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Results tagged with convex-geometry
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user 27013
A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...
3
votes
Accepted
Is the interior of the tensor product of two convex cones equal to the tensor product of the...
Yes, $(C \otimes D)^\circ = C^\circ \otimes D^\circ$ is correct.
Let us start by proving the inclusion $C^\circ \otimes D^\circ \subseteq (C \otimes D)^\circ$. To this end, it is enough to show that $ …
- 6,406
11
votes
Is every polytope combinatorially equivalent to the intersection of a simplex and a linear s...
Update: This answers the question without the extra condition on the subspace passing through the centre.
The answer is yes. The following stronger statement is an elementary fact of polyhedral geome …
- 6,406
14
votes
Structures of the space of neural networks
I would like to argue that the space of neural networks is a category with finite products, or more concretely a Lawvere theory. This expresses an important piece of structure, namely how neural netwo …
- 6,406