espnet2.asr.transducer.rnnt_multi_blank.utils.rnnt_helper.log_plus

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espnet2.asr.transducer.rnnt_multi_blank.utils.rnnt_helper.log_plus(p1: float, p2: float)

Compute the log of the sum of exponentials of two values.

This function calculates the logarithm of the sum of exponentials of two input probabilities, p1 and p2, using a numerically stable approach. This is particularly useful in applications such as log-probability calculations in machine learning, where directly computing the sum of exponentials can lead to overflow issues.

• Parameters:
  • p1 (float) – The first probability value, which may be negative infinity.
  • p2 (float) – The second probability value, which may be negative infinity.
• Returns: The log of the sum of exponentials of p1 and p2.
• Return type: float

Examples

>>> log_plus(0.5, 0.5)
0.6931471805599453  # log(2) = log(0.5 + 0.5)

>>> log_plus(-float('inf'), 1.0)
1.0  # log(0 + exp(1.0)) = 1.0

>>> log_plus(-1.0, -2.0)
-0.3132616875182228  # log(exp(-1.0) + exp(-2.0))

NOTE

If either p1 or p2 is negative infinity, the other value will be returned directly.