The advent of deep learning has yielded powerful tools to automatically compute gradients computations. This is because training a neural network equates iteratively updating its parameters using gradient descent find the minimum loss function. Deep then subset broader paradigm; workflow with free that end-to-end optimisable, provided one can keep track all way through. work introduces neos: an...

We consider learning of submodular functions from data. These functions are important in machine learning and have a wide range of applications, e.g. data summarization, feature selection and active learning. Despite their combinatorial nature, submodular functions can be maximized approximately with strong theoretical guarantees in polynomial time. Typically, learning the submodular function a...

We describe a class of cellular automata (CAs) that are end-to-end differentiable. DCAs interpolate the behavior of ordinary CAs through rules that act on distributions of states. The gradient of a DCA with respect to its parameters can be computed with an iterative propagation scheme that uses previously-computed gradients and values. Gradient-based optimization over DCAs could be used to find...

A differentiable semigroup is a topological semigroup (5, *) in which 5 is a differentiable manifold based on a Banach space and the associative multiplication function * is continuously differentiable. If e is an idempotent element of such a semigroup we show that there is an open set U containing e so that there is a C retraction of U into the set of idempotents of S so that (x)<$(y) =...

1. The bordism groups. This note presents an outline of the authors' efforts to apply Thorn's cobordism theory [ó] to the study of differentiable periodic maps. First, however, we shall outline our scheme for computing the oriented bordism groups of a space [ l ] . These preliminary remarks bear on a problem raised by Milnor [4]. A finite manifold is the finite disjoint union of compact connect...

A real-valued continuously differentiable function f on the unit interval is constructed such that ∞ ∑ k=1 βf (x, 2 −k) = ∞ holds for every x ∈ [0, 1]. Here βf (x, 2−k) measures the distance of f to the best approximating linear function at scale 2−k around x.

We introduce the use of high order automatic differentiation, implemented via the algebra of truncated Taylor polynomials, in genetic programming. Using the Cartesian Genetic Programming encoding we obtain a high-order Taylor representation of the program output that is then used to back-propagate errors during learning. The resulting machine learning framework is called differentiable Cartesia...

Prior work has shown that features which appear to be biologically plausible as well as empirically useful can be found by sparse coding with a prior such as a laplacian (L1) that promotes sparsity. We show how smoother priors can preserve the benefits of these sparse priors while adding stability to the Maximum A-Posteriori (MAP) estimate that makes it more useful for prediction problems. Addi...

astrophysics is becoming now an integral part of general physics. considering the black hole theory ,which is a new and exciting branch of relativistic astrophysics, we see many connections between elementary particle physics and astrophysics. in this article we attempt to explain the development of star physics ,in an easy ,understandable manner. previous knowledge of relativistic theory or cl...