Polynomial Neural Networks

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Overview

These networks replace or augment standard nonlinear layers with polynomial activations, multivariate polynomial units, or basis expansions such as orthogonal and learned recursive polynomials. Researchers study their approximation power and parameter identifiability using algebraic geometry, and develop training methods including derivative regularization, active queries, and constraints that encode physical conditions. Applications include differential-equation solving, vision and graph models, robotics, and compact edge inference. While theory clarifies when these models can represent functions and recover parameters, controlling numerical stability, optimization, and cost—and determining when polynomial models outperform ReLU or spline-based alternatives—remains a central challenge.

Latest papers

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24 papers6 papers in the last four weeks, up 100% on the four weeks before. 0.0% of all new papers.

  1. Polynomial Residual Networks are Generically Identifiable

    Oct 24, 2026Isabel Dahlgren, Giovanni Luca Marchetti, Kathlén KohnParameter IdentifiabilityPolynomial Neural Networks

  2. Linear Independence of Polynomial Compositions with Bounded Input Degree

    Oct 14, 2026Xiaotian Chang, Yacoub HendiRepresentation IdentifiabilityParameter Identifiability

  3. The Physics Is the Network: Fast, Training-Free Neural Emulation

    Oct 14, 2026Luka Todorovic, Kaushal Gianchandani, Sai RavelaNeural PDE SolversNeural Surrogate Modeling

    Department of Mathematics and Department of Statistics, University of Michigan, Ann Arbor, MI · NASA Postdoctoral Program Fellow, NASA Goddard Institute for Space Studies, New York, NY · Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA

  4. Trainable at Depth, Solvable at Small Size: What the Loss Surface of a Polynomial Activation Dictates for Designing, Initializing and Training Networks

    Oct 14, 2026Xiuyi YangNeural Network OptimizationNeural Network Training Dynamics

  5. Polynomial neural surrogates for designing photonic quantum experiments

    Oct 5, 2026Rohit Chaurasiya, Xuemei GuNeural Surrogate ModelingPolynomial Neural Networks

    Institute of Condensed Matter Theory and Optics, Friedrich Schiller University Jena, Max-Wien-Platz 1, 07743 Jena, Germany

  6. Beyond Overparameterization: Provable Learning of Input-Convex Multi-Layer Polynomial Networks with Active Queries

    Oct 4, 2026Jinqi Tang, Qian Chen, Shihong Ding +1Polynomial Neural NetworksInput Convex Neural Networks

    Peking University

  7. Algebraic Expressivity Certificates for Shallow Polynomial Neural Networks

    Sep 11, 2026Sepehr Akbari, Shahrzad JamshidiNeural Network ExpressivityShallow Neural Networks

    Dept. of Math & Computer Science Lake Forest College

  8. SW-KAN: Kolmogorov-Arnold Networks with Stieltjes-Wigert q-Orthogonal Polynomials

    Sep 3, 2026Amirhosein Azarpour, Seyyed Moein KazemiFunction ApproximationKolmogorov-Arnold Networks

    Faculty of Mathematical Sciences, Department of Computer Science, Shahid Beheshti University, Tehran · Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran

  9. RecKAN: Kolmogorov-Arnold Networks with a Learnable Recursive Polynomial Basis

    Sep 1, 2026Amirhosein AzarpourPolynomial Neural NetworksKolmogorov-Arnold Networks

    Department of Computer Science Shahid Beheshti University Tehran, Iran

  10. Linear Independence of Polynomial Compositions and Identifiability of Deep Neural Networks

    Aug 27, 2026Kathlén Kohn, Giovanni Luca Marchetti, Alex Massarenti +1Parameter IdentifiabilityPolynomial Neural Networks

    KTH Stockholm · AI4S AB Stockholm · University of Ferrara

  11. Bern2Edge: A Neurosymbolic Compiler for Edge Deployment via Bernstein Polynomial Networks

    Aug 20, 2026Malak Gamal El-Din, Yifan Zhang, Yasser Shoukry +2Edge InferenceFPGA-Based Neural Network Acceleration

