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| <p> $\mathcal{L}_{\mathrm{MMD}}(p_{M},p_{M^{\prime}})=\left(\mathbb{E}_{i,j}[k(\mu_% |
| {i},\mu_{j})-2k(\mu_{i},\mu_{j}^{\prime})+k(\mu_{i}^{\prime},\mu_{j}^{\prime})% |
| ]\right)^{\frac{1}{2}},$ </p> |
| <p> $\rho=400\,\mu m$ </p> |
| <p> $\lambda=1550\,\mu m$ </p> |
| <p> $\mathbf{y}_{d}$ </p> |
| <p> $\mathbf{z}\sim\pi(\mathbf{z})=\mathcal{N}(\mathbf{z};\mathbf{0},\mathbf{I}))$ </p> |
| <p> $\mathcal{L}_{\mathrm{NLL}}\simeq\frac{1}{2}\|h(\mathbf{x};\mathbf{c})\|_{2}^{2% |
| }-\log\left|\det\mathbf{J}_{h}(\mathbf{x})\right|$ </p> |
| <p> $\min_{\theta}\mathcal{L}_{\mathrm{MSE}}\left(\tilde{\mathbf{x}},f_{\phi}\left(% |
| g_{\theta}\left(\tilde{\mathbf{x}}\right)\right)\right),$ </p> |
| <p> $\mathbf{z}_{K}\sim\pi(\mathbf{z}_{K})=\mathcal{N}(\mathbf{z}_{K};\mathbf{0},% |
| \mathbf{I}_{K}))$ </p> |
| <p> ${\mathbf{x}_{s}}$ </p> |
| <p> $\mathcal{L}_{\mathrm{MSE}}=\mathbb{E}[(\mathbf{y}_{d}-h_{\mathbf{y}_{d}}(% |
| \mathbf{x}_{D}))^{2}]$ </p> |
| <p> $\mu^{\prime}\sim p_{M^{\prime}}$ </p> |
| <p> $p(\mathbf{x})=\pi(\mathbf{z}=h(\mathbf{x}))\left|\det\frac{\partial h(\mathbf{% |
| x})}{\partial\mathbf{x}^{T}}\right|,$ </p> |
| <p> $\mathbf{x}=h^{-1}(\mathbf{z};\mathbf{c})$ </p> |
| <p> $s:\mathbf{x}_{D}\in\mathbb{R}^{D}\mapsto\mathbf{y}_{d}\in\mathbb{R}^{d}$ </p> |
| <p> $\displaystyle\simeq\frac{1}{2}\|h(\mathbf{x})\|_{2}^{2}-\log\left|\det\mathbf{% |
| J}_{h}(\mathbf{x})\right|.$ </p> |
| <p> $(x_{\text{stim}},y_{\text{stim}})$ </p> |
| <p> $\mathbf{z}=h(\mathbf{x};\mathbf{c})$ </p> |
| <p> $\mathbf{z}=h(\mathbf{x})$ </p> |
| <p> $\mathbf{z}_{K}$ </p> |
| <p> $\mathcal{L}_{\mathrm{MMD}}(p(h(\mathbf{x}_{D})),p(\mathbf{y}_{d})p(\mathbf{z}_% |
| {K}))$ </p> |
| <p> $\mathbf{x}_{D}$ </p> |
| <p> $\mathbf{y}_{p}$ </p> |
| <p> $\mu\sim p_{M}$ </p> |
| <p> $\Psi\in\mathbb{R}^{z\times h}$ </p> |
| <p> $\bm{0.982}$ </p> |
| <p> $24.90$ </p> |
| <p> $\bm{0.861}$ </p> |
| <p> $\bm{0.044}$ </p> |
| <p> $z=8,192$ </p> |
| <p> $r:\Re\times\Re^{3}\rightarrow\Re^{3}$ </p> |
| <p> $24.88$ </p> |
| <p> $\bm{0.047}$ </p> |
| <p> $24.13$ </p> |
| <p> $\bm{0.018}$ </p> |
| <p> $\bm{32.70}$ </p> |
| <p> $\bm{W}_{\Psi}$ </p> |
| <p> $M^{\prime}_{\Delta}=(\bm{W}^{\prime}_{\Delta},\bm{b}^{\prime}_{\Delta})$ </p> |
| <p> $\bm{W}_{\gamma}$ </p> |
| <p> $27.89$ </p> |
| <p> $\bm{0.714}$ </p> |
