预测没变，只把米换成厘米，损失为什么涨了 4.605？

"""Gaussian density and NLL under a declared change of measurement units."""
import json
import math
from pathlib import Path


def nll(y, mean, variance, full=True):
    if variance <= 0:
        raise ValueError('variance must be positive')
    value = 0.5 * (math.log(variance) + (y - mean) ** 2 / variance)
    return value + (0.5 * math.log(2 * math.pi) if full else 0.0)


def interval_probability(low, high, mean, sigma):
    if sigma <= 0 or high < low:
        raise ValueError('invalid interval or sigma')
    return 0.5 * (math.erf((high-mean)/(sigma*math.sqrt(2))) - math.erf((low-mean)/(sigma*math.sqrt(2))))


def main():
    y, mean, sigma = 0.1, 0.0, 0.2
    factor = 100.0
    meters = nll(y, mean, sigma**2)
    centimeters = nll(y*factor, mean*factor, (sigma*factor)**2)
    delta = centimeters - meters
    assert math.isclose(delta, math.log(factor), abs_tol=1e-12)
    density_m, density_cm = math.exp(-meters), math.exp(-centimeters)
    assert density_m > 1
    assert math.isclose(density_m/factor, density_cm, abs_tol=1e-12)
    prob_m = interval_probability(-0.1,0.1,mean,sigma)
    prob_cm = interval_probability(-10,10,mean*factor,sigma*factor)
    assert math.isclose(prob_m, prob_cm, abs_tol=1e-12)
    omitted = nll(y, mean, sigma**2, full=False)
    wrong_variance = nll(y, mean, sigma)
    print(f'meters: variance={sigma**2:.6f}, full NLL={meters:.6f}, density={density_m:.6f} per meter')
    print(f'centimeters: variance={(sigma*factor)**2:.6f}, full NLL={centimeters:.6f}, density={density_cm:.6f} per centimeter')
    print(f'NLL difference={delta:.6f}; log(100)={math.log(factor):.6f}')
    print(f'interval probability: [-0.1,0.1] m={prob_m:.6f}; [-10,10] cm={prob_cm:.6f}')
    print(f'constant omitted NLL={omitted:.6f}; difference={meters-omitted:.6f}')
    print(f'incorrectly passing sigma as variance: NLL={wrong_variance:.6f}')
    exact_fit = [{'sigma':s, 'nll':nll(0,0,s*s)} for s in [1.0,0.1,0.01]]
    print('exact-fit NLL as sigma shrinks: '+', '.join(f"{r['nll']:.6f}" for r in exact_fit))
    assert all(a['nll'] > b['nll'] for a,b in zip(exact_fit,exact_fit[1:]))
    residual = y - mean
    optimum = residual**2
    assert nll(y,mean,optimum) < nll(y,mean,optimum/2)
    assert nll(y,mean,optimum) < nll(y,mean,optimum*2)
    try:
        nll(y,mean,0)
    except ValueError:
        pass
    else:
        raise AssertionError('zero variance must fail')
    report = {'meters':{'nll':meters,'density':density_m},'centimeters':{'nll':centimeters,'density':density_cm},
        'nll_delta':delta,'interval_probability':prob_m,'constant_omitted':omitted,
        'sigma_as_variance':wrong_variance,'exact_fit':exact_fit,
        'scope':'Fixed univariate Gaussian arithmetic; no network fitting, PyTorch execution or empirical calibration.'}
    Path('report.json').write_text(json.dumps(report, indent=2, allow_nan=False)+'\n', encoding='utf-8')
    print('checks passed: Jacobian scaling, interval invariance, constant, variance boundary')


if __name__ == '__main__':
    main()