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\} |