Approximation
神经网络优化篇：详解梯度的数值逼近（Numerical approximation of gradients）
在实施backprop时，有一个测试叫做梯度检验，它的作用是确保backprop正确实施。因为有时候，虽然写下了这些方程式，却不能100%确定，执行backprop的所有细节都是正确的。为了逐渐实现梯度检验，首先说说如何计算梯度的数值逼近。 先画出函数\(f\)，标记为\(f\left( \thet ......
Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited
目录概符号说明MotivationChebNetII代码 He M., Wei Z. and Wen J. Convolutional neural networks on graphs with chebyshev approximation, revisited. NIPS, 2022. 概 作 ......
Approximation with Gradient Descent Method
title: Approximation with Gradient Descent Method layout: page categories: data analysis Polynomial Approximation with Gradient Descent Method Suppose ......
理论的动态发展完完备与进化：数论Number Theory数域的进化史 与 Infinite Precision无限精度+Infinite Approximation无穷近似
Infinite Precision: (0)数是什么？以有限的数元，度量与表示无限的现象、事物与状态，作为整个数学科学理论的根基。 以Binary二进制为例, 有{0,1}, Constant/Dynamic系统建模上，两种state(状态)？0->1与1->0代表“change变化”？ 而Dec ......
Numerical Approximation Chapter 6 Notes
Weierstrass theorem approximation之间也有高低，所以我们在compact subset里面会有best approximation. 但是以polynomial interpolation为例，随着不断选更多的Chebyshev interpolation point ......
Approximation Theory and Method ch7
Approximation Theory and Method ch7 ~~part 1, part 2, part 3, ch7, 命名乱了——致敬微软~~ ... as the sign of $p(x)$. It follows that $p^{}$ is a best minimax ap ......
Approximation Theory and Method part 3
Approximation Theory and Method part 3 Basic properties of divided differences Let $\left{x_i ; i=0,1, \ldots, n\right}$ be any $(n+1)$ distinct point ......
Numerical Approximation Chapter 5 Notes
考虑在某个范围$[a,b]$上的$n+1$个点值所确定的插值$n$次多项式$p$满足 $$ p(x_i)=f(x_i) $$ 其中$f\in \mathscr L[a,b]$ , $p$是$\mathscr P_n$中满足条件的polynomial. 考虑到按照条件可以列出一个$n+1$元方程组，未 ......
Approximation Theory and Methods习题解答
2.1 $\Vert f\Vert\geq 0$ obvious $\Vert a-b\Vert=\Vert b-a\Vert$ by definition $f\in\mathscr A$ then $-f\in\mathscr A$ Triangle Inequality $\Vert a+b\ ......
Approximation Theory and Method part 2
Approximation Theory and Method part 2 Approximation operators 在前面的讨论中，我们得到了 best approximation 的一些性质. 但是实际上我们并不总是能有 best approximation 这么好的结果。那么我们能不能 ......