Results 1 to 10 of about 12,323,314 (203)

On an additive arithmetic function. [PDF]

Pacific Journal of Mathematics, 1977
Let \(n\) be a positive integer, \(n=\prod\limits_{i=1}^rp_i^{\alpha_i}\) in canonical form, and let \(A(n)=\sum\limits_{i=1}^r\alpha_ip_i\). Clearly \(A\) is an additive arithmetic function.
K. Alladi, P. Erdos
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Arithmetic in the developing brain: A review of brain imaging studies

Developmental Cognitive Neuroscience, 2018
Brain imaging studies on academic achievement offer an exciting window on experience-dependent cortical plasticity, as they allow us to understand how developing brains change when children acquire culturally transmitted skills. This contribution focuses
Lien Peters, Bert De Smedt
doaj   +2 more sources

On a arithmetic function

Monatshefte f�r Mathematik, 1959
P. McCarthy
semanticscholar   +2 more sources

An arithmetic function [PDF]

Bulletin of the American Mathematical Society, 1937
L. Carlitz
semanticscholar   +4 more sources

Objects generated by an arbitrary natural number. Part 3: Standard modal-topological aspect [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
The set Set(n), generated by an arbitrary natural number n, was defined in [3]. There, and in [4], some arithmetic functions and arithmetic operators of a modal type are defined over the elements of Set(n).
Krassimir Atanassov
doaj   +1 more source

Task Arithmetic in the Tangent Space: Improved Editing of Pre-Trained Models [PDF]

Neural Information Processing Systems, 2023
Task arithmetic has recently emerged as a cost-effective and scalable approach to edit pre-trained models directly in weight space: By adding the fine-tuned weights of different tasks, the model's performance can be improved on these tasks, while ...
Guillermo Ortiz-Jiménez, Alessandro Favero, P. Frossard   +2 more
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Objects generated by an arbitrary natural number. Part 4: New aspects [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
The set Set(n), generated by an arbitrary natural number n, was defined in [3]. There, and in [5, 6], some arithmetic functions and arithmetic operators of a modal and topological types are defined over the elements of Set(n).
Krassimir Atanassov
doaj   +1 more source

Teaching Arithmetic to Small Transformers [PDF]

arXiv.org, 2023
Large language models like GPT-4 exhibit emergent capabilities across general-purpose tasks, such as basic arithmetic, when trained on extensive text data, even though these tasks are not explicitly encoded by the unsupervised, next-token prediction ...
Nayoung Lee, Kartik K. Sreenivasan, Jason D. Lee, Kangwook Lee, Dimitris Papailiopoulos   +4 more
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A simple proof of generalizations of number-theoretic sums [PDF]

Songklanakarin Journal of Science and Technology (SJST), 2022
For positive integers 𝑘, 𝑚, and 𝑛, let 𝑆𝑘 𝑚(𝑛) be the sum of all elements in the finite set {𝑥 𝑘 : 1 ≤ 𝑥 ≤ 𝑛⁄𝑚 , (𝑥, 𝑛) = 1}. The formula for 𝑆𝑘 𝑚(𝑛) is established and simpler formulae for 𝑆𝑘 𝑚(𝑛) under some conditions on 𝑚 and 𝑛 are verified. The
Yanapat Tongron, Narakorn Rompurk Kanasri   +1 more
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Grokking modular arithmetic [PDF]

arXiv.org, 2023
We present a simple neural network that can learn modular arithmetic tasks and exhibits a sudden jump in generalization known as ``grokking''. Concretely, we present (i) fully-connected two-layer networks that exhibit grokking on various modular ...
A. Gromov
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