Post on 16-Oct-2020
Equivalence Queries: done by parallel exploration
Extraction
Extracting Automata from Recurrent Neural Networks Using Queries and CounterexamplesGail Weiss, Yoav Goldberg, and Eran Yahav
Supported by European Union’s Seventh Framework Programme (FP7) under grant agreement no. 615688 (PRIME)
Interaction Overview:
RNN
DynamicPartitioning
Membership Queries
Equivalence Queries
L*
Demonstration: Learning : (all words that start and end the same, over {a,b})ε |a(a |b)*a |b(a |b)*b
ε? a? b?
L*
RNN
ba
?
L*
RNN
bb? bab? baa? bba? …
L*
RNN
Equivalence queries can cause
refinements!
aba
?
L*
RNN
abb?abab? abba?aaa?aa? …
L*
RNN
?
L*
RNN
Demonstration:
Differentiating suffix (of states 0,2) is “ab”.Check “ab” (state 0 + “ab") and
“bab" (state 1 + “ab”).RNN agrees with L* on “ab” and on “bab”,
so partitioning is refined
(Could have not agreed, then counterexample would be returned)
L* DFA
-1-1
1
1
initial state - reached with “”
0
a
1 2
3
a,b
a
a
b
bb
1
10
a reached with “a”
0
a
1 2
3
a,b
a
a
b
bb
-1-1
1
1
0
a
0
a
1 2
3
a,b
a
a
b
bb
-1-1
1
10
a
1-1
-1
0
a
1 2
3
a,b
a
a
b
bb
0
a
1 2
3
a,b
a
a
b
bb
1
1
01
a b
reached with “b”
-1-1
1
101
a b
0
a
1 2
3
a,b
a
a
b
bb
-1-1
1
101
a b
0
a
1 2
3
a,b
a
a
b
bb2
-1-1
1
101
a b
0
a
1 2
3
a,b
a
a
b
bb2
a
reached with “aa”
-1-1
1
1
0
a
1 2
3
a,b
a
a
b
bb
-1-1
0
Cluster ConflictDifferentiating suffix (of states 0,1) is the empty word.
Check empty word (state 0) and “a" (state 1).RNN agrees with L* on empty word and on “a”,
ao partitioning is refined
Cluster Conflict Classification ConflictRNN disagrees with L* on “aa".
A counterexample is returned to L*.
Counterexample: aa
github.com/tech-srl/lstar_extraction contains also link to a Google Colaboratory notebookTry it yourself: