minimize_gd

std.optim.minimize_gd · Level L2

Plain gradient descent for any model, from zero weights, one step per entry of the learning-rate schedule lr: a Scan of gd_step. A template over the model's gradient df(w, X, y); bound to @grad of a loss, NOVA derives the gradient by reverse mode.

wₖ₊₁ = wₖ − ηₖ·∇f(wₖ), w₀ = 0

Signature

minimize_gd(X: f64[n, d], y: f64[n], lr: f64[s]) → 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 witness df = logistic_grad: s gradient steps from zero to 80 digits (100-digit arithmetic), on all 40 test cases.
All 145 float64 results inside the running error bound; the closest uses 7% 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 7% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 46%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 101

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

gd_step

Called by

—

sha256:ea43757f13823266da5f6b34339308534749593cd2a38130787aaa21f0f15516

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.minimize_gd[df=std.optim.logistic_grad]
Pins: sha256:74744c3ed525301c2356fb30d8430df3901509c62a08525478dee32caf89aacbthis graph and the 2 it reaches through calls
Evidence: sha256:22072b86cf80fc21cbfff9b04d0550be7028a0b52cbbbefcfcfc444b1f69c36cthe 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.