Related papers: Towards a classification of countable 1-transitive…
A major part of computability theory focuses on the analysis of a few structures of central importance. As a tool, the method of coding with first-order formulas has been applied with great success. For instance, in the c.e. Turing degrees,…
This paper describes a design that can be used for Explainable AI. The lower level is a nested ensemble of patterns created by self-organisation. The upper level is a hierarchical tree, where nodes are linked through individual concepts, so…
Although there is a somewhat standard formalization of computability on countable sets given by Turing machines, the same cannot be said about uncountable sets. Among the approaches to define computability in these sets, order-theoretic…
We provide a short combinatorial proof of Cayley's formula by means of a bijective map to an outcome space of an urn-drawing problem. Furthermore we introduce an algebraic structure on the set of labeled trees, which provides a more…
This work introduces a transformation-based learner model for classification forests. The weak learner at each split node plays a crucial role in a classification tree. We propose to optimize the splitting objective by learning a linear…
Many common sequential data sources, such as source code and natural language, have a natural tree-structured representation. These trees can be generated by fitting a sequence to a grammar, yielding a hierarchical ordering of the tokens in…
Connected acyclic graphs (trees) are data objects that hierarchically organize categories. Collections of trees arise in a diverse variety of fields, including evolutionary biology, public health, machine learning, social sciences and…
This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into two parts. The first one is a critical review of…
Latent tree learning(LTL) methods learn to parse sentences using only indirect supervision from a downstream task. Recent advances in latent tree learning have made it possible to recover moderately high quality tree structures by training…
For a labelled tree on the vertex set $[n]:=\{1,2,..., n\}$, define the direction of each edge $ij$ to be $i\to j$ if $i<j$. The indegree sequence of $T$ can be considered as a partition $\lambda \vdash n-1$. The enumeration of trees with a…
A congruence of the weak order is simple if its quotientope is a simple polytope. We provide an alternative elementary proof of the characterization of the simple congruences in terms of forbidden up and down arcs. For this, we provide a…
A grammar-compressed ranked tree is represented with a linear space overhead so that a single traversal step, i.e., the move to the parent or the i-th child, can be carried out in constant time. Moreover, we extend our data structure such…
Decision trees and systems of decision rules are widely used as classifiers, as a means for knowledge representation, and as algorithms. They are among the most interpretable models for data analysis. The study of the relationships between…
We introduce the concept of a class of graphs, or more generally, relational structures, being locally tree-decomposable. There are numerous examples of locally tree-decomposable classes, among them the class of planar graphs and all…
In many complex networks the vertices are ordered in time, and edges represent causal connections. We propose methods of analysing such directed acyclic graphs taking into account the constraints of causality and highlighting the causal…
We study the problem of learning properties of nodes in tree structures. Those properties are specified by logical formulas, such as formulas from first-order or monadic second-order logic. We think of the tree as a database encoding a…
The Classification Tree (CT) is one of the most common models in interpretable machine learning. Although such models are usually built with greedy strategies, in recent years, thanks to remarkable advances in Mixer-Integer Programming…
We introduce the new concept of computation coding. Similar to how rate-distortion theory is concerned with the lossy compression of data, computation coding deals with the lossy computation of functions. Particularizing to linear…
When trained on language data, do transformers learn some arbitrary computation that utilizes the full capacity of the architecture or do they learn a simpler, tree-like computation, hypothesized to underlie compositional meaning systems…
Higher-order pushdown systems and ground tree rewriting systems can be seen as extensions of suffix word rewriting systems. Both classes generate infinite graphs with interesting logical properties. Indeed, the model-checking problem for…