logistic_adam_step

std.optim.logistic_adam_step · Level L2

One training step of logistic regression with Adam (β₁ = 0.9, β₂ = 0.999, ε = 10⁻⁸): the gradient from logistic_grad, then adam_step at the step's (t, lr). The body that logistic_fit_adam scans.

state ← adam_step(state, ∇L(w), t, η)

Signature

logistic_adam_step(state: f64[3, d], tl: f64[2], X: f64[n, d], y: f64[n]) → f64[3, 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 logistic_grad, then Adam's update written out to 80 digits (100-digit arithmetic), on all 40 test cases.
All 588 float64 results inside the running error bound; the closest uses 70% 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 67% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 55%
bit-equal to the NumPy formula in float64: 93%
largest error, in units in the last place: 4.2e+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

Calls

adam_step logistic_grad

Called by

logistic_fit_adam

sha256:db2e33af6cafacfcd7391600d603b4f7cb5ca634d6dda28ebdd3883b71da817c

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_adam_step · Ω:logistic_adam_step
Pins: sha256:68f114212c698f390863b83771c534169e0875d403f5260ae4a3590896c53208this graph and the 2 it reaches through calls
Evidence: sha256:1f0d8328e8f00fd0b8193c9d63968c040f771a6f929f0a6db467bff4ae46cfd1the 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.