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There is an increased interest in solving complex constrained problems where part of the input is not given as facts but received as raw sensor data such as images or speech. We will use "visual sudoku" as a prototype problem, where the…
The algorithms that simple feedback neural circuits representing a brain area can rapidly carry out are often adequate to solve only easy problems, and for more difficult problems can return incorrect answers. A new excitatory-inhibitory…
The use of Neural Networks in quantum many-body theory has seen a formidable rise in recent years. Among the many possible applications, one surely is to make use of their pattern recognition power when dealing with the study of equilibrium…
The effects of payoffs and noise on the maintenance of cooperative behavior are studied in an evolutionary Prisoner's Dilemma game with players located on the sites of different two-dimensional lattices. This system exhibits a phase…
Infinite-state systems such as distributed protocols are challenging to verify using interactive theorem provers or automatic verification tools. Of these techniques, deductive verification is highly expressive but requires the user to…
Recently many neural models have been proposed to solve combinatorial puzzles by implicitly learning underlying constraints using their solved instances, such as sudoku or graph coloring (GCP). One drawback of the proposed architectures,…
Motivated by certain applications from physics, biochemistry, economics, and computer science, in which the objects under investigation are not accessible because of various limitations, we propose a trial-and-error model to examine…
Fourier phasing is the problem of retrieving Fourier phase information from Fourier intensity data. The standard Fourier phase retrieval (without a mask) is known to have many solutions which cause the standard phasing algorithms to…
We give a procedure that can be used to automatically satisfy invariants of a certain shape. These invariants may be written with the operations intersection, composition and converse over binary relations, and equality over these…
Complex computer simulations are commonly required for accurate data modelling in many scientific disciplines, making statistical inference challenging due to the intractability of the likelihood evaluation for the observed data.…
This paper introduces a node formulation for multistage stochastic programs with endogenous (i.e., decision-dependent) uncertainty. Problems with such structure arise when the choices of the decision maker determine a change in the…
The Winograd Schema Challenge is both a commonsense reasoning and natural language understanding challenge, introduced as an alternative to the Turing test. A Winograd schema is a pair of sentences differing in one or two words with a…
In this paper we investigate the complexity of abduction, a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining the world's behavior it aims at finding an explanation for some observed manifestation.…
Grover's algorithm solves the unstructured search problem. Grover's algorithm can find the target state with certainty only if searching one out of four. Designing the deterministic search algorithm can avoid any repetition of the…
A free-form Sudoku puzzle is a square arrangement of m times m cells such that the cells are partitioned into m subsets (called blocks) of equal cardinality. The goal of the puzzle is to place integers 1,...,m in the cells such that the…
We explore the problem of step-wise explaining how to solve constraint satisfaction problems, with a use case on logic grid puzzles. More specifically, we study the problem of explaining the inference steps that one can take during…
The Decodoku project seeks to let users get hands-on with cutting-edge quantum research through a set of simple puzzle games. The design of these games is explicitly based on the problem of decoding qudit variants of surface codes. This…
As increasingly complex AI systems are introduced into our daily lives, it becomes important for such systems to be capable of explaining the rationale for their decisions and allowing users to contest these decisions. A significant hurdle…
Finding actions that satisfy the constraints imposed by both external inputs and internal representations is central to decision making. We demonstrate that some important classes of constraint satisfaction problems (CSPs) can be solved by…
We present probabilistic neural programs, a framework for program induction that permits flexible specification of both a computational model and inference algorithm while simultaneously enabling the use of deep neural networks.…