cross_entropy

std.loss.cross_entropy · Level L1

Cross-entropy between a target distribution and the softmax of logits. Calls log_softmax.

−Σᵢ tᵢ·log softmax(z)ᵢ

Signature

cross_entropy(logits: f64[n], target: 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.

logitsf64[n]targetf64[n]log_softmaxlpMultiplytlReduceSumsNegatellf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference -np.sum(target * log_softmax(logits)) to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 20% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
65%
bit-equal to the NumPy formula in float64
63%
largest error, in units in the last place
2.18

Identity

Calls
log_softmax
Called by
—
sha256:33cf1fc43bfd545a043eea67d29a3f1c8bf0fc1251fe9171c47f73e53c80a2b1

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.cross_entropy · Ω:cross_entropy
Pins
sha256:04d7fcf938951750466c3749cac4da0edefdaca5c9704f0a5561b17211db6a86this graph and the 2 it reaches through calls
Evidence
sha256:9f220fa5fd6fd1dba9f194ad2ab4576052b1f7a9ef9a5b762968024aa6cf3b3fthe 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.