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text:
\section*{Acknowledgements}
We are thankful for enlightening discussions with Eyal Bairey and Giacomo Torlai.
We are grateful for financial support from the Swiss National Science Foundation, the NCCR QSIT. This work has received funding from the European Research Council under grant agreement no. 771503.

\vfill

\pagebreak
\clearpage
\widetext

\begin{center}
\textbf{\large Supplementary material: Correlation-Enhanced Neural Networks as Interpretable Variational Quantum States}
\end{center}

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\section{Architecture details: Toric code}
\label{app:architecture}

\begin{figure}[b]
\centering
\includegraphics[scale=2.9]{Loops}
\caption{Examples of vertical and horizontal non-contractible loops $L_v$ and $L_h$ are depicted here.}
\label{fig:loops}
\end{figure}

We explain and physically motivate the details of the architecture of the cRBM ansatz employed for the perturbed toric code. In particular, we begin by considering the toric code Hamiltonian (\ref{eq:Hamiltonian})
\begin{align}
H=-\sum \limits_{s} A_s -\sum \limits_{p} B_p,
\end{align}
where $A_s=\prod_{i \in s} \sigma^x_i$ and $B_p=\prod_{i \in p} \sigma^z_i$. When periodic boundary conditions are employed, the ground state (eigenstate of all stabilizer operators) is four-fold degenerate. In particular, the topological sectors differ by non-contractible loops: Let us consider the quantity $\Gamma=\prod_{i \in L} s_i$, where $L$ can be a horizontal or a vertical non-contractible loop as depicted in Fig.~\ref{fig:loops}.
As $[C,H]=0$, the ground state manifold can be separated in four sectors with different eigenvalues $\{\lambda_v,\lambda_h \}$ of the vertical or horizontal loop. Since $\{\lambda_v,\lambda_h \}=\{\pm 1,\pm 1 \}$, there are four possible sectors corresponding to the four degenerate ground states.

In \cite{deng2017machine}, an exact RBM representation of the toric code ground state has been given. The RBM representation is constructed with a hidden layer, where each hidden neuron is associated with either a specific vertex or a specific plaquette. In particular, the neuron is then connected to the spins associated to the vertex $s$ or plaquette $p$  with the weights  $W_{s,i}=i\pi /2$ for $i \in s$ and $W_{p,i}=i\pi /4$ for $i \in p$, respectively. As there are in total as many stabilizers as physical spins, the hidden neuron density is equal to $1$. The toric code ground state is recovered when setting all biases equal to zero. The obtained ground state corresponds to an equal superposition of the four topological sectors (the sign of a specific sector in the superposition differs for different lattice sizes).

\begin{figure}[tb]
\centering
\includegraphics[scale=1]{RBM_Network}
\caption{The structure of the cRBM ansatz: In addition to the visible layer (yellow) an RBM would normally have, we add additional visible neurons (blue and green) capturing the relevant correlations in the system and connect them to the already existing hidden neurons (grey).}
\label{fig:ansatz}
\end{figure}

We symmetrize the ansatz by imposing translational symmetries. In the case of a toric code, the lattice can be separated into $A$-and $B$-lattice and therefore has a two-atomic basis. In particular, we recall that a standard RBM ansatz can be factorized to
\begin{align}
\Psi(\{s_1, ...s_N\})=\exp(\sum \limits_{k} a_k s_k)\prod \limits_{j} \cosh (\sum \limits_k W_{k,j} s_k +b_j).
\end{align}
As a consequence, spin-spin correlations are encoded in the structure of the occuring cosine hyperbolicus. This property induces a restriction in the flexibility of the ansatz to represent correlations.
Let us denote the group of translational symmetries by $G$ and a group element by $g \in G$ defined by its action $g: k \to g(k)$ on a spin $k$. Then, the symmetrized ansatz is given by
\begin{align}
\Psi_{\rm symm}(\{s_1, ...s_N\}) =\exp(\sum \limits_{k} a_{{\rm bs}(k)} s_k)\prod \limits_{g \in G}\prod^{\alpha} \limits_{j=1} \cosh (\sum \limits_k W_{k,j} s_{g(k)} +b_j),
\end{align}
where ${\rm bs}(k)$ returns $0$ ($1$) if the spin $k$ is on $A$ ($B$)-sublattice. The parameter $\alpha$ denotes the number of hidden neurons. The toric code can be consequently written as symmetrized RBM with $\alpha=2$ and the weights
\begin{align}
W_{k,j}=\begin{cases} i\pi /2 &\text{if } j=0 \text{ and } k \in s_0, \\
i\pi /4 &\text{if } j=1 \text{ and } k \in p_0, \\
0 &\text{else.}
\end{cases}
\label{eq:toricweights}
\end{align}
Here, $s_0$ and $p_0$ correspond to an arbitrary vertex and plaquette. As the ansatz is symmetric, the choice of $s_0$ and $p_0$ does not matter.

The cRBM ansatz we choose includes generic correlators as well as correlators tailored to the toric code. In particular, we include
\begin{align}
C^{\rm bond}_{k,l}=s_k s_l, \ \ C^{\rm plaq}_{p}=\prod \limits_{k \in p} s_k, \ \ C^{\rm loop}_{L}=\prod \limits_{k \in L} s_k.
\end{align}
Here, $C^{\rm bond}_{k,l}$ corresponds to the product of nearest-neighbour spins. The correlator $C^{\rm plaq}_{p}$ consists of a product of all spins on the plaquette $p$, and non-contractible loops $L$ are included with $C^{\rm loop}_{L}$. The modifications are limited to the visible layer in order to preserve efficient sampling. The ansatz (only including bond- and plaquette correlators) is schematically depicted in Fig.~\ref{fig:ansatz}. Inserting the resulting energy functional into the symmetrized wave-function ansatz yields
\begin{align}
&\Psi_{{\rm cRBM},0}(\{s_1, ...s_N\})=\exp(\sum \limits_{k} a_{\rm bs}(k) s_k) \exp( \sum \limits_{\langle kl\rangle} a^{\rm bond}_{{\rm bsb}(k,l)} C^{\rm bond}_{k,l})\exp(\sum \limits_{p} a^{\rm plaq} C^{\rm plaq}_{p})
\exp(\sum \limits_{L} a^{\rm loop}_{{\rm bsL}(L)} C^{\rm loop}_{L}) \nonumber \\
&\times\prod \limits_{g \in G}\prod^{\alpha} \limits_{j=1} \cosh (b_j+\sum \limits_k W_{k,j} s_{g(k)} +\sum \limits_{\langle k,l\rangle} W^{\rm bond}_{kl,j}C^{\rm bond}_{g(k),g(l)} +\sum \limits_{p} W^{\rm plaq}_{p,j} C^{\rm plaq}_{g(p)} + \sum \limits_{L} W^{\rm loop}_{L,j} C^{\rm loop}_{g(L)}),
\label{eq:RBM_mod-app}
\end{align}
where we define the action of the symmetry operator $g$ on a set $M$ as the action of $g$ on all spins inside $M$, i.e.
\begin{align}
C^{\rm plaq}_{g(p)}:=\prod \limits_{k \in p} s_{g(k)}, \ \ C^{\rm loop}_{g(L)}:=\prod \limits_{k \in L} s_{g(k)}.
\end{align}
In addition, there can be identified four distinct ``bond-sublattices'', that are left invariant by the applied translational symmetry. As a consequence, four biases associated to bond correlators remain when applying symmetries to the ansatz. The map ${\rm bsb}(k,l)$ returns the respective sublattice of the bond between site $k$ and $l$. As any plaquette can obtained by applying a suitable translational symmetry operation $g$ to another arbitrary plaquette, only one visible bias $a^{\rm plaq}$ associated to plaquette correlators exists. Concerning non-contractible loops, the map ${\rm bsL}(L)$ returns $0$ ($1$) if the loop is horizontal (vertical).

Additional flexibility is achieved by adding hidden neurons only connected to a certain type of visible neurons. Here, we improve the representability of superpositions of the topological sectors by extending the ansatz to
\begin{align*}
\Psi_{\rm cRBM}&=\Psi_{{\rm cRBM},0} \times \prod \limits_{g \in G} \cosh \big(b^{\rm vert}+\sum \limits_{L \in {\rm \mathcal{L}_{vert}}} W^{\rm vert. loop}_{L,j} C^{\rm loop}_{g(L)} \big) \times\cosh \big(b^{\rm horiz}+\sum \limits_{L \in {\rm \mathcal{L}_{horiz}}} W^{\rm horiz. loop}_{L,j} C^{\rm loop}_{g(L)} \big).
\end{align*}
The set of vertical (horizontal) non-contractible loops is denoted by ${\rm \mathcal{L}_{vert}}$ (${\rm \mathcal{L}_{horiz}}$). We have thus introduced two additional hidden neurons only connected to the visible neurons associated to non-contractible loops.

With chosen number of hidden neurons $\alpha$, the total number of parameters of our ansatz therefore corresponds to $11+2L+(1+2L+7L^2)\alpha$ on a lattice with length $L$. Throughout this manuscript, we choose $\alpha=2$.
For the conducted simulations, we initialize the ansatz in the toric code ground state. In addition, we add random small deviations on the parameters, as the pure toric code ground state (\ref{eq:toricweights}) represents a local minimum.

