关于Michael Nielsen著作中feedforward函数的功能困惑求解

Hey there! Let's unpack this confusing behavior you're seeing—it's all about input shapes, I promise!

The Core Issue: Input Shape Differences #

Your feedforward function works exactly as intended, but the problem lies in how you're passing input when testing manually versus how the evaluate function uses the test data:

• In the evaluate function: Each x from test_data is a flattened 1D array representing a single image. For example, if your input layer maps to 30 features, x will have a shape like (30,). When you pass this to feedforward:

  a = sigmoid(np.dot(w, a)+b)
  

  The output layer's weight matrix w is shaped (10, 30) (10 classification neurons, 30 input features). The dot product np.dot(w, a) produces a 1D array of shape (10,), which is exactly the 10-class output you expect. np.argmax then picks the index (0-9) of the highest activation, matching your classification goal.

• In your manual test: You're passing an image that's a 2D array instead of a flattened 1D array. From your output being 10×30, it looks like your input image has a shape like (30, 30)—either 30 separate images each with 30 features, or an unflattened 30×30 image. When you run feedforward on this:

  • np.dot(w, a) (with w as (10, 30)) will produce a (10, 30) array—each column corresponds to the 10-class output for one of the 30 input samples/features.
  • When you call np.argmax(test) without specifying an axis, NumPy flattens the entire 2D array into a 1D array of 300 elements, so the index returned will be between 0-299 instead of 0-9.

How to Fix Your Manual Test #

To get the expected 0-9 output when testing a single image:

1. Flatten your input image into a 1D array first:

   flattened_image = image.flatten()  # or image.reshape(-1)
   test = net.feedforward(flattened_image)
   print(np.argmax(test))  # Now returns 0-9 as expected
   

2. If you're intentionally testing a batch of images, specify the axis in np.argmax to get per-sample results:

   # For a (10, 30) output array (30 samples, 10 classes each)
   predictions = np.argmax(test, axis=0)  # Returns an array of 30 elements (0-9)
   

内容的提问来源于stack exchange，提问作者Guenterino