[Term Entry] PyTorch Tensor Operations: .expm1()

content/pytorch/concepts/tensor-operations/terms/expm1/expm1.md

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+---
+Title: '.expm1()'
+Description: 'Calculates the exponential of each element in a tensor and then subtracts 1.'
+Subjects:
+  - 'Computer Science'
+  - 'Machine Learning'
+Tags:
+  - 'Functions'
+  - 'Machine Learning'
+  - 'Python'
+  - 'Tensor'
+CatalogContent:
+  - 'intro-to-py-torch-and-neural-networks'
+  - 'paths/computer-science'
+---
+
+In PyTorch, the **`.expm1()`** function takes in an input [tensor](https://www.codecademy.com/resources/docs/pytorch/tensors) and returns a tensor where each element is the exponential of the input element minus 1. It provides greater precision than performing $$exp(x) - 1$$ directly, especially for small values of `x`. The function computes each element as:
+
+$$y_i= e^{x_i}-1$$
+
+## Syntax
+
+```pseudo
+torch.expm1(input, *, out=None) → Tensor
+```
+
+Or,
+
+```pseudo
+torch.special.expm1(input, *, out=None) → Tensor
+```
+
+**Parameters:**
+
+- `input`: The input tensor.
+- `out` (Optional): A tensor to store the output. If provided, the result is written to this tensor.
+
+**Return value:**
+
+It returns a new tensor of the same shape as the input, containing the computed values for each corresponding element.
+
+## Example
+
+This example demonstrates the usage of the `.expm1()` function:
+
+```py
+import torch
+
+# Define a tensor
+x = torch.tensor([0, math.log(2.)])
+
+result = torch.special.expm1(x)
+
+print(result)
+```
+
+The output of this code is:
+
+```shell
+tensor([ 0.,  1.])
+```