Related papers: Tree Neural Networks in HOL4

In recent years, there has been considerable innovation in the world of predictive methodologies. This is evident by the relative domination of machine learning approaches in various classification competitions. While these algorithms have…

Computer Algebra Systems (e.g. Maple) are used in research, education, and industrial settings. One of their key functionalities is symbolic integration, where there are many sub-algorithms to choose from that can affect the form of the…

As data are increasingly modeled as graphs for expressing complex relationships, the tree pattern query on graph-structured data becomes an important type of queries in real-world applications. Most practical query languages, such as XQuery…

Since their recent introduction, process trees have been frequently used as a process modeling formalism in many process mining algorithms. A process tree is a tree-based model of a process, in which internal vertices represent behavioral…

Deep neural networks are widely used for nonlinear function approximation with applications ranging from computer vision to control. Although these networks involve the composition of simple arithmetic operations, it can be very challenging…

We introduce a neural network that represents sentences by composing their words according to induced binary parse trees. We use Tree-LSTM as our composition function, applied along a tree structure found by a fully differentiable natural…

This paper introduces a differentiable framework that embeds the axiomatic structure of Random Utility Models (RUM) directly into deep neural networks. Although projecting empirical choice data onto the RUM polytope is NP-hard in general,…

We show how neural models can be used to realize piece-wise constant functions such as decision trees. The proposed architecture, which we call locally constant networks, builds on ReLU networks that are piece-wise linear and hence their…

Recently, deep neural networks have expanded the state-of-art in various scientific fields and provided solutions to long standing problems across multiple application domains. Nevertheless, they also suffer from weaknesses since their…

Deep neural networks (DNNs) and decision trees (DTs) are both state-of-the-art classifiers. DNNs perform well due to their representational learning capabilities, while DTs are computationally efficient as they perform inference along one…

One of the main virtues of trees is to represent formal solutions of various functional equations which can be cast in the form of fixed point problems. Basic examples include differential equations and functional (Lagrange) inversion in…

Neural networks and tree ensembles are state-of-the-art learners, each with its unique statistical and computational advantages. We aim to combine these advantages by introducing a new layer for neural networks, composed of an ensemble of…

We present a recursive formulation of the Horn algorithm for deciding the satisfiability of propositional clauses. The usual presentations in imperative pseudo-code are informal and not suitable for simple proofs of its main properties. By…

In this article we propose a boosting algorithm for regression with functional explanatory variables and scalar responses. The algorithm uses decision trees constructed with multiple projections as the "base-learners", which we call…

Verifying programs that manipulate tree data structures often requires complex, ad-hoc proofs that are hard to generalize and automate. This paper introduces an automatic technique for analyzing such programs. Our approach combines automata…

We present a Fourier neural network (FNN) that can be mapped directly to the Fourier decomposition. The choice of activation and loss function yields results that replicate a Fourier series expansion closely while preserving a…

Deep neural networks (DNNs) lack the precise semantics and definitive probabilistic interpretation of probabilistic graphical models (PGMs). In this paper, we propose an innovative solution by constructing infinite tree-structured PGMs that…

Wood increment is critical information in forestry management. Previous studies used mathematics models to describe complex growing pattern of forest stand, in order to determine the dynamic status of growing forest stand in multiple…

The personnel rostering problem is the problem of finding an optimal way to assign employees to shifts, subject to a set of hard constraints which all valid solutions must follow, and a set of soft constraints which define the relative…

We describe here a simple application of rational trees to the implementation of an interpreter for a procedural language written in a logic programming language. This is possible in languages designed to support rational trees (such as…