long short term memory guide

long short term memory guide

I'll summarize the content across all pages, focusing on explaining LSTM networks in a clear, educational manner suitable for interactive visualization.

Understanding Long Short-Term Memory (LSTM) Networks: A Comprehensive Guide

Summary: This collection of technical explanations provides a detailed exploration of Long Short-Term Memory (LSTM) networks - a specialized type of recurrent neural network designed to overcome the limitations of traditional RNNs in processing sequential data. The content explains the architecture, components, and working mechanisms of LSTMs with clear illustrations and implementation examples suitable for interactive visualization.

Introduction to Recurrent Neural Networks

Traditional neural networks lack memory capabilities, making them unsuitable for sequential data processing. Recurrent Neural Networks (RNNs) address this limitation by incorporating loops that allow information to persist across time steps. This chain-like architecture makes RNNs naturally suited for sequence and list data.

The Problem with Standard RNNs

While RNNs can theoretically handle long-term dependencies, they struggle with this in practice due to:

1. Vanishing Gradient Problem: When backpropagating through many time steps, gradients become exponentially smaller, preventing effective weight updates.

2. Exploding Gradient Problem: Conversely, gradients can become exponentially larger, destabilizing the training process.

These issues limit RNNs' ability to connect information across long sequences, such as understanding the relationship between distant words in text.

LSTM Architecture and Components

LSTMs were specifically designed to overcome these limitations. Key components include:

Cell State

• Acts as a conveyor belt running through the entire chain

• Allows information to flow unchanged through the network

• Provides long-term memory capabilities

Gates

Gates are neural network layers that regulate information flow using sigmoid activation functions:

1. Forget Gate: Decides what information to discard from the cell state

2. Takes current input x(t) and previous hidden state h(t-1)

3. Outputs values between 0 (forget) and 1 (keep) for each element

4. Formula: f_t = σ(W_f · [h_{t-1}, x_t] + b_f)

5. Input Gate: Determines what new information to store

6. Consists of two parts:

   • Sigmoid layer: Decides which values to update

   • Tanh layer: Creates candidate values to add to state

7. Formulas:

   • i_t = σ(W_i · [h_{t-1}, x_t] + b_i)

   • C̃t = tanh(W_C · [h{t-1}, x_t] + b_C)

8. Output Gate: Controls what information to output

9. Filters the cell state to create the output

10. Formula:

    • o_t = σ(W_o · [h_{t-1}, x_t] + b_o)

    • h_t = o_t * tanh(C_t)

Cell State Update Mechanism

The cell state update combines the forget and input gate operations: - C_t = f_t * C_{t-1} + i_t * C̃_t - This allows selective forgetting of irrelevant information while adding relevant new information

LSTM Variants

Several LSTM variants have been developed:

1. Peephole Connections: Allow gate layers to look at the cell state

2. Coupled Forget and Input Gates: Make forgetting and input decisions together

3. Gated Recurrent Unit (GRU): Combines forget and input gates into a single "update gate" and merges cell state with hidden state

Implementation Example

The implementation involves: 1. Initializing weight matrices and biases 2. Computing forget gate outputs 3. Computing input gate outputs and creating new candidate values 4. Updating the cell state 5. Computing output gate values and creating the hidden state

```python import numpy as np

def sigmoid(x): return 1. / (1 + np.exp(-x))

Forward pass for a single LSTM cell

xc = np.hstack((x, h_prev)) # Combine input and previous hidden state f_gate = sigmoid(np.dot(W_f, xc) + b_f) # Forget gate i_gate = sigmoid(np.dot(W_i, xc) + b_i) # Input gate