    Department of Electrical Engineering and Computer Science, University of California, Irvine, CA 92697 USA

  12. PRISM: Polynomial Representations for Interaction-Structured Motor Control

    Jul 26, 2026Seung Hyun Lee, Stella X. YuRobotic ControlRL for Robotics

    University of Michigan

  13. A Polynomial Architecture-Attribution Co-Design Framework for Exact Aumann-Shapley Attribution in GNNs

    Jul 23, 2026Bizu Feng, Zhimu Yang, Shuming Wang +4Gradient-Based AttributionPolynomial Neural Networks

    Institute of Artificial Intelligence Innovation and Industry, Fudan University, Shanghai, China · Shanghai Academy of AI for Science, Shanghai, China · Human Phenome Institute, Fudan University, Shanghai, China +1

  14. Expressivity of Shallow Neural Networks Over Finite Fields

    Jul 19, 2026Maksym Zubkov, Carol Wu, Shiwei Yang +2Shallow Neural NetworksPolynomial Neural Networks

    Department of Mathematics, University of British Columbia, 1984 Mathematics Rd, Vancouver, V6T 1Z2, BC, Canada

  15. It's Much Easier for Neural Networks to learn Game of Life Dynamics with the Right Activation Function: Polynomial Kolmogorov-Arnold Networks

    Jun 22, 2026Tashin Ahmed, Q. Tyrell DavisPolynomial Neural NetworksCellular Automata

    Independent Researcher · Work completed while at Cross Labs, Cross Compass Ltd., Japan.

  16. Layer-wise Derivative Controlled Networks Achieve Competitive Accuracy and Gradient Stability Across Data Regimes

    Jun 6, 2026Rowan MartnishnNeural Network GeneralizationPolynomial Neural Networks

  17. ChainzRule: Sample-Efficient, Robust Deep Learning Across Tabular, NLP, and Vision Tasks

    May 23, 2026Rowan MartnishnPolynomial Neural NetworksNeural Network Robustness

    Sentivity AI

  18. Activation-Free Backbones for Image Recognition: Polynomial Alternatives within MetaFormer-Style Vision Models

    May 20, 2026Jeffrey Wang, Jonathan Gregory, Grigorios G. ChrysosPolynomial Neural NetworksNeural Network Activation Functions

    University of Wisconsin–Madison, Madison, WI, USA.

  19. Minimal Filling Architectures of Polynomial Neural Networks: Counterexamples, Frontier Search, and Defects

    May 10, 2026Kevin Dao, Jose Israel RodriguezPolynomial Neural NetworksNeural Network Approximation Theory

    Department of Mathematics, University of Wisconsin-Madison, Wisconsin, USA.

  20. The Geometry of Polynomial Group Convolutional Neural Networks

    Mar 31, 2026Yacoub Hendi, Daniel Persson, Magdalena LarforsConvolutional Neural NetworksPolynomial Neural Networks

    Uppsala University · Chalmers University of Technology

  21. Why ReLU? A Bit-Model Dichotomy for Deep Network Training

    Feb 22, 2026Ilan Doron-Arad, Elchanan MosselEmpirical Risk MinimizationReLU Neural Networks

    MIT, Cambridge, MA, USA

  22. Parameter-Minimal Neural DE Solvers via Horner Polynomials

    Feb 16, 2026T. Matulić, D. SeršićNeural PDE SolversPolynomial Neural Networks

    Dept. of Electronic Systems and Information Processing, Faculty of Electrical Engineering and Computing, University of Zagreb, Zagreb, Croatia

  23. SUPN: Shallow Universal Polynomial Networks for Efficient Function Approximation

    Nov 26, 2025Zachary Morrow, Michael Penwarden, Brian Chen +3Polynomial Neural NetworksNeural Network Approximation Theory

  24. The Alexander-Hirschowitz theorem for neurovarieties

    Nov 24, 2025A. Massarenti, M. MellaPolynomial Neural NetworksParameter Identifiability