\section{Optimization and training}
\label{app:optimization}

\begin{figure}[tb]
\includegraphics[scale=1]{Convergence_plot}
\caption{Variational energies of a cRBM ansatz during the optimization procedure for the magnetic field $(0.3,0,0)$ on a lattice with $N=18$ spins. The ground state energy obtained via exact diagonalization is depicted as grey dashed line. The inset shows the relative error of the variational energy to the ground state energy with number of iterations.}
\label{fig:convergence}
\end{figure}

\subsection{Optimization}
We obtain the ground state wave function approximation by minimizing
\begin{align}
\langle E \rangle =\frac{\langle \Psi | H| \Psi \rangle}{\langle \Psi | \Psi \rangle}.
\end{align}
As optimization procedure, we implement the method introduced by Sorella et al. \cite{sorella2007weak}, which can be interpreted as effective second order approximation to the imaginary time evolution method: In every iteration step, the weights $\Lambda$ (representing all network parameters) are updated as
\begin{align}
\Lambda \to \Lambda - \eta S^{-1} \nabla_{\Lambda}\langle H \rangle.
\end{align}
Here, $\eta$ denotes the learning rate and second order effects are included by the covariance matrix \cite{park2020geometry}
\begin{align}
S_{k,k'}=\langle O^{*}_k O_{k'} \rangle -\langle O^{*}_k \rangle \langle O_{k'}\rangle.
\end{align}
The variational derivatives of the neural network ansatz $\Psi(\{s_1,...s_N\}):=\Psi(\mathcal{S})$ with respect to the $k$-th variational parameter $\Lambda_k$ are given by
\begin{align}
O_k(\mathcal{S})=\frac{1}{\Psi(S)}\partial_{\Lambda_k}\Psi(\mathcal{S}).
\end{align}
In addition, the force $\nabla_{\Lambda}\langle H \rangle$ can be reformulated as
\begin{align}
\nabla_{\Lambda_k}\langle H \rangle=\langle E_{loc} O^{*}_k\rangle -\langle E_{loc} \rangle \langle O^{*}_k \rangle,
\end{align}
where the local energy $E_{loc}$ is defined as
\begin{align}
E_{loc}(\mathcal{S})=\frac{\langle \mathcal{S}|H|\Psi \rangle}{\Psi(\mathcal{S})}.
\end{align}
In order to ensure that the inverse of the covariance matrix $S^{-1}$ is well-defined, we employ the explicit regularization $S=S+\epsilon id$. Throughout our work, we have typically chosen the learning rate $\eta$ in between $10^{-2}$ and $10^{-3}$, reducing the learning rate with number of iterations, and the regularization $\epsilon \sim 10^{-4}$. We note here, that it can be beneficial to decrease the regularization with number of iterations \cite{becca2017quantum, carleo2017solving}.
Fig.~\ref{fig:convergence} shows an exemplary convergence plot for the cRBM ansatz applied on the toric code with magnetic field $(0.3,0,0)$. We initialized the ansatz with the parameters specified in (\ref{eq:toricweights}) and additional small random noise.

\subsection{Efficient calculation of expectation values}
Expectation values of an operator $M$ with respect to the wave function ansatz $\Psi(\mathcal{S})$ can be calculated using variational Monte Carlo \cite{mcmillan1965ground, becca2017quantum}
\begin{align}
\frac{\langle \Psi | M | \Psi \rangle}{\langle \Psi | \Psi \rangle}=\frac{1}{\langle \Psi |\Psi\rangle}\sum \limits_{\mathcal{S},\mathcal{S}'} \Psi^{*}(\mathcal{S}) M(\mathcal{S},\mathcal{S}'),\Psi(\mathcal{S}')=\frac{1}{\langle \Psi |\Psi\rangle}\sum \limits_{\mathcal{S}} M_{loc}(S) \Psi^{*}(\mathcal{S})\Psi(\mathcal{S}),
\label{eq:vmc1}
\end{align}
where $M(\mathcal{S},\mathcal{S}')$ denotes the matrix element $\langle \mathcal{S} |M |\mathcal{S}'\rangle$ and
\begin{align}
M_{loc}(S)=\frac{\langle \mathcal{S}|M|\Psi\rangle}{\Psi(\mathcal{S})}.
\end{align}
Reformulating eq. (\ref{eq:vmc1}) as
\begin{align}
\frac{\langle \Psi | M | \Psi \rangle}{\langle \Psi | \Psi \rangle}=\frac{\sum \limits_{\mathcal{S}} M_{loc}(\mathcal{S})|\Psi(\mathcal{S})|^2}{\sum \limits_{\mathcal{S}}|\Psi(\mathcal{S})|^2},
\end{align}
we see that the expectation value can be efficiently calculated sampling the quantity $ M_{loc}(\mathcal{S})$ over a Markov Chain with update probability
\begin{align}
p(\mathcal{S}_i \to \mathcal{S}_{i+1})={\rm min}\{\frac{|\Psi(\mathcal{S}_{i+1})|^2}{|\Psi(\mathcal{S}_{i})|^2}, 1\}.
\end{align}
For the toric model, we include vertex-flips and flipping of non-contractible loops in addition to single spin-flip updates in order to ensure ergodicity.

\subsection{Variational derivatives}
In order for the optimization described above to be feasible, it has to be possible to calculate the derivatives $O_k(\mathcal{S})$ efficiently. It has been shown in \cite{carleo2017solving}, that this statement holds for standard RBMs. We show here, that introducing correlators does not increase the complexity of the variational derivatives. Concretely, let us consider a generic cRBM ansatz of the form
\begin{align}
&\Psi(\mathcal{S})=\exp(\sum a_k s_k+\sum \limits_{i} a^{\rm corr}_{i} C_i)\prod \limits_{j} \cosh (\theta_j (\mathcal{S})),  \nonumber \\
&\theta_j(\mathcal{S})=\sum \limits_k W_{k,j} s_k+\sum \limits_{i} W^{\rm corr}_{i,j} C_i  +b_j.
\end{align}
The derivatives with respect to the network parameters are then gives by
\begin{align}
&\frac{1}{\Psi(\mathcal{S})}\partial_{a_k} \Psi(\mathcal{S})=s_k, \\
&\frac{1}{\Psi(\mathcal{S})}\partial_{a^{\rm corr}_i} \Psi(\mathcal{S})=C_i, \\
&\frac{1}{\Psi(\mathcal{S})}\partial_{b_j} \Psi(\mathcal{S})=\tanh(\theta_j(\mathcal{S})), \\
&\frac{1}{\Psi(\mathcal{S})}\partial_{W_{k,j}} \Psi(\mathcal{S})=s_k\tanh(\theta_j(\mathcal{S})), \\
&\frac{1}{\Psi(\mathcal{S})}\partial_{W^{\rm corr}_{i,j} }\Psi(\mathcal{S})=C_i\tanh(\theta_j(\mathcal{S})).
\end{align}

\section{Accuracy of RBM and cRBM for the toric code}
\label{app:energies}
In this section, we compare in detail the accuracies of the RBM and cRBM wave functions for different field directions of the toric code.
With the purpose to understand the influence of the field directions to the accuracy of the wave-function ansatz, we examine the fields separately in $x$-, $y$- and $z$-direction on a small lattice with $N=18$ spins.
Simulations for the standard RBM were partly done with the help of the {\it netket} library \cite{carleo2019netket}.

\begin{figure}[tb]
\centering
\includegraphics[scale=1]{RBM_Alpha_hx0p3}
\caption{RBM energies versus number of hidden neurons at $h_x=0.3$. The ground state and first excited state energy obtained using exact diagonalization are shown with grey dashed lines.}
\label{fig:alphahx}
\end{figure}

\paragraph{x-fields}
We have shown in the main text, that cRBMs achieve precisions several orders of magnitude higher than RBMs for the toric code with fields in $x$-direction (see Fig.~\ref{fig:L2}). In particular, we have compared an RBM and a cRBM with the same amount of parameters. In addition, increasing the hidden neuron density of the RBM ansatz does not lead to a significant increase in precision, as shown in Fig.~\ref{fig:alphahx} for $h_x=0.3$. Instead, as explained in the main text it represents a more relevant extension of the spanned sub-space to introduce correlators.

\begin{figure}[b]
\includegraphics[scale=1]{Energy_compare_hy}
\caption{RBM, cRBM energies for $(0,h_y,0)$ (left panel). The relative error with respect to the ground state energy obtained via exact diagonalization is plotted on the right hand side.}
\label{fig:energycomparehy}
\end{figure}

\begin{figure}[tb]
\includegraphics[scale=1]{RBM_Alpha_hy0p2}
\caption{RBM energies versus number of hidden neurons at $h_y=0.2$. The ground state and first excited state energy obtained using exact diagonalization are shown with grey dashed lines.}
\label{fig:alphahy2}
\end{figure}

\paragraph{y-fields}
We compare the energies of an RBM and a cRBM for fields in $(0,h_y,0)$-direction. As shown in Fig.~ \ref{fig:energycomparehy}, cRBMs again pose a significant improvement of the accuracy of the ansatz. It is in addition remarkable, that the RBM ansatz hardly learns any effect of the applied fields: For the ground state of the pure toric code $|\Psi_0\rangle$, the variational energy $\langle H \rangle$ is equal to $2L^2=18$ for any applied field. As we initialize the ansatz in the toric code ground state (plus small random deviations), $\langle H \rangle=18$ after optimization for nonzero $h_y$-fields corresponds to no net learning effect. As the ground state of the toric code with nonzero $h_y$ fields corresponds to a superposition of different topological sectors characterized by non-contractible loops, we deduce that including non-contractible loops as correlators mainly leads to the large improvement of the wave-function accuracy seen in Fig.~\ref{fig:energycomparehy} for the cRBM.
We tested again an increase of the hidden neuron density exemplary at $h_y=0.2$ for the RBM ansatz, and observed no significant improvement (see Fig.~\ref{fig:alphahy2}).

\paragraph{z-fields}
Let us consider the Hamiltonian
\begin{align}
H=-\sum \limits_{s} A_s - \sum \limits_{p} B_p + h_z \sum \limits_{i} \sigma^z_i.
\end{align}
For small $h_z$, we can approximate the Hamiltonian as \cite{castelnovo2008quantum}
\begin{align}
H_{M}&=-\sum \limits_{s} A_s - \sum \limits_{p} B_p+\sum \limits_{s} e^{h_z/2 \sum \limits_{i \in s} \sigma^z_i}\approx H+const.
\end{align}
The ground state of the model can be exactly represented as an RBM, starting from the exact representation of the toric ground state and assigning visible biases with values $a_i=-h_z$. As a consequence, an RBM ansatz yields a suitable approximation of the ground state of the original Hamiltonian $H$. Introducing additional correlators therefore yields only small improvements, if only $z$-fields are present.
\section{Topological phases}
\label{app:topphase}

\begin{figure}[b]
\centering
\includegraphics[scale=1]{Fidhxhz0p5hy0p2}
\caption{Fidelities for the fields $(h,0,h)$ and $(h,0.2h,0.5h)$ for $N=128$ spins.}
\label{fig:fids}
\end{figure}

\begin{figure}[tb]
\centering
\includegraphics[scale=1]{Wilson_Loops_hxhz_hy0p2}
\caption{Wilson loops and fidelity for the field direction $(h,0.2,h)$.}
\label{fig:fidloop}
\end{figure}

We probe the toric code phase diagram in different field directions and detect the topological phase transitions with a variety of methods. In the main text, we have examined the finite-size scaling behaviour of Wilson loops for selected field directions. We note here, as system sizes accessible to variational Monte Carlo methods are typically limited, finite size scaling analysis yields expectedly phase transition values slightly larger than the actual position (comparing e.g. the obtained transition around $h\sim 0.345$ on the self-dual line to literature values of $h\sim 0.340$ \cite{vidal2009low,wu2012phase}). In this section, we consider different methods and quantities in order to characterize the phase transitions and states in the respective phases further.

