added logit page

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

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+---
+Title: '.logit()'
+Description: 'Returns the logit of each element in the input tensor.'
+Subjects:
+  - 'Code Foundations'
+  - 'Computer Science'
+  - 'Data Science'
+Tags:
+  - 'Elements'
+  - 'Methods'
+  - 'PyTorch'
+  - 'Tensor'
+CatalogContent:
+  - 'learn-python-3'
+  - 'paths/data-science'
+---
+
+The **`torch.logit()`** function computes the logit (log-odds) of each element in the input [tensor](https://www.codecademy.com/resources/docs/pytorch/tensors). The logit function is the inverse of the logistic sigmoid function, defined as:
+
+$$\text{logit}(x) = \log\left(\frac{x}{1 - x}\right)$$
+
+This operation is widely used in statistics and machine learning, particularly in logistic regression and neural network transformations. This function is an alias for `torch.special.logit()`.
+
+## Syntax
+
+```pseudo
+torch.logit(input, eps=None, *, out=None)
+```
+
+**Parameters:**
+
+- `input` (Tensor): The input tensor, where each element should be in the range `(0, 1)` when `eps` is not provided.
+- `eps` (float, optional): A small value added for numerical stability. Values less than `eps` are clamped to `eps`, and values greater than `1 - eps` are clamped to `1 - eps`.
+- `out` (Tensor, optional): The output tensor to store the result.
+
+**Return value:**
+
+Returns a tensor containing the logit transformation of the input values.
+
+## Example 1
+
+In this example, probabilities are converted into logits and then passed through a sigmoid function to verify the inverse relationship:
+
+```py
+import torch
+
+probs = torch.tensor([0.2, 0.5, 0.8])
+logits = torch.logit(probs)
+recovered = torch.sigmoid(logits)
+
+print("probs:", probs)
+print("logits:", logits)
+print("sigmoid(logits):", recovered)
+```
+
+Expected output (values may vary slightly due to precision):
+
+```shell
+probs: tensor([0.2000, 0.5000, 0.8000])
+logits: tensor([-1.3863,  0.0000,  1.3863])
+sigmoid(logits): tensor([0.2000, 0.5000, 0.8000])
+```
+
+## Example 2
+
+In this example, the `eps` parameter is used to prevent infinities when the input contains 0 or 1:
+
+```py
+import torch
+
+x = torch.tensor([0.0, 1.0])
+
+# Without eps: produces -inf and +inf
+print(torch.logit(x, eps=None))
+
+# With eps: clamps input to [eps, 1 - eps] before applying logit
+print(torch.logit(x, eps=1e-6))
+```
+
+The output of this code is:
+
+```shell
+tensor([-inf, inf])
+tensor([-13.8155,  13.8023])
+```