Piecewise Polynomial Regression of Tame Functions via Integer Programming
Not on the map. Why?
Abstract (arXiv)
Tame functions are a class of nonsmooth, nonconvex functions, which feature in a wide range of applications: functions encountered in the training of deep neural networks with all common activations, value functions of mixed-integer programs, or wave functions of small molecules. We consider approximating tame functions with piecewise polynomial functions. We bound the quality of approximation of a tame function by a piecewise polynomial function with a given number of segments on any full-dimensional cube. We also present the first mixed-integer programming formulation of piecewise polynomial regression. Together, these can be used to estimate tame functions. We demonstrate promising computational results.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 17 of its 57 references that are in the map. First posted on arXiv 22 Nov 2023.
Builds on
17 of 57 references.
References · 17
- 2019Complexity of Linear Regions in Deep Networkscited by 167
- 2017Bounding and Counting Linear Regions of Deep Neural Networkscited by 161
- 2018Stochastic subgradient method converges on tame functionscited by 124
- 2019Conservative set valued fields, automatic differentiation, stochastic gradient method and deep learningcited by 72
- 2020A mathematical model for automatic differentiation in machine learningcited by 45
- 2022Optimal Sparse Regression Treescited by 13
- 2021Active manifolds, stratifications, and convergence to local minima in nonsmooth optimizationcited by 11
- 2019Adaptive Estimation of Multivariate Piecewise Polynomials and Bounded Variation Functions by Optimal Decision Treescited by 10
- 2022Progress in Mathematical Programming Solvers from 2001 to 2020cited by 10
- 2023ReLU Neural Networks, Polyhedral Decompositions, and Persistent Homologcited by 10
- 2020Nonsmoothness in Machine Learning: specific structure, proximal identification, and applicationscited by 9
- 2021Stochastic Subgradient Descent Escapes Active Strict Saddles on Weakly Convex Functionscited by 9
5 more
- 2017Nonconvex piecewise linear functions: Advanced formulations and simple modeling toolscited by 7
- 2023Global convergence of the gradient method for functions definable in o-minimal structurescited by 5
- 2023Taming Binarized Neural Networks and Mixed-Integer Programscited by 4
- 2021Lattice partition recovery with dyadic CARTcited by 2
- 2022Polynomial Matrix Inequalities within Tame Geometrycited by 2
Built on by
Citing papers per year: 2025: 1.
1 paper.