It has been shown, that the overlap between two ground states obtained at slightly varied field (``fidelity'') is a reliable tool to detect second-order symmetry-breaking quantum phase transitions \cite{zanardi2006ground,venuti2007quantum}. Numerical evidence suggests, that topological phase transitions can be detected as well by the fidelity \cite{hamma2008entanglement}. In particular, the fidelity is given by
\begin{align}
\mathcal{F}(h)=\frac{\langle \Psi_{h} | \Psi_{h+\Delta h} \rangle }{\sqrt{\langle \Psi_{h} | \Psi_{h} \rangle}\sqrt{\langle \Psi_{h+\Delta h} | \Psi_{h+\Delta h} \rangle} },
\label{eq:fid1}
\end{align}
where $\Psi_{h}$ denotes the ground state of a Hamiltonian $H(h)$.
At the position $h_C$ of the phase transition, the two states differ the most and the fidelity hence scales to zero.

We calculate the fidelity efficiently using a Monte Carlo Markov chain. In particular, we reformulate Eq.~(\ref{eq:fid1}) as
\begin{align}
&\mathcal{F}(h)=\frac{\sum \limits_{\mathcal{S}} \Psi^{*}_{h}(\mathcal{S}) \Psi_{h+\Delta h}(\mathcal{S})}{\sqrt{\sum \limits_{\mathcal{S}} \Psi^{*}_{h}(\mathcal{S}) \Psi_{h}(\mathcal{S})} \sqrt{\sum \limits_{\mathcal{S}} \Psi^{*}_{h+\Delta h}(\mathcal{S}) \Psi_{h+\Delta h}(\mathcal{S})} } =\frac{\sum \limits_{\mathcal{S}} \frac{\Psi_{h+\Delta h}(\mathcal{S})}{\Psi_{h}(\mathcal{S})}  |\Psi_{h}(\mathcal{S})|^2}{\sqrt{\sum \limits_{\mathcal{S}} 1 \cdot|\Psi_{h}(\mathcal{S})|^2} \sqrt{\sum \limits_{\mathcal{S}} \frac{|\Psi_{h+\Delta h}(\mathcal{S})|^2}{|\Psi_{h}(\mathcal{S})|^2}  |\Psi_{h}(\mathcal{S})|^2} }.
\label{eq:fid2}
\end{align}
A Markov chain with update probability $p(\mathcal{S}_{i} \to \mathcal{S}_{i+1})={\rm min}(1,|\Psi_{h}(\mathcal{S}_{i+1})|^2/|\Psi_{h}(\mathcal{S}_{i})|^2)$ can be used to calculate the quantities
\begin{align}
A_1=\frac{\sum \limits_{\mathcal{S}} \frac{\Psi_{h+\Delta h}(\mathcal{S})}{\Psi_{h}(\mathcal{S})}  |\Psi_{h}(\mathcal{S})|^2 }{\sum \limits_{\mathcal{S}} |\Psi_{h}(\mathcal{S})|^2}, \ \ \ A_2=\frac{\sum \limits_{\mathcal{S}} 1 \cdot  |\Psi_{h}(\mathcal{S})|^2 }{\sum \limits_{\mathcal{S}} |\Psi_{h}(\mathcal{S})|^2}=1, \ \ \ A_3=\frac{\sum \limits_{\mathcal{S}} \frac{|\Psi_{h+\Delta h}(\mathcal{S})|^2}{|\Psi_{h}(\mathcal{S})|^2}  |\Psi_{h}(\mathcal{S})|^2 }{\sum \limits_{\mathcal{S}} |\Psi_{h}(\mathcal{S})|^2}. \nonumber
\end{align}
The fidelity given in Eq.~\ref{eq:fid2} is then obtained as
\begin{align}
\mathcal{F}(h)=\frac{A_1}{\sqrt{A_2} \sqrt{A_3}}.
\end{align}
In order to account for a non-smooth gauge, we consider the norm of the fidelity $|\mathcal{F}(h)|$. Figure~\ref{fig:fids} shows the fidelity on the self-dual line for a lattice of $N=128$ spins as well as the fidelity for the field direction $h(1,0.2,0.5)$. The minimum in the fidelity indicates the respective second-order topological phase transition. We note here, that the fidelity scales to zero at the position of the phase transition with increasing system size. The critical field strenght is in accordance to the position of the phase transition obtained via finite-size scaling analysis of the quantity $W(m=4)$, see Fig.~\ref{fig:L2}.

We have probed the model for a variety of different field directions, exemplary discussing the self-dual line and the field direction $h(1,0.2,0.5)$. As another example, we show here the self-dual line for nonzero transverse field, i.e. $(h,0.2,h)$. The expectation values of the Wilson loop operator as well as the fidelity are depicted in Fig.~\ref{fig:fidloop}. The estimated critical field strength $h_C \sim 0.339$ is slightly smaller than the critical field strength for zero transverse field. This result is in agreement with the qualitative observation in Ref.~\cite{dusuel2011robustness}, that the critical field strength on the self-dual line decreases for increasing transverse field.

We further characterize the entanglement properties of the obtained states. In particular, we consider the generalized Renyi entanglement entropies
\begin{align}
S_n(\rho_A)=\frac{1}{1-n} \ln [{\rm Tr} (\rho^n_A)]
\end{align}
Here, $\rho_A$ is the reduced density matrix of the ground state on a subsystem $A$, obtained by tracing out a subsystem $B$. $A$ and $B$ correspond to a bipartition of the lattice. In the limit $n\to 1$, the van Neumann entanglement entropy is recovered
\begin{align}
S_1(\rho_A)=-{\rm Tr}(\rho_A \ln \rho_A).
\end{align}
The Renyi entropy for $n=2$ can be calculated efficiently via Variational Monte Carlo techniques. In particular, $S_2$ is given by
\begin{align}
S_2=-\frac{1}{2}\ln \bigg[  \sum \limits_{\mathcal{S}_{A1},\mathcal{S}_{A2},\mathcal{S}_{B1},\mathcal{S}_{B2}} \frac{\Psi(\mathcal{S}_{A2}\cup \mathcal{S}_{B1})\Psi(\mathcal{S}_{A1}\cup \mathcal{S}_{B2})}{\Psi(\mathcal{S}_{A1}\cup\mathcal{S}_{B1})\Psi(\mathcal{S}_{A2}\cup\mathcal{S}_{B2})} |\Psi(\mathcal{S}_{A1}\cup \mathcal{S}_{B1}) \Psi(\mathcal{S}_{A2}\cup \mathcal{S}_{B2})|^2 \nonumber \\
\times \big( 1/ \sum \limits_{\mathcal{S}_{A1},\mathcal{S}_{A2},\mathcal{S}_{B1},\mathcal{S}_{B2}} |\Psi(\mathcal{S}_{A1}\cup \mathcal{S}_{B1}) \Psi(\mathcal{S}_{A2}\cup \mathcal{S}_{B2})|^2\big)\bigg].
\label{eq:S2}
\end{align}

Here, spin-configurations on sub-partition $A$ ($B$) are denoted with subscript $A$ ($B$). A spin-configuration on the whole lattice with the configuration on subpartition $A$ ($B$) corresponding to $\mathcal{S}_A$ ($\mathcal{S}_B$) coincides with $\mathcal{S}_A \cup \mathcal{S}_B$.
The second Renyi entropy can therefore be obtained by considering two copies of the lattice and the state $|\Psi\rangle \otimes |\Psi \rangle$. We construct a Markov chain with update probability
\begin{align}
p(\mathcal{S}_i\to \mathcal{S}_{i+1})=\min (1, \frac{|\Psi(\mathcal{S}_{1,(i+1)}) \Psi(\mathcal{S}_{2,(i+1)})|^2}{|\Psi(\mathcal{S}_{1,(i)}) \Psi(\mathcal{S}_{2,(i)})|^2}),
\end{align}
where $\mathcal{S}_1$ ($\mathcal{S}_2$) corresponds to the spin-configuration on copy $1$ (copy $2$) of the lattice. In each step, either copy $1$ or copy $2$ is chosen and a spin-update proposed. Since the update probability factorizes, the efficiency of the computation is comparable to a standard Variational Monte Carlo calculation of any expectation value.
The obtained expression (\ref{eq:S2}) can be interpretated as the expectation value of a SWAP-operator, as detailed in Ref.~\cite{hastings2010measuring}.

We can derive expression (\ref{eq:S2}) by considering the reduced density matrix
\begin{align}
\rho_A=\sum \limits_{\mathcal{S}, \mathcal{S'}, \mathcal{S}_B} \langle \mathcal{S}_B|\mathcal{S} \rangle \langle \mathcal{S}'|\mathcal{S}_B\rangle \Psi^{*}(\mathcal{S})\Psi(\mathcal{S}')/\mathcal{N}^2,
\label{eq:rhoA}
\end{align}
where $\mathcal{N}$ denotes the normalization of the state $|\Psi\rangle$. The sum runs over all possible spin-configurations $\mathcal{S}$, $\mathcal{S}'$ on the whole lattice as well as all possible spin-configurations $\mathcal{S}_B$ on partition $B$. We reformulate expression~(\ref{eq:rhoA}) as
\begin{align}
\rho_A=\sum \limits_{\mathcal{S}_A, \mathcal{S}'_A, \mathcal{S}_B} \Psi^{*}(\mathcal{S}_A \cup \mathcal{S}_B) \Psi(\mathcal{S}'_A \cup \mathcal{S}_B) |\mathcal{S}_A \rangle \langle \mathcal{S}'_A|/\mathcal{N}^2, \nonumber
\end{align}
where $\mathcal{S}_A$ ($\mathcal{S}'_A$) denotes a spin-configuration on partition $A$.
Then,
\begin{align}
&{\rm Tr}(\rho^2_A) \nonumber \\
&=\frac{1}{\mathcal{N}^4} \sum \limits_{\mathcal{S}_A,\mathcal{S}_{A1},\mathcal{S}'_{A1},\mathcal{S}_{B1}}\langle \mathcal{S}_A |\mathcal{S}_{A1}\rangle \langle \mathcal{S}'_{A1} | \Psi^{*}(\mathcal{S}_{A1} \cup \mathcal{S}_{B1}) \Psi(\mathcal{S}'_{A1} \cup \mathcal{S}_{B1}) \sum \limits_{\mathcal{S}_{A2},\mathcal{S}'_{A2},\mathcal{S}_{B2}} |\mathcal{S}_{A2}\rangle \langle \mathcal{S}'_{A2} |\mathcal{S}_{A}\rangle \Psi^{*}(\mathcal{S}_{A2} \cup \mathcal{S}_{B2}) \Psi(\mathcal{S}'_{A2} \cup \mathcal{S}_{B2})  \nonumber \\
&=\frac{1}{\mathcal{N}^4}\sum \limits_{\mathcal{S}_{A1},\mathcal{A}_2,\mathcal{S}_{B1},\mathcal{S}_{B2}} \Psi^{*} (\mathcal{S}_{A1} \cup \mathcal{S}_{B1}) \Psi (\mathcal{S}_{A2} \cup \mathcal{S}_{B1}) \Psi^{*}(\mathcal{S}_{A2} \cup \mathcal{S}_{B2})\Psi (\mathcal{S}_{A1} \cup \mathcal{S}_{B2}). \nonumber
\end{align}
Inserting the obtained expression together with
\begin{align}
\mathcal{N}^4=\sum \limits_{\mathcal{S}_1} |\Psi(\mathcal{S}_1)|^2\sum \limits_{\mathcal{S}_2} |\Psi(\mathcal{S}_2)|^2 =\sum \limits_{\mathcal{S}_{A1},\mathcal{S}_{B1},\mathcal{S}_{A2},\mathcal{S}_{B2}} |\Psi(\mathcal{S}_{A1}\cup \mathcal{S}_{B1})  \Psi(\mathcal{S}_{A2}\cup\mathcal{S}_{B2})|^2
\end{align}
into the definition $S_2=-1/2 \ln[{\rm Tr} (\rho^2_A)]$ yields expression~(\ref{eq:S2}).

