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The normalized cell error for cell at time n
|V(Hc(1,1))|=25|E(Hc(1,1))|=40|V(Hc(2,1))|=21|E(Hc(2,1))|=24|V(Hc(3,1))|=9|E(Hc(3,1))|=8
|V(Hc(1,2))|=13|E(Hc(1,2))|=12|V(Hc(2,2))|=16|E(Hc(2,2))|=16|V(Hc(3,2))|=10|E(Hc(3,2))|=10
|V(Hc(1,3))|=35|E(Hc(1,3))|=32
|V(Hc(3,3))|=13|E(Hc(3,3))|=16
Collectively Cooperative Learning: Learning Group Sizes in Computer GoTae-Hyung “T” Kim Ganesh Kumar Venayagamoorthy Donald C. Wunsch II [email protected] [email protected] [email protected]
AcknowledgementAuthors would like to thank Intelligent Systems Center, Mary K. Finley Missouri Endowment, and National Science Foundation, contract number ECCS-0725382, for their financial support to perform this research. The authors also would like to thank Rui Xu, John Seiffertt, Sriram Chellapan and Sejun Kim for their insightful discussions.
Introduction• Collaborative learning is an educational approach that students team up to explore a question or create a meaningful project.• Cooperative learning is a subset of collaborative learning to learn a subject in cooperation with team members. The students at different levels not only are responsible for learning the subject, but also help teammates to learn via interactions. They are individually accountable for their work and the work group as a whole is also assessed.• Collectively cooperative learning (CCL) is a novel machine learning approach to learn a subject in cooperation with teams of learning agents. Both the individual and the group are assessed. The term collectively differentiates CCL from cooperative learning.
• Properties of CCL• Goal-oriented. There is a goal each individual and team should learn.• Independent. Each agent learns independently to meet the goal.• Interactive. A team of learning agents cooperates to learn the goal.• Adaptive. CCL can process various types of inputs.• Scalable. CCL can deal with various sizes of the arena.
Cell outputCTOP
CLEFT
CRIGHT
ManagerCell
Proc.1
Proc. 2
Cell input
CBOTTOM
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-1 0
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-1-
1-1
-1-
1-1
-1-
1-1
-1-
1-1
-1-
1-1
-1-
1-1
-1-
1-1
-1-
1-1
-1-
1-1
-1-
1-1
-1-
1-1
-1
-1
-1-
1-
1-1
-1-
1-1-
1
-1-
1-
1-1
-1-
1-
1-1
-1-
1
-1 -
1
-1 -
1
-1 -
1
-1 -
1
-1-
1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
timen=1
n=Nend
Syst
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inpu
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Lear
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Syst
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outp
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-1 0
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0 -4
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01
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-4-
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-4-
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5-5
-1
0-
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-1
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-1
0-
10-
10
-4-
4-4
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6-6
-1
-1
-2-
2-
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-5-
5-
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-1
0
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4-4
-4-
4-
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-7-
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-7 -
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-6 -
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-2 -
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-2 -
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-1-
1
-1
-1
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-1
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-1
-6
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-1
-1
-7
-4
-1
-1
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010
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0
10
10
.
Group size counting problem in computer Go
• A square lattice graph G=(V,E).
• The graph size set S of the graph G
• The size sn of a subgraph Hn=(Vn,En)
• The total number of subgraphs N in a graph G may vary.
• An autonomous processing unit (APU) learns the sub-graph size from zero-knowledge.
GHNnHVsS nnnn ;,,2,1 ,xeach verteon |)(|: (1)
• (Group size counting problem=a sub-problem in computer Go)| essential info. for judging the life and death of the group
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11
-1
0 0
0
00 1 0
1
0
0
01
0
3
32
-1
0 0
0
00 230
16
17
18QM N O P
The proposed approaches• Recursive approach
• Use function recursion giving a bird eye view of the board.
• Non-recursive approach• Local/myopic visibility.• Neighborhood status tree’s tree traversal mechanism is implemented via
baton passing concept.
