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| <p> $0.277\pm 0.004$ </p> |
| <p> $77.72\pm 0.59$ </p> |
| <p> $\mathcal{T}=\{x\in\mathcal{T}:d_{x}=2\}$ </p> |
| <p> $0.274\pm 0.016$ </p> |
| <p> $\displaystyle\mathcal{L}_{\text{ERM}}(f)=\mathbb{E}_{x\sim P_{S},x^{\prime}% |
| \sim\mathcal{A}_{\text{ft}}(\cdot\mid x)}[\ell(f(x^{\prime}),y_{x})].$ </p> |
| <p> $\mathbf{36.9\pm 0.7}$ </p> |
| <p> $\mathcal{A}_{\text{ft}}$ </p> |
| <p> $34.5\pm 1.4$ </p> |
| <p> $71.6\%\rightarrow 68.8\%$ </p> |
| <p> ${\beta}>{\gamma}$ </p> |
| <p> $\mathcal{L}_{0-1}(\widehat{f}_{\text{erm}})=1/3$ </p> |
| <p> $\mathbf{98.5\pm 0.0}$ </p> |
| <p> $\text{SNR}(x,x_{\text{err}})=\frac{|x|}{x_{\text{err}}}$ </p> |
| <p> $30.4\%\rightarrow 32.1\%$ </p> |
| <p> $x\in\{2,4,6,8\}$ </p> |
| <p> $\text{SNR}({\bm{X}}^{\prime}_{i,j},{\bm{X}}^{\prime}_{\text{err},i,j})\geq 5$ </p> |
| <p> $\displaystyle\mathcal{A}_{\text{ft}}({x^{\prime}}\mid x)=\begin{cases}1&\{{x^{% |
| \prime}},x\}\in\{1,4\},\{2,3\}\\ |
| 1&x={x^{\prime}}\text{ and }x\notin\{1,2\}\\ |
| 0&\text{otherwise}\end{cases}$ </p> |
| <p> $61.26\pm 1.10$ </p> |
| <p> $\widehat{f}_{\text{erm}}$ </p> |
| <p> $x,{x^{\prime}}$ </p> |
| <p> $\text{loss}_{\text{ft}}:\mathbb{R}^{n}\times\mathcal{Y}\rightarrow\mathbb{R}$ </p> |
| <p> $86.1\pm 1.3$ </p> |
| <p> $\tilde{x^{\prime}}$ </p> |
| <p> $96.7\%\rightarrow 98.5\%$ </p> |
| <p> $P_{U}=\beta P_{S}+(1-\beta)P_{T}$ </p> |
| <p> $\min\{{\alpha^{\prime}},{\beta^{\prime}}\}>{\gamma^{\prime}}$ </p> |
| <p> $F^{\prime},F^{\prime}_{\text{err}}$ </p> |
| <p> $z^{\prime}\sim\text{loguniform}(0.95z_{\text{orig}},\;\text{min}(1.5(1+z_{% |
| \text{orig}})-1,\;5z_{\text{orig}}))$ </p> |
| <p> $90.5\pm 0.4$ </p> |
| <p> $\widehat{f}(x)=\operatorname*{arg\,max}_{i\in[r]}(\widehat{B}\widehat{\phi}(x)% |
| )_{i}$ </p> |
| <p> $92.3\pm 0.2$ </p> |
| <p> ${x^{\prime}}\in\mathcal{X}$ </p> |
| <p> $65.2\rightarrow 91.4$ </p> |
| <p> $\tilde{{\bm{X}}^{\prime}}_{\text{err}}=10^{0.4(d(z^{\prime})-d(z_{\text{orig}}% |
| ))}\{F^{\prime}_{\text{err}}(t_{\text{new},i},w_{\text{new},j})\}_{i=1,j=1}^{T% |
| ,W},$ </p> |
| <p> $\alpha>\gamma+\beta$ </p> |
| <p> $\displaystyle\mathcal{L}_{\text{ft}}(h)=\mathbb{E}_{x\sim P_{S},y\sim p^{*}(% |
| \cdot\mid x),{x^{\prime}}\sim\mathcal{A}_{\text{ft}}(\cdot|x)}[\text{loss}_{% |
| \text{ft}}(h(\widehat{\phi}({x^{\prime}})),\;y;\;\theta)]$ </p> |
| <p> $\displaystyle\mathcal{L}_{\text{pretrain}}(\phi)=\mathbb{E}_{(x,x^{+})\sim S_{% |
| +}}[d_{+}(\phi(x),\phi(x^{+}))]-\mathbb{E}_{x,{x^{\prime}}\sim P_{U}}[d_{-}(% |
| \phi(x),\phi({x^{\prime}}))].$ </p> |
| <p> $93.8\%\rightarrow 94.9\%$ </p> |
| <p> $61.3\%\rightarrow 67.8\%$ </p> |
| <p> $d(z)$ </p> |
| <p> $0.32\rightarrow 0.28$ </p> |
| <p> $\{F_{\text{err}}(t_{i},w_{j})\}_{i=1,j=1}^{T,W}$ </p> |
| <p> $\mathcal{A}_{\text{pre}}(\cdot\mid x)$ </p> |
