log_softmax

std.nn.log_softmax · Level L1

Log of the softmax, computed as x − logsumexp(x) without forming the softmax. Calls logsumexp.

xᵢ − log Σⱼ e^(xⱼ)

Signature

log_softmax(x: f64[n]) → f64[n]

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.

xf64[n]logsumexplseSubtractyyf64[n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference x - np.log(np.sum(np.exp(x))) to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 148 float64 results inside the running error bound; the closest uses 55% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
67%
bit-equal to the NumPy formula in float64
78%
largest error, in units in the last place
6.0e+3

Large ulp counts appear where a result is tiny next to the numbers it is computed from (after cancellation, for example), so one unit in the last place is tiny too; the absolute error is still inside the bound. Results within their own error of zero are not counted.

Identity

sha256:b214602190583450717d4868470d0235a7027c1485154d8d7d3485078ac93ec2

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

Control handle

Symbol
Ω:std.nn.log_softmax · Ω:log_softmax
Pins
sha256:354f0e8273a7bc2dda8691f905ff52d28c0543745ef716a2317a6550c4cfcfdbthis graph and the 1 it reaches through calls
Evidence
sha256:59c29b1a6c76f98b063deb27cfbdca0f787600e53341c02fecc014665f8b752dthe 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.