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numbo

Goal: recreate FARG's Numbo in Clojure

See Fluid Concepts & Creative Analogies, p.131 onwards (Chapter 3)

Usage

lein run - kicks off and starts a run

lein run -- -t 114 -b 1,6,7,11,20 -i 1000 -c 10 -t : target value -b : bricks to use to make this value -i : number of iterations to run a single calculation before giving up -c : number of times to run this target/bricks combo

lein test - unit tests lein repl - loads all code, run (-main) to trigger the GUI and leave a REPL open

Dump CSV output at the end of the Raw data tab of https://docs.google.com/spreadsheets/d/1WZ5VMy2MDzJz80Jh93ApQpbrfS-tuu16n_Xqfur-Egk/edit#gid=0

(I'm using this spreadsheet to track and analyze runs - the two "Run Analysis" tabs let me do side-by-side comparisons)

Tags and experiments

I'm tagging a new version wherever things get noticeably better, and documenting experiments here. I'm keeping output of experiments in the runs/ directory

v1.01

first fully running version with automated tests

v1.02

  • played w/frequencies: dismantler 5->10, pump-target 5->10 pump-brick 5->10; didn't make much difference to speed
  • played w/frequencies: dismantler 5->2, pump-target 5->2 pump-brick 5->2; didn't make much difference to speed
  • made the random-creator 2 -> 1, everything else back to 5. Lots of failures in the first test
  • (2020.07.30-21.34.19) made the random-creator 1 -> 3, everything else on 5 - not much difference, maybe slightly worse
  • (2020.07.31-08.11.08) Slower decay, less pumping: cy/DEFAULT_ATTRACTION_DEC from 0.02 -> 0.01, pn/DEFAULT_DECAY 0.1 -> 0.05 core/brick and pump frequency 5->10 . Slows av # iterations but leads to more solutions and an uplift for 87 (8 3 9 10 7)
  • (2020.07.31-14.46.21) Allowed secondary targets to be fulfilled by single bricks, and slowed the decay/pumped less often - GREAT, went from solving 5 to 7 puzzles, run-times were up a little tho. MARKED v1.03

v1.03

  • tried lots of runs for "lein run -- -t 116 -b 20,2,16,14,6 -i 10000 -c 10000" - do we ever go for depth 3? No, we always find something sooner - e.g. ((6 * 20) - (20 - 16)) not (20 * 6)- (2 + (16 - 14)) (see 116-target-10k.csv). 3% failed, 0.5% found ((6 * 20)= (20 - 16)) or equivalent, rest were ((6 * 16) + 20) or equivalent
  • random-target2 now samples by attraction instead of pure randomness
  • (2020.08.01-08.44.10) 1000 attempts on 81 , (9 7 2 25 18), it never gets there.
  • (2020.08.03-22.00.58 v1.03-2-g29b4f1e) updated the worthiness calculator so if there's an activated node near the eval'd value we use it; this lengthens the calculation a lot but gets us 8/10 ( whilst degrading the solution %age for a few). I suspect that pnet activation and overly empty coderacks are a problem now (1/5 of our iterations for this run were nil, many must be just 1 codelet in the rack, so in practice we're never selecting between alternatives). MARKED 1.04

v1.04

  • Upped the frequency of events going into the coderack and implemented a decay there so it never has >32 items in it. IT RAN SO SLOW IT HURT - no debugging output at all, tho I could see stuff go past in the logs
  • Rewound a bit after getting poor result and started playing with the frequency of doing random stuff
  • (2020.08.09-09.03.26) do random stuff every iteration - 8/10 solved, but %ages solved low (1 @ 100%)
  • (2020.08.08-12.26.48) every 2 iterations, 8/10 solved and %ages higher (2 @ 100%, 1 @ 95, 1 @ 99)
  • (2020.08.09-11.42.53) every 3 iterations, 8/10 solved and still higher (3 @ 100%, 1 @ 99, many others in 80s) - also getting faster
  • (2020.08.09-19.38.38) every 5 iterations, 8/10 solved (2 @ 100, 5 in 90s, 1 at 89)
  • (2020.08.09-20.27.03) every 10 iterations, 8/10 solved but quality of a few seems to drop off. So it seems like the best is in between
  • (2020.08.09-20.59.37) every 7, a few drop, a few gain, but overall slower
  • (2020.08.10-07.15.19) seems best balance (MOVED to v1.05)