The non-recursive approach
1
Cell outputCTOP
CLEFT
CRIGHT
ManagerCell
Proc.1
Proc. 2
Cell input
CBOTTOM
1ˆ
0,ˆˆ
, sg
sro
n
nn
Estimated cell output at time n
Estimated root cell index
Estimated group sizenr
g
Feedback output of the neighboring cells at time n-1
CtopCbottom Cleft Cright
Ccenter
Ctop
Feedback output of the neighboring
cells at time n
Feedback output to the neighboring cells at time n+1Cbottom Cleft CrightCtop
no b s no b s no b s no b s
1ˆ no b s
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0 0
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00 1 0
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0 16
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18QM N O P
01
0
3
32
-1
0 0
0
00 230
Root cell discovery phase
Group sizecounting phase
Group sizePropagation phase
Phase 1
Phase 2
Phase 3
Non-steady-state s=0
Steady state s=1
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-1
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-1 -
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-1 -
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-1 -
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-1-
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-1
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-1
-1
-1
-1
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time
n=1
n=Nend
Syst
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inpu
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Lear
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Syst
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outp
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-1
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0
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01
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00
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00
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00
00
1
30
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02
00
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0
0
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0
00
00
01
01
00
0
30
00
0
00
00
00
00
00
00
00
00
-4
-4
-4
-4
-4
-4
-5
-5
-5
-5
-5
-5
-1
0-1
0-1
0
-1
0-1
0-
10
-4
-4
-4
-7
-7
-7
-7
-7
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-6
-6
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-6
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-1
-1
-2
-2
-5
-5
-5
-5-
10-
10
-6
-6
-4
-4
-4
-4
-7
-7
-7
-7
-7 -
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-6 -
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-2 -
2
-2 -
2
-1-
1
-1
-1
0-
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-1
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-1
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-1
-1
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-1
-11
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.
QM N O P
17
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16
1
• Baton passing concept ← recursive solutionHscattered
|V(Hscattered)|=1|E(Hscattered)|=0
Hspirangle
|V(Hspirangle)|=199|E(Hspirangle)|=198
Hc(row,col)row
col.
1
2
3
1 2 3
COUNT_AND_PROPAGATE_GROUP_SIZE(C) 1 if (C.b=1 and C.c1=0) or (C.b=2 and C.c2=0) 2 then if C.v=0 // The first time this cell is visited? 3 then C.v← 1 4 if C.b=1 5 then g← COUNT_GROUP_SIZE(C.g,C.id,C.r) 6 [C.V,C.n,leave]=IS_LEAVE_THIS_CELL(C.V,C.S,C.s) 7 if leave 8 then return C 9 if C.b=1 10 then C.c1← 111 C.V← zeros(1,4)12 else // if C.b=213 then C.c2← 114 if C.T=;[] // If trail is empty,15 then [C.n,C.T]=POP_STACK(C.T)16 elseif (C.b=1 and C.c1=1) or (C.b=2 and C.c2=1)17 then if C.T=;[]18 then [C.n,C.T]=POP_STACK(C.T)19 else20 then if C.b=121 C.b← 222 else23 then C.b← - 124 [C.V,C.n,leave]=IS_LEAVE_THIS_CELL(C.V,C.S,C.s)25 if leave26 then return C27 return C
UPDATE_CELL(C,R_Temp) 1 if C.s=0 // Empty status requires no action 2 then C.r← 0 3 else // C.s=1 or - 1 4 if C.p=0 // non- steady- state 5 then C← DISCOVER_ROOT_CELL(C,R_Temp) 6 elseif C.p=1 and C.b=;0 // Bypass a cell w/o a baton 7 then C=COUNT_AND_PROPAGATE_GROUP_SIZE(C) 8 return C // Note C is a structure or CELL{x,y}
DISCOVER_ROOT_CELL(C,R_Temp) 1 Tmp← C.r 2 for i← 1 to 4 3 do if C.S(i)=C.s 4 then Tmp← [Tmp R_Tmp(i)] 5 if min(Tmp) <C.r 6 then C.r← min(Tmp) 7 else 8 then C.w← C.w+1 9 if C.e < C.w10 then C.p← 111 if C.id=C.r12 then C.b← 113 return C
COUNT_GROUP_SIZE(g,id,r) 1 if id=r // Root cell? 2 then g← 1 3 else 4 then g← g+1 5 return g
IS_LEAVE_THIS_CELL(V,S,s) 1 leave← 0 2 n← 0 // if S(i)=;s 2 for i← 1 to 4 3 do if V(i)=0 // Not checked? 4 then V(i)← 1 5 if S(i)=s 6 then n← i 7 leave← 1 8 break 9 return [V,n,leave]
POP_STACK(Stack_trail) 1 index← length(Stack_trail) 2 output← Stack_trail(index) 3 Stack_trail(index)← [] 4 return [output, Stack_trail]
