Sequence Modeling: A Deep Dive into Neural Networks

This blog post summarizes a lecture on sequence modeling with neural networks, covering recurrent neural networks (RNNs) and the more advanced Transformer architecture. We'll explore how these models handle sequential data and their applications.

Understanding Sequence Modeling

Sequence modeling deals with data where the order matters. Consider predicting the next position of a moving ball. Without knowing the ball's past trajectory, it's a random guess. However, knowing its previous positions allows for a much more accurate prediction. This principle applies to various forms of sequential data, like:

• Audio: Speech waveforms are sequences of sound waves.
• Text: Language is a sequence of characters or words.
• Medical readings: EKGs capture sequential heart activity.
• Financial markets: Stock prices evolve over time.
• Biological sequences: DNA and protein sequences encode life's blueprints.

The key is that the order and relationship between elements within the sequence are crucial for understanding and predicting future events.

Neural Networks for Sequence Data

We can extend basic neural networks for sequence modeling. Instead of a single input producing a single output, we can have:

• Sequence in, single out: Analyzing a sentence for positive or negative sentiment.
• Single in, sequence out: Generating a caption for an image.
• Sequence in, sequence out: Translating text between languages.

Recurrent Neural Networks (RNNs): A Foundation

The Core Idea: Recurrence

RNNs are designed to handle sequential data by incorporating the concept of a 'state'. This state, represented as H(t), captures information about the sequence up to a specific time step 't'. The state is updated iteratively as the network processes the sequence.

The output at time step 't' depends on both the input at that time step (X(t)) and the state from the previous time step (H(t1)). This creates a relationship between time steps, allowing the network to learn patterns and dependencies within the sequence.

Unrolling the RNN

An RNN can be visualized as a loop or 'unrolled' across time steps. This shows how the same model is applied repeatedly to each element in the sequence, updating its internal state at each step.

Mathematical Formulation

The state update is defined by a recurrence relation:

H(t) = f(W * [X(t), H(t1)])

Where:

• H(t) is the hidden state at time t
• X(t) is the input at time t
• W is a learned weight matrix
• f is a nonlinear activation function (e.g., tanh)

The choice of activation function can influence the network's performance. Besides tanh, ReLu can be used.

Training RNNs: Backpropagation Through Time (BPTT)

RNNs are trained using backpropagation, but with a twist. Since the network processes data sequentially, the error is backpropagated through time (BPTT). The loss is calculated at each time step, summed across the entire sequence, and then used to update the weights.

The Vanishing/Exploding Gradient Problem

A challenge with BPTT is the potential for vanishing or exploding gradients. Repeated matrix multiplications during backpropagation can cause gradients to become extremely small or large, hindering learning. This is especially problematic for long sequences with longterm dependencies.

Mitigating Gradient Issues

Several strategies can be used to address vanishing/exploding gradients:

• Activation function selection: Choosing activation functions that mitigate gradient shrinkage (e.g., ReLU).
• Weight initialization: Initializing weights carefully to avoid extreme values.
• Gated Recurrent Units (GRUs) and Long ShortTerm Memory (LSTMs): Using more complex recurrent cells with gating mechanisms to selectively remember or forget information. LSTMs are particularly effective at capturing longterm dependencies.

Gating uses learned weights to decide what information to keep or discard, leading to more robust state updates.

Applications of RNNs

RNNs have been successfully applied to various tasks, including:

• Music generation: Creating new musical pieces based on learned patterns from existing music.
• Sentiment analysis: Classifying the sentiment of a sentence (positive, negative, neutral).

Beyond RNNs: The Limitations and the Rise of Attention

RNN Limitations

Despite their usefulness, RNNs have limitations:

• Limited memory capacity: Encoding very long sequences can be challenging due to the bottleneck in the hidden state size.
• Computational slowness: Processing sequences time step by time step can be computationally intensive, especially for long sequences.
• Difficulty capturing longterm dependencies: Vanishing gradients can hinder the network's ability to learn relationships between distant elements in the sequence.

The Attention Mechanism: A Paradigm Shift

The attention mechanism offers an alternative to time stepbytime step processing. It allows the model to focus on the most relevant parts of the input sequence, regardless of their position. This is done by weighing each input element based on its relevance to the current context.

SelfAttention: Attending to the Input Itself

Selfattention is a specific type of attention where the model attends to different parts of the same input sequence. It's the foundation of the Transformer architecture.

The Analogy: Searching for Information

The attention mechanism can be understood through an analogy with searching for information in a database. A query is compared to a set of keys, and the most relevant value is retrieved.

Key Components of SelfAttention

1. Positional Encoding: Adding information about the position of elements in the sequence.
2. Query, Key, Value (Q, K, V): Transforming the input into three different representations: query, key, and value. These transformations are learned linear layers.
3. Attention Scores: Computing a similarity score between the query and each key, often using a dot product (cosine similarity).
4. Attention Weights: Normalizing the attention scores using a softmax function to obtain probabilities between 0 and 1.
5. Weighted Sum: Multiplying the values by the attention weights and summing them to produce a contextaware representation.

Putting it Together: A Single Attention Head

These steps form a single selfattention 'head'. Multiple attention heads can be used in parallel to capture different aspects of the input sequence. These heads can then be combined to form a richer representation.

Transformers: Building on Attention

The Transformer architecture is built on the selfattention mechanism. It stacks multiple attention heads and feedforward layers to create a powerful model for sequence processing. Transformers overcome many of the limitations of RNNs, allowing for parallel processing, longer memory capacity, and improved performance on a variety of tasks.

Applications of Transformers

Transformers have revolutionized various fields, including:

• Natural Language Processing (NLP): Tasks like machine translation, text generation, and question answering. Models like GPT and BERT are based on the Transformer architecture.
• Biology: Analyzing DNA and protein sequences.
• Computer Vision: Image recognition and object detection.

Conclusion

Sequence modeling is a fundamental problem in machine learning with diverse applications. RNNs provide a good starting point, but the attention mechanism and Transformer architecture offer significant advantages in terms of memory capacity, computational efficiency, and performance. The field is constantly evolving, with new architectures and techniques emerging to address the challenges of sequential data processing.