Consider the feedforward neural network shown in the figure below. The weights are: w1 = -0.1, w2 = -0.1, w3 = 0.2 and b = -0.1. The transfer function f is sigmoid: f(x)=1/(1+exp(-x)).

The network receives the input x = [0.5, 0.1, 0.3]. What will be the network’s output?

If the result has more than 1 decimal points, round it to 1 decimal points, otherwise just write the number. Examples:

Result              What to write

0.246               0.2

0.26                 0.3

0.6                   0.6

Question

Consider the feedforward neural network shown in the figure below. The weights are: w1 = -0.1, w2 = -0.1, w3 = 0.2 and b = -0.1. The transfer function f is sigmoid: f(x)=1/(1+exp(-x)).

The network receives the input x = [0.5, 0.1, 0.3]. What will be the network’s output?

If the result has more than 1 decimal points, round it to 1 decimal points, otherwise just write the number. Examples:

Result              What to write

0.246               0.2

0.26                 0.3

0.6                   0.6

BlackTom AI · Accepted Answer

Compute the neuron's net input: z = w1*x1 + w2*x2 + w3*x3 + b.

1) Relevant knowledge points and concepts
- A single feedforward neuron sums weighted inputs plus a bias to get net input z.
- The sigmoid activation is f(z) = 1 / (1 + exp(-z)).
- After computing f(z) we apply the requested rounding to one decimal place.

2) Step-by-step reasoning and intermediate calculations
- Given: w1 = -0.1, w2 = -0.1, w3 = 0.2, b = -0.1 and x = [0.5, 0.1, 0.3].
- Compute each weighted term:
  w1*x1 = -0.1 * 0.5 = -0.05
  w2*x2 = -0.1 * 0.1 = -0.01
  w3*x3 = 0.2 * 0.3 = 0.06
- Sum these and add bias:
  z = (-0.05) + (-0.01) + 0.06 + (-0.1)
  First combine: -0.05 - 0.01 = -0.06
  Then -0.06 + 0.06 = 0
  Then 0 + (-0.1) = -0.1
  So z = -0.1

3) Apply the sigmoid activation and show intermediate work
- f(z) = 1 / (1 + exp(-z)) with z = -0.1
- exp(-z) = exp(0.1) ≈ 1.105170918
- f(-0.1) = 1 / (1 + 1.105170918) = 1 / 2.105170918 ≈ 0.4750208125

4) Why the correct answer is correct
- The computed output before rounding is approximately 0.47502. The problem asks to round to one decimal place, so 0.475... rounds to 0.5 (since the second decimal 7 rounds the first decimal up).

5) Why other possible numeric guesses would be incorrect
- Omitting the bias (b = -0.1) would give z = 0 and f = 0.5 exactly; including the bias gives z = -0.1 and f ≈ 0.475, so forgetting the bias can produce an incorrect 0.5 before rounding decisions.
- Computing exp(-0.1) instead of exp(0.1) (i.e., using the wrong sign) or arithmetic errors in weighted sums would produce values like 0.6 or 0.3 which do not match the correct sigmoid result.

6) Conclusion and final answer confirmation
- After summation, activation, and rounding to one decimal place, the network output is 0.5, which matches the provided answer.

类似问题

Which of the following statements about neural networks is not true?

Question at position 40 Like decision trees, neural networks can select inputs.TrueFalse

Question at position 11 What if in a neural network implementation we use a learning rate that’s too large?Network will not convergeNetwork will convergeCan’t say

Question at position 3 The number of nodes in the input layer of a neural network is 10 and the hidden layer is 5. What is the maximum number of connections from the input layer to the hidden layer?Less than 50It is an arbitrary value50More than 50

Which of the following best describes the structure of a neural network?

We have 3 neurons at the input layer, and 4 neurons in the first layer. These two layers are densely connected. How many parameters do we have between the input layer and the first layer? (Hint: bias are used)

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