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.
arXiv:2608. 09707v1 Announce Type: cross Abstract: Embedding trained neural networks as surrogates within optimisation problems is an established practice in operations research.
By Yu Liu, Jan Kronqvist, Fabricio Oliveira
arXiv:2607. 15525v1 Announce Type: cross Abstract: Kolmogorov--Arnold Networks (KANs) replace fixed node activations with learned one-dimensional edge functions, offering an explicit interface for interpretation and a possible alternative to transformer feed-forward networks.
By Felippe Alves, Renato Vicente
arXiv:2606. 02385v1 Announce Type: cross Abstract: Sparse Autoencoders (SAEs) have found success parsing neural representations into interpretable concepts, providing a basis for understanding and control.
By William Dorrell
arXiv:2608. 00859v1 Announce Type: new Abstract: Kolmogorov--Arnold Networks (KANs) replace scalar edge weights with learnable univariate functions parameterized by multiple basis coefficients.
By Kazi Ahmed Asif Fuad, Lizhong Chen
arXiv:2606. 27126v1 Announce Type: new Abstract: Kolmogorov Arnold networks (KAN) have recently been introduced as a (deep) neural network architecture whose trainable parameters adapt the activation functions, instead of the coefficients of the affine transformations at the core of traditional architectures such as deep multilayer perceptrons (MLPs).
By Miguel Jaraiz, Fermin Gutierrez, Pablo Yeste, Miguel S\'anchez-Dom\'inguez, Eusebio Valero, Gonzalo Rubio, Lucas Lacasa
arXiv:2512. 09084v3 Announce Type: replace Abstract: The Kolmogorov-Arnold representation theorem offers a theoretical alternative to Multi-Layer Perceptrons (MLPs) by placing learnable univariate functions on edges rather than nodes.
By Oscar Eliasson
arXiv:2602. 06737v2 Announce Type: replace Abstract: We present a generalized framework for the range verification of neural networks featuring non-linear activation functions.
By Noah Schwartz, Chandra Kanth Nagesh, Sriram Sankaranarayanan, Ramneet Kaur, Tuhin Sahai, Susmit Jha
arXiv:2608. 09523v1 Announce Type: new Abstract: Deep neural network (DNN) training with stochastic gradient descent (SGD) and its variants achieves strong empirical performance, yet classical optimization theory does not fully explain this success.
By Binchuan Qi
Over the past decade, deep neural networks (DNNs) have achieved remarkable success on complex machine-learning tasks, yet the theoretical foundations of their performance remain incomplete. From a statistical viewpoint, a natural question is: can DNNs attain feature-learning and prediction consistency comparable to that of classical models?
arXiv:2605. 08446v3 Announce Type: replace Abstract: Bayesian neural networks are typically trained against the evidence lower bound (ELBO), whose Jensen gap closes only when the variational posterior is exact.
By Pavel Prochazka
arXiv:2607. 09967v1 Announce Type: cross Abstract: Many neural networks operations have a multiplicative nature rather than additive: halving or doubling a norm are analogous relatively but require unequal optimization distances when taking linear steps.
By Ethan Smith