Results 61 to 70 of about 72,380 (161)

Grokking modular arithmetic

, 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 arithmetic tasks under vanilla gradient descent with the MSE loss function in the absence of any ...
openaire   +2 more sources

Modular Arithmetic Based on Boolean Functions: A Divide and Conquer Approach

IEEE Access
This paper introduces a new method for designing modular arithmetic units, for reduction ( $X (mod\ P)$ ), multiplication ( $(A\cdot B) (mod\ P)$ ), and multiplication by a constant ( $(constant\cdot A)(mod \ P)$ ).
Danila Gorodecky, Leonel Sousa
doaj   +1 more source

Distance between consecutive elements of the multiplicative group of integers modulo n [PDF]

Notes on Number Theory and Discrete Mathematics
For a prime number p, we consider its primorial P:=p# and U(P):=(ℤ/Pℤ)^× the set of elements of the multiplicative group of integers modulo P which we represent as points anticlockwise on a circle of perimeter P.
Steven Brown
doaj   +1 more source

Cost-Efficient Pipelined Modular Polynomial Multiplier for Post-Quantum Cryptography Saber

Quantum Reports
The development of quantum computers presents a great challenge for current cryptographic algorithms. Post-quantum cryptography has been proposed to secure against quantum computers in the near future.
Hua Li
doaj   +1 more source

Arithmetic Hilbert Modular Functions II

Revista Matemática Iberoamericana, 1985
This work is a continuation of the author's earlier papers on Hilbert modular functions and arithmetic Hilbert modular forms. Here a q- expansion principle is established necessary to obtain reciprocity laws for special values of arithmetic Hilbert modular functions (associated to a totally real algebraic number field k) which subsumes the classical ...
openaire   +2 more sources

SYNTHESIS AND ANALYSIS OF REED-SOLOMON CODES IN ISOMORPHIC SPACE OF IMAGES

Ìнформаційні технології в освіті, 2013
A training variant of Reed-Solomon codes, which greatly simplifies the process of synthesis of codewords and detection-fixes for corrupted data files. The algorithm is based on the transfer of variables and operations, in which the synthesis and analysis
A.J. Beletsky, А.А. Beletsky, O.I. Volyvach, M.A. Yakymchuk   +3 more
doaj  

NEURAL NETWORKS OF THE FINAL RING BASED ON THE REDUCTION SCHEME OF THE POSITION-MODULAR-CODE TRANSFORMATION

Informatika, 2018
The article studies the problem of creating a neural network of modular computing structures for highperformance expressions in the field of information security.
N. I. Chervyakov, A. A. Kolyada, N. A. Kolyada, V. A. Kuchukov, S. U. Protasenia   +4 more
doaj  

Factoring an integer with three oscillators and a qubit. [PDF]

Nat Commun
Brenner L, Caha L, Coiteux-Roy X, Koenig R.   +3 more
europepmc   +1 more source

Canonicalizing Zeta Generators: Genus Zero and Genus One. [PDF]

Commun Math Phys
Dorigoni D, Doroudiani M, Drewitt J, Hidding M, Kleinschmidt A, Schlotterer O, Schneps L, Verbeek B.   +7 more
europepmc   +1 more source