569 research outputs found
Redundant Sudoku Rules
The rules of Sudoku are often specified using twenty seven
\texttt{all\_different} constraints, referred to as the {\em big} \mrules.
Using graphical proofs and exploratory logic programming, the following main
and new result is obtained: many subsets of six of these big \mrules are
redundant (i.e., they are entailed by the remaining twenty one \mrules), and
six is maximal (i.e., removing more than six \mrules is not possible while
maintaining equivalence). The corresponding result for binary inequality
constraints, referred to as the {\em small} \mrules, is stated as a conjecture.Comment: 14 pages, 161 figures, to appear in TPL
Fusion rules for quantum reflection groups
We find the fusion rules for the quantum analogues of the complex reflection
groups . The irreducible representations can be
indexed by the elements of the free monoid , and their tensor
products are given by formulae which remind the Clebsch-Gordan rules (which
appear at ).Comment: 33 page
Scalable Coupling of Deep Learning with Logical Reasoning
In the ongoing quest for hybridizing discrete reasoning with neural nets,
there is an increasing interest in neural architectures that can learn how to
solve discrete reasoning or optimization problems from natural inputs. In this
paper, we introduce a scalable neural architecture and loss function dedicated
to learning the constraints and criteria of NP-hard reasoning problems
expressed as discrete Graphical Models. Our loss function solves one of the
main limitations of Besag's pseudo-loglikelihood, enabling learning of high
energies. We empirically show it is able to efficiently learn how to solve
NP-hard reasoning problems from natural inputs as the symbolic, visual or
many-solutions Sudoku problems as well as the energy optimization formulation
of the protein design problem, providing data efficiency, interpretability, and
\textit{a posteriori} control over predictions.Comment: 10 pages, 2 figures, 6 tables. Published in IJCAI'2023 proceeding
- …