讓我們逐一檢視。

Let’s take a look one by one.

對於第一幅影象，神經網路認為該圖為4的概率為96.66%。

For the first image, the neural networkdecided it was a 4 by 96.66% probability.

比較圖4-16中的左右兩幅影象，它們分別是神經網路的輸入和判斷輸出。

Compare the left and right images in Figure4-16, which are the input and the digit that the neural network selected,respectively.

圖4-16 左右影象分別是神經網路的輸入和判斷輸出Left and rightimages are the input and digit that the neural network selected, respectively

從兩幅圖的對比可以看出，輸入影象中的內容確實包含了數字4的重要特徵。

The input image indeed contains importantfeatures of the number 4.

雖然看起來也與1相似，但更與4接近。

Although it appears to be a 1 as well, itis closer to a 4.

分類看起來似乎是合理的。

The classification seems reasonable.

接下來，第二幅影象被認為是2的概率為99.36%。

Next, the second image is classified as a 2by 99.36% probability.

當我們比較輸入影象和訓練資料2時，看起來應該是合理的。

This appears to be reasonable when wecompare the input image and the training data 2.

它們之間只有一個畫素的差異。

They only have a one-pixel difference.

如圖4-17所示。

See Figure 4-17.

圖4-17 第二幅影象被判斷為2The second image isclassified as a 2

第三幅影象被認為是3的概率為97.62%。

The third image is classified as a 3 by97.62% probability.

當我們對比兩幅影象時，這也是很合理的。

This also seems reasonable when we comparethe images.

如圖4-18所示。

See Figure 4-18.

圖4-18 第三幅影象被判斷為3The third image isclassified as a 3

然而，當我們比較第二和第三幅輸入影象時，它們之間只有一個畫素的差別。（待判斷的輸入影象之間只有一個畫素的差別！！！）

However, when we compare the second andthird input images, the difference is only one pixel.

這種微小的差異導致了兩種完全不同的分類。

This tiny difference results in two totallydifferent classifications.

你可能沒有注意，影象2和3的訓練資料（即標準模板）也只有兩個畫素的差別。

You may not have paid attention, but thetraining data of these two images has only a two-pixel difference.

神經網路能捕捉到這種微小的差異，並將其應用到實踐中，這豈不是令人驚歎嗎？

Isn’t it amazing that the neural networkcatches this small difference and applies it to actual practice?

——本文譯自Phil Kim所著的《Matlab Deep Learning》

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