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arXiv_latex

TeX stringlengths 1 269k ⌀
O(n^{2})
f
n
G(v)
s_{o}\oplus s_{a}\in\mathbb{V}^{n+m}
Z\in\mathbb{R}^{m\times d_{\text{token}}}
E_{\psi}(s)
\displaystyle=F^{i}(E_{\psi}(s_{o})\oplus\text{Proj}_{\psi}(Z)).
\displaystyle\cos(v,v_{t}^{image})+\lambda\cos(v,v_{t}^{text})
\cos(\psi_{i},\psi_{j})
{}^{4}
v_{t}^{text}=F^{t}(E_{\psi}(s^{\prime}))
{}^{*}
\displaystyle\text{argmax}_{Z}
\rightarrow
\mathcal{A}(x,t,s_{o})
\displaystyle=F^{i}(E_{\psi}(s_{o}\oplus s_{a}))
{}^{1}
\text{Proj}_{\psi}(Z)_{i}=Z_{i}+\text{sg}(\psi_{j}-Z_{i})
x_{t}
500\times 20=10000
w_{i},w_{j}
v_{t}^{image}\leftarrow F^{i}(x_{t})
m=4
s_{a}=E_{\psi}^{-1}(\text{Proj}_{\psi}(Z))
{}^{5}
Z_{i}
{}^{1,*}
\text{Proj}_{\psi}(Z)
s
\displaystyle\text{argmax}_{s_{a}}
t
s^{\prime}\leftarrow
v_{t}^{image}
5\times 4\times 100=2000
{}^{1,2}
\psi\in\mathbb{R}^{\|\mathbb{V}\|\times d_{\text{token}}}
bestloss\leftarrow\mathcal{L},bestZ\leftarrow Z
G
\lambda=0
\text{Proj}_{\psi}:\mathbb{R}^{m\times d_{\text{token}}}\rightarrow\mathbb{R}^% {m\times d_{\text{token}}}
i\leftarrow 1
s\in\mathbb{V}^{*}
\displaystyle\text{argmax}_{s_{a}}\mathbb{E}_{x\sim G(F^{t}(E_{\psi}(s_{o}% \oplus s_{a})))}\mathcal{A}(x,t,s_{o})~{},
\displaystyle\cos(v,v_{t}^{image})+\lambda\cos(v,v_{t}^{text}),
\cos(a,b)=\frac{a^{T}b}{\\|a\\|\\|b\\|}
\eta
512\times 512
x
E_{\psi}(s_{o}\oplus s_{a})=E_{\psi}(s_{o})\oplus E_{\psi}(s_{a})
N
bestloss>\mathcal{L}
v_{t}^{image}=F^{i}(x_{t})
d_{\text{emb}}
\displaystyle\text{argmax}_{s_{a}}\cos(F^{i}(E_{\psi}(s_{o}\oplus s_{a})),v_{t% }).
s^{\prime}=
{}^{3,*}
Z\leftarrow Z-\eta\nabla_{Z}\mathcal{L}
100
s_{a}
s_{o}\oplus s_{a}
m
v
\displaystyle\text{s.t.}\quad v=F^{i}(E_{\psi}(s_{o}\oplus s_{a})),
\mathbb{V}=\{w_{1},w_{2},\cdots,w_{\|\mathbb{V}\|}\}
F^{i}
\psi
\displaystyle\text{s.t.}\quad v
s_{o}
F^{t}
{}^{2}
\oplus
E_{\psi}(s)_{i}=\psi_{j}
5\times 4=20
3\times 100
{}^{3}
v\leftarrow F^{t}(E_{\psi}(s_{o})\oplus\text{Proj}_{\psi}(Z))
\mathcal{L}=-\cos(v,v_{t}^{image})-\lambda\cos(v,v_{t}^{text})
s_{o}\in\mathbb{V}^{n}
s_{a}\leftarrow E_{\psi}^{-1}(\text{Proj}_{\psi}(bestZ))
bestloss\leftarrow\infty,bestZ\leftarrow Z
\displaystyle=F^{i}(E_{\psi}(s_{o}\oplus E_{\psi}^{-1}(\text{Proj}_{\psi}(Z))))
t\in\mathbb{V}
Z
(\cdot)
x\sim G(v)
d_{\text{token}}
s_{a}\in\mathbb{V}^{m}
v_{t}
\lambda
\mathbb{V}
w_{j}=s_{i}
t\in\mathcal{V}
x\sim G(F^{t}(E_{\psi}(s)))
E_{\psi}
j=\text{argmin}_{j^{\prime}}\\|\psi_{j^{\prime}}-Z_{i}\\|_{2}^{2}
\|s\|\times d_{\text{token}}
\displaystyle\text{argmax}_{v_{t}}\mathbb{E}_{x\sim G(v_{t})}\mathcal{A}(x,t,s% _{o})~{}.
E_{L}\cup E_{R}
E_{L}=\{(u,w)\|(u,w)\in E,w\neq v\}

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TeX data from arXiv

Using https://github.com/KyuDan1/TeX2Image code.
We have categories Math, Physics, Statistics, ComputerScience.

Domain	Size
Mathematics	4.22M
Computer Science	2.76M
Statistics	0.89M
Physics	0.78M
Total (unique)	7.17M

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