相关论文: Nested Intervals Tree Encoding with Continued Frac…

In this article, we give a precise mathematical meaning to `linear? time' that matches experimental behaviour of the algorithm. The sorting algorithm is not our own, it is a variant of radix sort with counting sort as a subroutine. The true…

Tree methods (recursive partitioning) are a popular class of nonparametric methods for analyzing data. One extension of the basic tree methodology is the survival tree, which applies recursive partitioning to censored survival data. There…

This paper considers metric spaces where distances between a pair of nodes are represented by distance intervals. The goal is to study methods for the determination of hierarchical clusters, i.e., a family of nested partitions indexed by a…

Forecasting is critical in areas such as finance, biology, and healthcare. Despite the progress in the field, making accurate forecasts remains challenging because real-world time series contain both global trends, local fine-grained…

We present an algorithm for the Merkle tree traversal problem which combines the efficient space-time trade-off from the fractal Merkle tree [3] and the space efficiency from the improved log space-time Merkle trees traversal [8]. We give…

Understanding the response of an output variable to multi-dimensional inputs lies at the heart of many data exploration endeavours. Topology-based methods, in particular Morse theory and persistent homology, provide a useful framework for…

The class of self-nested trees presents remarkable compression properties because of the systematic repetition of subtrees in their structure. In this paper, we provide a better combinatorial characterization of this specific family of…

This paper introduces the Partition Tree Weighting technique, an efficient meta-algorithm for piecewise stationary sources. The technique works by performing Bayesian model averaging over a large class of possible partitions of the data…

Bayesian phylogenetic inference is currently done via Markov chain Monte Carlo (MCMC) with simple proposal mechanisms. This hinders exploration efficiency and often requires long runs to deliver accurate posterior estimates. In this paper,…

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,…

In recent years, non-parametric methods utilizing random walks on graphs have been used to solve a wide range of machine learning problems, but in their simplest form they do not scale well due to the quadratic complexity. In this paper, a…

We define a mapping from transition-based parsing algorithms that read sentences from left to right to sequence labeling encodings of syntactic trees. This not only establishes a theoretical relation between transition-based parsing and…

Implicit Neural Representations for Videos (NeRV) have emerged as a powerful paradigm for video representation, enabling direct mappings from frame indices to video frames. However, existing NeRV-based methods do not fully exploit temporal…

In this paper we introduce a variation on the multidimensional segment tree, formed by unifying different interpretations of the dimensionalities of the data structure. We give some new definitions to previously well-defined concepts that…

We reformulate the problem of encoding a multi-scale representation of a sequence in a language model by casting it in a continuous learning framework. We propose a hierarchical multi-scale language model in which short time-scale…

We prime-encode the natural numbers via recursive factorisation, iterated to the exponents, generating a corpus of planar rooted trees equivalently represented as Dyck words. This forms a deterministic text endowed with internal rules.…

Natural language is hierarchically structured: smaller units (e.g., phrases) are nested within larger units (e.g., clauses). When a larger constituent ends, all of the smaller constituents that are nested within it must also be closed.…

Large language models achieve strong reasoning performance, yet existing decoding strategies either explore blindly (random sampling) or redundantly (independent multi-sampling). We propose Entropy-Tree, a tree-based decoding method that…

A dual approach to defining the triangle sequence (a type of multidimensional continued fraction algorithm, initially developed in NT/9906016) for a pair of real numbers is presented, providing a new, clean geometric interpretation of the…

In phylogenetics, evolution is traditionally represented in a tree-like manner. However, phylogenetic networks can be more appropriate for representing evolutionary events such as hybridization, horizontal gene transfer, and others. In…