\begin{figure}[b]
\centering
\includegraphics[scale=1]{Entropies}
\caption{Renyi entropies $S_2$ for  $(h,0,h)$ and $(h,0.2h,0.5h)$ for $N=72$ spins.}
\label{fig:S2}
\end{figure}

We have computed the Renyi entropy $S_2$ along the fields $(h,0,h)$ and $(h,0.2h,0.5h)$ for $N=72$ spins, as depicted in Fig.~\ref{fig:S2}. We observe, that the Renyi entanglement entropy is high in the topological phase, while approaching zero in the topologically trivial phase. This result is in accordance with long-range entanglement emerging as property of topological order. In addition, the calculation of the Renyi entropies explicitely shows, that the presented cRBM ansatz is able to capture the present long-range entanglement.

\section{Optimization with constraints}
\label{app:excstates}

\subsection{Excited states: Orthogonalizing}

\begin{figure}[tb]
\centering
\includegraphics[scale=1]{EXCstates}
\caption{The energies of the four lowest-lying states $|\Psi_0\rangle$, ..$|\Psi_3\rangle$ obtained via exact diagonalization on a lattice with $N=18$ spins are plotted for the field directions $(h,0,h)$ and $(h,0.2h,0.5h)$. The energies of the first excited state $|\Psi_1\rangle$ computed by optimizing a constrained cost function with a cRBM is in qualitative agreement with the exact diagonalization results.}
\label{fig:Exc}
\end{figure}

In this section, we detail the algorithm to obtain excited states presented in the main text. As explained in App.~\ref{app:optimization}, the ground state is obtained by minimizing the quantity (``cost function'')
\begin{align}
C(\Lambda):=\langle H \rangle.
\label{eq:C}
\end{align}
In order to find the first excited state, we extend the cost function by including the orthogonality constraint to the ground state.
Given the ground state $\Psi_0$ obtained in a first variational optimization procedure, we define the modified cost function
\begin{align}
C_{E}(\Lambda)=\frac{\langle \Psi |H| \Psi \rangle}{\langle \Psi | \Psi \rangle}+\kappa\frac{|\langle \Psi_0|\Psi \rangle|^2}{\langle \Psi_0|\Psi_0\rangle \langle \Psi|\Psi \rangle}.
\end{align}
The parameter $\kappa$ tunes the weight of the constraint. More concretely, minimizing $C_{E}$ yields the state with lowest possible energy orthogonal to the ground state if $\kappa$ is sufficiently large. The minimization of the modified cost function is implemented straightforwardly. In particular, the modification appears in the computation of the derivative of the cost function in every natural gradient descent step.
\begin{align}
\Lambda \to \Lambda - \eta S^{-1} \nabla_{\Lambda}C_{E}.
\end{align}
Reformulating the cost function as
\begin{align}
C_{E}=\frac{\langle \Psi |H| \Psi \rangle}{\langle \Psi | \Psi \rangle}+\kappa \frac{\langle \Psi \big| P\big|\Psi \rangle} { \langle \Psi | \Psi \rangle} , \ \ P=\frac{|\Psi_0\rangle \langle \Psi_0|}{\langle \Psi_0 | \Psi_0 \rangle},
\end{align}
 the derivative with respect to the $k$-th network parameter is given by
\begin{align}
\partial_{\Lambda_k}C_{E}=\langle E_{loc} O^{*}_k \rangle -\langle E_{loc} \rangle \langle O^{*}_k \rangle +\kappa (\langle P_{loc}O^{*}_k \rangle -\langle P_{loc} \rangle \langle O^{*}_k \rangle).
\end{align}
Here, $P_{loc}$ is defined as
\begin{align}
P_{loc}(\mathcal{S})=\frac{\langle \mathcal{S}|P|\Psi \rangle}{\Psi(\mathcal{S})}.
\end{align}
The calculation of occuring expectation values containing $P_{loc}$ is in direct analogy to the calculation of the fidelity $\mathcal{F}$ discussed in Sec.~\ref{app:topphase}.

\begin{figure}[b]
\centering
\includegraphics[scale=1]{Topdeg}
\caption{The energy gap between the ground state and the first excited state obtained with a cRBM ansatz is plotted for different lattice sizes. The exponential scaling of the magnitude of the gap in the topological phase is plotted with solid lines. The position of the phase transition is indicated via a grey dashed line.}
\label{fig:topdeg}
\end{figure}

We demonstrate the accuracy of the received first excited state energies by comparison with exact diagonalization on a small lattice. More specifically, the comparison of the first excited state energy is depicted in Fig.~\ref{fig:Exc} for several field directions, showing quantitative agreement.

We have examined the scaling of the energy gap in the main text of this work. In particular, the magnitude of the energy gap $\Delta$ between the ground state and the first excited state has been shown to scale as  $\Delta \sim \exp (-L)$ in the topological phase of the toric model \cite{kitaev2003fault} yielding a degeneracy in the thermodynamic limit. We verify this scaling in Fig.~\ref{fig:topdeg}.
In particular, we determine the proportionality constant $a(h)$ at field strength $\Delta(h) =a(h) \exp (-L)$ using exact diagonalization for a lattice of $N=18$ ($L=3$) spins. We plot $a(h) \exp (-L)$ together with the computed gap $\Delta(h)$ for each simulated lattice size and thus demonstrate the exponential decrease with system size of the energy gap in the topological phase.
The position of the phase transition coincides with the crossing of the energy gaps of different lattice size, as the decrease of the energy gap with increasing system size is a result of the ground state degeneracy in the thermodynamic limit, and thus only holds in the topological phase of the model.

\subsection{Excited states: Operator expectation values}
In this section, we examine the variational optimization procedure in the presence of constraints on the wave function. In particular, we consider a (hermitian) operator $M$ and aim to find the state with lowest variational energy fulfilling the constraint $\langle M \rangle=A$, where A is a (real) value. It has been shown in the main text, that such an optimization can be used to ``cherry-pick'' for an excited state with approximately known physical quantities. The procedure to obtain specific excited states consists of two steps: (1) determining the appropriate operator. Here, it is crucial that the operator is chosen such that no state with lower energy than the state of interest has a larger expectation value than the sought-after state (or, if states with larger expectation values and lower energies exist, no state with lower expectation value and lower energy should exist). This condition ensures, that indeed an eigenstate and not a superposition of eigenstates is obtained. (2) Optimizing for a large enough {\it range} of different values of $A$. The eigenstate(s) can be identified by considering the variance of the local energy or the norm of the local energy derivatives $||\nabla \langle H \rangle||$. Both quantities vanish for an eigenstate \cite{becca2017quantum}.

\begin{figure}[bt]
\centering{
\includegraphics[scale=1]{Enconstrained}}
\caption{The difference $E(\Delta_{AB})/N-E(0)/N$ of the variational energy constrained to $\Delta_{AB}=\langle A_s-B_p \rangle$ for the field strenghts $h=0.38$ (upper panel) and $h=0.6$ (lower panel) for two lattice sizes. On the first order transition line, the difference decreases with larger lattice size, in particular in the range ($-0.5 \leq \Delta_{AB} \leq 0.5$) indicating the values of the parameter $\Delta_{AB}$ in the two adjacent phases.}
\label{fig:enconstrained}
\end{figure}

A constrained optimization might also be useful for the consideration of first-order phase transitions, choosing $M$ to be the respective order parameter and therefore being able to identify an occuring level crossing.

We here detail the optimization procedure. The ground state in general is obtained by minimizing the cost function $C(\Lambda)$ (\ref{eq:C}).
In order to impose the given constraint, we extend the cost function. In particular, we consider the cost function of the form
\begin{align}
C_{M}(\Lambda):=\langle H \rangle+\kappa |\langle M \rangle-A|^2
\end{align}
The added constraint $|\langle M \rangle-A|^2$ is minimal, when the expectation value of the hermitian operator $M$ is equal to the real value $A$.
The parameter $\kappa$ tunes the weight of the constraint. More concretely, minimizing $C_{\Lambda}$ yields the state with lowest possible energy fulfilling the constraint $\langle M \rangle = A$ if $\kappa$ is sufficiently large. The optimization algorithm is straightforwardly adapted. More concretely, the weights are updated in each step by
\begin{align}
\Lambda \to \Lambda - \eta S^{-1} \nabla_{\Lambda}C_{M}.
\end{align}
The derivative of the cost function with respect to the $k$-th parameter is given as
\begin{align}
\partial_{\Lambda_k}C_{M}=\partial_{\Lambda_k}\bigg( \frac{\langle \Psi| H | \Psi \rangle}{\langle \Psi| \Psi \rangle}+\kappa \big|\frac{\langle \Psi | M| \Psi \rangle}{\langle \Psi | \Psi \rangle}-A\big|^2\bigg) \nonumber \\
=\langle E_{loc} O^{*}_k \rangle -\langle E_{loc} \rangle \langle O^{*}_k \rangle +2\kappa (\langle M_{loc} \rangle -A)(\langle M_{loc} O^{*}_k \rangle -\langle M_{loc} \rangle \langle O^{*}_k \rangle).
\label{eq:derivC}
\end{align}
Here, $M_{loc}$ is defined as
\begin{align}
M_{loc}(\mathcal{S})=\frac{\langle \mathcal{S}|M|\Psi \rangle}{\Psi(\mathcal{S})}.
\end{align}
Updating the gradient descent step accordingly to Eq.~(\ref{eq:derivC}) thus results in a minimization of the generalized cost function $C_M$.