• Pseudo-code of the non-recursive solution
The recursive approach
1 2
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8 9
Raw board status
COUNT_GROUP_SIZE_RECURSIVELY(p,x’,y’,D,V,g) 1 if p=D(x’,y’) and V(x’,y’)=;1 2 g← g+p // initialize G to a bxb matrix with zeros 3 V(x’,y’)← 1 // initialize D to a b’xb’ matrix with infinities 4 [g,V]=COUNT_GROUP_SIZE_RECURSIVELY(p,x’- 1,y’,D,V,g) // Up 5 [g,V]=COUNT_GROUP_SIZE_RECURSIVELY(p,x’+1,y’,D,V,g) // Down 6 [g,V]=COUNT_GROUP_SIZE_RECURSIVELY(p,x’,y’- 1,D,V,g) // Left 7 [g,V]=COUNT_GROUP_SIZE_RECURSIVELY(p,x’,y’+1,D,V,g) // Right 8 return [g,V]
1 1
1 1 1 1
1 1
1
- 1 - 1
- 1
- 1 - 1
- 1 - 1
- 1 - 1
0 0 0
0 0 0
0 0 0 0 0 0
0 0 00
0
0
x
y
Board representation B
x
y
00
0 0000
00 0000
00 0
00
0 0
0 0
0 0 0 0 0
0 0 00
0
0
0
0
0
Group size G
∞
∞
∞
∞
∞
∞
∞
∞
1
1 1 1
1 1
1
- 1
- 1
- 1 - 1
- 1 - 1
- 1 - 1
0 0
0 0
0 0 0 0 0
0 0 00
0
0
∞ ∞ ∞ ∞ ∞ ∞ ∞
1
1
- 1
0
0
0
∞ ∞ ∞ ∞ ∞ ∞ ∞
∞
∞
∞
∞
∞
∞
x’
y’
Dummy Board D
00
0 0000
00 0000
00 0
00
∞
∞
∞
∞
∞
∞
∞
∞
0 0
0 0
0 0 0 0 0
0 0 00
0
0
∞ ∞ ∞ ∞ ∞ ∞ ∞
0
0
0
∞ ∞ ∞ ∞ ∞ ∞ ∞
∞
∞
∞
∞
∞
∞
x’
y’
Visit Mark V (Initialized)
1
0 ∞ 11
1 ∞ - 1- 1 0 1 0- 1
(2,1)
(3,1) (2,2)
(2,1)(2,1)
g=1
g=2 g=3
Neighborhood status tree
Conclusions
1x
y
1 1
1
Board status B Dummy board D
∞
∞
∞
∞
∞
1
1
∞ ∞ ∞
1
1
x’
y’
∞ ∞ ∞ ∞
∞ 1
∞
1
1
∞1
∞
1
1
∞
1
1
∞
1
1
11
1
1
2 3
44 4
44
4
∞
1
1
∞
1
1
(1,1)
∞ 1
(2,1)
1 ∞ ∞ 1
(2,2)
11
(1,2)
1∞ 1
∞ 1
∞
∞ ∞
• Neighborhood status tree (NST)
• One baton per group
• Only a cell with a baton is activated.
Simulation configurations• Board size b=2~5 (all settings), 6 (sample), 19 (100 professional games).
1
0
0
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1 0
01
1 0
1 1
1
1 1
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0 0
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0 0
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1
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0
0
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0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
b=2
b=3
rowcol.
1
2
3
1 2 3
b=6 b=19
00
0
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-1
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-1-
1-1
-1-
1-1
-1-
1-1
-1-
1-1
-1-
1-1
-1-
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-1-
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-1-
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-1-
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-1-
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-1
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-1-
1-
1-1
-1-
1-1-
1
-1-
1-
1-1
-1-
1-
1-1
-1-
1
-1 -
1
-1 -
1
-1 -
1
-1 -
1
-1-
1
-1
-1
-1
-1
-1
-1
-1
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-1
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-1
-1
timen=1
n=Nend
Syst
em
inpu
t
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Lear
ning
Syst
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outp
ut
00
00
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0
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0
00
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-1
04
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03
0 -4
0
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0
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00
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0
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1
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00
01
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05
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00
00
00
00
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2
6
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00
00
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00
00
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00
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00
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00
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00
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00
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00
00
0
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00
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0
03
02
20
00
00
01
01
00
03
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00
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00
00
00
00
00
-4-
4-4
-4-
4-4
-5-
5-5
-5-
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-1
0-
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0
-1
0-
10-
10
-4-
4-4
-7-
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-7-
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-6-
6-6
-6-
6-6
-1
-1
-2-
2-
5-5
-5-
5-
10
-1
0
-6-
6-
4-4
-4-
4-
7-7
-7-
7
-7 -
7
-6 -
6
-2 -
2
-2 -
2
-1-
1
-1
-1
0-1
0
-7
-1
-4
-1
-6
-6
-1
-1
-7
-4
-1
-1
101
010
101
010
101
0
10
10
.
