logistic_loss

std.optim.logistic_loss · Level L5

Logistic regression's loss: the mean binary cross-entropy of the logits Xw against y, through bce_with_logits. Bind its gradient as @grad[f=std.optim.logistic_loss,wrt=w] and minimize_adam trains on the loss alone; NOVA derives the gradient by reverse mode.

L(w) = mean( bce(Xw, y) )

Signature

logistic_loss(w: f64[d], X: f64[n, d], y: 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.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size.
Agrees with the reference mean(t·log(1 + e^(−z)) + (1 − t)·log(1 + e^z)), z = Xw to 80 digits (100-digit arithmetic), on all 40 test cases.
All 40 float64 results inside the running error bound; the closest uses 32% 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 22% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 68%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 1.25

Identity

Calls

bce_with_logits

Called by

—

sha256:3a29dc3f47e6791565fd9ecbb901649c42f7bd29fda5d63d54fa69a199d6d74b

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_loss · Ω:logistic_loss
Pins: sha256:af50c553b03b6a4ec5c9f4aac87d519afb233df55f7e00aa1101ed32a43aad3athis graph and the 2 it reaches through calls
Evidence: sha256:0a7c0ca040765a82c39bb86a969927ce6f52e54f2ac1029ee7a69e53bb7f5498the 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.