In recent years, deep learning techniques have been developed to improve the performance of program synthesis from input-output examples. Albeit its significant progress, the programs that can be synthesized by state-of-the-art approaches are still simple in terms of their complexity. In this work, we move a significant step forward along this direction by proposing a new class of challenging t...

In recent years, deep learning techniques have been developed to improve the performance of program synthesis from input-output examples. Albeit its significant progress, the programs that can be synthesized by state-of-the-art approaches are still simple in terms of their complexity. In this work, we move a significant step forward along this direction by proposing a new class of challenging t...

Process-based modelling offers interpretability and physical consistency in many domains of geosciences but struggles to leverage large datasets efficiently. Machine-learning methods, especially deep networks, have strong predictive skills yet are unable answer specific scientific questions. In this Perspective, we explore differentiable as a pathway dissolve the perceived barrier between proce...

We prove that there exists a Lipschitz function from l into IR which is Gâteaux-differentiable at every point and such that for every x, y ∈ l, the norm of f (x) − f (y) is bigger than 1. On the other hand, for every Lipschitz and Gâteaux-differentiable function from an arbitrary Banach space X into IR and for every ε > 0, there always exists two points x, y ∈ X such that ‖f (x)−f (y)‖ is less ...

In this article we present an efficient algorithm to compute rotation intervals of circle maps degree one. It is based on the computation number a monotone map one with constant section. The main strength that it computes \emph{exactly} interval natural subclass continuous non-invertible maps. We also compare our other existing ones by plotting Devil's Staircase one-parameter family and Arnold ...

Invariants that incrementally maintain the value of expressions under assignments to their variables are a natural abstraction to build high-level local search algorithms. But their functionalities are not sufficient to allow arbitrary expressions as constraints or objective functions as in constraint programming. Differentiable invariants bridge this expressiveness gap. A differentiable invari...

A natural question, of great generality, various special forms of which are often asked in differential topology, is the following: Let Mi, Mi be differentiable w-manifolds, : M\—»M2 a continuous map which is a homotopy equivalence between M\ and M2. When is there a differentiable isomorphism <3>: Mi—> M2 in the same homotopy class as 0? For example, there is the Poincaré Conjecture which po...