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.
For a fixed parameter budget, should one build a deep-narrow or shallow-wide MLP? We systematically sweep depth (1--8 hidden layers) against width across three parameter budgets (5K, 20K, 50K) on two contrasting tasks: sparse parity (a compositional boolean function) and smooth regression.
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.
We systematically measure the memorization capacity of two-layer MLPs by sweeping model width and training on synthetic data with random vs.\ structured labels.
Benford's Law predicts that leading significant digits in naturally occurring datasets follow a logarithmic distribution, with digit 1 appearing approximately 30\% of the time. We investigate whether this law emerges in the weights of trained neural networks by training tiny MLPs on modular arithmetic and sine regression tasks, saving weight snapshots across 5{,}000 training epochs.
Random Matrix Theory (RMT) predicts that the eigenvalue spectrum of \frac{1}{M}W^\top W for an M \times N random matrix W follows the Marchenko-Pastur (MP) distribution. We use this null model to quantify how much structure trained neural network weight matrices have learned beyond random initialization.
We systematically map the phase diagram of "grokking" — the delayed transition from memorization to generalization — in tiny neural networks trained on modular addition (mod 97). By sweeping over weight decay (\lambda \in \{0, 10^{-3}, 10^{-2}, 10^{-1}, 1\}), dataset fraction (f \in \{0.
Random Matrix Theory (RMT) predicts that the eigenvalue spectrum of \frac{1}{M}W^\top W for an M \times N random matrix W follows the Marchenko-Pastur (MP) distribution. We use this null model to quantify how much structure trained neural network weight matrices have learned beyond random initialization.
We systematically map the phase diagram of "grokking" — the delayed transition from memorization to generalization — in tiny neural networks trained on modular addition (mod 97). By sweeping over weight decay (\lambda \in \{0, 10^{-3}, 10^{-2}, 10^{-1}, 1\}), dataset fraction (f \in \{0.