Ah, the classic "Hybrid Model of LSTM-GRU" gambit! It's like the Frankenstein of neural networks, stitching together Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) to conquer the stock market beast. Let's whip up those formulas, shall we?

LSTM Cell Equations:

1. Forget Gate:

   $$ f_t = \sigma(W_f \cdot [h_{t-1}, x_t] + b_f) $$

2. Input Gate:

   $$ i_t = \sigma(W_i \cdot [h_{t-1}, x_t] + b_i) $$

3. Candidate Layer:

   $$ \tilde{C}_t = \tanh(W_C \cdot [h_{t-1}, x_t] + b_C) $$

4. Cell State Update:

   $$ C_t = f_t * C_{t-1} + i_t * \tilde{C}_t $$

5. Output Gate:

   $$ o_t = \sigma(W_o \cdot [h_{t-1}, x_t] + b_o) $$

6. Hidden State:

   $$ h_t = o_t * \tanh(C_t) $$

GRU Cell Equations:

1. Update Gate:

   $$ z_t = \sigma(W_z \cdot [h_{t-1}, x_t] + b_z) $$

2. Reset Gate:

   $$ r_t = \sigma(W_r \cdot [h_{t-1}, x_t] + b_r) $$

3. Candidate Activation:

   $$ \tilde{h}_t = \tanh(W_h \cdot [r_t * h_{t-1}, x_t] + b_h) $$

4. Final Memory At Time t:

   $$ h_t = (1 - z_t) * h_{t-1} + z_t * \tilde{h}_t $$

Hybrid Model Concept:

In a hybrid model, you could utilize LSTM for its ability to remember longer sequences and GRU for its computational efficiency and capability to cope with smaller sequences, combining them in a custom architecture. A common approach is to stack them in layers:

• Send your input to an LSTM layer first.
• Feed the output of the LSTM into a GRU layer.
• Connect a dense layer to interpret the output for a prediction task, like stock prices.

The art of neural networks is like cooking; once you know the ingredients, you can season to taste!

For even more juicy tidbits and tips on deploying your neural network beast, remember to visit trituenhantao.io – where intelligence meets its artificial companions!