![NEURAL NETWORK IMPLEMENTATION:
AND GATE
- **Problem:**
- Input: Binary pairs (0, 1).
- Output: 1 if all inputs are 1; otherwise 0.
- **Weights and Bias:**
- Adjusted such that weighted sum > threshold only when both inputs are
1.
- **Example:**
- Input: [0, 0] -> Output: 0
- Input: [1, 1] -> Output: 1
- Linearly separable problem.](https://image.slidesharecdn.com/detailedbackpropagationandneuralnetworkimplementation-250706060108-764f43f9/85/Detailed_Back_Propagation_and_Neural_Network_Implementation-pptx-8-320.jpg)
![NEURAL NETWORK IMPLEMENTATION: OR
GATE
- **Problem:**
- Input: Binary pairs (0, 1).
- Output: 1 if any input is 1; otherwise 0.
- **Weights and Bias:**
- Adjusted such that weighted sum > threshold if either input is 1.
- **Example:**
- Input: [0, 0] -> Output: 0
- Input: [1, 0] -> Output: 1
- Linearly separable problem.](https://image.slidesharecdn.com/detailedbackpropagationandneuralnetworkimplementation-250706060108-764f43f9/85/Detailed_Back_Propagation_and_Neural_Network_Implementation-pptx-9-320.jpg)
![NEURAL NETWORK IMPLEMENTATION:
XOR GATE
- **Problem:**
- Input: Binary pairs (0, 1).
- Output: 1 if inputs are different; otherwise 0.
- **Weights and Bias:**
- Requires hidden layer to separate data points.
- **Example:**
- Input: [0, 1] -> Output: 1
- Input: [1, 1] -> Output: 0
- Non-linear problem solved by MLP.](https://image.slidesharecdn.com/detailedbackpropagationandneuralnetworkimplementation-250706060108-764f43f9/85/Detailed_Back_Propagation_and_Neural_Network_Implementation-pptx-10-320.jpg)
Detailed_Back_Propagation_and_Neural_Network_Implementation.pptx
- 1. BACK PROPAGATION ALGORITHMS AND NEURAL NETWORK IMPLEMENTATION Multi-Layer Perceptron (MLP), Back Propagation Algorithm, AND/OR/XOR Implementation
- 2. MULTI-LAYER PERCEPTRON (MLP): OVERVIEW - Structure: - Consists of input, hidden, and output layers. - Fully connected neurons. - Solves complex, non-linear problems. - Common activation functions: - Sigmoid: Output in range (0, 1). - ReLU: Introduces non-linearity. - Training involves forward and backward propagation.
- 3. MLP ARCHITECTURE - Input Layer: - Accepts raw data. - Number of neurons = Features of input data. - Hidden Layers: - Perform feature extraction. - Multiple layers for deep learning.
- 4. MLP ARCHITECTURE - Output Layer: - Final predictions. - Number of neurons = Number of output classes.
- 6. BACK PROPAGATION ALGORITHM: STEPS 1. **Forward Pass**: - Compute outputs for each layer. - Use activation functions for non-linearity. 2. **Error Calculation**: - Compute error (E) = (Target - Output). 3. **Backward Pass**: - Calculate gradients of E w.r.t weights using chain rule. 4. **Weight Update**: - Use gradient descent: w = w - * ∂E/∂w η - Repeat until error converges.
- 7. STOCHASTIC GRADIENT DESCENT (SGD) - Optimization method used in back propagation. - Updates weights after processing each training example. - Steps: 1. Shuffle training data. 2. Process one sample at a time. 3. Update weights using gradient of loss function. - Advantages: Fast updates, suitable for large datasets. - Drawback: High variance, which can lead to noisy convergence.
- 8. NEURAL NETWORK IMPLEMENTATION: AND GATE - **Problem:** - Input: Binary pairs (0, 1). - Output: 1 if all inputs are 1; otherwise 0. - **Weights and Bias:** - Adjusted such that weighted sum > threshold only when both inputs are 1. - **Example:** - Input: [0, 0] -> Output: 0 - Input: [1, 1] -> Output: 1 - Linearly separable problem.
- 9. NEURAL NETWORK IMPLEMENTATION: OR GATE - **Problem:** - Input: Binary pairs (0, 1). - Output: 1 if any input is 1; otherwise 0. - **Weights and Bias:** - Adjusted such that weighted sum > threshold if either input is 1. - **Example:** - Input: [0, 0] -> Output: 0 - Input: [1, 0] -> Output: 1 - Linearly separable problem.
- 10. NEURAL NETWORK IMPLEMENTATION: XOR GATE - **Problem:** - Input: Binary pairs (0, 1). - Output: 1 if inputs are different; otherwise 0. - **Weights and Bias:** - Requires hidden layer to separate data points. - **Example:** - Input: [0, 1] -> Output: 1 - Input: [1, 1] -> Output: 0 - Non-linear problem solved by MLP.
- 11. EXAMPLE
- 12. EXAMPLE
- 13. EXAMPLE
- 14. EXAMPLE
- 15. EXAMPLE
- 16. EXAMPLE
- 17. SUMMARY - MLPs use back propagation for learning. - Key steps: Forward pass, error calculation, backward pass, weight update. - SGD is an efficient optimization technique. - AND and OR gates are linearly separable, solvable by simple networks. - XOR requires non-linear separability, solved by MLPs with hidden layers.