sketch-oversampling

At its defaults it draws the error of a rank-4 tucker representation built from a sketch, against the columns of oversampling. The flat line is the deterministic decomposition — d matrix SVDs — at 8.81·10⁻⁴, and nothing random can go below it, since every curve here is a projection onto a subspace of the same size. The upper two are medians over five seeds: a dense Gaussian sketch, which the randomised field's bounds cover, and a Khatri–Rao sketch, whose columns are outer products of small random vectors and which no bound in that field applies to. With no oversampling the dense sketch is 3.65 times the deterministic answer; at twelve extra columns it is 1.15. The structured one costs 6.8 per cent more at four extra columns and 9.5 per cent at twelve — measured, because there is nothing else to say about it.

sketch-oversampling is one function in lib/figures/tsketch.js — sketching a tensor — a random matrix larger than the object, and the structured one that is not. 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.

The flat line is the deterministic decomposition — d matrix SVDs — at 8.81·10⁻⁴, and nothing random can go below it, since every curve here is a projection onto a subspace of the same size. The upper two are medians over five seeds: a dense Gaussian sketch, which the randomised field's bounds cover, and a Khatri–Rao sketch, whose columns are outer products of small random vectors and which no bound in that field applies to. With no oversampling the dense sketch is 3.65 times the deterministic answer; at twelve extra columns it is 1.15. The structured one costs 6.8 per cent more at four extra columns and 9.5 per cent at twelve — measured, because there is nothing else to say about it.

The flat line is the deterministic decomposition — d matrix SVDs — at 8.81·10⁻⁴, and nothing random can go below it, since every curve here is a projection onto a subspace of the same size. The upper two are medians over five seeds: a dense Gaussian sketch, which the randomised field's bounds cover, and a Khatri–Rao sketch, whose columns are outer products of small random vectors and which no bound in that field applies to. With no oversampling the dense sketch is 3.65 times the deterministic answer; at twelve extra columns it is 1.15. The structured one costs 6.8 per cent more at four extra columns and 9.5 per cent at twelve — measured, because there is nothing else to say about it.

The flat line is the deterministic decomposition — d matrix SVDs — at 0.0671, and nothing random can go below it, since every curve here is a projection onto a subspace of the same size. The upper two are medians over five seeds: a dense Gaussian sketch, which the randomised field's bounds cover, and a Khatri–Rao sketch, whose columns are outer products of small random vectors and which no bound in that field applies to. With no oversampling the dense sketch is 2.78 times the deterministic answer; at twelve extra columns it is 1.20. The structured one costs 39.4 per cent more at four extra columns and 6.6 per cent at twelve — measured, because there is nothing else to say about it.

The flat line is the deterministic decomposition — d matrix SVDs — at 4.09·10⁻⁹, and nothing random can go below it, since every curve here is a projection onto a subspace of the same size. The upper two are medians over five seeds: a dense Gaussian sketch, which the randomised field's bounds cover, and a Khatri–Rao sketch, whose columns are outer products of small random vectors and which no bound in that field applies to. With no oversampling the dense sketch is 6.40 times the deterministic answer; at twelve extra columns it is 1.37. The structured one costs 1.9 per cent more at four extra columns and -2.4 per cent at twelve — measured, because there is nothing else to say about it.

The flat line is the deterministic decomposition — d matrix SVDs — at 7.94·10⁻⁶, and nothing random can go below it, since every curve here is a projection onto a subspace of the same size. The upper two are medians over five seeds: a dense Gaussian sketch, which the randomised field's bounds cover, and a Khatri–Rao sketch, whose columns are outer products of small random vectors and which no bound in that field applies to. With no oversampling the dense sketch is 15.12 times the deterministic answer; at twelve extra columns it is 1.23. The structured one costs 34.8 per cent more at four extra columns and -1.0 per cent at twelve — measured, because there is nothing else to say about it.

Every figure above asserted its own claims on the way to being drawn, and a claim that failed would have failed the build rather than drawn a wrong picture. Those assertions 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.

10 distinct claims across 5 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.

It draws a decomposition and prints its residual. It calls oversamplingSweep, 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 146 of 287 generators — 131 print a residual and 15 are exempt with a published reason; 141 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.