Understanding GPT Training with Transformers: A Comprehensive Guide
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The field of neural networks has witnessed remarkable advancements over the last few decades, shifting from rudimentary models to intricate architectures adept at tackling a variety of tasks. Initially, neural networks were basic feed-forward networks characterized by a unidirectional flow of information from input to output. As challenges arose with early models, more advanced architectures were conceived to overcome these limitations.
- Feed-forward networks (FFNs): These are the most basic form of artificial neural networks, where connections between nodes do not create cycles. They are typically employed for tasks involving fixed-size input and output vectors.
- Convolutional Neural Networks (CNNs): Tailored for data structured in a grid format, like images, CNNs utilize convolutional layers to autonomously learn spatial hierarchies of features, excelling in image classification and computer vision applications.
- Recurrent Neural Networks (RNNs): RNNs are specifically built to manage sequential data by retaining a ‘memory’ of preceding inputs. They are commonly used in tasks such as language modeling and time-series forecasting. However, RNNs face difficulties with long-range dependencies, often due to problems like vanishing gradients.
- Transformers: The introduction of the Transformer model by Vaswani et al. in their 2017 paper, “Attention is All You Need,” represented a pivotal moment in deep learning, especially for sequence-to-sequence tasks such as language translation and text summarization. Unlike RNNs, Transformers do not require the sequential processing of data, enabling parallelization that drastically reduces training times.
In this article, we will delve deeply into Transformer architecture and demonstrate how to train a GPT-like model from the ground up utilizing this architecture.
Why Study Transformers?
Transformer models are among the most significant breakthroughs in technology over the past decade. Their influence on artificial intelligence and machine learning is profound, transforming numerous sectors by enabling capabilities that were once thought unattainable for computing systems:
- Text Generation (Natural Language Processing): Transformers can produce human-like text with impressive fluency and coherence. Notable examples include ChatGPT, Claude, and Gemini.
- Image Generation (Computer Vision): These models can create highly realistic images that are often indistinguishable from real photographs. Examples include Midjourney, Firefly, and Dall-E.
- Advanced AI Agent Systems: In specific applications, Transformer-based models exhibit the capability to autonomously plan and execute actions, such as developing a comprehensive travel system using AI agents based on Transformers.
By gaining a thorough understanding of Transformer architecture and its functionality, professionals can position themselves at the cutting edge of technological advancements. This knowledge equips individuals with the necessary tools to employ these powerful models to solve complex, real-world problems across various industries.
Core Components of Transformers
Transformers are built upon several essential components:
- Self-Attention Mechanism: This is the fundamental innovation of the Transformer architecture, enabling the model to assess the significance of various words in a sentence, irrespective of their order. Each word in the input sequence is converted into query, key, and value vectors. The self-attention mechanism computes attention scores by taking the dot product of the query with all keys, followed by applying a softmax function to derive weights. These weights are then utilized to calculate a weighted sum of the values, yielding the self-attention output.
- Multi-Headed Self Attention: This extends the self-attention mechanism, allowing the model to concentrate on different segments of the input sequence simultaneously. It employs multiple sets of query, key, and value vectors, enabling the model to capture diverse types of relationships and dependencies within the data.
- Positional Encoding: Since Transformers do not process sequences in order by default, positional encodings are added to input embeddings to convey information regarding the position of words within the sequence.
- Feed-Forward Networks: After the attention layers, the output is directed through a feed-forward neural network, which operates independently at each position.
- Layer Normalization and Dropout: These techniques are utilized to stabilize and regularize the training procedure.
The Rise of Transformers
Transformers have gained popularity due to their proficiency in managing long-range dependencies and their efficiency in processing sequences in parallel. This has established them as the preferred architecture for many state-of-the-art models in natural language processing, including BERT and GPT. Their adaptability has also led to applications beyond NLP, extending into computer vision and audio processing.
Imagining a World Without Self-Attention
The self-attention mechanism is critical for comprehending how Transformers process sequences:
To grasp the concept of a world without self-attention, consider that computers do not inherently understand text; therefore, we must convert it into numerical representations for processing. One approach is assigning a unique number to each word in the vocabulary and representing it as a one-hot encoded vector.
For instance, given a small text corpus containing the words “apple,” “banana,” and “orange,” the vocabulary would be:
- “apple” ? index 0
- “banana” ? index 1
- “orange” ? index 2
The one-hot encoded vectors would appear as follows:
- “apple” ? [1, 0, 0]
- “banana” ? [0, 1, 0]
- “orange” ? [0, 0, 1]
These vectors can be provided to the machine for further processing. However, this representation presents two notable challenges:
- High Dimensionality: One-hot encoding generates high-dimensional sparse vectors, especially with extensive vocabularies, leading to elevated computational demands.
- Absence of Semantic Relationships: This method fails to capture any semantic or contextual relationships among words. For instance, “apple” and “fruit” would have entirely distinct vectors, despite their related meanings.
