1. Description
Self-attention layers provide an efficient way to capture dependencies in sequential data such as time series. The key intuition behind using self-attention for time series/sequence analysis is its ability to assign different importance weights to different steps in the input sequence, enabling the model to focus on the most relevant parts of the input for prediction.
content
- How does it work? Simplified way of understanding
- the mathematics of self-attention
- location code
- Intuition behind calculating weights
- query, key and value
- Attention Layer Input: Word Embeddings
- multi-headed attention
- Self-Attention, RNN, 1D CONV
- Transformer model
2. How does it work? A simplified way of understanding.
Here's a simplified way to understand it:
- Capturing long-term dependencies: Traditional sequential models, such as recurrent neural networks (RNNs) and their variants (such as LSTMs and GRUs), sometimes struggle to resolve long-term dependencies due to issues such as vanishing gradients . However, self-attention can capture dependencies between any two points in a sequence, regardless of their distance. This capability is particularly valuable in time series analysis, since past events, even those in the distant past, can influence future forecasts.
- Weighted importance : Self-attention computes a weight that represents the importance or relevance of a particular timestep to other timesteps. For example, in a time series of stock prices, the model can learn to pay more attention to the time steps corresponding to major market events.
- Parallelization : Unlike RNNs, which process data sequentially, self-attention operates on the entire sequence simultaneously, allowing parallel computation. This makes it faster and more efficient when working with large time series.
- Interpretability: Self-attention layers can provide a form of interpretability , as attention weights provide insight into the time steps the model believes are important for each prediction.
3. The mathematics of self-attention
In the attention mechanism, given a set of vector values and a vector query, attention computes a weighted sum of values based on the query and a set of key vectors. Queries, keys, and values are all vectors; their dimensionality is a parameter of the model, and they are all learned during training.
The specific type of attention used in Transformers is called scaled dot product attention. Here's how it works:
- Compute the attention score: For each query and key pair, compute the dot product of the query and the key. This will generate a number representing a "match" between the query and the key. This is done for all query key pairs.
- Scaled score: The score is then scaled by dividing it by the square root of the query/key vector dimension. This is done to prevent the dot product from growing too large as the number of dimensions increases.
- Apply softmax: Next, a softmax function is applied to these scaled fractions for each query. This ensures that the fractions are positive and sum to 1. This allows them to be used as weights for weighted sums.
- Compute the output: Finally, the output of each query is computed as a weighted sum of value vectors, using the softmax outputs as weights.
Mathematically, it can be expressed as follows:
Note that (Q, K, V) = SoftMax((QKT)/sqrt(dk)) V
here:
- Q is the query matrix.
- K is a matrix of keys.
- V is a matrix of values.
- dk is the dimension of the query/key.
- The operation QK^T represents the dot product of Q and the transpose of K.
This process is performed for each position in the input sequence, allowing each position to pay attention to all other positions in a weighted manner, with weights determined by the compatibility between the query and each key.
4. Position code
Positional encoding is a technique used to provide the model with some information about the relative position of words in a sentence.
Transformers are based on a self-attention mechanism, which essentially does not take into account the order of words in a sentence. This is different from models like RNNs or LSTMs, which process the input sequentially and thus naturally incorporate word positions.
Positional encodings are added to the input embeddings (representing words) before being passed to the self-attention layer. Positional encodings are vectors that encode the position of words in a sentence. These vectors are designed in such a way that the model can easily learn to focus on words based on the distance between them.
The exact form of the location code may vary. In the original transformer model, positional codes are created using specific formulas involving sine and cosine functions. However, other forms of positional encodings, such as learned positional encodings, are also possible.
In the figure, the positional encoding is represented as a separate step after the input embedding, but in practice, the positional encoding is usually added to the embedding before passing to the self-attention layer.
5. The intuition behind calculating weights
In self-attention mechanisms, the importance of a step is intrinsically linked to the content of that step. For example, consider Transformer architectures that use self-attention in natural language processing tasks. The model computes for each word in the input a set of attention scores (the "importance" of a step) that indicate how many other words should be considered when encoding the current word into a context-sensitive representation.
The self-attention mechanism essentially considers the entire input sequence and determines the importance of each word to the current word based on its semantic and syntactic relationship. This relationship is determined by computing the dot product of the query vector (representing the current word) and the key vector (representing the other word). Then there is a SoftMax operation to ensure that the sum of all attention scores is 1.
These query, key (and value) vectors are learned during training, so the importance of a word (and its relation to another word) can vary depending on the context in which it is used. The attention weights essentially form a distribution over the input sequence, indicating which words are important in encoding the current word. Therefore, the learned importance weights (attention scores) are indeed content-dependent and associated with specific words. The context of each word (i.e. its relationship to other words in the sequence) determines how much attention the model pays to that word when encoding different words in the sequence. For example, if you are processing the sentence "the black cat sat on the mat", then when encoding the word "cat", the self-attention mechanism might assign high attention scores to "black" and "sat", indicating that these words are important for understanding The context of "cat" in this sentence is important.
