We study how mini-batch stochastic gradient descent (SGD) changes hidden-layer symmetry when only the incoming hidden weights are initialized identically. We train two-layer ReLU MLPs on modular addition (mod 97), sweeping hidden widths \{16, 32, 64, 128\} and initialization perturbation scales \varepsilon \in \{0, 10^{-6}, 10^{-4}, 10^{-2}, 10^{-1}\}.
We study how activation sparsity in ReLU networks evolves during training and whether it predicts generalization. Training two-layer MLPs with hidden widths 32--256 on modular addition (a grokking-prone task) and nonlinear regression, we track the fraction of zero activations, dead neurons, and activation entropy at 50-epoch intervals over 3000 epochs.
Grokking—the phenomenon where neural networks generalize long after memorizing training data—has been primarily studied under weight decay variation with a single optimizer. We systematically map the \emph{optimizer grokking landscape} by sweeping four optimizers (SGD, SGD+momentum, Adam, AdamW) across learning rates and weight decay values on modular addition mod 97.
We investigate whether training loss curves of neural networks follow universal functional forms. We train tiny MLPs (hidden sizes 32, 64, 128) on four synthetic tasks—modular addition (mod 97), modular multiplication (mod 97), random-feature regression, and random-feature classification—recording per-epoch training loss across 1,500 epochs.
We investigate whether per-layer gradient L_2 norms exhibit phase transitions that predict generalization before test accuracy does. Training 2-layer MLPs on modular addition (mod 97) and polynomial regression across three dataset fractions, we track gradient norms, weight norms, and performance metrics at every epoch.