As a result, a more effective method for word representation involves using word embeddings (e.g., Word2Vec, GloVe). These techniques encapsulate relationships between words through dense vectors, operating on the principle of “You shall be known by your neighbors.” This means words that frequently co-occur are positioned closer together in the embedding space. These models are trained on vast text corpuses from books and online documents to discern which words commonly appear together (or not).
In the illustration above, words with similar semantic meanings are located close to each other; for instance, "king" and "queen" are adjacent, as are "paint" and "color." Conversely, "paint" and "garden" are positioned further apart.
Word2Vec can also capture analogies through vector arithmetic. For example, the relationship “king is to queen as man is to woman” can be expressed as:
vector(king) - vector(man) + vector(woman) = vector(queen)
This illustrates how Word2Vec captures both semantic and syntactic relationships between words.
However, a limitation of Word2Vec is its assignment of a fixed vector to each word, regardless of context. Consider the following two sentences:
- The river bank is a great place for a picnic.
- The bank will close soon, so we should hurry to deposit the check.
In these sentences, the word “bank” would retain the same vector in any context, leading to ambiguity as Word2Vec fails to differentiate between “bank” as a financial institution and “bank” as the side of a river. Thus, Word2Vec lacks contextual comprehension.
Moreover, Word2Vec primarily focuses on local context (usually within a fixed window size), which may not suffice for capturing long-range dependencies in sentences or documents. Consider this example:
- She decided to run the marathon because she enjoys running.
Here, "marathon" and "running" are related concepts, yet Word2Vec may not effectively capture this connection.
Exploring Self-Attention in Depth
Self-attention is a mechanism employed in transformer models that allows them to concentrate on various parts of an input sequence to grasp the context and relationships between words.
Imagine reading a sentence and trying to interpret the meaning of each word based on surrounding words. Self-attention operates similarly, enabling a model to “pay attention” to different words in a sentence to discern their significance and relationships.
It is important to note that self-attention builds upon Word2Vec embeddings by updating these embeddings using contextual attention scores.
Mechanism Overview
- Each Word Evaluates Every Other Word: In a sentence, each word is compared with every other word to gauge how much attention it should give them. This is akin to asking, “How crucial is this word for understanding another word's meaning?”
- Assigning Importance: Each word is assigned a score relative to every other word in the sentence, with higher scores indicating greater importance for contextual understanding.
- Creating a Contextual Representation: The scores are utilized to generate a weighted sum of all words, yielding a new representation for each word that incorporates context from other words.
Consider the following example.
In this scenario, the word “history” is more closely associated with the word “subject” than with any other term. Similarly, “favorite” is more closely linked to “subject” than to anything else. This process is known as self-attention.
Now consider another instance involving the word "history."
In this case, “history” has a stronger connection with the words “late” and “she” than with any other word. Likewise, “meetings” is more associated with “she” than with anything else.
Essentially, the embeddings of the same word are influenced by other words in the current context, necessitating adjustments based on the context. This is what self-attention entails: computing how each word relates to every other word in the sentence and subsequently updating the original embeddings using this score. The new embeddings are now enriched with contextual relevance.
Here are the attention scores of every word concerning every other word in the sentence.
Below is a visual representation of the process for computing contextual embeddings from plain embeddings.
Multi-Headed Self-Attention
In the transformer architecture, a feed-forward layer is added atop the attention block. Multiple attention blocks can address different types of attention. For instance, one attention head could concentrate on syntactical aspects, while another might focus on semantic elements, and a third could tackle coreference attention.
Syntactic Attention
- Purpose: Concentrates on the grammatical structure of the sentence.
- Example: In the sentence “The quick brown fox jumps over the lazy dog,” syntactic attention might help identify that “quick” and “brown” describe “fox,” while “lazy” describes “dog.”
Semantic Attention
- Purpose: Examines the meanings and relationships between words based on their context.
- Example: In a sentence like “She poured the water into the glass,” semantic attention might connect “poured” with both “water” and “glass” to comprehend the action being described.
Coreference Attention
- Purpose: Assists in resolving references within the text.
- Example: In the sentences “John grabbed his coat. He was in a hurry,” coreference attention helps clarify that “He” refers to “John.”
Contextual Attention
- Purpose: Focuses on the broader context of the sentence or paragraph.
- Example: In a paragraph discussing a complex idea, contextual attention aids the model in maintaining a coherent understanding of the overall theme and how each sentence contributes to it.
Cross-Sentence Attention
- Purpose: Captures relationships between sentences in longer texts.
- Example: In a narrative, cross-sentence attention might help link the current sentence with a previous one that offers crucial background information.
Collaboration of Attention Heads
Each attention head processes the input sequence independently, concentrating on various aspects as detailed above. With multiple heads, the Transformer can capture a broad spectrum of relationships and features within the sequence.
