Related papers: Black Boxes
We study the mechanism design problem of allocating a set of indivisible items without monetary transfers. Despite the vast literature on this very standard model, it still remains unclear how do truthful mechanisms look like. We focus on…
We consider decompositions of the real line into pairwise disjoint Borel pieces so that each piece is closed under addition. How many pieces can there be? We prove among others that the number of pieces is either at most 3 or uncountable,…
We like to build Abelian groups (or R-modules) which on the one hand are quite free, say $\aleph_{\omega + 1}$-free, and on the other hand, are complicated in suitable sense. We choose as our test problem having no non-trivial homomorphism…
The Causal Set hypothesis asserts that spacetime, ultimately, is discrete and its underlying structure is that of a locally finite partial ordered set, and macroscopic causality reflects a deeper notion of order in terms of which all the…
Deep neural networks learn fragile "shortcut" features, rendering them difficult to interpret (black box) and vulnerable to adversarial attacks. This paper proposes semantic features as a general architectural solution to this problem. The…
We explain a highly efficient algorithm for playing the simplest type of dots and boxes endgame optimally (by which we mean "in such a way so as to maximise the number of boxes that you take"). The algorithm is sufficiently simple that it…
We explore the consequences of layering a Lambek proof system over an arbitrary (constraint) logic. A simple model-theoretic semantics for our hybrid language is provided for which a particularly simple combination of Lambek's and the proof…
The existence of exact solutions which represent a lattice of black holes at a scalar-field-dominated cosmological bounce suggests that black holes could persist through successive eras of a cyclic cosmology. Here we explore some remarkable…
Various simplicial complexes can be associated with a graph. Box complexes form an important families of such simplicial complexes and are especially useful for providing lower bounds on the chromatic number of the graph via some of their…
We consider extensive games with perfect information with well-founded game trees and study the problems of existence and of characterization of the sets of subgame perfect equilibria in these games. We also provide such characterizations…
We consider partially ordered sets of combinatorial structures under consecutive orders, meaning that two structures are related when one embeds in the other such that `consecutive' elements remain consecutive in the image. Given such a…
Black and white holes play remarkably contrasting roles in general relativity versus observational astrophysics. While there is overwhelming observational evidence for the existence of compact objects that are "cold, dark, and heavy", which…
In set theory without the axiom of regularity, we consider a game in which two players choose in turn an element of a given set, an element of this element, etc.; a player wins if its adversary cannot make any next move. Sets that are…
We consider black holes in an "unsuitable box": a finite cavity coupled to a thermal reservoir at a temperature different than the black hole's Hawking temperature. These black holes are described by metrics that are continuous but not…
Each market has its singular characteristic. Its inner structure is directly responsible for the observed distributions of returns though this fact is widely overlooked. Big orders lead to doubling the tails. The behavior of a market maker…
Recent work showing the existence of conflict-free almost-perfect hypergraph matchings has found many applications. We show that, assuming certain simple degree and codegree conditions on the hypergraph $ \mathcal{H} $ and the conflicts to…
Consider the following one-player game. Take a well-formed sequence of opening and closing brackets. As a move, the player can pair any opening bracket with any closing bracket to its right, erasing them. The goal is to re-pair (erase) the…
Four and five dimensional extremal black holes with nonzero entropy have simple presentations in M-theory as gravitational waves bound to configurations of intersecting M-branes. We discuss realizations of these objects in matrix models of…
We point out that neural networks are not black boxes, and their generalization stems from the ability to dynamically map a dataset to the extrema of the model function. We further prove that the number of extrema in a neural network is…
Understanding how "black-box" models arrive at their predictions has sparked significant interest from both within and outside the AI community. Our work focuses on doing this by generating local explanations about individual predictions…