binary_cross_entropy

std.loss.binary_cross_entropy · Level L1

Binary cross-entropy for probabilities strictly between 0 and 1.

−mean( t·log p + (1 − t)·log(1 − p) )

Signature

binary_cross_entropy(p: f64[n], t: f64[n]) → f64[]

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks a call to another library function; select it to open that function.

1.0pf64[n]tf64[n]SubtractqSubtractuLoglpLoglqMultiplyaMultiplycAddsMeanmNegatellf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference -np.mean(t * np.log(p) + (1 - t) * np.log(1 - p)) to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 13% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
60%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
1.54

Identity

Calls
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Called by
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sha256:2c5e3264274b6a3f35f403b9842ead1e382ca21e36b4b515e71f72580948f63d

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