| <p> ${\bm{t}}_{\text{new}}=\frac{1+z^{\prime}}{1+z_{\text{orig}}}{\bm{t}}$ </p> |
| <p> $\hat{p_{T}}(z^{\prime}|z)$ </p> |
| <p> $78.84\pm 0.97$ </p> |
| <p> $40.5\pm 1.6$ </p> |
| <p> $\mathcal{A}(\cdot|x)$ </p> |
| <p> $\mathcal{A}_{\text{prop}}$ </p> |
| <p> $78.9\%\rightarrow 68.8\%$ </p> |
| <p> $\gamma>\beta$ </p> |
| <p> $\hat{p_{T}}(z^{\prime}\mid z)$ </p> |
| <p> $46.4\pm 0.5$ </p> |
| <p> $0.286\pm 0.007$ </p> |
| <p> $30.4\rightarrow 31.2$ </p> |
| <p> $30.4\%\rightarrow 37.2\%$ </p> |
| <p> $10^{\text{Uniform}[-3,-2]}$ </p> |
| <p> $36.1\pm 0.7$ </p> |
| <p> $89.3\%\rightarrow 92.3\%$ </p> |
| <p> $30.4\pm 0.6$ </p> |
| <p> $\displaystyle\begin{cases}{\rho}&y_{1}=y_{2},d_{1}=d_{2}~{}\text{~{}~{}(same % |
| class, same domain)}\\ |
| {\alpha}&y_{1}=y_{2},d_{1}\neq d_{1}\text{~{}~{}(same class, different domain)% |
| }\\ |
| {\beta}&y_{1}\neq y_{2},d_{1}=d_{2}\text{~{}~{}(different class, same domain)}% |
| \\ |
| {\gamma}&y_{1}\neq y_{2},d_{1}\neq d_{2}\text{~{}~{}(different class and % |
| domain)}\\ |
| \end{cases},$ </p> |
| <p> $68.75\pm 0.95$ </p> |
| <p> $\mathbf{94.9\pm 0.4}$ </p> |
| <p> $10^{\text{Uniform}[-5,-2]}$ </p> |
| <p> $\mathcal{S}=\{1,2\}$ </p> |
| <p> $F,F_{\text{err}}:\mathbb{R}\times\mathbb{R}\rightarrow\mathbb{R}$ </p> |
| <p> $h:\mathbb{R}^{k}\rightarrow\mathbb{R}^{n}$ </p> |
| <p> $77.40$ </p> |
| <p> $\mathcal{Y}=\{1,\dots,k\}$ </p> |
| <p> $\mathbf{80.54\pm 1.20}$ </p> |
| <p> $S_{+}(x,{x^{\prime}})$ </p> |
| <p> $71.59\pm 1.10$ </p> |
| <p> $z_{\text{orig}}$ </p> |
| <p> $\displaystyle\mathbb{E}_{(x,x^{+})\sim S_{+}}\left[\phi(x)^{\top}\phi(x^{+})% |
| \right]+\mathbb{E}_{x,x^{\prime}\sim P_{U}}\left[\left(\phi(x)^{\top}\phi(x^{% |
| \prime})\right)^{2}\right].$ </p> |
| <p> $L_{T}(f)=\mathbb{E}_{x\sim P_{T},y\sim p^{*}(\cdot\mid x)}[\ell(f(x),y)]$ </p> |
| <p> $89.3\pm 0.9$ </p> |
| <p> $\mathbf{51.4\pm 0.6}$ </p> |
| <p> $\mathcal{A}_{\text{pre}}$ </p> |
| <p> ${\bm{X}}^{\prime},{\bm{X}}^{\prime}_{\text{err}}$ </p> |
| <p> $89.3\rightarrow 92.3$ </p> |
| <p> $65.15\pm 0.67$ </p> |
| <p> ${\bm{w}}_{\text{new}}=\frac{1+z^{\prime}}{1+z_{\text{orig}}}{\bm{w}}$ </p> |
| <p> $62.3\pm 1.9$ </p> |
| <p> $36.3\%\rightarrow 37.2\%$ </p> |
| <p> $47.5\pm 1.0$ </p> |
| <p> $y_{x}=-1$ </p> |
| <p> ${\rho},{\alpha},{\beta},{\gamma}$ </p> |
| <p> $46.4\rightarrow 46.4$ </p> |
| <p> $\mathbf{0.256\pm 0.005}$ </p> |
| <p> ${\bm{X}}_{\text{err}}\in\mathbb{R}^{T\times W}$ </p> |
| <p> $\epsilon\in\mathbb{R}^{W}$ </p> |
| <p> $\widehat{\phi}$ </p> |
| <p> $\widehat{\phi}:\mathcal{X}\to\mathbb{R}^{k}$ </p> |
| <p> $d_{+}$ </p> |
| <p> ${\bm{X}}\in\mathbb{R}^{T\times W}$ </p> |
| <p> ${\alpha}>{\gamma}$ </p> |
| <p> $({\bm{t}}_{\text{new}},{\bm{w}}_{\text{new}})$ </p> |
| <p> $31.2\pm 0.6$ </p> |
| <p> $0.289\pm 0.003$ </p> |
| <p> $0.310\pm 0.006$ </p> |
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