Deep Learning for Audio: Long Short-Term Memory Networks (LSTM) Lecture Notes

Introduction

• Welcome to the video series on deep learning for audio.
• This session focuses on Long Short-Term Memory (LSTM) networks.

Review of Previous Content

• Previous video covered simple Recurrent Neural Networks (RNNs).
• RNNs are effective for time series data but have limitations:
  • Lack of long-term memory.
  • Difficulty learning patterns with long dependencies.

Importance of LSTMs

• LSTMs introduced to address RNN limitations:
  • Can learn longer-term patterns.
  • Useful in tasks with long dependencies, such as audio/music generation.
• However, LSTMs still struggle with very long sequences (hundreds/thousands of steps).

LSTM vs. Simple RNN

• Comparison of LSTM architecture with simple RNNs.
• Simple RNN:
  • Composed of a dense layer with tanh activation.
  • Inputs at time T and previous state vector are concatenated.
  • Outputs are the new state vector and output.
• LSTM Structure:
  • Similar structure but includes additional components (memory cells).
  • Capable of learning longer-term patterns due to its architecture.

LSTM Cell Overview

• An LSTM cell has:
  • Memory cell for long-term information (cell state).
  • Hidden state for short-term information.
  • Gates: forget gate, input gate, output gate (act as filters).

Components of LSTM Cell

1. Input (XT): Data point in the sequence.
2. Output (HT): Output of the cell; linked to the hidden state.
3. Cell State (CT): Responsible for long-term memory storage.
4. Hidden State: Represents short-term memory.

Gate Functions

Forget Gate

• Decides what information to forget from the cell state.
• Uses sigmoid activation function to create a forget matrix (FT).
• Element-wise multiplication with previous cell state to determine what to retain.

Input Gate

• Decides what new information to add to the cell state.
• Combines the hidden state and input data using a sigmoid function to create an input matrix (IT).
• New cell state (CT') is calculated using tanh activation function.
• Element-wise multiplication with IT decides what to keep from the new input.

Update Cell State (CT)

• Element-wise sum of filtered previous cell state (CTF) and new input (CTI) gives the current cell state.

Output Gate

• Determines the next hidden state (HT) using the current cell state.
• Output is produced by applying the sigmoid function and tanh activation to the cell state and hidden state.

Summary

• LSTMs are efficient in retaining long-term and short-term memories.
• They have various components that work together to enhance learning from sequential data.
• Key concepts learned: cell states, hidden states, and gate functions (forget, input, output).

Next Steps

• Transition from theory to implementation.
• Upcoming video will focus on preprocessing data for RNNs.

Conclusion

• Encourage viewers to ask questions in the comments.
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