Layer-wise Derivative Controlled Networks

2026-05-14

AI Summary

This work addresses the fundamental trade-off among accuracy, hardware efficiency, and stability in complex machine learning models, particularly the issue of drastic output fluctuations caused by minor input perturbations. To this end, the authors propose ChainzRule, a novel architecture that embeds derivative-aware mechanisms directly into the network. It introduces a differential regularization (DREG)-based polynomial activation engine, replacing conventional global Lipschitz constraints with localized, fine-grained inter-layer derivative control. This approach preserves model expressivity while substantially enhancing stability. Empirical results demonstrate a 23.1% reduction in peak gradient fluctuations on MNIST, achieves 70.17% accuracy on the Yelp Full dataset, and surpasses standard models in performance despite using only 1/15.5 of their parameter count.

Abstract

As machine learning models grow in complexity, they increasingly struggle with three conflicting demands: the need for high accuracy, the requirement for hardware efficiency, and the necessity of functional stability. Traditional architectures often achieve performance at the expense of spiky or unpredictable behavior, where small changes in input lead to massive swings in output -- a critical flaw for real-world deployment in sensitive environments. This paper introduces ChainzRule (CR), a novel neural architecture designed to harmonize these competing goals. ChainzRule replaces standard piecewise-linear activations with a Polynomial Engine governed by Differential Regularization (DREG). Unlike traditional methods that impose global, coarse-grained constraints on a model's Lipschitz constant, DREG acts as a targeted regularization on intermediate derivatives. This approach suppresses extreme sensitivity without attenuating the representational power inherent in the Polynomial Engine. In head-to-head"Fair Fight"benchmarks, ChainzRule outperformed standard models while using 15.5x fewer parameters. On the MNIST dataset, it reduced peak gradient volatility by an average of 23.1%, ensuring a smoother and more predictable manifold. On Yelp Full ordinal regression under explicit DREG regularization, ChainzRule achieves 70.17% accuracy, validating that derivative-aware regularization is compatible with competitive performance on realistic tasks. By embedding gradient awareness into the architecture via DREG, ChainzRule demonstrates that stability and accuracy need not be competing objectives.

Problem

• accuracy
• hardware efficiency
• functional stability
• gradient volatility
• input sensitivity

Innovation

• Differential Regularization
• Polynomial Engine
• Derivative Control
• Stable Neural Networks
• Lipschitz Continuity