The outputs from all these heads are then concatenated and passed through a linear layer, allowing the model to amalgamate these diverse perspectives into a richer, more nuanced representation of the input. Finally, the outputs are processed through the softmax layer to convert logits into probabilities.
This multifaceted approach is one of the reasons why Transformers excel in tasks such as translation, summarization, and more, as they can simultaneously comprehend various layers of meaning and structure within the text.
Attention Score Computation Using Query (Q), Key (K), and Value (V) Vectors:
Let’s delve deeper into how attention scores are computed.
- Compute Q Vector: Initially, we take input embeddings and multiply them by the WQ vector to generate the Queries vector. The Queries vector has the same number of rows as the input vector but is smaller in size.
- Compute K Vector: Next, we take input embeddings and multiply them by the WK vector to produce the Key (K) vector. The Key vector also shares the same number of rows as the input vector but is smaller in size.
Both WQ and WK are hyperparameters that are optimized during training.
Intuition Behind Q and K Vectors: A Q vector functions like a question vector that can be posed to a word to obtain information about other words in a sentence. For instance, “What verbs are related to this word?” The Q vector embodies this inquiry. The K vector provides keys that answer these questions posed by queries. These two vectors facilitate understanding which queries correspond to which keys.
- Compute Similarity Between Q and K Vectors: Now, we need to ascertain which questions match the keys. We achieve this by computing the dot product of the Q and K vectors. A dot product close to 0 signifies similarity between the two vectors, and vice versa. We must transpose the K matrix to align the dimensions of the Q and K vectors.
We must normalize the dot product using the softmax function.
- Compute V Vector: The V vector is calculated by multiplying input embeddings with the WV vector.
We then multiply the normalized dot product with the V vector (Value vector). The resulting vector is now an updated embedding vector that incorporates an attention score.
Below is a diagram illustrating all three steps together.
This mechanism enables the Transformer to dynamically focus on various sections of the input sequence, capturing intricate dependencies and relationships.
Up to this point, we've examined attention score computation for a single head.
Multi-Headed Self-Attention: In models such as GPT, we typically compute multiple attention heads for different types of attention, including semantic attention, coreference attention, and syntactic attention, as previously outlined. This is accomplished by dividing input embeddings into multiple segments (denoted as N) and subsequently repeating the Q, K, and V vector computation for each segment. The Q, K, and V vectors are distinct for each attention segment. Ultimately, we concatenate the updated embeddings to form a new embedding vector that reflects attention from N different heads.
We have omitted finer details of how attention is computed to simplify the explanation. Now it's time to reintroduce them. Before applying softmax, we divide the dot product of Q and K by the square root of the size of K vectors. This is done to prevent attention scores from becoming excessively large, which could destabilize the model. The following equation represents the final attention score.
Masking
Transformers are trained using self-supervised data. We input a sequence of text and aim to predict the same sequence shifted by one token, as illustrated below.
Typically, we present a sequence to the Transformer that has access to future tokens. This could allow the model to "cheat" by leveraging future tokens. To prevent this, we implement preemptive masking and only provide attention scores that compute the next token. Here’s how masking is executed.
Recall that we calculate the dot product of the Q and K vectors as part of the attention score.
To restrict the model from accessing future tokens, we initialize the values below the diagonals to -infinity.
We can then pass these values through the softmax function, which converts these -inf values to 0.
Here’s an updated diagram of attention score computation where we incorporate this masking step just after the dot product calculation.
Dropout Layer
Transformers are generally deep models featuring multiple layers of attention mechanisms and feed-forward neural networks. Due to their complexity, they are susceptible to overfitting, particularly when trained on smaller datasets or when the model is exceptionally large (as is the case with large language models). Overfitting occurs when a model excels on training data but fails to generalize to unseen data. This often arises when the model's complexity exceeds the available training data, enabling it to memorize specific details rather than learning general patterns.
The Dropout layer aids in mitigating overfitting by randomly “dropping out” or zeroing a proportion of neurons (and their corresponding connections) during training. This compels the network to learn more robust features, as it cannot overly rely on any particular neuron. By preventing any individual neuron from becoming overly dominant or overly reliant on specific features during training, dropout fosters the model’s ability to distribute its learned features across multiple neurons. This generally leads to improved generalization when the model is applied to new data.
Dropout is implemented in various sections of the Transformer architecture, such as following the attention mechanisms and within the feed-forward layers, to ensure that the model does not become overly dependent on specific parts of its structure and to enhance its ability to generalize across diverse tasks and datasets.
Gaining expertise in training models with Transformer networks from scratch is crucial for comprehending the underlying mechanics of many modern deep-learning models. Their capacity to efficiently manage complex, long-range dependencies, along with their extensive applicability across various domains, makes them a vital subject of study in machine learning. We will continue to delve into the specifics of coding transformer training in the next installment.
References:
- NanoGPT repo by Andrej Karpathy