In the main text, we have shown how the procedure can be used to obtain excited states.
We here additionally use the constrained optimization procedure to characterize a first order quantum phase transition. In particular, we examine the first-order transition line on the self-dual line $h(1,0,1)$ of the toric code. Previous studies have shown, that a first order transition from the vortex condensed to the charge condensed phase occurs on the self dual line in the regime $0.34<h< 0.418$ \cite{wu2012phase, tupitsyn2010topological}. We examine the field strengths $h=0.39$ and $h=0.6$ together with the expectation value $\Delta_{AB}:=\langle A_s -B_p \rangle$. In the charge-condensed phase, $ \Delta_{AB}<0$ whereas $ \Delta_{AB}>0$ in the vortex-condensed phase. The quantity thus serves as parameter defining the present phase. A first-order transition is characterized by a phase coexistence. In particular, we here expect in the thermodynamic limit a ground state degeneracy of two states with different value of $\Delta_{AB}$. However, for finite lattice size a different (symmetric) state with $\Delta_{AB}=0$ might have a lower energy than the degeneracy of the two states with $\Delta_{AB}\neq 0$. When optimizing at $h=0.39$ with the constraint $\Delta_{AB}\neq 0$, we expect the difference of the obtained variational energy to the ground state energy to decrease for larger lattice sizes such that degeneracy arises in the thermodynamic limit. As an exemplary illustration, we plot the difference $E(A)/N-E(0)/N$ for two lattice sizes ($N=32$ and $N=72$ spins) for $-1\leq A \leq 1$. Here, $E(A)$ is the variational energy optimized under the constraint $\Delta_{AB}=A$. Figure~\ref{fig:enconstrained} shows $E(A)/N-E(0)/N$ for the cases $h=0.38$ and $h=0.6$. The difference indeed decreases (for $\Delta_{AB}$ in a certain range) on the first-order transition line ($h=0.38$), whereas no change in energy difference is observed outside of the first-order transition line.

\section{Heisenberg model on a triangular lattice}
\label{app:Heisenberg}

\begin{figure}[tb]
\centering
\includegraphics[scale=0.9]{Lattice_triangular}
\caption{Triangular lattice, A-,B- and C-sublattices are indicated in blue, red and green.}
\label{fig:lattice_triangular}
\end{figure}

\begin{figure}[b]
\centering
\includegraphics[scale=1]{Heisenberg_Triangular}
\caption{Relative error of the variational energies obtained with an RBM and cRBM anatz for the triangular Heisenberg model on a model with $36$ spins.}
\label{fig:L5}
\end{figure}

We employ the cRBM ansatz for an example of a frustrated model, the antiferromagnetic Heisenberg model on a triangular lattice.

The Hamiltonian is given by
\begin{align}
H=J \sum \limits_{\langle i, j \rangle} \vec{\sigma}_i \cdot \vec{\sigma}_j,
\end{align}
where $J\geq 0$ is the antiferromagnetic interaction strength and $\vec{\sigma}=(\sigma^x,\sigma^y,\sigma^z)$. The sum is conducted over nearest-neighbors in the triangular lattice. Periodic boundary conditions as detailed in \cite{leung1993spin} are employed. Obtaining the ground state wave function has been proven to be a formidable challenge due to the Quantum Monte Carlo sign problem induced by the frustration in the system. In addition, variational ansätze have to overcome the difficulty to find the nontrivial sign structure of the real ground state wave function \cite{iqbal2016spin}.
The most accurate approximations of the ground state energy include the Green's function Monte Carlo (GFMC) result of \cite{capriotti1999Long} and Gutzwiller-projected wave functions with Jastrow or RBM factor \cite{ferrari2019neural}.

We compare the energies obtained using a standard RBM on a 6x6-cluster with the energies obtained using the modified cRBM ansatz. In order to achieve better accuracies, the RBM is initialized in the $120^{\circ}$ Neel state. This classical state can be written as RBM by using the expression introduced in \cite{miyashita1984variational} and \cite{huse1988simple}:
\begin{align}
| \Psi \rangle_{\rm Neel}=\sum \limits_{s} \exp (\tilde{H}_0) |s\rangle, \ \ \ \ \tilde{H}_0=\frac{1}{3}\pi i (\sum \limits_{i \in B} s_i-\sum \limits_{i \in C} s_i)
\end{align}
with $|s\rangle$ a basis state in spin-$z$-basis and $s_i \in \{-1,1\}$ the value of the spin in $z$-direction at lattice site $i$. The sublattices are denoted with $A$, $B$ and $C$ as illustrated in Fig.~\ref{fig:lattice_triangular}.
As a consequence, $| \Psi \rangle_{\rm Neel}$ corresponds to an RBM with the parameters $b_j=0$, $W_{kj}=0$ and visible biases
\begin{align*}
a_k=\begin{cases} 1/3 \pi i &\text{if } k \in $B$, \\
-1/3 \pi i &\text{if } k \in $C$, \\
0 &\text{else.}
\end{cases}
\end{align*}
We employ symmetries on the RBM ansatz compatible with the symmetries of the Neel state and the periodic boundary conditions detailed in \cite{schulz1996magnetic}: translational symmetry which keeps the sublattice invariant and $C_{3v}$ symmetry.
Due to the $SU(2)$ symmetry of the Heisenberg Hamiltonian, a more accurate ground state wave function is obtained by restricting to the subspace with $S_z=0$. This constraint is enforced by restricting the Monte Carlo sampling to configurations with total $z$-magnetization $\sum s_z=0$, only allowing (nearest-neighbor) spin-exchange updates.
The relative errors of the variational energies of the RBM ansatz are plotted in Fig.~\ref{fig:L5}. As parameters (hidden neurons) are increased, similar energies as the Gutzwiller-RBM ansatz are obtained. We perform the simulations on a $6\times 6$- lattice and compare with exact diagonalization \cite{schulz1996magnetic,capriotti1999Long}.

We compare the variational energies obtained with the RBM ansatz with a cRBM ansatz. The cRBM ansatz includes physical as well as generic extensions. In particular, we make use of the a correction introduced to the Neel state by Huse and Elser \cite{huse1988simple}
\begin{align}
| \Psi \rangle_{\rm Neel}=\sum \limits_{s} \exp (\tilde{H}_0+\tilde{H}_1 + \tilde{H}_2) |s\rangle, \\
\tilde{H}_1=-\sum \limits_{i,j} K_{i,j} s_i s_j, \ \ \ \tilde{H}_2=i L \sum \limits_{i,j,k} \gamma_{ijk} s_i s_j s_k,
\end{align}
where $\tilde{H}_1$ and $\tilde{H}_2$ correspond to two-body and three-body corrections, respectively. In particular, $\exp (\tilde{H}_1)$ takes the form of the Jastrow factor.  The sum in the expression for $\tilde{H}_1$ runs over nearest neighbors, while the sum in $\tilde{H}_2$ runs over distinct triplets: the sites $i$ and $k$ are second neighbours to one another while being both nearest neighbours of $j$. The parameters $K_{i,j}$ and $L$ determine the accuracy of the Huse-Elser wave function. The value of the sign factor $\gamma_{ijk}=\gamma_{kji}=\pm 1$ changes sign under rotations by $\pi/3$ or $\pi$. The corrections to the Neel state induce a significant improvement in the wave function accuracy and consitute an early and simple approach to a variational wave function for the triangular Heisenberg antiferromagnet.

The Huse-Elser corrections can be naturally implemented as cRBM ansatz. In particular, we introduce $2$-body and $3$-body correlators as in $\tilde{H}_1$ and $\tilde{H}_2$: nearest-neighbor correlators $C^b=s_i s_j$ and triplet correlators $C^t=s_i s_j s_k$. Here, the index $b$ denotes the bond between site $i$ and $j$ and $t$ marks the triplet defined by $i,j,k$. The Huse-Elser wavefunction can be recovered by choosing the biases on $C^b$ and $C_t$ appropriately. In particular, the optimal parameters found in \cite{huse1988simple} correspond approximately to the biases
\begin{align*}
a^b_{i,j}=-\frac{1.45}{8}, \ \
a^t_{i,j,k}=\frac{0.13}{8}\gamma_{ijk} \bf{i},
\end{align*}
where $a^b_{i,j}$ and $a^t_{i,j,k}$ correspond to the biases related to the correlators $C^b$ and $C^t$. We found the influence of the triplet correlators to occur mainly in the biases and therefore set all weights connecting triplet correlators to hidden neurons equal to zero in order to reduce parameters.
The relative error of the variational energies obtained with such a cRBM are compared with the energies of an RBM ansatz in Fig.~\ref{fig:L5}.  For the same amount of parameters, the cRBM ansatz provides significantly lower energies. In addition, the slope of the relative error curves with increasing number of parameters is steeper for the cRBM, indicating that the extension of the spanned Hilbert sub-space is more efficient when introducing correlators.

