Problema
A small neural network has a hidden layer and an output layer. Data flows forward through them:
- Hidden layer: h_j = ReLU(inputs · hidden_weights[j] + hidden_biases[j]), where ReLU(z) = max(0, z)
- Output layer: y_k = sigmoid(h · output_weights[k] + output_biases[k]), where sigmoid(z) = 1 / (1 + e^(-z))
Implement forward_pass(inputs, hidden_weights, hidden_biases, output_weights, output_biases).
Input
inputs: The n input values.
hidden_weights, hidden_biases: The hidden layer, one row and one bias per hidden neuron.
output_weights, output_biases: The output layer, one row and one bias per output; each row has one weight per hidden neuron.
Output
Return the list of network outputs y.
Vincoli
1 ≤ inputs, hidden neurons, outputs ≤ 50
-10 ≤ each value ≤ 10
Esempi
Input:
inputs = [1.0, 0.5]
hidden_biases = [0.0, 0.5]
output_biases = [0.0]
hidden_weights = [
[1.0, -2.0],
[0.5, 1.0]
]
output_weights = [
[1.0, -1.0]
]
Output atteso:
expected = [0.182426]Input:
std::vector<double> inputs = {1.0, 0.5};
std::vector<double> hidden_biases = {0.0, 0.5};
std::vector<double> output_biases = {0.0};
std::vector<std::vector<double>> hidden_weights = {
{1.0, -2.0},
{0.5, 1.0}
};
std::vector<std::vector<double>> output_weights = {
{1.0, -1.0}
};
Output atteso:
std::vector<double> expected = {0.182426};Input:
double[] inputs = new double[] {1.0, 0.5};
double[] hidden_biases = new double[] {0.0, 0.5};
double[] output_biases = new double[] {0.0};
double[][] hidden_weights = new double[][] {
new double[] {1.0, -2.0},
new double[] {0.5, 1.0}
};
double[][] output_weights = new double[][] {
new double[] {1.0, -1.0}
};
Output atteso:
double[] expected = new double[] {0.182426};Spiegazione
Hidden: ReLU(1×1 + 0.5×(-2) + 0) = ReLU(0) = 0 and ReLU(1×0.5 + 0.5×1 + 0.5) = 1.5. Output: sigmoid(0×1 + 1.5×(-1) + 0) = sigmoid(-1.5) ≈ 0.182426.
Input:
inputs = [2.0]
hidden_biases = [0.0, 0.0]
output_biases = [-1.0, 0.0]
hidden_weights = [
[1.0],
[-1.0]
]
output_weights = [
[0.5, 0.5],
[-0.5, 2.0]
]
Output atteso:
expected = [0.5, 0.268941]Input:
std::vector<double> inputs = {2.0};
std::vector<double> hidden_biases = {0.0, 0.0};
std::vector<double> output_biases = {-1.0, 0.0};
std::vector<std::vector<double>> hidden_weights = {
{1.0},
{-1.0}
};
std::vector<std::vector<double>> output_weights = {
{0.5, 0.5},
{-0.5, 2.0}
};
Output atteso:
std::vector<double> expected = {0.5, 0.268941};Input:
double[] inputs = new double[] {2.0};
double[] hidden_biases = new double[] {0.0, 0.0};
double[] output_biases = new double[] {-1.0, 0.0};
double[][] hidden_weights = new double[][] {
new double[] {1.0},
new double[] {-1.0}
};
double[][] output_weights = new double[][] {
new double[] {0.5, 0.5},
new double[] {-0.5, 2.0}
};
Output atteso:
double[] expected = new double[] {0.5, 0.268941};Spiegazione
Hidden: ReLU(2) = 2 and ReLU(-2) = 0. Output 1: sigmoid(2×0.5 + 0 - 1) = sigmoid(0) = 0.5. Output 2: sigmoid(2×(-0.5) + 0) = sigmoid(-1) ≈ 0.268941.
Come affrontarlo
Prova prima da solo, poi apri un suggerimento alla volta.
Suggerimento 1
First compute all hidden activations from the inputs, then use those hidden outputs for the final layer.
Suggerimento 2
Each layer is a batch of dot products plus biases, with ReLU in the hidden layer and sigmoid at the output.
Suggerimento 3
Do not mix original inputs into the second layer; it only sees the hidden layer outputs.
Complessità attesa
O(hn + oh) time, O(h + o) extra space
Riferimenti
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