nll_labels

std.loss.nll_labels · Level L3

Negative log-likelihood with integer class labels: minus the mean of each row's log-probability at its label.

−(1/n)·Σᵢ log pᵢ,yᵢ

Signature

nll_labels(logp: f64[n, c], labels: i64[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.

logpf64[n, c]labelsi64[n]ReshapecolGatherAlongpickedMeanmeanNegatenllnllf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference -np.take_along_axis(logp, labels[:, None], axis=1).mean() in exact rational arithmetic, on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 18% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
90%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
2.12

Identity

Calls
—
Called by
cross_entropy_labels
sha256:de840122e34ea4e864b098c053ed384f670a6c3eb08fa01d98d5dc59d1c52d61

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