PyTorch .logit()

The torch.logit() function computes the logit (log-odds) of each element in the input tensor. 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

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:

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)

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Expected output (values may vary slightly due to precision):

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])

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Example 2

In this example, the eps parameter is used to prevent infinities when the input contains 0 or 1:

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))

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The output of this code is:

tensor([-inf, inf])
tensor([-13.8155,  13.8023])

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