Statistical Methods
Normalize log weights without overflowing exponentials
Define the task
Some calculations produce weights on a logarithmic scale because the untransformed values are extremely large or small. Confirm that the inputs are natural logarithms of nonnegative weights. A collection of arbitrary scores becomes a different model when exponentiated, so retain the origin and intended meaning of each weight.
Carry out the check
Subtract the largest log weight from every entry, exponentiate the shifted values and divide each by their sum. The common shift cancels in normalized weights. Recover the log of the original total by adding the maximum back to the log of the shifted sum. Extremely small relative weights may still underflow to zero in finite precision.
Worked hypothetical example
For hypothetical log weights 1000 and 1001, direct exponentiation exceeds common floating-point range. The shifted values are −1 and 0, giving normalized weights about 0.268941 and 0.731059. The log total is about 1001.313262. Adding the same constant to both inputs leaves the normalized weights unchanged. Stable arithmetic does not validate the scientific assumptions that produced the weights.
Method checked 14 November 2026 against SciPy documentation: logsumexp.