v1.05

  • added 20 + 20 = 40 to pnet which ought to help with 41 5,16,22,25,1 (it did: 6 --> 63%)
  • played with pnet deactivation: 0.1, 0.2, 0.9 for nneighbor, neighbor and activated node, decay 0.02 (basically, make highly activated nodes nonlinearly more likely - focus on a single idea more readily) (also cyto nodes start less attractive, are pumped 0.7, decay more slowly) (worse)
  • dropped iterations to 2000, it's more important for us to test fast than be exhaustive.
  • looked into some solutions, really struggled with 31. Tried modifying rand-syntactic-comparison
  • we have a ton of wasted iterations where there's nothing in the coderack. Started logging these, they're a smell...
  • ok, rewrote get-temperature, started running random operations based on temperature at the same frequency. Coderack more rarely empty. So how important are individual random operations?
  • (2020.08.22-12.19.07) disabled rand-block: avg solutions=1, avg time=1213, % solved=48, % blank=30
  • (2020.08.22-12.40.49) nothing disabled: avg solutions=2.7, avg time=1351, % solved=43, % blank=15
  • (2020.08.22-13.21.54) disabled seek-facsimile: avg solutions=3.1, avg time=1573, % solved=27, % blank=34
  • (2020.08.22-13.47.00) disabled rand-target-match: avg solutions=3, avg time=1368, % solved=40, % blank=28
  • (2020.08.22-14.21.03) disabled rand-syntactic-comparison: avg solutions=2.8, avg time=976, % solved=, 68, % blank=10
  • Conclusions: seek-facsimile seems important for solving. rand-block ensures more exploration at the cost of dead ends. syntactic-comparison is harmful. target-match useful occasionally.
  • Next steps: make syntactic-comparison + target-match v rare (1/10?), keep rand-block as-is, seek facsimile as-is
  • (2020.08.22-15.00.28) avg solutions=2.8, avg time=1056, % solved=, 63, % blank=29
  • Hmm. make rand-syntactic even less frequent? Try again with same config to get a feel for variance
  • (2020.08.22-15.47.23) avg solutions=2.8, avg time=1111, % solved=, 61, % blank=30
  • (diversion) - can't understand why 81 , (9 7 2 25 18) isnt getting 9 * (7+2) and added a pnet line to try and make this connection. If there's a pnet calculation with the result of a target, we should try and make it no?
  • (???) changed seek-facsimile and rand-block to be considered every cycle (rather than every 2): avg solutions=2.6, avg time=1250, % solved=54, , % blank=3.55 - so good for blanks but that's it
  • forced a seek-facsimile whenever we regularly pump the pnet+cyto, to be a bit more "intentional" - "go look here"
  • (2020.08.23-19.01.00) avg solutions=3.1, avg time=1072, % solved=61, , % blank=29
  • tried with both the seek-facsimile when pumping and a random one
  • (2020.08.23-20.28.34) little difference, avg solutions=2.5, avg time=1124, %solved=61, % blank=9
  • will we just randomly find answers by spending a long time? did 100 runs to 25k iterations each on 31 , (3 5 24 3 14) - no answers anywhere. SO WE NEED NEW CODELETS yay
  • OK, made it so rand-block can use sub-blocks
  • (2020.09.08-13.07.57) Did a full test. A bit better, avg solutions=3.1, time=989, %age solved=64%, % blank = 19% (TAGGED to v1.06)

