameters are N = 4 104,σ = 5, η = 0.01. The number of test samples is Ntest = 104. Additional details regarding the experiments can be found in App. K.
Hardware Specification No The paper does not specify any particular hardware (CPU, GPU, etc.) used for running the experiments.
Software Dependencies No The paper mentions "using adaptive momentum based optimizers like ADAM (Kingma & Ba, 2017)" in Section 3.5 and "ADAM optimizer with Py Torch s default parameters" in Fig. 11, but it does not specify version numbers for these software components.
Experiment Setup Yes The parameters are N = 4 104,σ = 5, η = 0.01. The direction of S(t = 0) was drawn isotropically with S0 = 0.1 and b(t = 0) = 0. (...) using ADAM optimizer (with β1 = 0.8, β2 = 0.9), instead of GD. The parameters are λ = d/N = 0.495, N = 4000 and σ = 1.