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| <p> $\displaystyle\mathcal{L}_{\text{MAE}}(\phi)=\mathbb{E}_{x\sim P_{U},{x^{\prime% |
| }}\sim\mathcal{A}_{\text{pre}}(\cdot\mid x)}[(\phi({x^{\prime}})-x)^{2}]$ </p> |
| <p> $\mathbf{0.246\pm 0.015}$ </p> |
| <p> $\frac{{\alpha}}{{\gamma}}$ </p> |
| <p> $\tilde{{\bm{X}}^{\prime}}=10^{0.4(d(z^{\prime})-d(z_{\text{orig}}))}\{F^{% |
| \prime}(t_{\text{new},i},w_{\text{new},j})\}_{i=1,j=1}^{T,W},$ </p> |
| <p> $\mathcal{S}=\{x\in\mathcal{X}:d_{x}=1\}$ </p> |
| <p> $92.3\%\rightarrow 96.7\%$ </p> |
| <p> $\displaystyle\mathcal{L}(B)=\mathbb{E}_{x\sim P_{S}}\left[\ell(B\widehat{\phi}% |
| (x),y_{x})\right]+\eta\|B\|_{F}^{2},$ </p> |
| <p> $x\sim P_{S}$ </p> |
| <p> $({\bm{t}},{\bm{w}})$ </p> |
| <p> $\text{Uniform}[0.5,0.9]$ </p> |
| <p> $S_{+}(x,x^{+})=\mathbb{E}_{\bar{x}\sim P_{U}}[\mathcal{A}_{\text{pre}}(x\mid% |
| \bar{x})\mathcal{A}_{\text{pre}}(x^{+}\mid\bar{x})]$ </p> |
| <p> $\{F^{\prime}(t_{\text{new},i},w_{\text{new},j})\}_{i=1,j=1}^{T,W}$ </p> |
| <p> $\widehat{h}=\operatorname*{arg\,min}_{h}\mathcal{L}_{\text{ft}}(h)$ </p> |
| <p> $5Ã$ </p> |
| <p> $0.8\AA$ </p> |
| <p> $\left(\,\overline{\text{Ch.}},\text{Ch.}\,\right)$ </p> |
| <p> $match(Ch.,\cdot{})$ </p> |
| <p> $\left(\,\text{Ch.},\overline{\text{Ch.}}\,\right)$ </p> |
| <p> $\\ |
| A$ </p> |
| <p> $\min(match)$ </p> |
| <p> $\left(\,\text{H.2},\overline{\text{H.2}}\,\right)$ </p> |
| <p> $10\AA$ </p> |
| <p> $\max(d_{\rho})$ </p> |
| <p> $match(\cdot{},Ch.)$ </p> |
| <p> $B(\mathbf{p},\rho_{\mathbf{p}})$ </p> |
| <p> $\gamma:M\rightarrow M^{\prime}$ </p> |
| <p> $d_{\rho}(C,C^{\prime}):=\sqrt{\sum_{\mathbf{p}\in M}|\,\rho_{\mathbf{p}}-\rho_% |
| {\gamma(\mathbf{p})}\,|^{2}},$ </p> |
| <p> $\overline{\text{H.1}}$ </p> |
| <p> $\AA$ </p> |
| <p> $\mathbf{p}^{\prime}\in C^{\prime}$ </p> |
| <p> $d_{\rho}(C,C^{\prime})$ </p> |
| <p> $d_{\rho}$ </p> |
| <p> $\overline{\text{Ch.}}$ </p> |
| <p> $1.4\AA$ </p> |
| <p> $\mathbf{p}_{N}$ </p> |
| <p> $match(C,C^{\prime})$ </p> |
| <p> $\left(\,\overline{\text{H.1}},\text{H.1}\,\right)$ </p> |
| <p> $\alpha-\pi$ </p> |
| <p> $V(C,\rho):=\iiint_{\bigcup_{\mathbf{p}\in{}C}B(\mathbf{p},\rho_{\mathbf{p}})}1dxdydz.$ </p> |
| <p> $\overline{\text{H.2}}$ </p> |
| <p> $\left(\,\overline{\text{H.2}},\text{H.2}\,\right)$ </p> |
| <p> $L(C):=\sum_{j=1}^{N}\|\mathbf{p}_{j}-\mathbf{p}_{j-1}\|_{2}.$ </p> |
| <p> $s(C):=\dfrac{1}{tortuousness(C)},$ </p> |
| <p> $\left(\,\text{H.1},\overline{\text{H.1}}\,\right)$ </p> |
| <p> $-\mathbf{v}$ </p> |
| <p> $\alpha_{t}x_{t}+\beta_{t}\epsilon_{t}$ </p> |
| <p> $\max_{x^{adv}}\ \ J(x^{adv},y)\ \ \ \ s.t.\left\|x-x^{adv}\right\|_{\infty}<\epsilon.$ </p> |
| <p> $\max_{x^{adv}}\ \ \left\|f^{m}(x,p)-f^{m}(x^{adv},p)\right\|_{2}\ \ \ \ s.t.% |
| \left\|x-x^{adv}\right\|_{\infty}<\epsilon.$ </p> |
| <p> $f^{m}(\cdot)$ </p> |
| <p> $\epsilon^{\prime}=0.01$ </p> |
| <p> $\left\|x-x^{adv}\right\|_{p}<\epsilon$ </p> |