v1.06

  • Updating to use samplers
  • Turned down FREQ_PUMP_TARGET to 20 to avoid overfocusing on a solution
  • (2020.09.09-10.23.47) avg solutions=1.2, avg time=1136, % solved=52, % blank=59
  • Turned FREQ_PUMP_TARGET back to 10 - that %age blank is hideous
  • (2020.09.10-07.28.07) avg solutions=1.2, avg time=1032, % solved=58, % blank=36
  • So something about sampling must be broken....
  • In seek-facsimile, 20+20=40 maps to 22+22, which cannot be satisfied
  • Error is in (map (comp cy/closest-node misc/int-k) (pn/filter-links-for (:links calc) :param))
  • This allows the same parameter to be pulled twice - cy/closest-node needs to take multiple parameters
  • Rewrote and fixed!
  • (2020.09.10-09.37.51) avg solutions=2.6, avg time=844, % solved=70, % blank=15 - MUCH BETTER
  • shuffle inputs to closest-nodes
  • (2020.09.10-10.03.20) avg solutions=3.1, avg time=891, % solved=69, % blank=15
  • Pinned misc.normalized minimal value to 0.01 so that there's always a chance of getting 0-activated items and when we have nothing but zeros something can be chosen. Got an NPE when running this but can't repro it, seems rare...
  • OCCASIONAL NULLPOINTEREXCEPTION. Added some debugging to see what's going on, repro's v occasionally
  • (2020.09.10-10.52.25) avg solutions=3.2, avg time=910, % solved=68, % blank=16 - pinning didn't do much
  • We were allowing some poor solutions (9 7 2 25 18 --> 9 * 9). Fixed the get-solutions so it checks against a second count of actual bricks, stored in :original-bricks
  • (2020.09.10-12.47.50) avg solutions=2.7, avg time=964, % solved=66, % blank=16 - pretty good (TAGGED to v1.07)

v1.07

  • 41 (5 16 22 25 1) had a tiny success rate. 22+25 wasn't started from 20+20 because 16 and 22 are both nearer 20 than 25 is... so I made fuzzy-closest-nodes which occasionally looks beyond the obvious choices
  • (2020.09.10-19.52.48) avg solutions=3.4, avg time=879, % solved=73, % blank=17 - BEST YET, with an 86% success rate for 41, up from 6%
  • Looking at 31 (3 5 24 3 14) - ((5 * 3) * 3) - 14)
  • We frequently make 3 * 5 = 15 but never go with it. I've added 3 * 15 = 45 to the pnet, no joy.
  • Now activate the pnet with the results of any block we make, initially but not periodically, to "suggest" calculations be tried from this block?
  • Updated seek-facsimile to use blocks as well as bricks for inputs. Seems to solve t=31
  • (2020.09.11-10.03.30) avg solutions=4.8, avg time=815, % solved=75, % blank=4
  • But trialled in visualizer with t=114, and it's crazy
  • seek-facsimile over-triggers a lot - e.g. 3 * 4 = 12 leads to 20 * 143 = 2860 because that's all there is
  • stopped it and rand-block from ever multiplying by 1
  • tweaked seek-facsimile so the result of the made calculation has to be within 50% of the calc we're trying to facsimile
  • Noted (9 7 2 25 18) never gets 9 * ( 7 + 2)
  • Set the minimal dismante config to 0.4
  • (2020.09.11-11.33.52) avg solutions=4.4, avg time=885, % solved=70, % blank=29
  • (looks like it screwed t=31, helped t=114)
  • Set the minimal dismante config to 0.3 - makes little difference to t=31 (18% success still), t=114 is 57% (down
  • Raised it to 0.5, t=114 is 73%, t=31 is 9%
  • (2020.09.11-12.06.34) avg solutions=4.1, avg time=882, % solved=69, % blank=28

parallel

  • Did a trial of evolving 10 children/generation for 10 generations. Parallelized with pmap, it ran in 31 hours(!). Results were a little better: average solutions= 4.5, average time= 851.8 %age solved=72.4, )

  • The same thing run in serial took 49h, but some of these hours were at the same time (i.e. parallel one suffered). Serial results were not so great, but maybe in the same error: 4.8 solutions, average 898.4 iterations, 70.2% solved

  • Tried again, in parallel, evolving more aggressively: made it 6 children/generation, 20 generations, 20% likely that any parameter changed. Started from the 72.4 point {:FUZZY_CLOSEST_MID 0.9, :PN_INC 21/100, :PN_DECAY 2/25, :ATTR_INC 83/100, :FREQ_DISMANTLE 7, :URGENCY_LOW 1, :ATTR_DEFAULT 77/100, :PN_SELF 259/50, :CODERACK_SIZE 31, :FREQ_PUMP_TARGET 13, :PN_DEFAULT 1/25, :FREQ_RAND_SYNTACTIC_COMPARISON 11, :URGENCY_MEDIUM 8, :FREQ_PUMP_BRICK 10, :FREQ_SEEK_FACSIMILE 10, :ATTR_DEC 1/25, :PN_NNEIGHBOR 113/100, :FREQ_RAND_BLOCK 4, :PN_NEIGHBOR 323/100, :FUZZY_CLOSEST_TOP 21/25, :URGENCY_HIGH 6, :FREQ_RAND_TARGET_MATCH 13}

