Related papers: Carry Value Transformation (CVT) - Exclusive OR (X…

Carry Value Transformation (CVT) is a model of discrete dynamical system which is one special case of Integral Value Transformations (IVTs). Earlier in [5] it has been proved that sum of two non-negative integers is equal to the sum of…

The notion of Carry Value Transformation (CVT) is a model of Discrete Deterministic Dynamical System. In this paper, we have studied some interesting properties of CVT and proved that (1) the addition of any two non-negative integers is…

A decision tree looks like a simple directed acyclic computational graph, where only the leaf nodes specify the output values and the non-terminals specify their tests or split conditions. From the numerical perspective, we express decision…

We show that an algorithmic construction of sequences of recursive trees leads to a direct proof of the convergence of random recursive trees in an associated Doob-Martin compactification; it also gives a representation of the limit in…

The Tsetlin Machine (TM) is a novel machine learning algorithm with several distinct properties, including transparent inference and learning using hardware-near building blocks. Although numerous papers explore the TM empirically, many of…

Given a boolean n by n matrix A we consider arithmetic circuits for computing the transformation x->Ax over different semirings. Namely, we study three circuit models: monotone OR-circuits, monotone SUM-circuits (addition of non-negative…

Learning vector representations for programs is a critical step in applying deep learning techniques for program understanding tasks. Various neural network models are proposed to learn from tree-structured program representations, e.g.,…

Decoder-only models generate tokens autoregressively by caching key/value vectors, but as the cache grows, inference becomes memory-bound. To address this issue, we introduce CLOVER (Cross-Layer Orthogonal Vectors), a novel approach that…

Working with generating functions, the combinatorics of a recurrence relation can be expressed in a way that allows for more efficient calculation of the quantity. This is true of the Catalan numbers for an ordered binary tree…

The tree based representation described in this paper, hereditarily binary numbers, applies recursively a run-length compression mechanism that enables computations limited by the structural complexity of their operands rather than by their…

Decision trees are popular machine learning models that are simple to build and easy to interpret. Even though algorithms to learn decision trees date back to almost 50 years, key properties affecting their generalization error are still…

Integral Value Transformation (IVT) is a family of transformations from N0kto N0. An algebraic result has been established in p-adic IVT systems and an application of the result is described in this paper. The result in this paper provides…

We propose a new topological invariant of unlabeled trees of N nodes. The invariant is a set of Nx2 matrices of integers, with sum_j k^{d_{i,j}} and v_i as the matrix elements, where d_{i,j} are the elements of the distance matrix and v_i…

We describe the set V of all real valued valuations v on the ring C[[x,y]] normalized by min{v(x),v(y)}=1. It has a natural structure of an R-tree, induced by the order relation v is less than v' iff v(f) is less than v'(f) for all f. It…

As a challenging vision-language task, Zero-Shot Composed Image Retrieval (ZS-CIR) is designed to retrieve target images using bi-modal (image+text) queries. Typical ZS-CIR methods employ an inversion network to generate pseudo-word tokens…

We describe an adaptive context tree weighting (ACTW) algorithm, as an extension to the standard context tree weighting (CTW) algorithm. Unlike the standard CTW algorithm, which weights all observations equally regardless of the depth, ACTW…

As part of work to connect phylogenetics with machine learning, there has been considerable recent interest in vector encodings of phylogenetic trees. We present a simple new "ordered leaf attachment" (OLA) method for uniquely encoding a…

Equational Unification is a critical problem in many areas such as automated theorem proving and security protocol analysis. In this paper, we focus on XOR-Unification, that is, unification modulo the theory of exclusive-or. This theory…

This study introduces and evaluates the Quantile Regressor Tree (QRT), a novel methodology merging the robust characteristics of quantile regression with the versatility of decision trees. The quantile regressor tree introduces…

A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with…