## 2 Background  
### Restricted Boltzmann Machines (RBMs)  
We use Restricted Boltzmann Machine (RBM) models [19] to learn the relevant features before we use an IR technique to select the subset of relevant instances to send to the server. RBMs are generative models [19; 20] and undirected probabilistic graphical models that are applied to a wide range of applications, including feature extraction, collaborative filtering, and image reconstruction [21]. RBMs are composed of two layers [15] as shown in Figure 1. The visible layer represents the observable variables like training data, while the hidden layer represents the latent variables of the extracted features from the visible data [22].  
These two layers are linked to each other via weighted connections [19]. Furthermore, there are no links between the units of each layer [15]. The training dataset is presented to the network's visible layer, while the network's hidden layer learns how to represent these data in a low-dimensional probabilistic way [23]. For every pairing of visible and hidden units, the network assigns the following Boltzmann probability distribution \(P(v,h)\)[19]:  
\[p(v,h)=\frac{1}{z}\text{exp}(-E(v,h)) \tag{1}\]  
where \(v\) represents visible layer inputs, \(v\equiv\{v_{1}\),..., \(v_{n}\}\); and \(h\) represents the hidden layer outputs, \(h\equiv\{h_{1}\),..., \(h_{m}\}\). \(Z\) is the partition function obtained by summing all possible pairs of \(v\) and \(h\). \(E\) is the energy of the joint configuration of \((v,h)\) given as:  
\[E(v,h)=-\sum_{i\in visible}a_{i}v_{i}-\sum_{j\in hidden}b_{j}h_{j}-\sum_{i,j}v_{ i}h_{j}w_{ij} \tag{2}\]  
Figure 1: Restricted Boltzmann Machine [15].  
where \(a_{i}\) and \(b_{j}\) are biases, and \(w_{ij}\) is the weight between visible unit \(i\) and hidden unit \(j\). RBMs use Gibbs Sampling to generate and sample units in the visible layer and hidden layer [22]. Gibbs Sampling is an algorithm that involves many steps, and in each step, a variable's value is replaced with a value taken from its distribution that is conditioned on the values of the remaining variables [24]. RBMs are trained using the Contrastive Divergence Algorithm, which iteratively applies Gibbs sampling until convergence [25].  
Restricted Boltzmann Machines can be employed to create new samples by learning the probability distribution of the visible layer \(P(v)\). Also, RBMs can be used to extract features and reduce dimensionality by learning the probability distribution of the hidden layer \(P(h)\)[23]. The probability distribution of these layers is given as [23]:  
\[p(v)=\frac{1}{z}\sum\
olimits_{h}\exp(-E(v,h)) \tag{3}\]  
\[p(h)=\frac{1}{z}\sum\
olimits_{v}\exp(-E(v,h)) \tag{4}\]  
In this study, our focus lies on exploring the latent space representation of the input data, specifically the hidden layer's representation. We term these representations as \"encodings\" due to their ability to capture and encode the crucial features present within the input instances. These encodings serve as a condensed representation that captures the salient information from the input instances, allowing us to use them for training a global model instead of using the original instances.