sgd_step

std.optim.sgd_step · Level L0

One step of gradient descent: params − lr·grad.

θ ← θ − η·g

Signature

sgd_step(params: f64[n], grad: f64[n], lr: f64[]) → f64[n]

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.
Equal to the reference params - lr * grad in exact rational arithmetic, on all 40 test cases.
All 154 float64 results inside the running error bound; the closest uses 87% 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 81% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 89%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 4.00

Identity

Calls

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Called by

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sha256:14d32786b9b0010c44ed7c6f66df95aeaaa19435f11a8b876d7d9b9e18c57e12

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.sgd_step · Ω:sgd_step
Pins: sha256:aeb9900b0da7df13e13e74f22b74a6916e29662a3aff0ac109e79cdbd245c80athis graph alone
Evidence: sha256:e4451ff73812ccac21d9840c4035af4b1f3863664ef369c4c681a316b43c6782the 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.