Generator

Three filters at their own optima, on one problem

One function in the compose library, called 1 time across 1 essay. Below: what it draws at its defaults, what it draws at every value an essay asks for, the 4 claims it put to the test while drawing them, and where it stands against the rule this site is named for.

At its defaults it draws three filters at their own optima, on one problem. Filter factors against the singular-value index. Truncation at K = 21 is a step from one to zero; Tikhonov at λ = 0.0215 is a smooth descent; the 20-step conjugate gradient filter rises above one and changes direction 5 times. The three reach errors within a few per cent of each other while differing by up to 0.99 in individual factors.

filter-comparison is one function in lib/figures/compose.js — four knobs — one floor under them, and a fifth that is not a knob at all. Everything below came out of it during this build, at arguments taken from the essays rather than invented for this page. A figure here is the figure a reader meets in an essay, and if the generator changes, this page changes with it.

At its defaults

Drawn even though every essay passes arguments — which on this site is every essay, at 100% of placements since the standard pass. A default nothing exercises is a trap for the next essay to call this with none, and this is the page where a default that has drifted from the figures around it becomes visible.

Three filters at their own optima, on one problemFilter factors against the singular-value index. Truncation at K = 21 is a step from one to zero; Tikhonov at λ = 0.0215 is a smooth descent; the 20-step conjugate gradient filter rises above one and changes direction 5 times. The three reach errors within a few per cent of each other while differing by up to 0.99 in individual factors.081624324048566400.250.50.7511.25index kfilter factortruncation K = 21TikhonovCGLS, 20 stepsone floor, three weightingstruncation vs Tikhonov0.77truncation vs CGLS0.99reversals in the CGLS filter5the same error, to a few per centby three different weightings

Filter factors against the singular-value index. Truncation at K = 21 is a step from one to zero; Tikhonov at λ = 0.0215 is a smooth descent; the 20-step conjugate gradient filter rises above one and changes direction 5 times. The three reach errors within a few per cent of each other while differing by up to 0.99 in individual factors.

noise: 0.01

The arguments are the ones Four knobs and one floor passes. A value nobody placed would be a picture no essay asked for and no claim was ever checked against.

Three filters at their own optima, on one problemFilter factors against the singular-value index. Truncation at K = 21 is a step from one to zero; Tikhonov at λ = 0.0215 is a smooth descent; the 20-step conjugate gradient filter rises above one and changes direction 5 times. The three reach errors within a few per cent of each other while differing by up to 0.99 in individual factors.081624324048566400.250.50.7511.25index kfilter factortruncation K = 21TikhonovCGLS, 20 stepsone floor, three weightingstruncation vs Tikhonov0.77truncation vs CGLS0.99reversals in the CGLS filter5the same error, to a few per centby three different weightings

Filter factors against the singular-value index. Truncation at K = 21 is a step from one to zero; Tikhonov at λ = 0.0215 is a smooth descent; the 20-step conjugate gradient filter rises above one and changes direction 5 times. The three reach errors within a few per cent of each other while differing by up to 0.99 in individual factors.

What it checked while drawing

Every figure above checked its own claims on the way to being drawn, and a claim that failed would have stopped the picture rather than shipped a wrong one. Those checks used to leave no trace at all: a passing one returned true and the only evidence the figure had checked anything was that nothing crashed. The list below is what they actually said, collected by running this generator with an observer installed — not a description of what it is believed to check.

4 distinct claims across 2 sets of arguments, grouped below by shape — because most of them are one sentence with a different number in it, and how many separate times that sentence was put to the test is the informative part.

a noise level small enough to be noise

a size the SVD is affordable at

and the CGLS filter is not monotone

the filters differ substantially at their own optima

Against the rule

It draws a decomposition and prints its residual. It calls cgls, and every figure above carries the badge — which residualcheck verifies by looking for it in the emitted SVG rather than by finding the call that builds one. A badge that is constructed and then left out of the body is the failure that check exists for.

Across the library: the rule bites on 217 of 397 generators — 199 print a residual and 18 are exempt with a published reason; 180 factorise nothing. Read from lib/residual-rule.js, which is the same body the gate enforces from, and the gate's last check fails the build if this page and it disagree about any generator.

Where it is called

Changing this generator changes every figure on this list. That is what makes the list worth publishing rather than keeping in a check script.

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