One subspace, solved and regularised, at 1.0% noise

At its defaults it draws one subspace, solved and regularised, at 1.0% noise. Two error curves against the number of bidiagonalisation steps, on a logarithmic vertical axis. The unregularised iterate reaches 0.1426 at step 20 and then climbs to 161 — a factor of 1127. The iterate with a penalty on the projected problem reaches 0.1429 and stays within 0.00% of it for the rest of the run.

hybrid-curves is one function in lib/figures/hybrid.js — hybrid regularisation — a penalty inside the subspace, and the rule that transfers to it. 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.

Two error curves against the number of bidiagonalisation steps, on a logarithmic vertical axis. The unregularised iterate reaches 0.1426 at step 20 and then climbs to 161 — a factor of 1127. The iterate with a penalty on the projected problem reaches 0.1429 and stays within 0.00% of it for the rest of the run.

Two error curves against the number of bidiagonalisation steps, on a logarithmic vertical axis. The unregularised iterate reaches 0.1426 at step 20 and then climbs to 161 — a factor of 1127. The iterate with a penalty on the projected problem reaches 0.1429 and stays within 0.00% of it for the rest of the run.

Two error curves against the number of bidiagonalisation steps, on a logarithmic vertical axis. The unregularised iterate reaches 0.1675 at step 3 and then climbs to 1607 — a factor of 9598. The iterate with a penalty on the projected problem reaches 0.1720 and stays within 14.17% of it for the rest of the run.

Two error curves against the number of bidiagonalisation steps, on a logarithmic vertical axis. The unregularised iterate reaches 0.1498 at step 10 and then climbs to 322 — a factor of 2146. The iterate with a penalty on the projected problem reaches 0.1500 and stays within 2.02% of it for the rest of the run.

Two error curves against the number of bidiagonalisation steps, on a logarithmic vertical axis. The unregularised iterate reaches 0.1114 at step 24 and then climbs to 32.2 — a factor of 289. The iterate with a penalty on the projected problem reaches 0.1180 and stays within 0.00% of it for the rest of the run.

Two error curves against the number of bidiagonalisation steps, on a logarithmic vertical axis. The unregularised iterate reaches 0.1056 at step 27 and then climbs to 16.1 — a factor of 153. The iterate with a penalty on the projected problem reaches 0.1079 and stays within 0.00% of it for the rest of the run.

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.

5 distinct claims across 6 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.

The rule does not apply to it. It factorises nothing, so there is no residual it could be withholding. That is worth stating rather than leaving blank: a site that reported the rule as satisfied by every generator would be counting mostly generators the rule never reached.

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.