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Numerically Stable Softmax

Source: R/00_constants.R
softmax.Rd

Computes the softmax transformation of a numeric vector, returning a probability vector that sums to 1.

Usage

softmax(x)

Arguments

x

Numeric vector of log-odds or arbitrary real values.

Value

Numeric vector of probabilities summing to 1.

Details

The softmax function is defined as: $$p_i = \frac{\exp(x_i)}{\sum_j \exp(x_j)}$$

This implementation subtracts the maximum value before exponentiating to ensure numerical stability for extreme inputs.

Special cases:

  • If x contains Inf values, the probability mass is split uniformly across all Inf entries.

  • Empty vector throws an error.

Examples

softmax(c(1, 2, 3))
#> [1] 0.09003057 0.24472847 0.66524096
sum(softmax(c(1, 2, 3)))
#> [1] 1

# Works with extreme values
softmax(c(1000, 1001, 1002))
#> [1] 0.09003057 0.24472847 0.66524096

# Inf handling
softmax(c(1, Inf, Inf))
#> [1] 0.0 0.5 0.5