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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…
Merkle trees have become a widely successful cryptographic data structure. Enabling a vast variety of applications from checking for inconsistencies in databases like Dynamo to essential tools like Git to large scale distributed systems…
Rank and select queries on bitmaps are essential building bricks of many compressed data structures, including text indexes, membership and range supporting spatial data structures, compressed graphs, and more. Theoretically considered yet…
We perform experimental studies on data structures that answer path median, path counting, and path reporting queries in weighted trees. These query problems generalize the well-known range median query problem in arrays, as well as the…
The decision tree recursively partitions the input space into regions and derives axis-aligned decision boundaries from data. Despite its simplicity and interpretability, decision trees lack parameterized representation, which makes it…
An indexed sequence of strings is a data structure for storing a string sequence that supports random access, searching, range counting and analytics operations, both for exact matches and prefix search. String sequences lie at the core of…
Tree-based data structures are ubiquitous across applications. Therefore, a multitude of different tree implementations exist. However, while these implementations are diverse, they share a tree structure as the underlying data structure.…
This work presents a discovery to advance the wisdom in a particular Succinct Data Structure: Wavelet Tree (Grossi, Gupta, and Vitter 2003). The discovery is first made by showing the feasibility of Reversed Indexes = Values: for integers…
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…
Leveraging the symmetries inherent to specific data domains for the construction of equivariant neural networks has lead to remarkable improvements in terms of data efficiency and generalization. However, most existing research focuses on…
In this paper, a new data structure named group-list is proposed. The group-list is as simple as the inverted index. However, the group-list divides document identifiers in an inverted index into groups, which makes it more efficient when…
We study the properties of ultrametric matrices aiming to design methods for fast ultrametric matrix-vector multiplication. We show how to encode such a matrix as a tree structure in quadratic time and demonstrate how to use the resulting…
Tree-structured multi-task architectures have been employed to jointly tackle multiple vision tasks in the context of multi-task learning (MTL). The major challenge is to determine where to branch out for each task given a backbone model to…
Tree-structured neural networks encode a particular tree geometry for a sentence in the network design. However, these models have at best only slightly outperformed simpler sequence-based models. We hypothesize that neural sequence models…
We show that the problem of constructing tree-structured descriptions of data layouts that are optimal with respect to space or other criteria from given sequences of displacements, can be solved in polynomial time. The problem is relevant…
Traversals are commonly seen in tree data structures, and performance-enhancing transformations between tree traversals are critical for many applications. Existing approaches to reasoning about tree traversals and their transformations are…
Neural networks with tree-based sentence encoders have shown better results on many downstream tasks. Most of existing tree-based encoders adopt syntactic parsing trees as the explicit structure prior. To study the effectiveness of…
In social networks, information and influence diffuse among users as cascades. While the importance of studying cascades has been recognized in various applications, it is difficult to observe the complete structure of cascades in practice.…
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…
Texture is the term used to characterize the surface of a given object or phenomenon and is an important feature used in image processing and pattern recognition. Our aim is to compare various Texture analyzing methods and compare the…