| <p> $\bm{0.070}$ </p> |
| <p> $\bm{0.025}$ </p> |
| <p> $\bm{0.911}$ </p> |
| <p> $\bm{h}^{\prime}_{\Delta}$ </p> |
| <p> $\bm{28.14}$ </p> |
| <p> $32.53$ </p> |
| <p> $\bm{b}=\{\bm{b}_{\Delta},\bm{b}_{c},\bm{b}_{\psi}$ </p> |
| <p> $29.57$ </p> |
| <p> $\bm{h}_{c}$ </p> |
| <p> $M^{\prime}_{\Delta}$ </p> |
| <p> $\bm{W}=\{\bm{W}_{\Delta},\bm{W}_{c},\bm{W}_{\psi}$ </p> |
| <p> $\bm{0.991}$ </p> |
| <p> $\bm{0.093}$ </p> |
| <p> $\bm{W}_{\mu},\bm{W}_{\gamma},\bm{W}_{\Psi},\bm{W}^{\prime}_{\Delta},\bm{W}^{% |
| \prime}_{c}\}$ </p> |
| <p> $\bm{37.72}$ </p> |
| <p> $\bm{b}_{\Psi}$ </p> |
| <p> $\bm{0.988}$ </p> |
| <p> $\bm{35.41}$ </p> |
| <p> $26.11$ </p> |
| <p> $\bm{f}_{\Delta}=\sigma\left(\bm{h}_{\Delta}\right),$ </p> |
| <p> $\bm{0.029}$ </p> |
| <p> $\bm{h}_{c}^{\prime}=[\bm{\Psi}\otimes\bm{f}_{c},\mathbf{d}].$ </p> |
| <p> $\bm{0.956}$ </p> |
| <p> $\bm{32.34}$ </p> |
| <p> $\bm{31.13}$ </p> |
| <p> $\bm{26.51}$ </p> |
| <p> $26,29$ </p> |
| <p> $27.31$ </p> |
| <p> $\bm{20.80}$ </p> |
| <p> $\bm{\mu}=\bm{f}_{\mu}\otimes\bm{\gamma}.$ </p> |
| <p> $\bm{36.76}$ </p> |
| <p> $\bm{W}_{\psi}$ </p> |
| <p> $\bm{\gamma}=tanh\left({\bm{W}_{\gamma}[\bm{h}_{\Delta},\bm{h}_{c}]+\bm{b}_{% |
| \gamma}}\right),$ </p> |
| <p> $\bm{27.56}$ </p> |
| <p> $\bm{b}_{\mu},\bm{b}_{\gamma},\bm{b}_{\Psi},\bm{b}^{\prime}_{\Delta},\bm{b}^{% |
| \prime}_{c}\}$ </p> |
| <p> $\bm{W}_{\mu}$ </p> |
| <p> $23.49$ </p> |
| <p> $\bm{0.007}$ </p> |
| <p> $\bm{h}_{\Delta}$ </p> |
| <p> $\bm{0.103}$ </p> |
| <p> $\bm{f}_{c}=\sigma\left({\bm{h}_{c}}\right),$ </p> |
| <p> $\bm{0.068}$ </p> |
| <p> $MSE(\cdot)$ </p> |
| <p> ${\cal L}=MSE(r(\Delta,\bm{c}),\bm{g}),$ </p> |
| <p> $32.45$ </p> |
| <p> $\bm{0.009}$ </p> |
| <p> $\bm{f}_{\psi}=\sigma\left({\bm{W}_{\psi}\bm{[h}_{\Delta},\bm{h}_{c}]+\bm{b}_{% |
| \psi}}\right),$ </p> |
| <p> $\bm{0.026}$ </p> |
| <p> $\mathbf{l}=(x,y,z)$ </p> |
| <p> $\bm{f}_{\mu}=\sigma\left({\bm{W}_{\mu}[\bm{h}_{\Delta},\bm{h}_{c}]+\bm{b}_{\mu% |
| }}\right),$ </p> |
| <p> $\bm{0.882}$ </p> |
| <p> $\bm{0.837}$ </p> |
| <p> $[\bm{h}_{\Delta},\bm{h}_{c}]$ </p> |
| <p> $\bm{f}_{\Delta}$ </p> |
| <p> $\bm{26.06}$ </p> |
| <p> $\bm{b_{\mu}}$ </p> |
| <p> $29.56$ </p> |
| <p> $\bm{27.01}$ </p> |
| <p> $26.05$ </p> |
| <p> $F_{\Theta}:(\mathbf{l},\mathbf{d})\rightarrow(\mathbf{c},\Delta)$ </p> |
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