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Regression trees and their ensemble methods are popular methods for nonparametric regression: they combine strong predictive performance with interpretable estimators. To improve their utility for locally smooth response surfaces, we study…

By fundamental results of Sch\"utzenberger, McNaughton and Papert from the 1970s, the classes of first-order definable and aperiodic languages coincide. Here, we extend this equivalence to a quantitative setting. For this, weighted automata…

Entity alignment (EA) aims to merge two knowledge graphs (KGs) by identifying equivalent entity pairs. While existing methods heavily rely on human-generated labels, it is prohibitively expensive to incorporate cross-domain experts for…

The problem of identifying a probabilistic context free grammar has two aspects: the first is determining the grammar's topology (the rules of the grammar) and the second is estimating probabilistic weights for each rule. Given the hardness…

A simple linear-time algorithm for constructing a linear context-free tree grammar of size O(rg + r g log (n/r g))for a given input tree T of size n is presented, where g is the size of a minimal linear context-free tree grammar for T, and…

Tree-of-Thought (ToT) reasoning boosts the problem-solving abilities of Large Language Models (LLMs) but is computationally expensive due to semantic redundancy, where distinct branches explore equivalent reasoning paths. We introduce…

An automatic word classification system has been designed which processes word unigram and bigram frequency statistics extracted from a corpus of natural language utterances. The system implements a binary top-down form of word clustering…

The HOM problem, which asks whether the image of a regular tree language under a given tree homomorphism is again regular, is known to be decidable [Godoy & Gim\'enez: The HOM problem is decidable. JACM 60(4), 2013]. However, the problem…

In codeswitching contexts, the language of a syntactic head determines the distribution of its complements. Mahootian 1993 derives this generalization by representing heads as the anchors of elementary trees in a lexicalized TAG. However,…

We present an algorithm for extraction of a probabilistic deterministic finite automaton (PDFA) from a given black-box language model, such as a recurrent neural network (RNN). The algorithm is a variant of the exact-learning algorithm L*,…

Transformers are ubiquitous models in the natural language processing (NLP) community and have shown impressive empirical successes in the past few years. However, little is understood about how they reason and the limits of their…

Example weighting algorithm is an effective solution to the training bias problem, however, most previous typical methods are usually limited to human knowledge and require laborious tuning of hyperparameters. In this paper, we propose a…

Agentic large language model (LLM) training often involves multi-turn interaction trajectories that branch into multiple execution paths due to concurrent tool use, think-mode, sub-agent, context management and other runtime designs. As a…

This thesis concerns the implementation of Lambda Prolog, a higher-order logic programming language that supports the lambda-tree syntax approach to representing and manipulating formal syntactic objects. Lambda Prolog achieves its…

We introduce a new complexity measure for finite strings using probabilistic finite-state automata (PFAs), in the same spirit as existing notions employing DFAs and NFAs, and explore its properties. The PFA complexity $A_P(x)$ is the least…

Simulations of weighted tree automata (wta) are considered. It is shown how such simulations can be decomposed into simpler functional and dual functional simulations also called forward and backward simulations. In addition, it is shown in…

Search-optimization problems are plentiful in scientific and engineering domains. Artificial intelligence has long contributed to the development of search algorithms and declarative programming languages geared toward solving and modeling…

In this paper we present a new tree-rewriting formalism called Link-Sharing Tree Adjoining Grammar (LSTAG) which is a variant of synchronous TAGs. Using LSTAG we define an approach towards coordination where linguistic dependency is…

In this paper, we propose a novel approach to combine \emph{compact directed acyclic word graphs} (CDAWGs) and grammar-based compression. This leads us to an efficient self-index, called Linear-size CDAWGs (L-CDAWGs), which can be…

In this paper, a new learning algorithm for Federated Learning (FL) is introduced. The proposed scheme is based on a weighted gradient aggregation using two-step optimization to offer a flexible training pipeline. Herein, two different…