ChainzRule cuts parameters 15.5× while stabilizing gradients

ChainzRule (CR), a neural architecture introduced in a new arXiv preprint, replaces standard piecewise-linear activations with a polynomial engine governed by differential regularization. The approach targets a persistent problem in deep learning: models that achieve high accuracy often exhibit unpredictable sensitivity, where small input changes trigger massive output swings. Traditional Lipschitz-constraint methods impose global smoothness but blunt the model's expressive power. ChainzRule's Differential Regularization (DREG) instead applies targeted regularization to intermediate derivatives, suppressing extreme sensitivity without crippling the polynomial engine's representational capacity.

In head-to-head benchmarks the authors call "Fair Fight" comparisons, ChainzRule used 15.5 times fewer parameters than standard models while maintaining competitive accuracy. On MNIST, it reduced peak gradient volatility by an average of 23.1 percent. On Yelp Full ordinal regression under explicit DREG regularization, the architecture hit 70.17 percent accuracy, demonstrating that derivative-aware regularization works on realistic tasks.

What stands out

• 15.5× parameter reduction — ChainzRule matched or beat standard architectures in Fair Fight benchmarks while using a fraction of the weights.
• 23.1% drop in gradient volatility — MNIST experiments showed peak gradient swings fell by nearly a quarter on average, producing a smoother decision manifold.
• 70.17% accuracy on Yelp Full — Ordinal regression under explicit DREG regularization reached competitive performance, validating the method on a real-world text dataset.
• Layer-wise derivative control — Unlike global Lipschitz constraints, DREG acts on intermediate derivatives, preserving the polynomial engine's expressive range while stabilizing gradients.