Anti-regularization introduces a reward term with a reversed sign into the loss function, deliberately amplifying model expressivity in small-sample regimes while ensuring that the intervention gradually vanishes as the sample size grows through a power-law decay schedule. We formalize spectral safety conditions and trust-region constraints, and we design a lightweight safeguard that combines a projection operator with gradient clipping to guarantee stable intervention. Theoretical analysis extends to linear smoothers and the Neural Tangent Kernel regime, providing practical guidance on the choice of decay exponents through the balance between empirical risk and variance. Empirical results show that Anti-regularization mitigates underfitting in both regression and classification while preserving generalization and improving calibration. Ablation studies confirm that the decay schedule and safeguards are essential to avoiding overfitting and instability. As an alternative, we also propose a degrees-of-freedom targeting schedule that maintains constant per-sample complexity. Anti-regularization constitutes a simple and reproducible procedure that integrates seamlessly into standard empirical risk minimization pipelines, enabling robust learning under limited data and resource constraints by intervening only when necessary and vanishing otherwise.

翻译：反正则化通过在损失函数中引入符号相反的奖励项，在小样本场景下刻意增强模型表达能力，同时通过幂律衰减机制确保干预效果随样本量增加而逐渐消失。我们形式化地建立了谱安全条件与信赖域约束，并设计了一种结合投影算子与梯度裁剪的轻量级保护机制以保证干预稳定性。理论分析拓展至线性平滑器与神经正切核体系，通过经验风险与方差的权衡为衰减指数的选择提供实践指导。实验结果表明，反正则化在回归与分类任务中均能缓解欠拟合现象，同时保持泛化能力并改善校准效果。消融研究证实衰减机制与保护措施对避免过拟合和不稳定性具有关键作用。作为替代方案，我们同时提出一种保持恒定样本复杂度的自由度目标调度机制。反正则化构成了一种简单且可复现的流程，能够无缝集成至标准经验风险最小化框架中，通过仅在必要时实施干预并在其他情况下自然消退的方式，实现在有限数据与资源约束下的稳健学习。