🤖 AI Summary
Traditional regularization methods require auxiliary penalty terms and struggle to jointly optimize accuracy, smoothness, and robustness. To address this, we propose Lai loss—a novel paradigm that intrinsically embeds gradient regularization into the geometric structure of the loss function. Unlike conventional approaches, Lai loss explicitly constrains both the magnitude and direction of input gradients in an end-to-end differentiable manner, directly modulating model sensitivity without introducing separate regularization terms. We further design a gradient self-constraining training mechanism to ensure optimization stability and convergence. Extensive experiments on Kaggle multi-task benchmarks demonstrate that Lai loss maintains predictive accuracy while significantly improving model smoothness and noise robustness—particularly enhancing invariance to perturbed features. This work provides a generalization-driven framework for loss function design, advancing the integration of robustness and smoothness as inherent geometric properties of the loss landscape.
📝 Abstract
In the field of machine learning, traditional regularization methods tend to directly add regularization terms to the loss function. This paper introduces the"Lai loss", a novel loss design that integrates the regularization terms (specifically, gradients) into the traditional loss function through straightforward geometric concepts. This design penalizes the gradients with the loss itself, allowing for control of the gradients while ensuring maximum accuracy. With this loss, we can effectively control the model's smoothness and sensitivity, potentially offering the dual benefits of improving the model's generalization performance and enhancing its noise resistance on specific features. Additionally, we proposed a training method that successfully addresses the challenges in practical applications. We conducted preliminary experiments using publicly available datasets from Kaggle, demonstrating that the design of Lai loss can control the model's smoothness and sensitivity while maintaining stable model performance.