6. Query, key and value
The layer's input is transformed into query, key, and value vectors by multiplying by three different weight matrices learned during training. The query and key vectors are used to compute attention scores, which determine how much attention is paid to each part of the input. A vector of values is then used to create weighted combinations based on these scores. This weighted combination is the output of the self-attention layer.
The key and value vectors in the attention mechanism are derived from the input embeddings, and both play different roles:
- Key Vectors (K): Key vectors are used to compute attention scores. In the context of a sentence or sequence, they represent the "contextual identity" of a word and are used for attention scoring. Each word in a sentence is associated with a key, which is used to compute the dot product over the query to compute the attention score. This score reflects the relevance of the word associated with that key to the word represented by the query.
- Value Vector (V): The value vector is used for the calculation of the weighted sum after applying the SoftMax function to the attention scores. They are what are averaged together to form the output of the attention layer. In a way, you can think of the value vector as "content" weighted by the attention score.
Essentially, the keys are used to determine "how to pay attention", i.e. they compute a compatibility score with the query, and the values are used to determine "what to pay attention to", i.e. they contribute to the final output based on the attention score.
In a sentence, compute a query, a key, and a value for each word. A word-specific query interacts with all keys (including itself) to compute an attention score, which is then used to weight the values.
For example, if we have the sentence "the cat sat on the mat", when processing the word "sat", the model will use the query associated with "sat", and use the query associated with "The", "cat", "sat", "on ", "the" and "mat" to compute their dot product. This will result in an attention score indicating that the model should focus on each of these words when trying to understand the meaning of "sat". These scores are then used to weight the value vectors associated with each word and summed to produce the output.
It's important to note that queries, keys, and values are not explicitly linked to specific words or meanings. They are learned during training, and the model determines how best to use them to accomplish the task for which it was trained.
Seven, attention layer input: word embedding
In machine learning, a model does not "understand" or "remember" words the way humans do. Instead, they represent words numerically and learn patterns in those representations. There are various ways to numerically represent words, such as bag-of-words, TF-IDF, and word embeddings.
The most common approach in deep learning models, such as Transformers, is to use word embeddings. Here's a simplified explanation of how it works:
- Word Embeddings: Each word in the vocabulary is mapped to a real vector, forming its word embedding . This vector is typically several hundred dimensions long. These vectors are initially assigned randomly.
- Contextual learning: During training, the model adapts word embeddings based on the context in which each word occurs. Words that frequently appear in similar contexts will have similar embeddings. So, for example, "cat" and "kitten" might end up with similar embeddings because they are both frequently used in sentences about pets.
- Backpropagation and Optimization: Learning is done through a process called backpropagation . The model makes predictions based on the current embedding, and then calculates the error between those predictions and the actual value. This error is then used to adjust the embeddings so that the predictions are closer to the actual values.
- Capturing meaning: Over time, these word embeddings begin to capture both semantic and syntactic meaning . For example, the model might learn that "cat" and "dog" are more similar to each other (both are pets) than "cat" and "car".
In a self-attention model like Transformers, these word embeddings are then used as input to a self-attention layer, where the relationships between different words are further modeled. Each word is not only represented by its own embedding, but also influenced by the embeddings of the words it interacts with in the sentence, allowing a rich, context-sensitive representation of each word.
It is important to note that the model will not "understand" words the way humans do. It doesn't know that cats are small, typically furry, domesticated, carnivorous mammals. It only knows representations of numbers it has learned and the patterns in those numbers. The semantic relationships it learns are purely based on patterns in the data it was trained on.
Eight, multi-headed attention
Multi-head attention is a key component of the Transformer model architecture, used to allow the model to focus on different types of information.
The intuition behind multi-head attention is that by applying the attention mechanism multiple times in parallel (these parallel applications are "heads"), the model can capture different types of relationships in the data.
Each attention head has its own learned linear transformation that is applied to the input embeddings to obtain its queries, keys and values. Because these transitions are learned separately, each head has the potential to learn to focus on different things. In the context of natural language processing, this might mean that one head learns to pay attention to syntactic relations (such as subject-verb agreement), while another head can learn to pay attention to semantic relations (such as word synonyms or topic roles).
For example, when processing the sentence "the cat sat on the mat," one attention head might focus on the relationship between "cat" and "sitting," capturing the information that the cat is the person sitting, while the other head might focus more on the relationship between "cat" and "sitting." Focus on the relationship between "sit" and "cushion", capturing information about where sitting occurs.
Then, the outputs of all heads are concatenated and linearly transformed to form the final output of the multi-head attention layer. This means that the different types of information captured by each header are combined to form a unified representation.
By using multiple heads, Transformers allow for a more complex and nuanced understanding of the input than can be achieved with a single attention mechanism application. This helps in part to increase their effectiveness on a wide range of tasks.
