{xi∈Rn}Ni=1

$\{{\mathbf{x}}_i\in {\mathbb{R}}^n{\}}_{i=1}^N$

$\{\mathbf{x}_i \in \mathbb{R}^n \}_{i=1}^N$N

$N$

$N$ n−

$n-$

$n-$X

$X$

$X$x1,…,xN

${\mathbf{x}}_1,\dots ,{\mathbf{x}}_N$

$\mathbf{x}_1,\dots,\mathbf{x}_N$

$$\begin{align} \mathbf{h}_1 & = \mathbf{W}_1\mathbf{x} + \mathbf{b}_1 \\ \hat{\mathbf{x}} & = \mathbf{W}_2\mathbf{h}_1 + \mathbf{b}_2 \end{align}$$

x^

$\hat{\mathbf{x}}$

$\hat{\mathbf{x}}$W1∈Rn×m

$W_1\in {\mathbb{R}}^{n\times m}$

$W_1\in \mathbb{R}^{n \times m}$W2∈Rm×n

$W_2\in {\mathbb{R}}^{m\times n}$

$W_2\in \mathbb{R}^{m \times n}$m<n

$m<n$

$m < n$

m

$m$

$m$W2

$W_2$

$W_2$m

$m$

$m$X

$X$

$X$

W2

$W_2$

$W_2$m

$m$

$m$X

$X$

$X$X

$X$

$X$n×N

$n\times N$

$n \times N$W2

$W_2$

$W_2$m×n

$m\times n$

$m\times n$W2

$W_2$

$W_2$O(m2n)

$O(m^{2}n)$

$O(m^2n)$X

$X$

$X$O(n2N)

$O(n^{2}N)$

$O(n^2N)$m<n

$m<n$

$m < n$

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