| <p> $\displaystyle\mathbb{E}[\sum_{t=0}^{m}\gamma^{t}r(y_{{\mathrm{LM}},t})],{\rm s% |
| .t.,}y_{{\mathrm{LM}},t}\sim M_{\mathrm{LM}}(\cdot|\hat{s_{t}},x),$ </p> |
| <p> $c_{i}=Z_{1}(f_{i})$ </p> |
| <p> ${}^{\clubsuit,\heartsuit}$ </p> |
| <p> $M_{\mathrm{LM}}$ </p> |
| <p> $\rm answer$ </p> |
| <p> $s_{0}=[-1]$ </p> |
| <p> $P^{\prime\prime}=\{c_{i}\}_{i=0}^{n-1}$ </p> |
| <p> $S_{\mathrm{semantic}}$ </p> |
| <p> $V=\{v_{1},...,v_{m}\}$ </p> |
| <p> $P^{\prime}=\{f_{i}\}_{i=0}^{n-1}$ </p> |
| <p> $\rm question$ </p> |
| <p> $k=a_{t}$ </p> |
| <p> $(\rm question,\rm context,\rm answer)$ </p> |
| <p> $q=Z_{2}(l)$ </p> |
| <p> $\zeta(y,\hat{y})=\lambda\cdot S_{\mathrm{textual}}(y,\hat{y})+(1-\lambda)\cdot |
| S% |
| _{\mathrm{semantic}}(y,\hat{y}),$ </p> |
| <p> $\displaystyle\underset{\theta}{\mathrm{max}}$ </p> |
| <p> $r=\alpha\cdot\zeta(y,\hat{y})$ </p> |
| <p> $l=\mathrm{concat}(g,h)$ </p> |
| <p> $P=\{p_{i}\}_{i=0}^{n-1}$ </p> |
| <p> $\rm context$ </p> |
| <p> $\hat{s_{t}}\sim\prod_{i=0}^{t}\pi_{\theta}(a_{i}|s_{<i},x)$ </p> |
| <p> $S_{\mathrm{textual}}$ </p> |
| <p> $\{v_{i}\}_{i=0}^{m}$ </p> |
| <p> $s_{t}=\mathrm{append}(s_{t-1},a_{t})$ </p> |
| <p> $\pi_{\theta}(a_{t}|s_{<t},x)$ </p> |
| <p> $v_{t+1}=p_{k}$ </p> |
| <p> $y_{\mathrm{LM}}$ </p> |
| <p> ${}^{*~{}\heartsuit}$ </p> |
| <p> $M_{\mathrm{LM}}(\cdot|v_{0},v_{1},...,v_{m},x)$ </p> |
| <p> $(v_{0},...,v_{t})\times a_{t}\rightarrow(v_{0},...,v_{t},v_{t+1})$ </p> |
| <p> $\underset{V\subset P}{\mathrm{max}}R(y_{\mathrm{LM}}\sim M_{\mathrm{LM}}(\cdot% |
| |v_{0},v_{1},...,v_{m},x)),$ </p> |
| <p> $s_{0}=(v_{0},x)$ </p> |
| <p> $\begin{cases}1&\text{ if }S\left({V_{\left(i,j\right)}}\right)>1,\\ |
| x_{(i,j)}&\text{ if }S\left({V_{\left(i,j\right)}}\right)=1,\\ |
| 0&\text{otherwise}\end{cases}$ </p> |
| <p> $x_{\left(i,j\right)}$ </p> |
| <p> $Q:\{0,1\}$ </p> |
| <p> $u{\left({x}\right)}^{t}$ </p> |
| <p> $MFA=\left\langle{\mathbb{Z}^{2},Q,V,F,w}\right\rangle$ </p> |
| <p> $Q:{Wb}_{i}=0$ </p> |
| <p> $f(0,x_{i+1},x_{i+2})=f(1,x_{i+1},x_{i+2})$ </p> |
| <p> $\left[0,51,204,255\right]$ </p> |
| <p> $\left({x_{i-1},x_{i},x_{i+1},x_{i+2}}\right)$ </p> |
| <p> $\Delta m_{\text{init}-t}=\sum_{i=0}^{n}{x_{i}^{t_{0}}}-\sum_{i=0}^{n}{x_{i}^{t}}$ </p> |
| <p> $f(x_{i},x_{i+1},x_{i+2})$ </p> |
| <p> $\displaystyle x^{t+1}_{i}=\begin{cases}x^{t}&\text{if }w^{t}=1\\ |
| f\left({u\left({x_{i}}\right)}^{t}\right)&\text{otherwise}\end{cases}$ </p> |
| <p> $Q:{Wb}_{i}=1$ </p> |
| <p> $f(x_{i-1},x_{i},x_{i+1})$ </p> |
| <p> $\begin{split}&\delta_{t}=\frac{\Delta(X_{t-1},X_{t})}{n}\quad\text{with}\quad t% |
| \geq 1,n\in\mathbb{N}\quad\text{and}\\ |
| &\Delta(X_{t-1},X_{t})=X_{t-1}\oplus X_{t}\end{split}$ </p> |
| <p> $m_{t}=\sum_{i=0}^{n}{x_{i}^{t}}$ </p> |
| <p> $V\left(i_{0},j_{0}\right)=\left\{{\left({i,j}\right):\mid{i-i_{0}}\mid+\mid{j-% |
| j_{0}}\mid\leq 1}\right\}$ </p> |
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