Related papers: All elementary functions from a single binary oper…
We study acquisition functions for active learning (AL) for text classification. The Expected Loss Reduction (ELR) method focuses on a Bayesian estimate of the reduction in classification error, recently updated with Mean Objective Cost of…
They run our lives, if you believe the hype in the news, but there is no precise definition of "algorithms" which is generally accepted by the mathematicians, logicians and computer scientists who create and study them. My main aims here…
In this note we discuss trees similar to the Calkin-Wilf tree, a binary tree that enumerates all positive rational numbers in a simple way. The original construction of Calkin and Wilf is reformulated in a more algebraic language, and an…
Boolean functions and binary arithmetic operations are central to standard computing paradigms. Accordingly, many advances in computing have focused upon how to make these operations more efficient as well as exploring what they can…
We consider the multiplicative complexity of Boolean functions with multiple bits of output, studying how large a multiplicative complexity is necessary and sufficient to provide a desired nonlinearity. For so-called $\Sigma\Pi\Sigma$…
We study enumeration problems for multi-operator monomials generated from one indeterminate by an associative multiplication together with finitely many unary operators. We consider four regimes, according to whether multiplication is…
Formulae of the Lambek calculus are constructed using three binary connectives, multiplication and two divisions. We extend it using a unary connective, positive Kleene iteration. For this new operation, following its natural…
By considering generalized logarithm and exponential functions used in nonextensive statistics, the four usual algebraic operators : addition, subtraction, product and division, are generalized. The properties of the generalized operators…
We introduce Nominal Matching Logic (NML) as an extension of Matching Logic with names and binding following the Gabbay-Pitts nominal approach. Matching logic is the foundation of the $\mathbb{K}$ framework, used to specify programming…
As we rapidly approach the frontiers of ultra large computing resources, software optimization is becoming of paramount interest to scientific application developers interested in efficiently leveraging all available on-Node computing…
Higher-point functions of gauge invariant composite operators in N=4 super Yang-Mills theory can be computed via triangulation. The elementary tile in this process is the hexagon introduced for the evaluation of structure constants. A…
We provide a novel transcription of monotone operator theory to the non-Euclidean finite-dimensional spaces $\ell_1$ and $\ell_{\infty}$. We first establish properties of mappings which are monotone with respect to the non-Euclidean norms…
Maps are polygonal cellular networks on Riemann surfaces. This paper analyzes the construction of closed form general representations for the enumerative generating functions associated to maps of fixed but arbitrary genus. The method of…
Causal functions of sequences occur throughout computer science, from theory to hardware to machine learning. Mealy machines, synchronous digital circuits, signal flow graphs, and recurrent neural networks all have behaviour that can be…
Regular expressions are commonly understood in terms of their denotational semantics, that is, through formal languages -- the regular languages. This view is inductive in nature: two primitives are equivalent if they are constructed in the…
Mixture-of-Experts (MoE) has become a dominant architecture for scaling Large Language Models (LLMs) efficiently by decoupling total parameters from computational cost. However, this decoupling creates a critical challenge: predicting the…
The current paper studies sample-efficient Reinforcement Learning (RL) in settings where only the optimal value function is assumed to be linearly-realizable. It has recently been understood that, even under this seemingly strong assumption…
We introduce and study the arithmetic function E_m(n), defined as the sum of the remainders of n when divided by the first m positive integers. Although the definition is elementary, the function encodes rich arithmetic structure. In this…
We present a theoretical analysis and empirical evaluations of a novel set of techniques for computational cost reduction of test time operations of network classifiers based on extreme learning machine (ELM). By exploring some…
Euler's formula, an extraordinary mathematical formula, establishes a vital link between complex-valued operations and trigonometric functions, finding widespread application in various fields. With the end of Moore's Law, electronic…