Reshaping Tensors with torch.Tensor.expand_as() in PyTorch

Purpose

• Achieves this by expanding dimensions of size 1 in self to the corresponding dimensions in other.
• Reshapes a tensor (self) to match the size of another tensor (other).

Key Points

• Broadcasting Compatibility
  The expanded tensor must be broadcastable with other for operations to work correctly.
• Singleton Dimensions
  Only dimensions with a size of 1 in self can be expanded.
• In-place Operation
  It creates a new view on the original self tensor, not a copy. This means it modifies the view of the underlying data without allocating new memory.

Example

import torch

# Create tensors
tensor1 = torch.tensor([1, 2, 3])
tensor2 = torch.zeros(2, 3)

# Expand tensor1 to match tensor2 size
expanded_tensor = tensor1.expand_as(tensor2)
print(expanded_tensor)

This will output:

tensor([[1, 2, 3],
        [1, 2, 3]])

Here, the singleton dimension (size 1) in tensor1 is expanded to match the second dimension (size 3) of tensor2.

Equivalence with expand()

torch.Tensor.expand_as() is functionally equivalent to:

expanded_tensor = tensor1.expand(tensor2.size())

When to Use expand_as()

• Common use case is when you have a small tensor that needs to be used in an operation with a larger tensor. By expanding the smaller tensor, you enable broadcasting for element-wise operations.

Cautions

• Expanding tensors with multiple dimensions of size 1 might not be intuitive.
• Be mindful of broadcasting rules to ensure correct calculations.

• If you need a true copy of the expanded tensor with allocated memory, use .clone().
• For more complex reshaping, consider using torch.view() or torch.reshape().

---

Example 1: Expanding a Scalar for Element-wise Operations

import torch

# Scalar value
weight = torch.tensor(3.14)

# Input data with multiple dimensions
data = torch.randn(2, 3)

# Expand weight to match data dimensions
expanded_weight = weight.expand_as(data)

# Element-wise multiplication using broadcasting
result = data * expanded_weight
print(result)

This code expands the scalar weight to the same size as data (2x3). The resulting element-wise multiplication is possible due to broadcasting.

Example 2: Expanding a 1D Tensor for Matrix Multiplication

import torch

# 1D tensor (row vector)
embedding = torch.tensor([0.5, 1.2, -0.8])

# Input data (matrix)
inputs = torch.randn(4, 3)

# Expand embedding to match the first dimension of inputs
expanded_embedding = embedding.expand_as(inputs[:, 0])  # Expand to match row size

# Matrix multiplication (broadcasting across columns)
output = expanded_embedding.unsqueeze(1) @ inputs  # Unsqueeze for proper matrix multiplication
print(output)

Here, the 1D tensor embedding is expanded to match the number of rows in inputs. Unsqueezing adds a new dimension (column) to expanded_embedding for compatible matrix multiplication.

Example 3: Expanding for Conditional Operations

import torch

# Condition tensor
condition = torch.tensor([True, False])

# Input data
data = torch.randn(2, 3)

# Expand condition to match data dimensions
expanded_condition = condition.expand_as(data)

# Conditional operation using broadcasting (where)
output = torch.where(expanded_condition, data * 2, data / 2)
print(output)

In this example, the boolean tensor condition is expanded to match the size of data. The torch.where function performs element-wise conditional operations based on the corresponding values in expanded_condition.

---

torch.repeat()

• Example:
• Unlike expand_as(), it creates a new tensor with replicated data, potentially consuming more memory.
• Use torch.repeat() when you need to create multiple copies of a tensor along a specific dimension.

import torch

tensor = torch.tensor([1, 2, 3])
repeated_tensor = tensor.repeat(2, 1)  # Repeat twice along the first dimension
print(repeated_tensor)

Broadcasting

• Example:
• It's often more efficient than creating new tensors.
• If your tensors are already compatible for element-wise operations, broadcasting can handle dimension mismatches automatically.

import torch

tensor1 = torch.tensor([1, 2, 3])
tensor2 = torch.ones(2, 3)
result = tensor1 * tensor2  # Broadcasting will handle size difference
print(result)

torch.view() or torch.reshape()

• Example:
• These functions change the view of the underlying data to a new shape without creating a copy as long as the total number of elements remains the same.
• Use torch.view() or torch.reshape() for more complex reshaping operations.

import torch

tensor = torch.arange(6)
reshaped_tensor = tensor.view(2, 3)  # Reshape to 2x3 matrix
print(reshaped_tensor)

torch.unsqueeze()

• Example:
• This can be helpful for making tensors compatible for certain operations.
• Use torch.unsqueeze() to add a new dimension of size 1 to a tensor.

import torch

tensor = torch.tensor([1, 2, 3])
unsqueeze_tensor = tensor.unsqueeze(1)  # Add a new dimension (column)
print(unsqueeze_tensor)

• Consider the following factors when deciding between these alternatives:
  • Memory Usage
    expand_as() and view()/reshape() are memory-efficient if dimensions match the total number of elements. repeat() creates copies and might consume more memory.
  • Complexity
    Broadcasting is most efficient for simple element-wise operations. expand_as(), view(), and reshape() offer more control for reshaping.
  • Dimensionality
    unsqueeze() is useful for adding specific dimensions.