Scaling Laws in the Tiny Regime: How Small Models Change Their Mistakes

Abstract

Neural scaling laws describe how model performance improves as a power law with size, but existing work focuses on models above 100M parameters. The sub-20M regime -- where TinyML and edge AI operate -- remains unexamined. We train 90 models (22K--19.8M parameters) across two architectures (plain ConvNet, MobileNetV2) on CIFAR-100, varying width while holding depth and training fixed. Both follow approximate power laws in error rate: $\alpha = 0.156 \pm 0.002$ (ScaleCNN) and $\alpha = 0.106 \pm 0.001$ (MobileNetV2) across five seeds. Since prior work fit cross-entropy loss rather than error rate, direct exponent comparison is approximate; with that caveat, these are 1.4--2x steeper than $\alpha \approx 0.076$ for large language models. The power law does not hold uniformly: local exponents decay with scale, and MobileNetV2 saturates at 19.8M parameters ($\alpha_{\mathrm{local}} = 0.006$). Error structure also changes. Jaccard overlap between error sets of the smallest and largest ScaleCNN is only 0.35 (25 seed pairs, $\pm 0.004$) -- compression changes which inputs are misclassified, not merely how many. Small models concentrate capacity on easy classes (Gini: 0.26 at 22K vs. 0.09 at 4.7M) while abandoning the hardest (bottom-5 accuracy: 10% vs. 53%). Counter to expectation, the smallest models are best calibrated (ECE = 0.013 vs. peak 0.110 at mid-size). Aggregate accuracy is therefore misleading for edge deployment; validation must happen at the target model size.