…
• Games in SGF format is reformatted and converted to a board status matrix B.
x y
x y
x y
x y
x y
N
x
N
y
yx
N
x
N
y
yxn
yx
N
x
N
y
yx
N
x
N
y
yxn
nnN
x
N
y
yxnn ee
1 1
),(
1 1
),(),(
1 1
),(
1 1
),(
1 1
),(
ˆ
ˆ
G
GG
G
G
G
GG
G
G
),(
),(),(
),(
),(),(
ˆ
yx
yxn
yx
yx
yxnyx
neG
GG
G
G
The normalized system error at time n
),( yxne
00
0
00
00
00
00
00
00
00
0
00
0
00
0
00
11
10
00
0
00
1
-1
01
11
10
10
00
1
01
1
00
0
01
10
01
0 -1
11
00
00
10
00
00
11
10
00
01
00
00
0
10
11
00
11
01
00
11
00
1
11
11
00
1
00
01
11
11
01
1
1
00
0
00
00
10
1
1
00
0
00
01
00
00
11
00
00
0
10
10
00
01
01
00
00
00
0
00
00
10
01
00
00
0
00
0
00
00
01
00
0
00
0
00
01
11
11
00
00
0
00
0
11
10
01
01
0
10
1
01
01
01
10
00
0
01
01
00
10
10
00
0
00
0
00
00
00
10
00
00
0
-1-
1-1
-1-
1-1
-1-
1-1
-1-
1-1
-1-
1-1
-1-
1-1
-1-
1-1
-1-
1-1
-1-
1-1
-1-
1-1
-1-
1-1
-1
-1
-1-
1-
1-1
-1-
1-1-
1
-1-
1-
1-1
-1-
1-
1-1
-1-
1
-1 -
1
-1 -
1
-1 -
1
-1 -
1
-1-
1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1n=1
time n
Syst
em
inpu
t
.
.
.
.
Lear
ning
Syst
em
outp
ut
00
00
00
00
00
00
00
00
00
0
00
00
00
0
00
13
30
00
0
00
30
-1 0
44
44
03
00
03
02
0
2
00
0
05
50
03
0 -4
0
54
00
00
50
00
00
0
54
40
00
05
00
00
0
50
41
00
55
06
00
0
55
00
1
55
66
00
60
00
01
55
55
05
5
6
00
00
00
00
50
2
6
00
00
00
02
00
00
21
00
00
00
10
20
00
00
10
00
0
00
00
00
00
10
0
00
00
0
00
00
00
00
0
00
0
00
00
00
02
2
00
00
0
00
00
1
30
01
02
00
20
1
0
03
02
20
00
00
01
01
00
03
00
00
00
00
00
00
00
00
00
00
-4-
4-4
-4-
4-4
-5-
5-5
-5-
5-5
-1
0-
10
-1
0
-1
0-
10-
10
-4-
4-4
-7-
7-7
-7-
7-7
-6-
6-6
-6-
6-6
-1
-1
-2-
2-
5-5
-5-
5-
10
-1
0
-6-
6-
4-4
-4-
4-
7-7
-7-
7
-7 -
7
-6 -
6
-2 -
2
-2 -
2
-1-
1
-1
-1
0-1
0
-7
-1
-4
-1
-6
-6
-1
-1
-7
-4
-1
-1
101
010
101
010
101
0
10
10
.
ne
x
y
nG
B
),( yxG
),(ˆyx
nG
),( yxnG
Simulation results
1
1
0
0
0
1 0
01
1 0
1 1
1
1 1
1
g=|V|
1
2
3
4
1
0
0
0
2 0
02
3 0
3 3
4
4 4
4
GB
1 2 3 4 5 6 7 8 9 10 110
0.2
0.4
0.6
0.8
1
g=1 g=2 g=3 g=4
Epoch n
Nor
mal
ized
sys
tem
err
or e
n
b=2,epsilon=1
id.
