How to sample from softmax with temperature

Here is how to sample from a softmax probability vector at different temperatures.

import numpy as np
import matplotlib.pyplot as plt
import matplotlib as mpl
import seaborn as sns
mpl.rcParams['figure.dpi']= 144
trials = 1000
softmax = [0.1, 0.3, 0.6]
def sample(softmax, temperature):
    EPSILON = 10e-16 # to avoid taking the log of zero
    (np.array(softmax) + EPSILON).astype('float64')
    preds = np.log(softmax) / temperature
    exp_preds = np.exp(preds)
    preds = exp_preds / np.sum(exp_preds)
    probas = np.random.multinomial(1, preds, 1)
    return probas[0]
temperatures = [(t or 1) / 100 for t in range(0, 101, 10)]
probas = [
    np.asarray([sample(softmax, t) for _ in range(trials)]).sum(axis=0) / trials
    for t in temperatures
plt.plot(temperatures, probas)

Notice how the probabilities change at different temperatures. The softmax probabilities are [0.1, 0.3, 0.6]. At the lowest temperatures of 0.01, the dominant index (value 0.6) has near 100% probability of being sampled. At higher temperatures, the selection probabilities move towards the softmax values, e.g. 60% probability for the third index.

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