Answers.Body: <p>Yes, for some applications, the spatial component of the tensor is indeed very important, but not for the examples you mentioned. The first point to clarify is that even though the <strong><code>torch.nn.Linear</code></strong> class can accept a tensor with multiple dimensions, it effectively performs the linear layer operation on a matrix, not on a multi-dimensional tensor.</p>
  <p>In reality, if you change the tensor from shape (240, 1) to (10, 24, 1), what PyTorch does is interpret (10, 24, 1) as (10*24, 1), and then performs the matrix multiplication. After that, it reshapes it back to the original input shape.</p>
  <p>The mathematical operation of the linear layer is described by this formula from the <a href="https://pytorch.org/docs/stable/generated/torch.nn.Linear.html" rel="nofollow noreferrer">PyTorch documentation</a>:</p>
  <p><span class="math-container">$y = xA^T + b$</span></p>
  <p>where <span class="math-container">$x$</span> is the data vector and <span class="math-container">$A^T$</span> is the weight matrix for the layer.</p>
  <p>Answering your question about the advantages of providing multi-dimensional input to PyTorch modules: it depends on the operation you're performing. A common technique that utilizes this is the Convolutional Layer. Convolutional layers work by taking a sliding kernel tensor to compute convolutions, allowing it to gather data from different parts of the tensor in a non-sequential way. Another method is Tensor Decomposition, similar to matrix decompositions, which breaks tensors into an outer product of vectors to create rank-1 tensors and sums them together.</p>
  <p>In general, these methods are applied primarily to image data. Using multi-dimensional operations on <a href="https://en.wikipedia.org/wiki/Independent_and_identically_distributed_random_variables" rel="nofollow noreferrer">i.i.d.</a> data or sequential data doesn't make much sense, because you will lose the sequential or independent distributed property. However, you can still use Conv layers for sequential data if using kernels shaped as an array to process sequential data, such as in audio processing models.</p>
  
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Answers.CreationDate: 2023-11-17T17:13:46.607Z
Answers.LastActivityDate: 2023-11-17T17:13:46.607Z
Answers.UserDisplayName: Cesar Ruiz
Body: <p>Most layer types in torch.nn such as torch.nn.Linear accept input with more than one dimension. Is there any advantage in doing so if you can shape your data to represent a certain arrangement in order to encode positional information?</p>
  <p>For example, given you have only one type of data (feature dimension = 1) and 240 samples in the form of subsequent time slots of 1 hour. Is there any potential benefit in changing this from (240, 1) to (10, 24, 1) in order to assign hours to days or will torch still view this just as a sequence of time slots/hours? Any source would also be appreciated.</p>
  
Tags: <pytorch><time-series><features><dimensionality>
Title: Is there any advantage to providing multi-dimensional input to torch modules?
UserDisplayName: kot
ThreadText: # Is there any advantage to providing multi-dimensional input to torch modules?
  
  (Asked by: username_0 on 2023-11-12)
  
  Most layer types in torch.nn such as torch.nn.Linear accept input with more than one dimension. Is there any advantage in doing so if you can shape your data to represent a certain arrangement in order to encode positional information?
  
  For example, given you have only one type of data (feature dimension = 1) and 240 samples in the form of subsequent time slots of 1 hour. Is there any potential benefit in changing this from (240, 1) to (10, 24, 1) in order to assign hours to days or will torch still view this just as a sequence of time slots/hours? Any source would also be appreciated.
  
  **Tags:** pytorch, time-series, features, dimensionality
  
  
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  ## 1 answers
  
  ### Answer by username_1 on 2023-11-17. Score: 2 | Accepted answer
  
  Yes, for some applications, the spatial component of the tensor is indeed very important, but not for the examples you mentioned. The first point to clarify is that even though the **`torch.nn.Linear`** class can accept a tensor with multiple dimensions, it effectively performs the linear layer operation on a matrix, not on a multi-dimensional tensor.
  
  In reality, if you change the tensor from shape (240, 1) to (10, 24, 1), what PyTorch does is interpret (10, 24, 1) as (10\*24, 1), and then performs the matrix multiplication. After that, it reshapes it back to the original input shape.
  
  The mathematical operation of the linear layer is described by this formula from the [PyTorch documentation](https://pytorch.org/docs/stable/generated/torch.nn.Linear.html):
  
  $y = xA^T + b$
  
  where $x$ is the data vector and $A^T$ is the weight matrix for the layer.
  
  Answering your question about the advantages of providing multi-dimensional input to PyTorch modules: it depends on the operation you're performing. A common technique that utilizes this is the Convolutional Layer. Convolutional layers work by taking a sliding kernel tensor to compute convolutions, allowing it to gather data from different parts of the tensor in a non-sequential way. Another method is Tensor Decomposition, similar to matrix decompositions, which breaks tensors into an outer product of vectors to create rank-1 tensors and sums them together.
  
  In general, these methods are applied primarily to image data. Using multi-dimensional operations on [i.i.d.](https://en.wikipedia.org/wiki/Independent_and_identically_distributed_random_variables) data or sequential data doesn't make much sense, because you will lose the sequential or independent distributed property. However, you can still use Conv layers for sequential data if using kernels shaped as an array to process sequential data, such as in audio processing models.
  
  
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