  • fixdc unworthy-block sampler

  • only take items from the next generation which are better than the current one. Take 5 then the best of that

  • Iteration= 3 percent= 76.4 cfg= {:FUZZY_CLOSEST_MID 0.9, :PN_INC 21/100, :PN_DECAY 13/100, :ATTR_INC 83/100, :FREQ_DISMANTLE 7, :URGENCY_LOW 1, :ATTR_DEFAULT 17/20, :PN_SELF 521/100, :CODERACK_SIZE 31, :FREQ_PUMP_TARGET 13, :PN_DEFAULT 1/25, :FREQ_RAND_SYNTACTIC_COMPARISON 11, :URGENCY_MEDIUM 8, :FREQ_PUMP_BRICK 12, :FREQ_SEEK_FACSIMILE 10, :ATTR_DEC 3/25, :PN_NNEIGHBOR 6/5, :FREQ_RAND_BLOCK 4, :PN_NEIGHBOR 323/100, :FUZZY_CLOSEST_TOP 21/25, :URGENCY_HIGH 6, :FREQ_RAND_TARGET_MATCH 13}

  • Changed evolve-config to evolve 50% of the time, not 20%; 1000 iterations per round

  • Best now (after 1x250-mutation iteration) Iteration= 1 percent= 67.7 cfg= {:FUZZY_CLOSEST_MID 0.9, :PN_INC 1/4, :PN_DECAY 33/100, :ATTR_INC 49/50, :FREQ_DISMANTLE 9, :URGENCY_LOW 3, :ATTR_DEFAULT 17/20, :PN_SELF 539/100, :CODERACK_SIZE 31, :FREQ_PUMP_TARGET 15, :PN_DEFAULT 13/100, :FREQ_RAND_SYNTACTIC_COMPARISON 17, :URGENCY_MEDIUM 13, :FREQ_PUMP_BRICK 15, :FREQ_SEEK_FACSIMILE 11, :ATTR_DEC 8/25, :PN_NNEIGHBOR 6/5, :FREQ_RAND_BLOCK 8, :PN_NEIGHBOR 323/100, :FUZZY_CLOSEST_TOP 0.9, :URGENCY_HIGH 10, :FREQ_RAND_TARGET_MATCH 14}

After another, still the best {:FUZZY_CLOSEST_MID 0.9, :PN_INC 1/4, :PN_DECAY 33/100, :ATTR_INC 49/50, :FREQ_DISMANTLE 9, :URGENCY_LOW 3, :ATTR_DEFAULT 17/20, :PN_SELF 539/100, :CODERACK_SIZE 31, :FREQ_PUMP_TARGET 15, :PN_DEFAULT 13/100, :FREQ_RAND_SYNTACTIC_COMPARISON 17, :URGENCY_MEDIUM 13, :FREQ_PUMP_BRICK 15, :FREQ_SEEK_FACSIMILE 11, :ATTR_DEC 8/25, :PN_NNEIGHBOR 6/5, :FREQ_RAND_BLOCK 8, :PN_NEIGHBOR 323/100, :FUZZY_CLOSEST_TOP 0.9, :URGENCY_HIGH 10, :FREQ_RAND_TARGET_MATCH 14}

  • I'm not mutating any of the priorities of individual codelets. I tried that:

Iteration= 4 percent= 65.4 urgencies= {:check-done 5, :test-block 3, :rand-syntactic-comparison 1, :rand-target-match 1, :create-target2 10, :activate-pnet 1, :inc-attraction 1, :load-brick 12, :fulfil-target2 4, :dismantler 1, :probe-target2 8, :seek-facsimile 3, :load-target 1, :rand-block 1}

  • Kicked of three attempts to start from random positions. All quickly make it to ~ 65 %, then hang there.
  • Wrote run-epoch-random to start from 500 random positions and choose the first 5 > 60%, all end up in the same place.

Next

  • consider blocks as input to seek-facsimile

81 (9 7 2 25 18) - never gets 9 * (7+2). Why is 9 * 9 not tried early, 9 as a target2?

