如果你做单调神经网络或者KAN相关研究，这篇论文提出了一个既有理论保障又有实际效果的MKAN，在基准上不输现有方法，而且保持了KAN的可解释性。
论文提出MKAN，一种通过指数重参数化B样条系数、正边权和单调基激活函数实现硬单调性保证的KAN变体，训练可用无约束梯度下降。理论贡献是表示代价定理：任何C^K特征提取器（语义邻域分划为球状）存在单调实现，节点数N'=N*+k≤2N*，其中k为原始非单调坐标数。在SMM/ICML-2024基准上，MKAN与SOTA单调神经网络竞争力相当，且是唯一兼具硬单调性与KAN边缘功能透明性的方法。在4个真实数据集的自监督特征尺寸扫描中验证了2N*预测，在受控单调生成数据集上MKAN的Spearman对齐显著高于KAN、MLP和线性基线。
Monotonic Kolmogorov-Arnold Networks: A Theoretical and Empirical Study of Monotonicity as an Inductive Bias
Monotonicity has been a long-running architectural inductive bias for neural networks, motivated by tabular, scientific, and economic settings where outputs are known to respond monotonically to certain inputs. Existing approaches are MLP- or flow-based and lack per-edge functional transparency; the only Kolmogorov--Arnold Network (KAN) variant with monotonicity, MonoKAN, enforces the constraint only on a restricted parameter subset and requires a projection-style training procedure. We close this gap with \textbf{MKAN}, a KAN with hard monotonicity guaranteed for \emph{all} parameter values via exponential reparameterization of B-spline coefficients, positive edge weights, and a monotone base activation. Training reduces to standard unconstrained gradient descent. Our headline theoretical contribution is a \emph{representation-cost} theorem: any $C^K, K >0$ feature extractor inducing a ball-shaped semantic-neighborhood partition admits a monotone realization of the equivalent neighborhood structure at $N' = N^* + k \le 2N^*$, where $k$ is the number of non-monotone coordinates of the original. The bound is architecture-agnostic and gives a principled sizing rule for monotone encoders. Empirically, MKAN is competitive with state-of-the-art monotone NNs on the SMM/ICML-2024 benchmark while being the only method that combines hard unconstrained monotonicity with KAN's per-edge functional transparency; the $2N^*$ prediction is validated in a self-supervised feature-size sweep on four real datasets, and on a controlled monotone-generative dataset MKAN recovers ground-truth factors with substantially higher Spearman alignment than KAN, MLP, and linear baselines.