logistic_grad

std.optim.logistic_grad · Level L1

The gradient of logistic regression's mean binary cross-entropy in the weights: Xᵀ(σ(Xw) − y)/n. Written out; a test checks it against NOVA's reverse mode applied to bce_with_logits.

∇L(w) = Xᵀ(σ(Xw) − y) / n

Signature

logistic_grad(w: f64[d], X: f64[n, d], y: f64[n]) → f64[d]

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.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size.
Agrees with the reference X.T @ (sigmoid(X @ w) - y) / n to 80 digits (100-digit arithmetic), on all 40 test cases.
All 135 float64 results inside the running error bound; the closest uses 17% of it.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them inside the running error bound at u = 2⁻²⁴; the closest uses 12% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 50%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 291

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

Calls

—

Called by

logistic_adam_step

sha256:5e2b2cfbe479404905ebb65bb6f3b1784afb76779f35e668627d00925d621067

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

Control handle

Symbol: Ω:std.optim.logistic_grad · Ω:logistic_grad
Pins: sha256:f48f0ba8749e0973c34842a0b645da9a97e80e78cbaaca03e8abc397543ab813this graph alone
Evidence: sha256:1e94e6f92bfb184a5c0722070be4cba67475c4ed119e473fdb4b8c465ebbf387the 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.