Concatenation and Linear Transformation

In GPT-J, the concatenation and linear transformation step of the attention mechanism is typically implemented using matrix multiplication and addition operations. Specifically, the output vectors from each head are concatenated along the feature dimension, resulting in a tensor of shape (batch_size, sequence_length, hidden_size x num_heads), where hidden_size is the dimensionality of the input and output vectors for each head, and num_heads is the number of attention heads.

The concatenated tensor is then multiplied by a learned weight matrix WO of shape (hidden_size x num_heads, hidden_size) to obtain a tensor of shape (batch_size, sequence_length, hidden_size). This matrix multiplication applies a separate linear transformation to each feature dimension of the concatenated tensor, allowing the model to learn a separate set of weights for each head.

Finally, the transformed tensor is passed through a bias vector bO of shape (hidden_size,), which is added element-wise to each vector along the feature dimension. This bias term is also learned during training and allows the model to learn a separate bias for each feature dimension.

The overall operation can be written as follows, using matrix notation:

# Input tensors
Q, K, V # shape (batch_size, sequence_length, hidden_size)
WQ, WK, WV, WO # learned weight matrices
bO # learned bias vector

# Compute attention weights
scores = tf.matmul(Q, K, transpose_b=True) / tf.math.sqrt(tf.cast(hidden_size, tf.float32))
weights = tf.nn.softmax(scores, axis=-1)
attention = tf.matmul(weights, V)

# Concatenate and transform output vectors
concatenated = tf.concat(tf.unstack(attention, axis=1), axis=-1)
transformed = tf.matmul(concatenated, WO) + bO

# Output tensor
output = transformed

In this code snippet, Q, K, and V represent the query, key, and value matrices, respectively, while WQ, WK, WV, and WO represent the learned weight matrices. The bias vector bO is added to the transformed output. The output tensor output represents the attended representation of the input sequence with respect to the query. Note that this code is TensorFlow-specific and may need to be adapted for other deep learning frameworks.

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Where is the code that performs this task?

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The code to perform the attention mechanism in GPT-J is typically implemented in the model architecture code, which is typically defined in a Python file. In the case of GPT-J, the model architecture is defined in a file called model.py, which is part of the official GPT-J GitHub repository.

The model.py file contains the implementation of the GPT-J model using the JAX deep learning framework. The attention mechanism is defined as a function called dot_product_self_attention, which takes as input the query, key, and value tensors, as well as the number of attention heads and the dimensionality of the hidden representation.

Here is an example of how the dot_product_self_attention function is defined in model.py:

def dot_product_self_attention(qkv, mask, dropout_rate):
q, k, v = split_heads(qkv, num_heads)
depth = (hidden_size // num_heads)
logits = np.matmul(q, k.transpose((0, 1, 3, 2)))
logits = logits / np.sqrt(depth)
if mask is not None:
mask = np.expand_dims(mask, axis=(1,2))
logits += (mask * -1e9)
weights = np.exp(logits - np.max(logits, axis=-1, keepdims=True))
weights = weights / np.sum(weights, axis=-1, keepdims=True)
weights = dropout(weights, dropout_rate)
attention_output = np.matmul(weights, v)
return attention_output.reshape((batch_size, sequence_length, hidden_size))

In this code, qkv is a tensor representing the concatenated query, key, and value matrices. The function first splits this tensor into separate tensors for each component, using the split_heads function. It then computes the dot product of the query and key matrices, and scales the resulting logits by the square root of the hidden size. If a mask is provided, it is applied to the logits to mask out invalid positions. The logits are then converted to weights using the softmax function, and dropout is applied to the weights. Finally, the attention output is obtained by multiplying the weights by the value matrix, and reshaping the result to the original tensor shape.

Overall, the attention mechanism in GPT-J is a complex operation that involves several steps, including matrix multiplication, softmax, and dropout. The code to perform this operation is typically implemented in the model architecture file, such as model.py in the case of GPT-J.