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 another library function this one runs — called once, or by Scan once per element; 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 14% 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
—
Called by
—
sha256:2c5e3264274b6a3f35f403b9842ead1e382ca21e36b4b515e71f72580948f63d

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol
Ω:std.loss.binary_cross_entropy · Ω:binary_cross_entropy
Pins
sha256:e37694313e848e59293b0f194afb670f0199f2d12d112903da59f35f14b2a2fathis graph alone
Evidence
sha256:ad69106db507d51f8eb92acb4de449a3886eebf9c7c4df599d3a3d35bfa8db62the hash of its verification record
Needs
no capability: a pure function

Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.