The article "Diversity of EML-type operators" discusses the EML operator, which can evaluate standard explicit purely transcendental elementary functions, and notes that while most research has focused on the binary EML, many similar variants exist. It enumerates and classifies these variants, clarifies common misconceptions, and proposes a M"obius layer that replaces matrix operations with rational functions. The paper also showcases the activation function eml(x,1/x), enabling separate recovery of exp(x) and ln(x) and thus evaluation of all elementary functions within a rational neural‑network generalization.
By Andrzej Odrzywo{\l}ek
arXiv:2402. 00094v3 Announce Type: replace-cross Abstract: We introduce a new class of deep neural networks (DNNs) with multilayered tree-like architectures.
By W. A. Z\'u\~niga-Galindo
arXiv:2606. 20325v1 Announce Type: new Abstract: Classical approximation theorems ask for a new neural network whenever the target accuracy is improved.
By Valentin Abadie, Clemens Hutter, Helmut B\"olcskei
arXiv:2606. 21497v2 Announce Type: replace-cross Abstract: Modern deep neural networks are trained using error backpropagation, which requires sequential forward and backward computations across network layers.
By Neeraj Mohan Sushma, Aditya Nagarsekar, Cabrel Teguemne Fokam, Robin Schiewer, Amit Kumar Pal, Anand Subramoney, David Kappel
arXiv:2606. 26705v1 Announce Type: cross Abstract: Feedforward neural network (NN) expressivity is typically studied by emulating optimal basis-expansion schemes.
By Anastasis Kratsios, Simone Brugiapaglia, Bum Jun Kim, Gregory Cousins, Haitz S\'aez de Oc\'ariz Borde
arXiv:2606. 08727v1 Announce Type: cross Abstract: Many classically studied function classes are known to be approximated optimally by superpositional methods, i.
By Dennis Elbr\"achter, Philipp Petersen
arXiv:2511. 14953v2 Announce Type: replace-cross Abstract: Discrete structures are currently second-class in differentiable programming.
By Joey Velez-Ginorio, Nada Amin, Konrad Kording, Steve Zdancewic
arXiv:2609.25874v1 Announce Type: new
Abstract: Deep neural networks approximate functions by composing affine maps with nonlinear activations, but how composition itself creates approximation power...
By Wentao Huang, Haizhang Zhang
arXiv:2609.24746v1 Announce Type: new
Abstract: Existing approaches to solving differential equations, such as symbolic regression, physics informed neural networks, and neural operators, typically f...
By Xiyue Fan, Adam Prugel-Bennett, Stuart E. Middleton
arXiv:2602.13106v2 Announce Type: replace-cross
Abstract: In recent years, there has been growing interest in understanding neural architectures' ability to learn to execute discrete algorithms, a li...
By Solveig Wittig, Antonis Vasileiou, Robert R. Nerem, Timo Stoll, Floris Geerts, Yusu Wang, Christopher Morris
NeuralCert presents a framework that learns high‑dimensional variational trial functions in a compact separable form, then spectrally diagnoses, prunes, and exactly certifies them via multimodular evaluation. The method is fully explicit and independently verifiable, and can run on a standard personal computer. Applied to three extremal problems, it demonstrates that neural optimization can discover better constructions, reveal empirical invariants useful for proofs, and expose optimization barriers that inspire new analytic or numerical approaches.
By Mark Patrick Roeling
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