\bibliographystyle{unsrt}

redpajama_set_name: RedPajamaArXiv


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Sergei Bobrovsky, Anton Stralman, Brett Connolly and Noel Acciari are now playing for the Florida Panthers. (Photo by THE ASSOCIATED PRESS)
Bobrovsky says he came to Florida to win the Stanley Cup
Jul. 3, 2019 7:43 a.m.
SUNRISE, Fla. — Sergei Bobrovsky already has two Vezina Trophies, the award handed out at the end of each season to the NHL's top goaltender.
He's not looking for a third.
For the Florida Panthers' new goalie, only one trophy matters now.
Bobrovsky and Florida's three other free agent signings — defenceman Anton Stralman, and forwards Brett Connolly and Noel Acciari — put on their new Panthers sweaters for the first time Tuesday in their official introduction to South Florida. When they're back to begin training camp in just over two months, the Stanley Cup will be the singular goal for the long-struggling Panthers.
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Bobrovsky was the biggest acquisition for the Panthers this summer, at least from a player sense. Florida's off-season began with a coaching change and the hiring of three-time Stanley Cup champion Joel Quenneville, who said having a great goaltender is "the biggest ingredient" when putting together a team that can truly win a title.
And the Panthers think they got the best goalie in the game, someone who led the NHL with nine shutouts last season and then backstopped Columbus to a stunning sweep of Tampa Bay in the opening round of the playoffs — after the Lightning were far and away the league's best team during the regular season.
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Bobrovsky was long believed to be Florida's top free-agent target, and it was widely presumed that he would pick the Panthers. He decided last week that he would indeed sign with Florida, and a $70 million, seven-year offer got it done.
"With the bright future this team has, with the great coach, with the great management, and with the really talented group of guys I'm excited to be here," Bobrovsky said. "I think we can make something special here."
Bobrovsky will replace Roberto Luongo as Florida's No. 1 goaltender, following Luongo's retirement. Sam Montembeault, who made his first 10 NHL starts last season with the Panthers, is likely going be the backup.
Florida has missed the playoffs in 16 of the last 18 seasons, hasn't won a playoff series since 1996 and will have had 16 coaches in 26 seasons when Quenneville makes his debut. But the Panthers touted a promising young core for years, had one of the NHL's top offences last season and believe Bobrovsky will be the difference-maker on the defensive end of the ice now.
"It's a process," the 30-year-old Bobrovsky said. "It's not going to be easy. Nobody says this is going to be smooth and nice. We're going to have to overcome some adversity. But those things will make us stronger."
Mexico outlasts Haiti 1-0 in Gold Cup semifinals
Top players looking to grow at U16 Hockey Alberta Summer Development Camp
Edmonton-Red Deer-Calgary bullet train waiting for provincial blessing
A high-speed train project between Edmonton and Calgary, proposed in April 2018,… Continue reading
Home selling and building markets reflecting a tough economy, but hope in sight
Real estate sales and new home builds still lagging 2018
Former Sylvan Lake bank employee sentenced to three years in prison for $1M fraud
Red Deer woman was ordered to pay nearly $830,000 in restitution
All that jazz back at Sylvan Lake
17th annual Jazz at the Lake runs Aug. 16 to 18
Plenty of family fun to be had at Westerner Days in Red Deer
Tim Hortons Kids Day and Servus Credit Union Family Day are discount days
Court of Appeal dismisses Paradise Shores arguments
A court will not hear arguments; sticks with appeal board's ruling
Schitt's Creek' and its stars among Canadians with Emmy nominations
TORONTO — Eugene Levy thought the highlight of his Tuesday would be… Continue reading
Singh sees Quebec as 'fertile ground' for NDP as he hits province for tour
OTTAWA — The province of Quebec offers the federal New Democrats fertile… Continue reading
ST. JOHN'S, N.L. — Four occupants of a downed float plane remained… Continue reading
New developments in text-messaging controversy involving Manitoba chief
WINNIPEG — The women's council of the Assembly of Manitoba Chiefs says… Continue reading
N.S. minister holds off comment on wrongful conviction case due to past as Mountie
HALIFAX — Nova Scotia's justice minister — a retired Mountie — says… Continue reading
Cuts to Legal Aid Ontario will cause hearing delays: Immigration and Refugee Board
OTTAWA — Cuts to legal-aid funding imposed by the Doug Ford government… Continue reading
Crown wants 2 years for man who took girl to U.S. to marry polygamous member
CRANBROOK, B.C. — A special prosecutor is recommending up to two years… Continue reading
Red Deer's Jared Howse qualifies for national track and field meet
Red Deer's Jared Howse is no stranger to the national stage, only…
LOS ANGELES — HBO's Game of Thrones slashed its way to a…
No guarantee voters will flip in this fall's federal election
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Canadian Pacific Railway Ltd. announced record second-quarter revenues of nearly $2 billion…
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Snapchat is currently the fastest growing social media platform, and with its ever expanding growth and popularity, it provides another marketing channel for many businesses to take advantage of. Like other social media platforms, it appeals to a certain demographic, and there are methods specific to Snapchat that may not be so successful on other networks. This article has been written with the intention of giving you some ideas on how to maximize the power of the current social media darling.
The attraction of Snapchat to its millions of users is the spontaneity and realism of the content produced. On virtually every other network, the content is polished, edited, and reviewed constantly for fear of damaging the brand. Snapchat, on the other hand, is faster and close to real-time, providing raw content.
Snapchat users feel more connected with the brands they follow, which makes it the perfect platform for behind the scenes styled content. The purpose is to make your followers feel personally connected to your brand, providing them with exclusive content or promotions that are only available on Snapchat. Your aim should be to build a tribe of rabid followers, hungry for every piece of information you provide.
This method can take some research and time because it is essential that you find the right match for your brand. The concept is to let someone else run your Snapchat account for a specified period. The ideal person to hand over the reigns to your account will be someone who has already established a huge following on Snapchat, of maybe 300,000 followers.
If you choose the right partner for this process, your brand will benefit from being "recommended" by that person, and the popularity and respect of their followers, will hopefully transfer to your brand. It is a similar concept to a friend recommending a film or book; you are much more likely to consider engaging with it, if it was recommended by someone whose opinion you respect and trust.
When Apple launches a new iPhone, there is always limited space in the audience. Apple has the resources and finances to stream their launches live on their website to meet demand,but for most companies, this is not a feasible option.
This is where Snapchat can provide the perfect solution. It is reasonable to assume that anyone who follows your brand on Snapchat is passionate and enthusiastic about your brand. Make your followers feel special by bringing them into the audience at any launches or special events. This can easily be accomplished by live streaming the event on your Snapchat channel. It is little things like this that will help grow your fanbase and their loyalty.
The scarcity of a product has long been used as a sales technique to encourage people to purchase a product. The fear of missing out on a special deal of promotion will be enough to convince someone to pull the trigger and make that purchase.
The fact that videos on Snapchat only last for 24 hours means that you can run a promotion safe in the knowledge that it will automatically be time limited. If you put some time and thought into this style of promotion, it can reap huge dividends, as you are promoting a time limited offer, to your biggest fans.
The above ideas are just some of the benefits that Snapchat can bring to your business. There are many more ways to utilize Snapchat for your business, but that comes with experience and success. As with everything, using Snapchat for your business comes with practice – luckily it is one of the easiest social media tools to use. If properly executed, any social media platform can help your business reach new customers and grow your following. Investing and learning the intricacies of the various social media platforms is time well spent, and could potentially benefit your brand for many years to come. To learn more about how to incorporate social media into your business, check out our other social media posts.


Kathy, This home was wonderful for our needs. My brothers and I were treating our parents for their 40th wedding anniversary. It was clean, quiet and just as described in the listing. We have rented before and the photos and listing weren't as accurate as yours were. Thank you for your great customer service and clean, comfortable beach home.
Thank you Kathy, the house was very nice and we had a great time. We will use OceanAire Rentals in the future and will refer your company to our friends and family.
Thanks so much, Kathy, we absolutely loved staying there! I'll definitely get in touch with you next time we're looking for a place down there.


