MKAN：具有硬单调性保证的KAN网络
Monotonic Kolmogorov-Arnold Networks: A Theoretical and Empirical Study of Monotonicity as an Inductive Bias
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.
This report is categorized under AITOP's "Models" desk. Key entities and technical topics under continuous tracking include MKAN, KAN, 单调性, 表示代价定理.
Source attribution: curated from arXiv cs.LG (@Mikhail Krasnov, Carolina Fortuna, Blaž Bertalanič).
