Understanding Transformers and Sequence Modeling in Machine Learning

The Evolution of Sequence Modeling in Machine Learning

Sequence modeling is a fundamental task in machine learning that deals with data points that are sequences. Each data point in a sequence model is a series of vectors, typically represented as X = (x1, x2, ..., xT), where each xj is a D-dimensional vector. Common examples of sequence data include:

• Sentences (sequences of linguistic tokens)
• Speech signals (sequences of frequency domain vectors)
• Industrial time series data
• Videos (sequences of image frames)

The goal of sequence modeling is to solve either discriminative or generative problems on these sequences. Some key applications include:

• Machine translation
• Text summarization
• Video classification
• Spam detection

Over the years, researchers have developed increasingly sophisticated approaches to handle sequential data. Let's explore the evolution of sequence modeling techniques, culminating in the powerful Transformer architecture that underlies modern large language models.

Early Approaches: Autoregressive Models

In the early days of sequence modeling, simple autoregressive (AR) models were a common approach. The basic idea was to model each element in the sequence as a linear combination of previous elements:

xt = a1xt-1 + a2xt-2 + ... + ak*xt-k

Where a1, a2, etc. are coefficients learned from data. This allowed the model to capture short-term dependencies in the sequence. However, AR models were limited in their ability to model complex, long-range dependencies.

Hidden Markov Models

Hidden Markov Models (HMMs) were a major advancement in sequence modeling, particularly for tasks like speech recognition. HMMs model the sequence as a Markov chain of hidden states, with each state emitting an observable symbol.

The key components of an HMM are:

• A set of hidden states
• Transition probabilities between states
• Emission probabilities for observing symbols given a state

HMMs could capture more complex dependencies than simple AR models. However, they still made strong independence assumptions that limited their power for many real-world sequences.

Recurrent Neural Networks

The rise of deep learning led to Recurrent Neural Networks (RNNs) becoming the dominant approach for sequence modeling in the 2010s. RNNs addressed a key limitation of feedforward neural networks - the ability to handle variable-length input sequences.

The core idea of RNNs is to share parameters across different time steps in the sequence. A basic RNN cell takes the current input xt and the previous hidden state ht-1 to produce an output yt and the next hidden state ht:

ht = tanh(Wxh * xt + Whh * ht-1 + bh) yt = Why * ht + by

Where W and b are learnable weight matrices and bias vectors.

This recurrent structure allows RNNs to theoretically capture long-range dependencies in sequences. In practice, vanilla RNNs struggled with issues like vanishing gradients for very long sequences. This led to more advanced architectures like Long Short-Term Memory (LSTM) networks.

Encoder-Decoder RNNs

For sequence-to-sequence tasks like machine translation, encoder-decoder RNN architectures became popular. These models consist of:

• An encoder RNN that processes the input sequence and produces a fixed-length context vector
• A decoder RNN that generates the output sequence conditioned on the context vector

While powerful, these models still faced challenges in capturing very long-range dependencies and handling very long sequences.

Attention Mechanisms

A key breakthrough came with the introduction of attention mechanisms. The core idea is to allow the decoder to focus on different parts of the input sequence when generating each output element.

Instead of encoding the entire input into a single fixed-length vector, attention allows the model to create a different context vector for each decoding step. This context vector is a weighted sum of the encoder hidden states, where the weights are learned based on relevance to the current decoding state.

Mathematically, for decoding step t:

context_t = sum(alpha_ti * h_i)

Where h_i are the encoder hidden states and alpha_ti are attention weights computed based on the relevance of h_i to the current decoder state.

Attention mechanisms dramatically improved performance on tasks like machine translation, allowing models to handle much longer sequences effectively.

The Transformer Architecture

The Transformer architecture, introduced in the landmark 2017 paper "Attention Is All You Need", took the idea of attention to its logical conclusion - what if we build a model using only attention, without any recurrence?

The key innovation of Transformers is the self-attention mechanism. Unlike previous attention models that computed attention between encoder and decoder states, self-attention allows a sequence to attend to itself.

Self-Attention in Transformers

The self-attention mechanism in Transformers works as follows:

1. For each input token xi, compute query, key, and value vectors:

   • qi = Wq * xi
   • ki = Wk * xi
   • vi = Wv * xi

2. For each position j, compute attention scores with every other position:

   • score_ij = (qi * kj) / sqrt(dk)

3. Apply softmax to get attention weights:

   • alpha_ij = softmax(score_ij)

4. Compute the weighted sum of values:

   • zi = sum(alpha_ij * vj)

This allows each position to attend to all other positions in the sequence, capturing complex dependencies without the need for recurrence.

Multi-Head Attention

Transformers use multi-head attention, which involves running multiple self-attention operations in parallel and concatenating the results. This allows the model to attend to information from different representation subspaces.

Positional Encoding

Since Transformers don't have an inherent notion of sequence order, positional encodings are added to the input embeddings to inject information about token positions.

Transformer Blocks

A full Transformer model consists of stacked encoder and decoder blocks. Each block contains:

• Multi-head self-attention layers
• Feed-forward neural networks
• Layer normalization
• Residual connections

This architecture allows Transformers to process entire sequences in parallel, making them much faster to train than RNNs on modern hardware.

Training Large Language Models

The Transformer architecture forms the backbone of modern large language models (LLMs) like GPT-3. The typical training process for these models involves:

1. Self-supervised pre-training on massive text corpora
2. Supervised fine-tuning on specific downstream tasks

Self-Supervised Pre-training

The pre-training phase typically uses a masked language modeling objective:

1. Take a text sequence and randomly mask some tokens
2. Train the model to predict the masked tokens

This allows the model to learn rich contextual representations of language without requiring labeled data.

Supervised Fine-tuning

After pre-training, the model can be fine-tuned on specific tasks using supervised learning. This often involves adding task-specific layers on top of the pre-trained Transformer.

For very large models, fine-tuning all parameters may be impractical. Techniques like low-rank adaptation (LoRA) allow efficient fine-tuning by updating a small number of parameters.

Conclusion

The evolution of sequence modeling techniques from simple autoregressive models to sophisticated Transformer architectures has revolutionized natural language processing and many other domains. Transformers and their variants now power state-of-the-art models for a wide range of tasks, from machine translation to protein structure prediction.

As research continues, we can expect further innovations in architecture design, training techniques, and applications of these powerful sequence models. The rapid progress in this field highlights the importance of understanding the fundamental principles behind these models, even as they grow in scale and capability.

Article created from: https://youtu.be/6eKnv52CTPM?feature=shared