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glasses Warby Parker serial number Not exclusively can an amazing suit of glasses look terrific, yet they can relax easy, allow you to see remarkable to anything you ever have, and could affect you to overlook that also you are using them. All the same, there are, clearly, a great deal of eyewear brands available and also they're not all equal.
glasses Warby Parker serial number That, along with glasses, could get fairly costly so you'll most likely should think about the glasses you acquire before you get them.
Parker Warby eyeglass frames offer single-vision as well as bifocal centerpieces. It does not normally provide trifocal focal factors, so you'll have to bear in mind that glasses Warby Parker serial number .
glasses Warby Parker serial number Parker Warby eyeglass frames have a lot putting it all on the line including sharp retro-hip cases, a smooth website, outstanding service highlighting a residence try the program, totally free sending as well as returns, and anarchical buzz that has actually been benefiting a considerable size of time.
One more obvious offering factor for customers is value: without a doubt most of Warby Parker glasses offers a sensible and inquisitively at a price of $95.
glasses Warby Parker serial number One of the ideal points about Warby Parker Sunglasses is that it boasts an attempt on-at-home program. glasses Warby Parker serial number The program essentially enables you to select a solid five structures, after which you'll obtain five days to check them out.
glasses Warby Parker serial number Determining the size is the least demanding part taking into account the truth that one of the most important estimation is the width of the framework. When you understand where you continue to be within the scope of thin to broad, you ought to have a number of options. Some of which can be rather well balanced.
The glasses it provides are of great and excellent quality. Every set of glasses includes anti-glare and anti-scratch finishes in addition to UV protection at no extra price, which is an extremely good option.
Looking through the coverings available at the site is really easy too.
Next off, you need to guarantee you're selecting a form that compliments your face. A rounder face could should try a square shape as well as vice versa.
A distinction in the color of a side could influence the shape to look absolutely adjusted. It's crucial to attempt a number of tones in the shape and also size that fits you finest. Concentrating on the tone of your skin is important considering that a couple of colors could be excessively severe, or in reality clean you out.
Consider your own design while choosing a casing. On the occasion that you incline toward quirkier clothing, you can likely attract off a crazy side. Although that no matter whether your design is routinely excellent – loco glasses can be an awesome method to produce an impact!
They're concentrated on bringing you spectacles at a sensible expense, despite whether your remedy is extra entangled than the majority of.
The frames are light as well as thin. You can get the perfect fit making use of Warby Parker's internet estimating instruments.
Try not to give the reasonable expenses a possibility to deceive you. These spectacles are not efficiently made. Warby Parker utilizes just the most effective products accessible. Despite whether they're making the structures from Japanese titanium or Italian cellulose acetic acid derivation, the developers visit the globe to bring customers the most effective high quality product. glasses Warby Parker serial number Amid the growth procedure, every acetic structure is cleaned up manually with a German wax compound before being tumbled for at the very least three days.
At Warby Parker, their motto is acquired a set as well as gives a pair. Regularly, they figure exactly what number of glasses has actually been sold at that point coordinate that number as a gift to their non-benefit partners. The act of generally giving eyeglasses is on a regular basis a temporary remedy. Nevertheless, preparing team participants to disperse spectacles has long-haul benefits. By offering these individuals function abilities, they've been made it possible for to have an enduring result.
Glasses have actually made some remarkable progress considering that the burdensome structures you wore as a child or the specs your grandfather could never ever show up to find. Huge and also square or magnificently round housings in tortoiseshell, dark or perhaps great colors have actually progressed towards ending up being a fad and not just for stylish individuals and also library sweethearts.
The very best top qualities Warby Parker sunglasses are modest and wise; along with they are quickly available online. Along these lines, not solely will you look wonderful in your brand-new Warby Parker designs; nonetheless you'll furthermore understand that your cash is being made use of in the direction of fantastic inspirations.
glasses Warby Parker serial number Not specifically can an unbelievable match of glasses look excellent, yet they could relax easy, allow you to see above anything you ever have, and also can influence you to forget that also you are wearing them. However, there are, obviously, a great deal of eyewear brands around as well as they're not all equal.
glasses Warby Parker serial number That, in addition to eyeglasses, could obtain quite costly so you'll presumably have to consider the glasses you acquire before you obtain them.
Parker Warby eyeglass frames use single-vision in addition to bifocal prime focus. It does not normally offer trifocal centerpieces, so you'll should keep in mind that glasses Warby Parker serial number .
glasses Warby Parker serial number Parker Warby eyeglass frames have a lot placing it all on the line including sharp retro-hip housings, a smooth website, incredible service highlighting a home try the program, complimentary sending out as well as returns, as well as insurgent buzz that has been helping a substantial size of time.
An additional undeniable offering point for customers is value: by much the majority of Warby Parker glasses uses a sensible and also inquisitively at a price of $95.
glasses Warby Parker serial number Among the finest features of Warby Parker Sunglasses is that it boasts an attempt on-at-home program. The program essentially allows you to select a solid 5 structures, after which you'll get 5 days to evaluate them out. After the 5 days, pop the glasses back in the casing with the label of shipping as well as you're all set.
It in addition has excellent plans on the off opportunity that you do not such as the ordered frames; you could return them in 30 days.
glasses Warby Parker serial number Determining the size is the least requiring part because of that the most critical estimation is the width of the frame. When you understand where you continue to be within the extent of slim to large, you ought to have a few options. Several of which can be rather well balanced.
The glasses it offers are of great and also excellent quality. Every set of glasses includes anti-glare as well as anti-scratch layers together with UV protection at no added cost, which is an exceptionally suitable choice.
Next, you have to guarantee you're picking a form that compliments your face. A rounder face may have to attempt a square form as well as the other way around.
A difference in the color of a side can affect the shape to look completely adjusted. It's essential to attempt a couple of colors in the sizes and shape that fits you best. Concentrating on the tone of your skin is essential since a few shades can be excessively extreme, or in actuality wash you out.
Consider your personal style while choosing a case. In the event that you incline towards quirkier clothing, you could likely draw off a crazy edge. Although that despite whether your style is routinely excellent – loco glasses could be a remarkable technique to develop an impression!
Different designers could place you out lots of bucks; nevertheless, Parker Warby eyeglass frames are very economical.
They're concentrated on bringing you glasses at a reasonable expense, despite whether your remedy is more entangled than the majority of.
Warby Parker's spectacles are understandable. The frameworks are light and slim. Meant to secure your eyes, the prime focus are made utilizing UV defense, hostile to scratch, as well as versus glow advancement.
You can obtain the excellent fit utilizing Warby Parker's internet estimating instruments. There's a casing for each and every face create! They run in size from slim, medium, and large, furthermore, to determining amongst conventional and low nose connect fits.
Warby Parker uses simply the ideal materials easily accessible. Regardless of whether they're making the frameworks from Japanese titanium or Italian cellulose acetic acid derivation, the developers check out the globe to bring clients the best quality item.
Warby Parker's sites make glasses on order and also are available online. All you need is a new solution from an optometrist. You can look online for Warby Parker locations in the USA. Parker Warby eyeglass frames are likewise offered cost-free shipping and also returns. Merely guarantee that you maintain the very first invoice.
At Warby Parker, their adage is acquired a pair and also provides a set. The act of generally giving eyeglasses is routinely a short-term service.
Spectacles have made some outstanding development considering that the challenging frameworks you put on as a youngster or the specifications your grandfather can never show up to discover. Huge and also square or magnificently rounded housings in tortoiseshell, dark or even great colors have actually advanced toward becoming a trend and also not just for trendy individuals and also library sweeties.
The very best high qualities Warby Parker sunglasses are moderate and wise; along with they are easily available online. Along these lines, not exclusively will you look fabulous in your new Warby Parker styles; nonetheless you'll additionally understand that your cash money is being utilized in the direction of terrific motivations.
glasses Warby Parker serial number Not solely could an incredible suit of glasses look great, yet they can relax very easy, enable you to see above anything you ever have, and also could affect you to overlook that even you are wearing them. Be that as it may, there are, clearly, a lot of eyewear brands available as well as they're not all equivalent.
glasses Warby Parker serial number That, along with eyeglasses, can get rather costly so you'll probably have to take into consideration the glasses you acquire prior to you obtain them.
Parker Warby eyeglass frames supply single-vision along with bifocal centerpieces. It does not typically offer trifocal prime focus, so you'll need to remember that glasses Warby Parker serial number .
glasses Warby Parker serial number Parker Warby eyeglass frames have a good deal putting all of it on the line including sharp retro-hip housings, a smooth website, amazing solution highlighting a house attempt the program, complimentary sending as well as returns, and insurgent buzz that has been helping a substantial size of time.
Another undeniable offering point for purchasers is worth: without a doubt a lot of Warby Parker glasses supplies a sensible and also inquisitively at a rate of $95.
glasses Warby Parker serial number One of the best points concerning Warby Parker Sunglasses is that it brags an attempt on-at-home program. glasses Warby Parker serial number The program basically allows you to select a strong five structures, after which you'll obtain five days to evaluate them out.
glasses Warby Parker serial number Figuring out the size is the least requiring part in light of the truth that the most vital evaluation is the width of the framework. When you make sense of where you remain within the range of slim to broad, you ought to have a couple of choices. A few of which could be rather well balanced.
The glasses it supplies are of good as well as top quality. Every pair of glasses has anti-glare as well as anti-scratch finishings in addition to UV security at no added price, which is a remarkably suitable alternative.
Next, you should ensure you're selecting a form that praises your face. A rounder face may require to try a square form and vice versa.
A difference in the shade of a side could affect the shape to look totally readjusted. It's vital to attempt a couple of hues in the form as well as dimension that fits you best. Concentrating on the tone of your skin is necessary since a couple of tones could be excessively severe, or in actuality wash you out.
Consider your very own style while choosing a case. In the event that you incline toward quirkier attire, you could likely drain a crazy side. Although that no matter whether your design is on a regular basis excellent – loco glasses can be an outstanding method to create a perception!
Various designers can put you out numerous bucks; nonetheless, Parker Warby eyeglass frames are extremely affordable.
They're concentrated on bringing you glasses at an affordable cost, despite whether your solution is a lot more entangled than most.
Warby Parker's spectacles are easy to understand. The frameworks are light as well as thin. Intended to shield your eyes, the centerpieces are made utilizing UV defense, hostile to scratch, and also against glare advancement.
You could get the optimal fit utilizing Warby Parker's web estimating tools as well. There's a casing for each and every face create! They run in width from slim, tool, and large, furthermore, to making a decision amongst typical as well as reduced nose attach fits.
Warby Parker makes use of simply the finest materials easily accessible. Regardless of whether they're making the frameworks from Japanese titanium or Italian cellulose acetic acid derivation, the developers see the world to bring clients the best quality product.
Warby Parker's sites make glasses on order as well as are available online. All you require is a new treatment from an eye doctor. You could browse online for Warby Parker areas in the USA. Parker Warby eyeglass frames are likewise offered complimentary shipping as well as returns. Simply make certain that you maintain the very first invoice.
At Warby Parker, their motto is acquired a pair and offers a set. The act of generally giving spectacles is consistently a temporary service.
Eyeglasses have actually made some remarkable development because the burdensome frameworks you wore as a child or the specs your grandfather could never ever appear to find. Significant and square or wonderfully round coverings in tortoiseshell, dark and even fantastic colors have actually progressed towards becoming a trend as well as not only for trendy individuals as well as collection sweethearts.
The most effective top qualities Warby Parker sunglasses are moderate as well as smart; in enhancement to they are quickly available online. Along these lines, not exclusively will you look fantastic in your brand-new Warby Parker designs; nevertheless you'll in addition recognize that your cash is being used towards wonderful inspirations.
glasses Warby Parker serial number Not specifically can an extraordinary match of glasses look fantastic, yet they could rest very easy, allow you to see above anything you ever have, and also could influence you to overlook that also you are using them. However, there are, obviously, a great deal of glasses brand names out there as well as they're not all equivalent.
glasses Warby Parker serial number That, along with eyeglasses, can get quite expensive so you'll presumably require to take into consideration the glasses you acquire prior to you obtain them.
Parker Warby eyeglass frames provide single-vision in addition to bifocal focal factors. It doesn't normally supply trifocal centerpieces, so you'll need to keep in mind that glasses Warby Parker serial number .
glasses Warby Parker serial number Parker Warby eyeglass frames have a terrific offer putting all of it on the line including sharp retro-hip housings, a smooth website, incredible service highlighting a house try the program, cost-free sending out and returns, as well as anarchical buzz that has actually been working for a significant size of time.
Another undeniable offering point for buyers is value: by far many of Warby Parker glasses offers a practical and inquisitively at a rate of $95.
glasses Warby Parker serial number One of the ideal aspects of Warby Parker Sunglasses is that it boasts an attempt on-at-home program. The program basically enables you to choose a strong five frames, after which you'll get five days to examine them out. After the 5 days, stand out the glasses back in case with the label of delivery as well as you're ready.
glasses Warby Parker serial number Identifying the dimension is the least demanding part taking into account the truth that the most crucial estimate is the width of the framework. When you make feeling of where you stay within the extent of thin to vast, you should certainly have a number of options. Some of which can be somewhat balanced.
The glasses it uses are of great as well as top quality. Every set of glasses has anti-glare and anti-scratch finishings together with UV protection at no additional price, which is an incredibly suitable choice.
Next, you need to guarantee you're choosing a form that compliments your face. A rounder face could should try a square form and also vice versa.
A difference in the color of an edge could influence the shape to look totally readjusted. It's essential to attempt a few tones in the sizes and shape that fits you finest. Concentrating on the tone of your skin is vital considering that a couple of hues can be excessively harsh, or in actuality laundry you out.
Consider your own design while picking a casing. In the event that you incline towards quirkier outfit, you can likely draw off an insane edge. Regardless of the truth that despite whether your style is routinely excellent – loco glasses can be a remarkable approach to create an impression!
Various designers can put you out several dollars; nevertheless, Parker Warby eyeglass frames are extremely economical.
They're focused on bringing you eyeglasses at a reasonable price, no matter whether your solution is a lot more entangled than many.
When it come to glasses styles, Warby Parker is a brilliant. They deliver a variety of designs, including retro, classic, pilot, vintage and also cat-eye.
From metal to pastels, the design is available in a selection of colors. Two-tone as well as turtle ranges are furthermore obtainable.
Try not to offer the affordable expenses a chance to fool you. These spectacles are not successfully made. Warby Parker makes use of just the very best products available. Despite whether they're making the structures from Japanese titanium or Italian cellulose acetic acid derivation, the developers visit the world to bring clients the best high quality item. glasses Warby Parker serial number Amid the advancement treatment, every acetic framework is cleaned manually with a German wax substance before being rolled for a minimum of three days.
Warby Parker's sites make glasses on order as well as are offered online. Parker Warby eyeglass frames are likewise offered cost-free shipping as well as returns.
At Warby Parker, their adage is purchased a pair as well as offers a set. Constantly, they figure exactly what number of glasses has actually been cost that point coordinate that number as a present to their non-benefit partners. The act of generally offering spectacles is on a regular basis a temporary solution. Nonetheless, preparing team participants to disperse eyeglasses has long-haul benefits. By offering these individuals function capabilities, they've been enabled to have an enduring result.
Glasses have made some amazing progression considering that the challenging structures you put on as a kid or the specs your grandpa can never ever appear to locate. Huge and also square or magnificently round cases in tortoiseshell, dark or even great colors have advanced toward ending up being a pattern and not just for classy people as well as collection sweeties.
The very best top qualities Warby Parker sunglasses are small as well as clever; in addition to they are easily offered online. Along these lines, not exclusively will you look fabulous in your brand-new Warby Parker styles; nonetheless you'll furthermore realize that your cash money is being made use of towards terrific motivations as well.