There is no straightforward mechanism to ensure that each attention head learns something different during training. Instead, this behavior emerges naturally from the stochastic (stochastic) nature of the training process and the fact that each attention head starts with different random initialization parameters.
The reasons are as follows:
- Random initialization: Weights in neural networks are usually initialized with small random values. Since each attention head has its own set of weights, they start at different positions in the weight space.
- Stochastic Gradient Descent: Neural networks are often trained using a variant of stochastic gradient descent. This involves showing the model a small randomly selected batch of training data, calculating the error the model made on this batch, and adjusting the model's weights to reduce this error. Because of the randomness involved in choosing these batches, each head may see slightly different patterns in the data, causing them to learn different things.
- Backpropagation: During backpropagation, each head receives a different error signal (gradient) due to the different initial parameters and the nature of the learning process. These different error signals push the weight of each head in a different direction, further encouraging them to learn different things.
It's worth noting, however, that the aforementioned factors just predispose each mind to learn different things. Not guaranteed. In practice, some heads may learn similar or even redundant representations. This is an ongoing area of research in deep learning, with various regularization techniques proposed to encourage more diversity in the representations learned by each head.
Furthermore, while the goal is to have different principals learn different aspects of the data, it is important that they all learn useful information for the task at hand. So it's a balance between encouraging diversity and ensuring that each head contributes to the overall performance of the model.
9. Self-attention, RNN, 1D CONV
9.1 Self-focus
Pros : Self-attention, especially in the form of Transformer models, allows parallel computation, which greatly speeds up training. It also captures dependencies between elements regardless of their distance in the sequence, which is beneficial for many NLP tasks.
Cons : Self-attention has quadratic computational complexity with respect to sequence length, which can make it inefficient for very long sequences. Furthermore, it does not capture positional information in the sequence by itself, thus requiring positional encoding.
Applications : Self-attention is widely used in NLP tasks such as translation, summarization, and sentiment analysis. The self-attention-based Transformer model is the basis of models such as BERT, GPT, and T5.
Computational requirements: Due to its quadratic complexity, self-attention requires more memory, but it allows parallel computation , which can speed up training.
9.2 RNN
Pros : RNNs are good at processing sequences and can capture dependencies between elements that are close together in a sequence. They are also relatively simple and have been widely used for many years.
Cons : RNNs suffer from vanishing and exploding gradient problems, which make them difficult to train on long sequences. They also process sequences sequentially, which prevents parallel computation and slows down training.
Applications : RNNs are used in many NLP tasks, including language modeling, translation, and speech recognition.
Computational requirements : RNNs have lower memory requirements than self-attention, but their inability to process sequences in parallel makes training slower.
9.3 Transform 1D
Pros : Conv1D can capture local dependencies and is more efficient than RNNs because it allows parallel computation. It is also less prone to vanishing and exploding gradient problems.
Cons : Conv1D has a fixed receptive field, which means it may not be able to capture long-term dependencies as well as self-attention or RNNs. It also requires careful choice of kernel size and number of layers.
Applications : Conv1D is often used for tasks involving time-series data, such as audio signal processing and anomaly detection in IoT data. In NLP, it can be used for text classification and sentiment analysis.
Computational requirements: Conv1D is more efficient than RNNs and self-attention in terms of memory and computation , especially for tasks involving local dependencies.
10. Transformer model
The transformer model introduced by Vaswani et al. in the paper "Attention is all you need" consists of an encoder and a decoder, each of which consists of a bunch of identical layers. In turn, these layers mainly consist of two sublayers: a multi-head self-attention mechanism and a positional fully-connected feed-forward network.
Let's review each component:
- Multi-head self-attention mechanism : The self-attention mechanism allows the model to weigh and encode different words in the input sequence according to their relevance to the word currently being processed. Multi-head attention allows the model to capture different types of relationships (e.g., syntactic, semantic) between words.
- Fully Connected Feedforward Network by Location: This is a standard feedforward neural network that is applied independently to each location. It is used to transform the output of the self-attention layer. While the self-attention layer helps the model understand the contextual relationship between words, the feed-forward network helps the model understand the words themselves.
- Residual connections and layer normalization: Each of the two sublayers (self-attention and feed-forward) in the Transformer layer has residual connections around it, followed by layer normalization . This helps alleviate the vanishing gradient problem and enables efficient training of models when stacked into deep architectures.
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The architecture of the transformer layer. Layers with trainable parameters are shown in orange
The key intuition behind stacking multiple Transformer layers is the same as in any deep learning model: each layer in the model has the potential to learn to capture a different level of abstraction. In the context of language, lower layers might learn to understand simple syntactic structures, while higher layers might learn to understand more complex semantics.
For example, in the sentence "the black and white cat sat on the mat", lower layers might focus on understanding local relationships between adjacent words, while higher layers might learn to understand the overall structure of the sentence and the "black and white" provided Facts with additional information about "cat".