How Contextual are Contextualized Word Representations?

!4
w {s1, . . . , sn}
{i1, . . . , in}
w = s1[i1] = . . . = sn[in]
fl(s, i) s[i]
l
SelfSiml(w) =
1
n2 − n ∑
j
∑
k≠j
cos
(
fl (sj, ij), fl (sk, ik))

!5
s ⟨w1, . . . , wn⟩
fl(s, i) s[i]
l
IntraSiml(s) =
1
n ∑
i
cos ( ⃗sl, fl(s, i))
where ⃗sl =
1
n ∑
i
fl(s, i)

!6
w {s1, . . . , sn}
{i1, . . . , in}
w = s1[i1] = . . . = sn[in]
fl(s, i) s[i] l
MEVl(w) =
σ2
1
∑i
σ2
i
[fl(s1, i1) . . . fl(sn, in)]
σ1 . . . σm

!7
Baseline (fl) = 𝔼x,y∼U(𝒪) [cos (fl(x), fl(y))]
𝒪
fl( ⋅ )
l

!8
𝒪
fl( ⋅ )
 
 
 
 
 
SelfSiml(w) = 0.95
Baseline(fl) = 0.00
Baseline(fl) = 0.99
Baseline(fl) = 0.00
Baseline(fl) = 0.99

!9
𝒪
fl( ⋅ )
 
 
 
 
 
SelfSiml(w) = 0.95
Baseline(fl) = 0.00
Baseline(fl) = 0.99
Baseline(fl) = 0.00
Baseline(fl) = 0.99

!10
𝒪
fl( ⋅ )
 
 
SelfSim*l
(w) = SelfSiml(w) − Baseline (fl)

!11

!12

!13

!14
SelfSiml(w) =
1
n2 − n ∑
j
∑
k≠j
cos
(

!15
SelfSiml(w) =
1
n2 − n ∑
j
∑
k≠j
cos
(

!16
SelfSiml(w) =
1
n2 − n ∑
j
∑
k≠j
cos
(

!17
IntraSiml(s) =
1
n ∑
i
where ⃗sl =
1
n ∑
i
fl(s, i)

!18
IntraSiml(s) =
1
n ∑
i
where ⃗sl =
1
n ∑
i
fl(s, i)

!19
MEVl(w) =
σ2
1
∑i
σ2
i

!20
MEVl(w) =
σ2
1
∑i
σ2
i

!21
MEVl(w) =
σ2
1
∑i
σ2
i

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