text:
So far, the best thing I've ever done, that's for sure!
Aart van Asseldonk
Aart van Asseldonk, together with diederendirrix, was responsible for the interior design during the renovation of Weverij De Ploeg in Bergeik. Aart was inspired by the architecture of Gerrit Rietveld, the designer of De Ploeg: "I immersed myself totally in this project and once again fell in love with De Stijl and Rietvelds' work. I really enjoyed transporting myself back to the spirit of the age. How Rietveld at the time made those decisions. That's extremely interesting to see and then to map out my own plan on that basis. A project like this really inspires you to do your very best. There's so much history involved. Really amazing that, as a youngster, you can start sketching in the drawings – and fantastic to work on them. And then as soon as it's finished the whole world has something to say about it …"
Breughelian tableau
Aart is delighted that the client − Bruns − gave him the opportunity of designing the interior. "In the design world everyone wanted the commission. These are the most interesting projects". He received the commission through the exhibition of his work at the Dutch Design Week, a Breughelian tableau in the Paterskerk church, and ended up talking to Jan Burgmans, Director of Bruns. "Rather cunningly I managed to arrange an appointment with Jan and he then invited me for De Ploeg. Diederendirrix was already involved in the project. I joined the team one week later. At the time Rob Meurders had already been working on the project for several months."
A free hand
For Aart, who studied product design in Arnhem, this was his first major interior assignment. "I wasn't yet experienced in interior design, but I do have a good sense of form and materialisation. What's more, my method of working fits in well with Jan Burgmans. We share the same love of material and handmade designs. I was really lucky that Jan allowed me a free hand to do as I wanted with the design of the interior." During the assignment Aart worked closely with project architect Rob Meurders and architect Thorsten Schneider. "The collaboration between Rob, Thorsten and myself was very important. It was a pleasant collaboration and we got along well." Both Aart and Rob had to adjust their ideas on occasion. "You first imagine what you plan to do but when putting it into practice, you sometimes have to acknowledge that there are other possible solutions. That was the game – negotiating these points with Rob, Thorsten, the client Bruns, and the contractor Aqualon. The construction meetings were extremely important in this context."
Playing with lines
Aart studied and reused many of the building's details. Some of them are not conspicuous , but that does not apply to the characteristic linear pattern of the exterior wall and the striking outer doors, which Rietveld decorated with a pattern derived from De Stijl. Aart also used this façade pattern in the wooden interior walls, but in a style entirely his own. "This façade is very significant. It's the building's most frequently-photographed façade. I turned the pattern around and started playing with the grid. I also blew everything up and made it thicker. This has produced a new, unique form that people recognise. In order to obtain this form I printed out a large number of views and then started sketching in them. I turned the plates in an alternating pattern to study the effect of the light. There's a high level of furniture quality in the wooden walls. If an interior contractor had devised this the smaller details wouldn't have received so much attention. Bruns is also really good with details. In this respect it was a match made in heaven."
Grand gestures
Aart, however, is not only interested in details, he also makes grand gestures. The spatial dimensionality of the building is excellently suited to this. "Bruns first had small spaces and they needed one large space, an open-plan office. This required grand expressions not small, unattractive bits and pieces." One of these grand expressions is the air-conditioning system − an autonomous element − suspended in the space. "I worried about the installationsplit. right from day one. The end result is super and really individual. It matches Bruns and the building perfectly." And it totally carries Aarts' signature. "We worked very well together and it was one of the biggest challenges in the project. We went really deep. The installers ended up saying 'there's that man again – the one with the hat'. It was a great game!"
Swearing in church
The design of the canteen also posed an unusual challenge whereby Aart drew his inspiration from the furniture designs, of Rietveld, among others. The large lamps, the green wall, the seating and the industrial kitchen design. "You can find multiple influences in the canteen, which is a bit like swearing in church. I wanted to create the Dudok feeling." But the height of the canteen really proved problematic in creating that atmosphere. "The building is high everywhere and yet you still want to feel you can sit comfortably with a large group of people. But the ceiling is very high and that feels uncomfortable. So we were busy with the lighting. I made several suggestions for factory lamps, at any rate my own interpretation of them. This finally resulted in large wooden lamps, which had the integral refinement that they're made of wood. But making such huge lamps is nevertheless another reference to Bruns: playing with the proportions and the space. And we wanted to make a BIG statement." Aart is very pleased with the design of the canteen and the kitchen. "Also with the furnishings made by Lensvelt, and the entire colour choice works extremely well. Somehow you want to create the feeling that they're all individual seats in the middle of a compartment. I think I've managed to make this work well."
Photo credits: Vincent van den Hoven
RepurposingRenovationMultifunctionalWorkingRelaxing


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Travel Bucket List
Travel All Over The World Together
The Toughest Countries to Visit
Hardest Countries to Visit
Here is a list of the toughest countries to visit where you need to be really patient and go about getting their visa expecting the unexpected. Traveling for sightseeing can be fun and exciting for all of us. Travel to historical, recreational places. However, traveling overseas are not as easy. The first and most important thing is getting a visa and knowing the general safety of that place.
Saudi Arabia with lots of Restrictions
Saudi Arabia is at the forefront of toughest countries to visit. This place issues visa for tourists with a lot of restrictions. Perhaps one of the reasons is that Saudi Arabia has huge oil reserves, which makes it no longer needing tourist dollars, but Saudi Arabia hosts 2 million Muslim pilgrims annually.
Kiribati a Beautiful Island in The Pacific
It is a beautiful island in the central Pacific, but getting a visa to travel to this island is very difficult and you have to endure a lot of trouble getting that visa. It is interesting to know that this country is on both side of the international line of history, meaning that time of day is the same as the one of Hawaii, however, the date is one day ahead. For this reason, the government of the country moved the east line in 1995 so that the entire country follows the same date. Because of that, on January 1st 2000, this country was the first place on earth to enter the third millennium.
Republic of Chad in The Center of The Africa
Chad has a population of 12 million people and you will find it in the center of the African continent. To get a visa to enter this country, you must first get a letter from a sponsor or a hotel in the capital inviting you to travel there. The letter should also mention the relationship between the two sides and the purpose of the trip. In addition, only a few hotels issue such a letter and you must reserve a room in advance and deposit the money. This makes it one of the toughest countries to visit as well as not a very safe one since there is always some kind of war is taking place here.
Nauru in The Heart of The Pacific
A beautiful with amazing weather in the heart of the Pacific, called the Republic of Nauru. The island, which is home to vast phosphate sources, is surrounded by coral reefs that flow out of the water during the ebb and create a special beauty in the waters of the Pacific.
Russia with lots of Historical and Natural Beauties
Russia, the largest country in the world, is a country with abundance of historical and natural tourist Attractions. To enter this country where is in the fifth place of most difficult visa countries. Moreover, to enter you must answer a list of questions. The name of the person or organization paying the trip. Name all the countries you've traveled to in the past 10 years. The place where the person is currently working and the two previous jobs. Any educational institution where the person has participated in.
Any charity in which one is a member of. Details of family members residing in Russia. Also, details of any training in explosives, nuclear weapons, etc. and details of national service. After all that, you may be approved and be given a visa.
Somalia a War Torn Country
This African country, which has been weakened by war and terrorism in recent decades. It makes this country one of most unsafe countries to visit. Therefore, the government does not want tourists to be abducted and killed. Perhaps the main reason is that the country is very difficult to issue visas to tourists.
Sudan Found in Africa
It is said that since the country was accused of killing tourists in 2003 and then the president of the country was accused of that, the country is not keen on bringing tourists with their cameras here. Therefore, Sudan might be one of toughest countries to visit in Africa so need more attention to safety details before planning to go there.
Yemen located in The Middle East
Yemen is a country in southwest Asia and south of the Arabian Peninsula in the Middle East. This country has been plagued with wars and conflicts has a very warm climate. That's why it's not an attractive place to travel and not one of those easy countries to visit.
Angola an Emerging Economic Country
Africa's third economy is Angola, which sees itself as an emerging economic world. Half of the adult population is engaged in agriculture, mainly producing food products. Its main export product is coffee. Much of the country's population is engaged in the cultivation of corn and coffee.
Angola has very rich underground resources, such as oil, diamonds, iron, manganese, copper and gold, and more than half of the country's revenue comes from oil sales. The country's strict visa policy has led to the belief among Angolans that every tourist who wants to travel to Angola is going to steal Angolan diamonds.
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text:
Die taiwanische Futsalnationalmannschaft ist eine repräsentative Auswahl taiwanischer Futsalspieler. Die Mannschaft vertritt den taiwanischen Fußballverband bei internationalen Begegnungen.

Abschneiden bei Turnieren
Das Futsalnationalteam Taiwans trat erstmals 2001 bei der Futsal-Asienmeisterschaft in Erscheinung und nimmt seither regelmäßig am kontinentalen Turnier teil. Siebenmal startete das Team bei der Finalrunde, überstand aber kein einziges Mal die Gruppenphase.

2004 war Taiwan Gastgeber der Futsal-Weltmeisterschaft und daher automatisch für die Endrunde qualifiziert. Gegen Spanien, die Ukraine und Ägypten blieb man ohne Punktgewinn und schied als Tabellenletzter nach der Vorrunde aus.

Futsal-Weltmeisterschaft

 1989 – nicht eingeladen
 1992 – nicht teilgenommen
 1996 – nicht teilgenommen
 2000 – nicht teilgenommen
 2004 – Vorrunde
 2008 – nicht qualifiziert
 2012 – nicht qualifiziert

Futsal-Asienmeisterschaft

 1999 – nicht teilgenommen
 2000 – nicht teilgenommen
 2001 – Vorrunde
 2002 – Vorrunde
 2003 – Vorrunde
 2004 – Vorrunde
 2005 – nicht qualifiziert
 2006 – Vorrunde
 2007 – nicht qualifiziert
 2008 – Vorrunde
 2010 – Vorrunde
 2012 – Vorrunde
 2014 – Vorrunde
 2016 – Vorrunde

Weblinks
 Auflistung aller Spiele auf futsalplanet.com

Futsalnationalmannschaft
Futsal
Nationalmannschaft

redpajama_set_name: RedPajamaWikipedia