adam_descent_step

std.optim.adam_descent_step · Level L2

One Adam step (β₁ = 0.9, β₂ = 0.999, ε = 10⁻⁸) for any model, given its gradient df(w, X, y): a template over df. With df = logistic_grad it is logistic_adam_step.

state ← adam_step(state, df(w, X, y), t, η)

Signature

adam_descent_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 witness df = logistic_grad: its gradient, then Adam's update written out to 80 digits (100-digit arithmetic), on all 40 test cases.
All 438 float64 results inside the running error bound; the closest uses 77% 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 72% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 58%
bit-equal to the NumPy formula in float64: 90%
largest error, in units in the last place: 1.4e+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_step

Called by

minimize_adam

sha256:be48fa2db2b310bc2931865bd3e7005a343119b04ff40103eee65ada09e75ec1

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.adam_descent_step[df=std.optim.logistic_grad]
Pins: sha256:e95e84182396ab75f4e2b9ab5fe1f8f4f575f694c82755ec0e63d72a2b0cc10dthis graph and the 2 it reaches through calls
Evidence: sha256:96c2fbff79ab808b2bb645a0e258fb78f34d0ac16f738e93ba977998a1299100the 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.