标签还是那两个类别，换成one-hot后平均损失为什么翻倍？

"""Documented reduction formulas, not an execution of torch.nn.CrossEntropyLoss."""
from math import isclose, isfinite, log


def require(condition, message):
    if not condition:
        raise AssertionError(message)


def compare(weights):
    probabilities = ((0.8, 0.2), (0.6, 0.4))
    labels = (0, 1)
    one_hot = ((1.0, 0.0), (0.0, 1.0))
    if not isinstance(weights, (list, tuple)) or len(weights) != 2:
        raise ValueError("need two class weights")
    if any(type(w) not in (int, float) or not isfinite(w) or not 0 < w <= 100
           for w in weights):
        raise ValueError("finite positive weights at most 100 required")
    indexed_terms = [-weights[y] * log(row[y]) for row, y in zip(probabilities, labels)]
    probability_terms = [-sum(weights[c] * target[c] * log(row[c]) for c in range(2))
                         for row, target in zip(probabilities, one_hot)]
    require(all(isclose(a, b, abs_tol=1e-12) for a, b in zip(indexed_terms, probability_terms)),
            "one-hot and index unreduced terms agree")
    numerator = sum(indexed_terms)
    weight_sum = sum(weights[y] for y in labels)
    return numerator, numerator / weight_sum, sum(probability_terms) / len(labels)


def main():
    print("fixed correct-class probabilities=[0.8, 0.4]; N=2; no ignored labels; label_smoothing=0")
    for weights in ([1, 3], [2, 6], [1, 1]):
        total, index_mean, onehot_mean = compare(weights)
        print(f"weights={weights}; sum={total:.6f}; index_mean={index_mean:.6f}; onehot_mean={onehot_mean:.6f}")
        print(f"denominators: index={sum(weights)}; onehot=2; ratio={onehot_mean / index_mean:.6f}")
    count = 0
    for relative in (0.1, 1, 3, 10):
        for scale in (0.1, 1, 2, 10):
            weights = [scale, relative * scale]
            _, indexed, probability = compare(weights)
            require(isclose(probability / indexed, sum(weights) / 2, abs_tol=1e-12), "ratio oracle")
            require(isclose(indexed, compare([1, relative])[1], abs_tol=1e-12), "common scale cancellation")
            count += 1
    for invalid in ([0, 1], [-1, 1], [True, 1], [float('inf'), 1], [1]):
        try:
            compare(invalid)
        except ValueError:
            pass
        else:
            raise AssertionError("invalid weights accepted")
    print(f"PASS: {count} reduction-ratio cases; matching unreduced terms; weight-scale invariance")


if __name__ == '__main__':
    main()