minimize_adam

std.optim.minimize_adam · Level L3

Training for any model with Adam, from zero weights, one step per entry of the learning-rate schedule lr: a Scan of adam_descent_step. A template over the model's gradient df(w, X, y). With df = logistic_grad it is logistic_fit_adam, bit for bit.

w = params( adam_descent_step[df]^s (0) )

Signature

minimize_adam(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: the same s Adam steps written out to 80 digits (100-digit arithmetic), on all 40 test cases.
All 161 float64 results inside the running error bound; the closest uses 1% of it.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 33 of them inside the running error bound at u = 2⁻²⁴; the closest uses 3% of it. Uncertified, too ill-conditioned at float32 for a finite bound: 7.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 16%
bit-equal to the NumPy formula in float64: 52%
largest error, in units in the last place: 1.3e+4

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_descent_step

Called by

—

sha256:0d779ebe820726d47a4b74278bafd83d3ca615eb331dbbcb1ddbfe5faf7a47bc

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_adam[df=std.optim.logistic_grad]
Pins: sha256:88a3c71653e33bbec3ce85d1099985a173721630d3a77f26c2759d8d3b44af5dthis graph and the 3 it reaches through calls
Evidence: sha256:cee03608e8b3fcad58aeeed511d8f9b376f30588994369d55b12d510763e8c8dthe 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.