torch.multinomial

ELiv 2025

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06-03-2025

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PyTorch's torch.multinomial function is a powerful tool for performing categorical sampling based on probabilities. This means you can use it to randomly select indices from a set of possibilities, with the probability of selecting each index determined by a given probability distribution. This article will delve into the intricacies of torch.multinomial, providing practical examples and explanations to enhance your understanding.

What does torch.multinomial do?

At its core, torch.multinomial draws random samples from a multinomial distribution. Imagine you have a set of categories (e.g., different types of fruits), each with an associated probability of being selected. torch.multinomial allows you to efficiently sample from this distribution, returning the indices of the selected categories. The number of samples drawn is specified by the user.

The function takes a probability tensor as input. This tensor must be 1D or 2D. Each element in the tensor represents the probability of selecting the corresponding index. The probabilities should sum to 1 along the specified dimension.

torch.multinomial Syntax and Parameters

The basic syntax is:

torch.multinomial(input, num_samples, replacement=False, out=None)

Let's break down the parameters:

• input (Tensor): A 1D or 2D tensor containing the probabilities for each category. The values must be non-negative. If 2D, sampling is performed independently across each row.

• num_samples (int): The number of samples to draw.

• replacement (bool, optional): If True, samples are drawn with replacement (meaning the same index can be selected multiple times). Defaults to False.

• out (Tensor, optional): The output tensor. Useful for in-place operations to save memory.

Example: Simple Categorical Sampling

Let's say we have three categories with probabilities [0.2, 0.5, 0.3]:

import torch

probabilities = torch.tensor([0.2, 0.5, 0.3])
num_samples = 10

samples = torch.multinomial(probabilities, num_samples, replacement=True)
print(samples)

This will output a tensor of 10 samples, each representing the index of a selected category (0, 1, or 2). Because replacement=True, the same index may appear multiple times.

Example: Sampling from Multiple Distributions

With a 2D input tensor, torch.multinomial draws samples independently for each row:

probabilities = torch.tensor([[0.1, 0.2, 0.7],
                             [0.8, 0.1, 0.1],
                             [0.3, 0.3, 0.4]])
num_samples = 5

samples = torch.multinomial(probabilities, num_samples, replacement=True)
print(samples)

This will return a 3x5 tensor, where each row contains 5 samples drawn from the corresponding row's probability distribution.

Handling Errors

torch.multinomial will raise a RuntimeError if:

• The input probabilities are negative.
• The probabilities do not sum to 1 (or very close to 1 due to floating-point precision). You might need to normalize your probabilities before using the function.

Applications of torch.multinomial

torch.multinomial has wide applicability in various machine learning tasks, including:

• Sampling from a vocabulary in natural language processing: Selecting words based on their predicted probabilities.
• Reinforcement learning: Choosing actions based on action probabilities given by a policy network.
• Generating random data: Simulating categorical data for experiments or testing.
• Creating weighted random samples: Biasing selection towards specific categories based on their importance.

Conclusion

torch.multinomial is a vital function in PyTorch for probabilistic sampling. Understanding its functionality and parameters empowers you to build more sophisticated and powerful machine learning models. Remember to normalize your probabilities and carefully consider whether you need sampling with or without replacement. By mastering this function, you unlock a crucial building block for various probabilistic applications within your PyTorch projects.