  • 7+2 = 9
  • TODO: test-block should see whether the result is part of a calc leading to the entry, if so probe-target2
  • TODO: probe-target2 should look for multipliers

No solutions for: 127 (7 6 4 22 25) - (((25 - (6 + 4)) * 7) + 22)

TODO stack

  • TODO: move sampler code into its own file
  • TODO: make the ratios in misc/fuzzy-closest-nodes configurable parameters
  • TODO: cy/format-block and cl/-format-block are the same, resolve
  • TODO: make the constant in dismantler configurable

Future ideas

Memory

What I'm noticing now: Numbo gets fixated on a possible, reasonable path and doesn't try others e.g. when trying to get to 31, 3 * 14 = 42 comes up again and again. Just 11 different! But we can't make 11.

Solution: introduce a memory:

  1. Whenever you dismantle, add the block you're dismantling to memory (count=1) or up its count
  2. Before creating a block, if it exists in memory. If it does, it has a count% (capped at 95) chance of being silently dropped.

Bricks as starting points

We need to consider bricks as starting points to calculations, not just blocks, to cover the 9 * (7 + 2) = 81 case If seek-facsimile gets a brick 9, it should make a block 9 * 9, with that second 9 being a secondary target. This should stimulate a 7+2 to occur. To do this

  • seek-facsimile --> make-block (brick1 op)
  • make-block sees if we can make a block using brick1 and op, sets it up, adds brick2 as a secondary target

Evolve parameters

I've got a lot of config params in config.clj

Evolve them:

  1. Do a run with 10 different variants of parameters
  2. Take the best 3 (measured by % complete)
  3. Do 6 evolutions of #1, 3 of #1, 1 of #3
  4. Repeat; should be O(7) runs in 24h
  5. Get good results on 1-4; drop the # iterations; repeat (?)

Bugs

  • If "3" is a secondary target in block A, but also a component of block B, when B is dismantled "3" is never returned to the bricks (because we assume it's a secondary target right). Solution: when dismantling, count how many times a brick is used in all blocks, not the current one?

Improvements

Strategies:

  • if things decay slower we don't need to pump them so often, so can reduce the activation-refresh and focus on calculations?
  • counterargument: if things decay faster we'll get rid of them quicker so can try new theories out faster!
  • break out the different things in random-creator and run them at separate timings
  • Break out the noise. If a thing makes less difference, just do it less anyway. (e.g. reduce frequencies as far as poss? map impact of reduction over many runs?)
  • 81 , (9 7 2 25 18) never gets (9 * 7) + 18 - same problem? - or ((18 * (7 - 2)) - 9) (WOULD ADDING 7 * 9 HELP?)
  • 31 (3 5 24 3 14) never gets (((5 * 3) * 3) - 14) - complex tho
  • 116 , (20 2 16 14 6) never gets (20 * 6)- (2 + (16 - 14)) - but has simpler solutions
  • 127 (7 6 4 22 25) never gets ((25 - (6 + 4)) * 7) + 22)
  • Start measuring the # of iterations where there's nothing on the coderack - this is a smell that we're underpopulating it/running too cool, and are effectively linear
  • Activation is linear, make it nonlinear - i.e important things should be way more likely to get sampled

Viz:

  • Make the current iteration an input field which you can put a value into
  • work out how to make scroll bars appear on canvas
  • input target and initial bricks in the visualizer

PNet:

  • Why does activation of :times not spread? Because it's got no pnet links. Seems bad
  • In pn/activate-node, take into account the weights of nodes

Cyto:

  • add more rules to rand-syntactic-comparison
  • drop-off in activation
  • see also p234 of paper for more. I think we could do more target comparisons (B)
  • we have 2 cy/random-target2 methods

Codelets:

  • cl/rand-op can multiply by 1, which doesn't seem so useful - never do this

License

Copyright © 2020 Tom Hume

This program and the accompanying materials are made available under the terms of the Eclipse Public License 2.0 which is available at http://www.eclipse.org/legal/epl-2.0.

This Source Code may also be made available under the following Secondary Licenses when the conditions for such availability set forth in the Eclipse Public License, v. 2.0 are satisfied: GNU General Public License as published by the Free Software Foundation, either version 2 of the License, or (at your option) any later version, with the GNU Classpath Exception which is available at https://www.gnu.org/software/classpath/license.html.

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Implementation of Numbo, a cognitively plausible number puzzle solver

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