New answers tagged optimization
2
53,268 29,596 29,306 total precision
Private communication with @A.Rex led to this solution, in which we construct a neural net that memorizes the answers. The core idea is that every function \$f\colon S\to\mathbf{R}\$ over a finite set \$S\$ enjoys the decomposition
$$ f(x) = \sum_{s\in S}f(s)\cdot \left\{\begin{array}{cl}1&\text{if }x=s\\0&\...
5
14,674,000,667 5,436,050 5,403,448 10,385 5,994 4,447 3,806 total precision
For a baseline, I investigated the following approach: Select \$M,\delta,\epsilon>0\$ such that if we sample the polynomial \$p(x)=x^3+ax^2+bx+c\$ at
$$ S:=\{-M,-M+\delta,-M+2\delta,\ldots,M\}, $$
then the largest sample point \$s^\star\in S\$ satisfying \$p(s^\star)<\...
1
182 white squares
Inspired by Robin Ryder's answer, I tried to squeeze in a couple more white squares. I believe this solution is unique, and I will soon post verification code accordingly.
Computer-readable grid:
HETERONORMATIVE
OVEROPINIONATED
POSSESSEDNESSES
B##############
INCOMMUNICATIVE
NEUROANATOMICAL
DETERMINATENESS
###############
...
13
Octave, 96 88 87 84 76 54 50 weights & biases
This 6-layer neural net is essentially a 3-step sorting network built from a very simple min/max network as a component. It is basically the example network from wikipedia as shown below, with a small modification: The first two comparisons are done in parallel. To bypass negative numbers though the ReLU, ...
9
180 white squares
My strategy was simply to find a smaller rectangle with no black squares, such that it can be filled in uniquely. All 2×k rectangles have multiple solutions. For 3×k rectangles, there are multiple solutions for k between 3 and 14, but there is a exactly one solution for k=15.
I then fit 4 such rectangles in the grid. This means that ...
0
[Python 3] (644449*2+0) 1288898 points
Perfect accuracy in only 644449 bytes
import zlib,base64 as s
t=enumerate(zlib.decompress(s.b64decode(b'###')).decode());a=lambda c:next(t)[1]
The full code cannot fit in an answer, so I have put it here and replaced the large binary string literal with b'###' in the answer text.
This is generated with the ...
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