TeX stringlengths 8 256 |
|---|
O(n^{2}) |
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}) |
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})) |
\text{Proj}_{\psi}(Z)_{i}=Z_{i}+\text{sg}(\psi_{j}-Z_{i}) |
500\times 20=10000 |
w_{i},w_{j} |
v_{t}^{image}\leftarrow F^{i}(x_{t}) |
s_{a}=E_{\psi}^{-1}(\text{Proj}_{\psi}(Z)) |
{}^{1,*} |
\text{Proj}_{\psi}(Z) |
\displaystyle\text{argmax}_{s_{a}} |
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 |
\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\|} |
512\times 512 |
E_{\psi}(s_{o}\oplus s_{a})=E_{\psi}(s_{o})\oplus E_{\psi}(s_{a}) |
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} |
s_{o}\oplus s_{a} |
\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}|}\} |
\displaystyle\text{s.t.}\quad v |
E_{\psi}(s)_{i}=\psi_{j} |
5\times 4=20 |
3\times 100 |
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} |
x\sim G(v) |
d_{\text{token}} |
s_{a}\in\mathbb{V}^{m} |
\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\} |
v_{1},v_{2}\in\overline{V_{m}} |
|\Delta E|^{\prime}=w^{*} |
1\leq j\leq k |
{\mathcal{R}} |
\pi\left(G^{\prime}\right)\leq\pi(G)-d |
\displaystyle\underbrace{n_{R}\times|y-C|\times k^{\prime}}_{\text{between the%
subpath of }w_{2}\text{ and the vertices in }u}+\underbrace{n_{R}\times|y-B-C%
|\times k}_{{\text{between the subpath of }w_{2}\text{ and the vertices in }v}}+ |
\operatorname{min}(\mathcal{E}(M_{L}^{*}),\mathcal{E}(M_{R}^{*})) |
E_{m}=\{e^{*}\} |
\displaystyle n_{L}\times n_{R}\times|x+y-A-B-C|\xrightarrow{n_{R}=0} |
v_{i}\in V_{L} |
M_{R}^{*}\xleftarrow[]{}\emptyset |
\alpha_{1}=A-x+x-A-B<B\xrightarrow{}0<2B |
u,v\in V |
\left|\sum_{k=i}^{j-2}(w_{k}+\epsilon_{k})-w^{*}-\sum_{k=i}^{j-2}w_{k}\right|=%
\left|w^{*}-\sum_{k=i}^{j-2}\epsilon_{k}\right| |
n_{L}(|x-A|+|x-A-B|) |
\mathcal{E}_{L}^{(i+1)}-\mathcal{E}_{L}^{(i)}=n_{L}\times\big{(}(i+1)\;w_{i+1}%
-(k-i)\;w_{i+1}\big{)} |
w^{\prime}(e_{i})=w(e_{i})+w(e^{*}) |
S_{R}\xleftarrow{}\sum_{\forall e_{i}\in E_{R}}R_{i} |
u,v\in G_{1} |
\Delta({\text{MARK\_RIGHT}}) |
\operatorname{min}(\mathcal{E}(M_{R}^{*}),\mathcal{E}(M_{L}^{*}))\leq\mathcal{%
E}(M) |
{\mathcal{L}}-(\frac{{\mathcal{L}}{n_{L}}+{n_{R}}(1-{\mathcal{R}})}{2{n_{L}}})%
=\frac{{\mathcal{L}}{n_{L}}-{n_{R}}(1-{\mathcal{R}})}{2{n_{L}}} |
T_{j}^{R} |
\varphi(x)=x/\alpha-\beta |
\mathcal{E}=\mathcal{E}_{R} |
S_{R}-S_{L}\leq R_{i} |
n_{L}\geq 0 |
c_{2}\geq\epsilon |
{n^{2}_{L}}\times((i+1)({\mathcal{L}}-i-1)-i({\mathcal{L}}-i))={n^{2}_{L}}%
\times(i{\mathcal{L}}-i^{2}-i+{\mathcal{L}}-i-1-i{\mathcal{L}}+i^{2})={n^{2}_{%
L}}\times({\mathcal{L}}-2i-1) |
e^{*}_{k}=(u_{j},u_{j+1}) |
|\Delta E|=|\overline{V_{m}}|(w^{*}_{1}+\dots+w^{*}_{k})=(n-2k)(w^{*}_{1}+%
\dots+w^{*}_{k}) |
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- 3