sequence of four inputs, carrying every hidden state forward yourself. 🔄

1. Given

Four inputs X1 to X4, recurrent weights and biases for hidden layers a, b, c, and an output layer y. 📊

2. Initialize

Let us set the hidden states a0, b0, c0 to zeros. Nothing has been read yet. 🛑

3. First hidden layer (a)

We build the transformation matrix by laying the input weights, the state weights and the biases side by side. We stack X1, the previous state a0, and an extra 1 underneath. Multiply the two, and a1 = [0, 1]. 🧮

4. Second hidden layer (b)

Let us do it again, one layer up. Now a1 is the input, and b0 is the previous state. Multiply: b1 = [1, -1]. ⬆️

5. Third hidden layer (c)

Once more. b1 is the input, c0 is the previous state, and c1 = [1, 1]. 🔁

6. Output layer (y)

Let us read the answer off the top of the stack. Weights and biases against [c1; 1], and Y1 = [3, 0, 3]. 📝

7. Carry the states forward

We copy a1, b1, c1 across. This is the whole trick of a recurrent network: the states are the only thing the next input gets to see. 🚀

8. Process X2

Repeat steps 3 to 6 for the second input: three hidden layers, then the output. Y2 = [5, 0, 4]. 🔢

9. Carry the states forward

Let us copy a2, b2, c2 across, exactly as before. 🔄

10. Process X3

Same four moves, third input. Y3 = [13, -1, 9]. 🧩

11. Carry the states forward

We copy a3, b3, c3 across, one last time. ⏭️

12. Process X4

Repeat once more. Y4 = [15, 7, 2]. ✅

You have just run a Deep RNN over a whole sequence by hand. ✍️

The outputs:
Y1: [3, 0, 3]
Y2: [5, 0, 4]
Y3: [13, -1, 9]
Y4: [15, 7, 2]

The takeaway: the hidden states are the memory, and they are the only memory there is. Everything the network learns from X1 has to fit in those little two-cell columns and get handed forward, one step at a time. 🧠

#RNN #DeepLearning #AI #MachineLearning #NeuralNetworks #Tech

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