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Hierarchical tree structures are common in many real-world systems, from tree roots and branches to neuronal dendrites and biologically inspired artificial neural networks, as well as in technological networks for organizing and searching…

Most deep learning models are limited to specific datasets or tasks because of network structures using fixed layers. In this paper, we discuss the differences between existing neural networks and real human neurons, propose association…

Contour trees offer an abstract representation of the level set topology in scalar fields and are widely used in topological data analysis and visualization. However, applying contour trees to large-scale scientific datasets remains…

Higher-order data with high dimensionality arise in a diverse set of application areas such as computer vision, video analytics and medical imaging. Tensors provide a natural tool for representing these types of data. Although there has…

Machine learning-based applications are increasingly prevalent in IoT devices. The power and storage constraints of these devices make it particularly challenging to run modern neural networks, limiting the number of new applications that…

Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…

Tensor data with rich structural information becomes increasingly important in process modeling, monitoring, and diagnosis. Here structural information is referred to structural properties such as sparsity, smoothness, low-rank, and…

Tree-based machine learning techniques, such as Decision Trees and Random Forests, are top performers in several domains as they do well with limited training datasets and offer improved interpretability compared to Deep Neural Networks…

Suffix trees are a fundamental data structure in stringology, but their space usage, though linear, is an important problem for its applications. We design and implement a new compressed suffix tree targeted to highly repetitive texts, such…

Sequential data such as time series, video, or text can be challenging to analyse as the ordered structure gives rise to complex dependencies. At the heart of this is non-commutativity, in the sense that reordering the elements of a…

We proposed the tensor-input tree (TT) method for scalar-on-tensor and tensor-on-tensor regression problems. We first address scalar-on-tensor problem by proposing scalar-output regression tree models whose input variable are tensors (i.e.,…

Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…

Tensor networks have proven to be a valuable tool, for instance, in the classical simulation of (strongly correlated) quantum systems. As the size of the systems increases, contracting larger tensor networks becomes computationally…

Artificial Intelligence (AI) has long pursued models, theories, and techniques to imbue machines with human-like general intelligence. Yet even the currently predominant data-driven approaches in AI seem to be lacking humans' unique ability…

We study the problem of learning a latent tree graphical model where samples are available only from a subset of variables. We propose two consistent and computationally efficient algorithms for learning minimal latent trees, that is, trees…

Structure learning is a core problem in AI central to the fields of neuro-symbolic AI and statistical relational learning. It consists in automatically learning a logical theory from data. The basis for structure learning is mining…

Regression trees are one of the oldest forms of AI models, and their predictions can be made without a calculator, which makes them broadly useful, particularly for high-stakes applications. Within the large literature on regression trees,…

This paper is a manual with tips and tricks for programming tensor network algorithms with global $SU(2)$ symmetry. We focus on practical details that are many times overlooked when it comes to implementing the basic building blocks of…

The paper presents a REDUCE program for the simplification of tensor expressions that are considered as formal indexed objects. The proposed algorithm is based on the consideration of tensor expressions as vectors in some linear space. This…

In this report, we propose Triton-distributed, an extension of existing Triton compiler, to overcome the programming challenges in distributed AI systems. Triton-distributed is the first compiler that supports native overlapping…