Deep Sequence Modeling: Building Foundations for Large Language Models

Welcome to the second lecture of 6.S191 on Deep Sequence Modeling! This lecture builds upon the basics of neural networks introduced in the first lecture and delves into applying these networks to problems involving sequential data. The goal is to provide a solid foundation in sequence modeling, preparing you for upcoming guest lectures on cuttingedge Large Language Models (LLMs).

Motivating Sequence Modeling with an Intuitive Example

Imagine tracking a ball in 2D space. Without any prior information, predicting its next position is simply a random guess. However, if you know the ball's past locations, the task becomes much easier. This illustrates the core concept of sequence modeling: predicting future states based on past history.

The Ubiquity of Sequential Data

Sequential data is everywhere. Examples include:

• Audio (sequences of sound waves)
• Text (sequences of characters or words)
• Medical signals (ECGs)
• Stock prices
• Biological sequences (DNA, protein)
• Weather patterns
• Motion video

Sequence modeling unlocks a wide range of applications for deep learning in the real world.

Problem Formulations in Sequence Modeling

Unlike basic classification problems that map a single input to a single output, sequence modeling deals with sequences of inputs and/or outputs. Examples include:

• Sentiment analysis: Processing a sentence and classifying its sentiment (positive or negative).
• Image captioning: Taking an image as input and generating a sequence of text to describe it.
• Machine translation: Translating a sequence of words from one language to another.

Recurrent Neural Networks (RNNs): The Foundation of Sequence Modeling

So, how do we build a neural network to handle sequential data? We'll start with **Recurrent Neural Networks (RNNs)**. The key idea behind RNNs is maintaining an **internal state** (h(t)) that is updated at each time step as the sequence is processed. This state acts as a form of memory, storing information about the past.

From Perceptron to RNN: Building Intuition

Consider a perceptron, which takes a set of inputs (X1...Xm) and produces an output (Yhat). While a perceptron can handle multiple inputs, it operates on a single time step, lacking a notion of sequence. A naive approach might be to feed sequential data to a perceptron at each time step independently. However, this ignores the inherent dependencies between time steps.

To address this, we introduce the concept of linking the neuron's internal state from a previous time step to the computation at a later time step. This internal state, h(t), is passed on across time, imbuing the network with a form of memory. Now, the prediction Yhat(t) depends not only on the current input but also on this past state.

This is a recurrence relation, where the output is a function of both the current input and the past state. This recurrent loop, visualized through time steps, is a foundational concept in sequence modeling.

Formalizing RNN Operations

The cell state h(t) is defined by a function parameterized by weights (W) that depends on both the input at time t and the prior state from time t1. This function is applied iteratively to update the cell state as the sequence is processed.

In pseudocode, an RNN can be visualized as looping through each word in a sentence, using the RNN to take that word, the last hidden state, predict some output, and then update the hidden state. This process is repeated iteratively.

The RNN updates its internal memory (hidden state) and produces a prediction (output) at each time step. The weights are reused at each time step in the sequence.

Training RNNs: Backpropagation Through Time

Training an RNN involves defining a loss function to measure the difference between predictions and desired behavior. A loss is computed at each time step, and the total loss is the sum of these individual losses. To train, we use **backpropagation through time**, where errors are backpropagated across individual time steps.

**Important consideration:** Standard RNNs can be difficult to train stably due to vanishing or exploding gradients, which makes tracking longterm dependencies challenging.

RNNs in Action: Music Generation

One compelling application of RNNs is music generation. By training an RNN on existing music, the model can learn to predict the next musical note in a sequence, effectively generating new pieces of music.

Limitations of RNNs and the Rise of Attention

Despite their capabilities, RNNs have limitations:

• The fixedlength state vector (h(t)) creates a bottleneck for information capacity.
• Sequential processing makes parallelization difficult.
• The encoding bottleneck can prevent longterm memory capacity.

These limitations have led to the development of new architectures, most notably those based on the **attention mechanism**.

Attention: Focusing on What Matters

The core idea of attention is to enable the model to focus on the most important parts of the input sequence. Instead of processing data time step by time step, attention allows the model to identify and attend to the relevant parts of the sequence in parallel.

The Search Analogy

Think of attention as a search process. You have a query (what you're looking for) and a database of keys (potential matches). The attention mechanism determines how similar the query is to each key and then extracts the value (the relevant information) associated with the best match.

SelfAttention in Detail

In sequence modeling, we use **selfattention**. Here's a breakdown:

1. Positional Embeddings: Add information about the position of words in the sequence.
2. Query, Key, and Value: Generate these matrices using neural network layers applied to the positionallyaware input.
3. Similarity Computation: Calculate the similarity between the query and key matrices (using dot product and scaling).
4. Attention Weights: Apply a softmax function to obtain weights representing the relative importance of each component in the sequence.
5. Weighted Value: Multiply the value matrix by the attention weights to extract the most important features.

Transformers: Attention is All You Need

The **Transformer** architecture, introduced in the 2017 paper "Attention is All You Need," relies heavily on the attention mechanism. It stacks multiple attention heads to increase network capacity and capture more complex feature relationships.

RealWorld Applications of Attention and Transformers

Attention and Transformers have revolutionized various fields:

• Natural Language Processing: Large Language Models (LLMs) like GPT utilize Transformers.
• Biological Sequences: Attention is used in modeling biological data.
• Computer Vision: Vision Transformers (ViTs) have emerged as powerful image processing models.

Conclusion

This lecture provided a foundational understanding of deep sequence modeling, starting with RNNs and culminating in the powerful attention mechanism used in Transformers. Stay tuned for upcoming lectures and handson labs exploring Large Language Models!