42 citations · 122 across the 36 of their papers we have counts for
39 papers
Fractal Gadgets for Neural Networks: The Complexity of the Narrow Regime
Olivier Bournez, Johanne Cohen, Laura Cohen +1
We study the verification problem for deep narrow ReLU neural networks: given a network of bounded width computing a piecewise-affine map on [0,1], does some input satisfy a prescr…
Relating the Computational and Logical Difficulty of Solving ODEs: From Polynomial to Discontinuous Right-Hand Sides
Olivier Bournez, Alonso Núñez
When a computer algebra system fails to solve an Ordinary Differential Equation, is this a limitation of its implementation, or a genuine computational barrier? Three traditions be…
Primitive Recursion without Composition: Dynamical Characterizations, from Neural Networks to Polynomial ODEs
Olivier Bournez
What do recurrent neural networks, polynomial ODEs, and discrete polynomial maps each bring to computation, and what do they lack? All three operate over the continuum--real-valued…
Toward higher-order infinite time Turing machines: simulational -machines
Olivier Bournez, Olivier Finkel, Johan Girardot
Infinite time Turing machines (ITTMs) have been introduced by Hamkins and Lewis in their seminal article arXiv:math/9808093. The strength of the model comes from a limit rule which…
Set Descriptive Complexity of Solvable Functions
Riccardo Gozzi, Olivier Bournez
In a recent article, we introduced and studied a precise class of dynamical systems called solvable systems. These systems present a dynamic ruled by discontinuous ordinary differe…
Solvable Initial Value Problems Ruled by Discontinuous Ordinary Differential Equations
Olivier Bournez, Riccardo Gozzi
We study initial value problems having dynamics ruled by discontinuous ordinary differential equations with the property of possessing a unique solution. We identify a precise clas…