Smoothness is a key inductive bias in machine learning and is closely related to generalization. Existing smoothness-inducing methods typically rely either on explicit gradient regularization, which often incurs substantial computational and memory overhead, or on data-mixing strategies, which are less naturally applicable to unsupervised and self-supervised settings. In this work, we propose $\textit{Dual Reconstruction Smoothing}$ (DReS), a nonparametric regularization framework that induces smoothness through a spline-based auxiliary branch with shared model parameters. The method introduces no additional trainable parameters and can be applied to arbitrary submodules, making it suitable for unsupervised, self-supervised, and supervised regimes. We show theoretically that the discrepancy between the target function and its DReS approximation is controlled by higher-order smoothness quantities of the function, establishing the method as an implicit higher-order smoothness regularizer. Empirically, DReS improves representation learning across several self-supervised methods, improves generation quality in generative modeling, and achieves strong performance relative to competitive baselines in supervised learning.

翻译：平滑性是机器学习中的关键归纳偏好，且与泛化能力密切相关。现有的平滑性诱导方法通常依赖于显式梯度正则化（这会带来显著的计算和内存开销）或数据混合策略（后者在无监督和自监督场景中天然适用性较低）。本文提出**双重重构平滑**（DReS），一种通过共享模型参数的样条辅助分支来诱导平滑性的非参数正则化框架。该方法不引入可训练参数，可应用于任意子模块，适用于无监督、自监督和有监督场景。我们从理论上证明，目标函数与其DReS近似之间的差异受该函数的高阶平滑量控制，从而将该方法确立为隐式高阶平滑正则化器。实验表明，DReS在多种自监督方法中提升表征学习质量，改善生成建模中的生成质量，并在有监督学习中相对于强基线取得优异性能。