Related papers: Ordered Functional Decision Diagrams: A Functional…
We address the problem of complementing higher-order patterns without repetitions of existential variables. Differently from the first-order case, the complement of a pattern cannot, in general, be described by a pattern, or even by a…
Existing end-to-end autonomous driving models rely heavily on purely data-driven inductive reasoning. This "black-box" nature leads to a lack of interpretability and absolute safety guarantees in complex, long-tail scenarios. To overcome…
Functional decomposition is the process of breaking down a function $f$ into a composition $f=g(f_1,\dots,f_k)$ of simpler functions $f_1,\dots,f_k$ belonging to some class $\mathcal{F}$. This fundamental notion can be used to model…
We introduce a new nameless representation of lambda terms inspired by ordered logic. At a lambda abstraction, number and relative position of all occurrences of the bound variable are stored, and application carries the additional…
Numerous formalisms and dedicated algorithms have been designed in the last decades to model and solve decision making problems. Some formalisms, such as constraint networks, can express "simple" decision problems, while others are designed…
Bayesian network classifiers are used in many fields, and one common class of classifiers are naive Bayes classifiers. In this paper, we introduce an approach for reasoning about Bayesian network classifiers in which we explicitly convert…
As a contribution to interpretable machine learning research, we develop a novel optimization framework for learning accurate and sparse two-level Boolean rules. We consider rules in both conjunctive normal form (AND-of-ORs) and disjunctive…
A longstanding open problem is whether there exists a non-syntactical model of untyped lambda-calculus whose theory is exactly the least equational lambda-theory (=Lb). In this paper we make use of the Visser topology for investigating the…
We explore a new class of end-to-end learnable models wherein data processing nodes (or network layers) are defined in terms of desired behavior rather than an explicit forward function. Specifically, the forward function is implicitly…
Labeling neural network submodules with human-legible descriptions is useful for many downstream tasks: such descriptions can surface failures, guide interventions, and perhaps even explain important model behaviors. To date, most…
Classical representations of quantum states and operations as vectors and matrices are plagued by an exponential growth in memory and runtime requirements for increasing system sizes. Based on their use in classical computing, an…
We present several results on comparative complexity for different variants of OBDD models. - We present some results on comparative complexity of classical and quantum OBDDs. We consider a partial function depending on parameter k such…
We propose a new approach, called as functional deep neural network (FDNN), for classifying multi-dimensional functional data. Specifically, a deep neural network is trained based on the principle components of the training data which shall…
Motivated by energy management for micro-grids, we study convex optimization problems with uncertainty in the objective function and sequential decision making. To solve these problems, we propose a new framework called ``Online…
The categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential…
Nondeterminism introduced by race conditions and message reorderings makes parallel and distributed programming hard. Nevertheless, promising approaches such as LVars and CRDTs address this problem by introducing a partial order structure…
Deep neural networks are a family of computational models that are naturally suited to the analysis of hierarchical data such as, for instance, sequential data with the use of recurrent neural networks. In the other hand, ordinal regression…
The ability to learn disentangled representations that split underlying sources of variation in high dimensional, unstructured data is important for data efficient and robust use of neural networks. While various approaches aiming towards…
Two-level logic minimization is a central problem in logic synthesis, and has applications in reliability analysis and automated reasoning. This paper represents a method of minimizing Boolean sum of products function with binary decision…
The paper examines hierarchies for nondeterministic and deterministic ordered read-$k$-times Branching programs. The currently known hierarchies for deterministic $k$-OBDD models of Branching programs for $ k=o(n^{1/2}/\log^{3/2}n)$ are…