1
B
00
000
0 0
0
0 1
00
000
0 0
0
0
00
000
0 0
0
0
00
000
0 0
0
0
00
000
0 0
0
0
00
000
0 0
0
0
G
2
3
4 00
000
0 0
0
0 1
00
000
0 0
0
0
00
000
0 0
0
0
00
000
0 0
0
0
00
000
5 0
0
0
00
000
0 0
0
0
5
6
7
8
9
10
11
12
1 1
1 21 2
1 31 3 31
1 41 4 41
1 4
1 51 5 51
1 5
1 1
0 00 5 001 61 6 61
1 6
1 1
1 5
1 61 6
00
000
0 0
0
0
00
000
0 0
0
00 00 5 001 71 7 71
1 7
1 1
1 71 71 7
00
000
0 0
0
0
00
000
0 0
0
00 00 5 001 81 8 81
1 8
1 1
1 81 81 8
1 8
0
000
0 0
0
0
0
000
0 0
0
00 00 5 001 91 9 91
1 9
1 1
1 91 91 9
1 91 9
00
000
0 0
0
0
00
000
0 0
0
01 31 3
1 3
00
000
0 0
0
0
00
000
0 0
0
01 41 4
1 41 4
00
000
0 0
0
0
00
000
5 0
0
01 51 5 51
1 5
1 1
1 5
00
000
0 0
0
0
00
000
0 0
0
01 51 5
1 5
00
000
0 0
0
0
00
000
0 0
0
01 61 6
1 61 6
00
000
0 0
0
0
00
000
5 0
0
01 61 6 61
1 6
1 1
1 6
51
1 513
14
15
1 6
1 6
1 6
00
000
0 0
0
0
00
000
0 0
0
00 00 5 001 71 7 71
1 7
1 1
1 7
1 71 7
00
000
0 0
0
0
00
000
0 0
0
00 00 5 001 71 7 71
1 7
1 1
1 71 7
1 7
00
000
0 0
0
0
00
000
0 0
0
00 00 5 001 81 8 81
1 8
1 1
1 81 81 8
1 8
16
17
18
5 10 15 20 25 30 350
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9
1011
12
13
141516
17
18
Epoch n
Nor
mal
ize
d sy
ste
m e
rro
r e n
b=3,epsilon=4
• System input, system output and learning curve. (2x2 & 3x3)
5 10 15 20 25 30 350
0.2
0.4
0.6
0.8
1
1
2 3
4
Epoch n
Nor
mal
ize
d sy
ste
m e
rro
r e n
b=4,epsilon=0
1
• All the system outputs are correct. (4x4)
id.
1
B
00
000
0 0
0
0
G1
0
0
0
000 0
00
000
0 0
0
04
0
0
0
000 0
1 41 41 4
200
000
0 0
0
01
0
0
0
000 0
00
000
0 0
0
04
0
0
0
000 0
1 41 41 4
1 41 41 41 44
00
000
0 0
0
01
0
0
0
000 0
00
000
0 0
0
06
0
0
0
000 0
1 61 61 6
1 61 6
00
000
0 0
0
01
0
0
0
000 0
00
000
0 0
0
06
0
0
0
000 0
1 61 61 6
1 61 6
1 61 61 61 6
1 1 6 6
3
4
5 10 15 20 25 30 350
0.2
0.4
0.6
0.8
1
1
23
4
Epoch n
Nor
mal
ized
sys
tem
err
or e
n
b=4,epsilon=3
1
rowcol.
