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Language models generate reasoning sequentially, preventing them from decoupling irrelevant exploration paths during search. We introduce Tree-Structured Language Modeling (TSLM), which uses special tokens to encode branching structure,…

Computation and Language · Computer Science 2026-02-02 Doyoung Kim , Jaehyeok Doo , Minjoon Seo

We study the complexity of the problem of searching for a set of patterns that separate two given sets of strings. This problem has applications in a wide variety of areas, most notably in data mining, computational biology, and in…

Computational Complexity · Computer Science 2016-12-20 Giuseppe Lancia , Luke Mathieson , Pablo Moscato

Estimating phylogenetic trees is an important problem in evolutionary biology, environmental policy and medicine. Although trees are estimated, their uncertainties are discarded by mathematicians working in tree space. Here we explicitly…

Methodology · Statistics 2017-10-16 Amy D. Willis , Rayna C. Bell

Recursive neural networks (RvNN) have been shown useful for learning sentence representations and helped achieve competitive performance on several natural language inference tasks. However, recent RvNN-based models fail to learn simple…

Computation and Language · Computer Science 2021-04-13 Atul Sahay , Ayush Maheshwari , Ritesh Kumar , Ganesh Ramakrishnan , Manjesh Kumar Hanawal , Kavi Arya

Structural probes learn a linear transformation to find how dependency trees are embedded in the hidden states of language models. This simple design may not allow for full exploitation of the structure of the encoded information. Hence, to…

Computation and Language · Computer Science 2024-02-27 Avik Pal , Madhura Pawar

Interpretable machine learning is essential in high-stakes domains where decision-making requires accountability, transparency, and trust. While rule-based models offer global and exact interpretability, learning rule sets that…

Machine Learning · Computer Science 2026-03-10 Hans Farrell Soegeng , Sarthak Ketanbhai Modi , Thomas Peyrin

Trees are fundamental data structure for many areas of computer science and system engineering. In this report, we show how to ensure eventual consistency of optimistically replicated trees. In optimistic replication, the different replicas…

Data Structures and Algorithms · Computer Science 2012-01-10 Stéphane Martin , Mehdi Ahmed-Nacer , Pascal Urso

Early in training, LMs can behave like n-gram models, but eventually they often learn tree-based syntactic rules and generalize hierarchically out of distribution (OOD). We study this shift using controlled grammar-learning tasks: question…

Machine Learning · Computer Science 2025-09-30 Tian Qin , Naomi Saphra , David Alvarez-Melis

Since they became observable, neuron morphologies have been informally compared with biological trees but they are studied by distinct communities, neuroscientists, and ecologists. The apparent structural similarity suggests there may be…

Neurons and Cognition · Quantitative Biology 2023-07-06 Roozbeh Farhoodi , Phil Wilkes , Anirudh M. Natarajan , Samantha Ing-Esteves , Julie L. Lefebvre , Mathias Disney , Konrad P. Kording

Predicting the ancestral sequences of a group of homologous sequences related by a phylogenetic tree has been the subject of many studies, and numerous methods have been proposed to this purpose. Theoretical results are available that show…

Populations and Evolution · Quantitative Biology 2013-09-05 Olivier Gascuel , Mike Steel

Modern industrial applications require robots to be able to operate in unpredictable environments, and programs to be created with a minimal effort, as there may be frequent changes to the task. In this paper, we show that genetic…

Robotics · Computer Science 2020-11-09 Matteo Iovino , Jonathan Styrud , Pietro Falco , Christian Smith

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…

Methodology · Statistics 2025-12-01 Maria Alejandra Valdez Cabrera , Amy D Willis , Armeen Taeb

Explaining predictions based on multivariate time series data carries the additional difficulty of handling not only multiple features, but also time dependencies. It matters not only what happened, but also when, and the same feature could…

Machine Learning · Computer Science 2023-05-31 Joseph Enguehard

Random forests are decision tree ensembles that can be used to solve a variety of machine learning problems. However, as the number of trees and their individual size can be large, their decision making process is often incomprehensible. In…

Artificial Intelligence · Computer Science 2022-11-22 Nico Potyka , Xiang Yin , Francesca Toni

We congratulate Lee, Nadler and Wasserman (henceforth LNW) on a very interesting paper on new methodology and supporting theory [arXiv:0707.0481]. Treelets seem to tackle two important problems of modern data analysis at once. For datasets…

Applications · Statistics 2008-07-28 Nicolai Meinshausen , Peter Bühlmann

Standard methods of using categorical variables as predictors either endow them with an ordinal structure or assume they have no structure at all. However, categorical variables often possess structure that is more complicated than a linear…

Machine Learning · Statistics 2020-04-17 Brian Lucena

Language exhibits inherent structures, a property that explains both language acquisition and language change. Given this characteristic, we expect language models to manifest their own internal structures as well. While interpretability…

Computation and Language · Computer Science 2026-05-19 Haruki Sakajo , Frederikus Hudi , Yusuke Sakai , Hidetaka Kamigaito , Taro Watanabe

Tree ensembles (TEs) find a multitude of practical applications. They represent one of the most general and accurate classes of machine learning methods. While they are typically quite concise in representation, their operation remains…

Artificial Intelligence · Computer Science 2026-04-01 Yacine Izza , Alexey Ignatiev , Xuanxiang Huang , Peter J. Stuckey , Joao Marques-Silva

Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…

Methodology · Statistics 2017-06-29 Christina Heinze-Deml , Marloes H. Maathuis , Nicolai Meinshausen

Tree structures appear in many fields of the life sciences, including phylogenetics, developmental biology and nucleic acid structures. Trees can be used to represent RNA secondary structures, which directly relate to the function of…

Machine Learning · Computer Science 2026-01-22 Pengyu Liu , Mariel Vázquez , Nataša Jonoska
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