Related papers: Ohana trees, linear approximation and multi-types …

In the first part of this paper, we define two resource aware typing systems for the {\lambda}{\mu}-calculus based on non-idempotent intersection and union types. The non-idempotent approach provides very simple combinatorial…

We investigate a natural generalization to trees of Hennie machines, a known automaton model for regular string functions. Tree-to-tree Hennie machines are tree-walking tree transducers with the ability to rewrite the node labels of their…

We consider combinatorial aspects of $\lambda$-terms in the model based on de Bruijn indices where each building constructor is of size one. Surprisingly, the counting sequence for $\lambda$-terms corresponds also to two families of binary…

We introduce inference trees (ITs), a new class of inference methods that build on ideas from Monte Carlo tree search to perform adaptive sampling in a manner that balances exploration with exploitation, ensures consistency, and alleviates…

Tabular neural network (NN) has attracted remarkable attentions and its recent advances have gradually narrowed the performance gap with respect to tree-based models on many public datasets. While the mainstreams focus on calibrating NN to…

Tree embedding has been a fundamental method in algorithm design with wide applications. We focus on the efficiency of building tree embedding in various computational settings under high-dimensional Euclidean $\mathbb{R}^d$. We devise a…

We estimate the size of a labelled tree by comparing the amount of (labelled) nodes with the size of the set of labels. Roughly speaking, a exponentially big labelled tree, is any labelled tree that has an exponential gap between its size,…

Formal transformations somehow resembling the usual derivative are surprisingly common in computer science, with two notable examples being derivatives of regular expressions and derivatives of types. A newcomer to this list is the…

The algebraic $\lambda$-calculus is an extension of the ordinary $\lambda$-calculus with linear combinations of terms. We establish that two ordinary $\lambda$-terms are equivalent in the algebraic $\lambda$-calculus iff they are…

We propose an implementation of lambda+, a recently introduced simply typed lambda-calculus with pairs where isomorphic types are made equal. The rewrite system of lambda+ is a rewrite system modulo an equivalence relation, which makes its…

Decision trees are widely used for non-linear modeling, as they capture interactions between predictors while producing inherently interpretable models. Despite their popularity, performing inference on the non-linear fit remains largely…

We propose and study a multi-scale approach to vector quantization. We develop an algorithm, dubbed reconstruction trees, inspired by decision trees. Here the objective is parsimonious reconstruction of unsupervised data, rather than…

In this paper, we consider establishing a formal connection between two distinct tree-abstraction problems inspired by the information-bottleneck (IB) method. Specifically, we consider the hard- and soft-constrained formulations that have…

An efficient approximate version of implicit Taylor methods for initial-value problems of systems of ordinary differential equations (ODEs) is introduced. The approach, based on an approximate formulation of Taylor methods, produces a…

Retrieval systems rely on representations learned by increasingly powerful models. However, due to the high training cost and inconsistencies in learned representations, there is significant interest in facilitating communication between…

We establish that the bisimulation invariant fragment of MSO over finite transition systems is expressively equivalent over finite transition systems to modal mu-calculus, a question that had remained open for several decades. The proof…

Ensembles of decision trees perform well on many problems, but are not interpretable. In contrast to existing approaches in interpretability that focus on explaining relationships between features and predictions, we propose an alternative…

We provide a proof of strong normalisation for lambda+, a recently introduced, explicitly typed, non-deterministic lambda-calculus where isomorphic propositions are identified. Such a proof is a non-trivial adaptation of the reducibility…

This paper presents a type theory with a form of equality reflection: provable equalities can be used to coerce the type of a term. Coercions and other annotations, including implicit arguments, are dropped during reduction of terms. We…

Slot and van Emde Boas' weak invariance thesis states that reasonable machines can simulate each other within a polynomially overhead in time. Is lambda-calculus a reasonable machine? Is there a way to measure the computational complexity…