Related papers: Reverse derivative categories
Reversible algorithms play a crucial role both in classical and quantum computation. While for a classical bit the only nontrivial reversible operation is the bit-flip, nature is far more versatile in what it allows to do to a quantum bit.…
While backpropagation--reverse-mode automatic differentiation--has been extraordinarily successful in deep learning, it requires two passes (forward and backward) through the neural network and the storage of intermediate activations.…
Reinforcement learning (RL) offers significant promise for machinery fault detection (MFD). However, most existing RL-based MFD approaches do not fully exploit RL's sequential decision-making strengths, often treating MFD as a simple…
The conformable derivative has been promoted in numerous publications as a new fractional derivative operator. This article provides a critical reassessment of this claim. We demonstrate that the conformable derivative is not a fractional…
We view a conic optimization problem that has a unique solution as a map from its data to its solution. If sufficient regularity conditions hold at a solution point, namely that the implicit function theorem applies to the normalized…
Following ideas of Lawvere and Linton we prove that classical varieties are precisely the exact categories with a varietal generator. This means a strong generator which is abstractly finite and regularly projective. An analogous…
A novel class of derivative-free optimization algorithms is developed. The main idea is to utilize certain non-commutative maps in order to approximate the gradient of the objective function. Convergence properties of the novel algorithms…
We discuss the functional lazy techniques in generation and handling of arbitrarily long sequences of derivatives of numerical expressions in one ``variable''; the domain to which the paper belongs is usually nicknamed ``Automatic…
Cartesian reverse derivative categories (CRDCs) provide an axiomatic generalization of the reverse derivative, which allows generalized analogues of classic optimization algorithms such as gradient descent to be applied to a broad class of…
A relational structure is called reversible iff every bijective endomorphism of that structure is an automorphism. We give several equivalents of that property in the class of disconnected binary structures and some its subclasses. For…
This is a mostly expository paper, intended to explain a very natural relationship between two a priori distinct notions appearing in the literature: Generic Vanishing in the context of vanishing theorems and birational geometry, and…
In this paper we prove that local fractional derivatives of differentiable functions are integer-order derivative or zero operator. We demonstrate that the local fractional derivatives are limits of the left-sided Caputo fractional…
The pseudoinverse of a matrix, a generalized notion of the inverse, is of fundamental importance in linear algebra and, thereby, in many different fields. Despite its proven existence, an algorithmic approach is typically necessary to…
Deep learning has seen tremendous success over the past decade in computer vision, machine translation, and gameplay. This success rests in crucial ways on gradient-descent optimization and the ability to learn parameters of a neural…
The inverse problem of special geometry (Seiberg-Witten geometry of 4d N=2 SCFT) asks for a recursive construction of all such geometries in rank $r$ by assembling together known lower-rank ``strata''. This leads to a program to…
Backward simulation is an approximate inference technique for Bayesian belief networks. It differs from existing simulation methods in that it starts simulation from the known evidence and works backward (i.e., contrary to the direction of…
The paper presents derivation and interpretation of one type of variable order derivative definitions. For mathematical modelling of considering definition the switching and numerical scheme is given. The paper also introduces a numerical…
A derived operation is a bilinear operation on a commutative associative algebra $A$ defined intrinsically out of its product and several derivations of the product. We show that operators of left (or right) multiplications of a derived…
Function regression/approximation is a fundamental application of machine learning. Neural networks (NNs) can be easily trained for function regression using a sufficient number of neurons and epochs. The forward-forward learning algorithm…
We present Sparse Backdoor, a supply-chain attack that plants a \emph{provably undetectable} backdoor in pre-trained image classifiers, including convolutional networks and Vision Transformers. The attack injects a structured sparse…