The general structure of how weights interact with inputs in a neural network layer often follows a similar form, . However, the specific nature of this interaction can vary slightly depending on the type of layer. Let's break this down:
Fully Connected (Dense) Layers
For fully connected (dense) layers, the relationship is:
Where:
- is the weight matrix.
- is the input vector.
- is the bias vector.
- is the output vector after applying the weights and biases.
This form is used in fully connected layers, where every input is connected to every output through a weight.
Convolutional Layers
In convolutional layers, the interaction between the input and the weights is different because the weights (often called filters or kernels) are applied locally over small patches of the input. However, the core idea is similar:
Here:
- is a set of convolutional filters (small matrices).
- is the input (often a multi-dimensional tensor, like an image).
- denotes the convolution operation.
- is a bias term, often added to the result of each convolution.
- is the output feature map.
Recurrent Layers (RNN, LSTM, GRU)
Recurrent layers involve a different type of interaction because they have a temporal or sequential component. However, they still involve a linear combination of the input with weights:
Where:
- is the hidden state at time .
- is the weight matrix for the hidden state.
- is the weight matrix for the input at time .
- is the input at time .
- is the bias.
- is the activation function.
Pooling Layers
- Interaction: Pooling layers reduce the spatial dimensions of the data by summarizing regions of the input.
- Operation: The most common types are max pooling and average pooling.
- Max Pooling: Takes the maximum value in each region.
- Average Pooling: Takes the average of the values in each region.
- Data Interaction: The pooling operation reduces the size of the feature map while retaining the most important information, making the model more robust to spatial variations.
Normalization Layers (Batch Normalization, Layer Normalization)
- Interaction: Normalization layers standardize the input to have a specific mean and variance.
- Operation: Where ΞΌ and Ο are the mean and standard deviation of the input, and Ξ³ and Ξ² are learnable parameters.
- Data Interaction: The input data is normalized across batches or features, and then scaled and shifted to allow the network to learn appropriate ranges for each feature.
Dropout Layer
- Interaction: Dropout layers randomly set a fraction of the input units to zero during training.
- Operation: Where p is the dropout rate.
- Data Interaction: During training, some neurons are randomly "dropped out," which forces the network to be more robust and reduces overfitting.
Attention Layers
- Interaction: Attention mechanisms compute a weighted sum of input features based on their relevance to a particular task.
- Operation:
Where Q (queries), K (keys), and V (values) are the input matrices.
- Data Interaction: The attention layer calculates how much focus should be given to each part of the input data, dynamically adjusting based on the task.
Summary
- Fully Connected Layers perform linear transformations across all inputs.
- Convolutional Layers focus on local regions and patterns.
- Recurrent Layers handle sequential data with temporal dependencies.
- Pooling Layers reduce spatial dimensions, summarizing information.
- Normalization Layers standardize inputs, stabilizing learning.
- Dropout Layers improve generalization by introducing randomness.
- Attention Layers dynamically weigh inputs for more focused processing.
Each type of layer interacts with the data in ways that suit its specific role in the network, allowing for flexible and powerful models that can handle a wide range of tasks.