1
2
3
1 2 3
1
2
3
4
5
6
7
8
b=6
b=11
b=10
10 20 30 40 50 60 70 80 90 1000
0.2
0.4
0.6
0.8
1
123 4 5
6 78
Epoch n
Nor
mal
ize
d sy
ste
m e
rro
r e n
b=5,epsilon=8
20 40 60 80 100 120 1400
0.2
0.4
0.6
0.8
1
b=6,epsilon=1 b=10,epsilon=23b=11,epsilon=8
Epoch n
Nor
mal
ize
d sy
ste
m e
rro
r e n
5 10 15 20 25 30 35 400
0.2
0.4
0.6
0.8
1
Epoch n
Nor
mal
ize
d sy
ste
m e
rro
r e n
b=19,epsilon=3
0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 00 0 0 0 0 1 3 3 0 0 0 00 0 3 0-1 0 4 4 4 4 0 3 0 0 0 30 2 02 0 0 0 0 5 5 0 0 30 -4 05 4 0 0 0 0 5 0 0 00 0 05 4 4 0 0 0 0 5 0 00 0 05 0 4 1 0 0 5 5 0 60 0 05 5 0 0 1 5 5 6 60 0 6 00 0 0 1 5 5 5 5 0 5 5 60 0 0 00 0 0 0 5 0 2 60 0 0 00 0 0 2 0 0 0 0 2 1 0 00 0 0 01 0 2 0 0 0 0 0 1 0 0 0 00 0 0 00 0 0 0 1 0 0 0 0 0 0 00 0 0 00 0 0 0 0 0 0 00 0 0 00 0 0 2 2 0 0 0 0 00 0 0 01 3 0 0 10 2 0 02 0 1 0 0 3 0 2 2 00 0 0 00 1 0 1 0 0 0 3 0 0 0 00 0 0 00 0 0 0 0 0 0 0 0 0 0 0
-4-4-4
-4-4-4 -5
-5-5
-5-5-5
-10-10-10
-10-10
-10
-4-4-4
-7-7-7
-7-7-7
-6-6-6
-6-6-6
-1
-1
-2-2
-5-5
-5-5
-10-10
-6-6
-4-4-4
-4-7-7
-7-7
-7 -7
-6 -6
-2 -2
-2 -2
-1
-1
-1
-10
-10
-7
-1
-4
-1
-6
-6
-1
-1
-7
-4
-1
-1
101010
101010
1010
1010
0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 00 0 0 0 0 1 1 1 0 0 0 00 0 1 0-1 0 1 1 1 1 0 1 0 0 0 10 1 01 0 0 0 0 1 1 0 0 10 -1 01 1 0 0 0 0 1 0 0 00 0 01 1 1 0 0 0 0 1 0 00 0 01 0 1 1 0 0 1 1 0 10 0 01 1 0 0 1 1 1 1 10 0 1 00 0 0 1 1 1 1 1 0 1 1 10 0 0 00 0 0 0 1 0 1 10 0 0 00 0 0 1 0 0 0 0 1 1 0 00 0 0 01 0 1 0 0 0 0 1 0 1 0 0 0 00 0 0 00 0 0 0 1 0 0 1 0 0 0 0 00 0 0 00 0 0 0 0 1 0 0 00 0 0 00 0 0 1 1 1 1 1 0 0 0 0 00 0 0 01 1 1 0 0 10 1 0 01 0 1 0 1 0 1 0 1 1 00 0 0 00 1 0 1 0 0 1 0 1 0 0 0 00 0 0 00 0 0 0 0 0 1 0 0 0 0 0 0
-1-1-1
-1-1-1 -1
-1-1
-1-1-1
-1-1-1
-1-1-1
-1-1-1
-1-1-1
-1-1-1
-1-1-1
-1-1-1
-1
-1
-1-1
-1-1
-1-1
-1-1
-1-1
-1-1-1
-1-1-1
-1-1
-1 -1
-1 -1
-1 -1
-1 -1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
• We proposed collectively cooperative learning (CCL) as a novel machine learning approach to learn a subject in cooperation with teams of learning agents. • Initially unknown group size/graph size is successfully learned by the proposed recursive/non-recursive solution.• The excess waiting time ε trades off the accuracy and learning speed.• There exists a region of ε, i.e. εg, guarantees correct an answer.• A guideline to set ε is suggested, which is a convenient second order equation.• The properties of CCL are: goal-oriented, independent, interactive, adaptive, scalable.
• Life and death of a group significantly impacts the entire game.
• Some Go rules: connectivity (↕ & ↔), black & white stones placed alternately
…
…
…
…
• Performance metric),( yxC
The normalized system error at time n
• All system outputs are correct and symmetry holds.
• Only interesting system inputs are shown here.• Temperature map shows the system
behavior.
Recent contributions• New experiments with novel performance metric: normalized cell error and
normalized system error• Temperature map that visualizes the system level progress of learning is
developed and applied to experiments.
