# View-Aware Contrastive Learning for Incomplete Tabular Data with Low-Label Regimes
## 3 Materials and Method
### Proposed Method
#### 3.3.3 Consistency Fusion and Loss Function Design  
Within the proposed multi-view consistency-based self-supervised representation learning framework, the module for consistency fusion and loss function design serves as the critical component that connects the previous two modules and enables unified objective optimization. Its primary function is to integrate multi-view embeddings and apply information-theoretic loss functions for joint training, thereby enhancing the semantic density and structural alignment of the representation space. As shown in the architectural diagram, this module consists of three sub-processes: encoding-projection, variable soft discretization, and information entropy maximization. Inspired by contrastive learning and variational inference, the design emphasizes mining cross-view mutual information while preserving local consistency constraints within individual views, as shown in Figure 3.  
In practice, each embedding \(z_{d}^{i}\) produced by the multi-view encoder is passed into a projection network \(\psi_{i}(\cdot)\). This projection network adopts a three-layer fully connected architecture. The first layer has parameters \([\text{width}=64,\text{height}=1,\text{channels}=128]\), followed by [128; 64] in the second layer, and [64; 32] in the third. Each layer is followed by a ReLU activation and a dropout operation to prevent overfitting and improve expressive capacity. The projected output \(\hat{z}_{d}^{i}=\psi_{i}(z_{d}^{i})\) is then used as the intermediate representation  
Figure 3: Illustration of the consistency fusion and loss function design module. Two augmented views \(X^{\prime}\) and \(X^{\prime\prime}\) are encoded and projected into a latent space, followed by soft variable discretization to produce segment-wise variable groups \(v_{1}^{\prime},\dots,v_{4}^{\prime}\) and \(v_{1}^{\prime\prime},\dots,v_{4}^{\prime\prime}\).  
entering the variable soft discretization module. The soft discretization stage aims to map the continuous latent vector \(\hat{z}_{d}^{i}\) into a finite probabilistic discrete set \(v_{1},v_{2},\ldots,v_{m}\), thereby enhancing the controllability of the information structure. The Gumbel-Softmax operation with a learnable temperature parameter is adopted as the discretization mechanism, expressed as follows:  
\[q_{ij}=\frac{\exp((\hat{z}ij+gij)/\tau)}{\sum_{k=1}^{m}\exp((\hat{z}ik+gik)/ \tau)}, \tag{14}\]  
where \(g_{ij}\) denotes Gumbel noise, \(\tau\) is the annealing temperature, and \(q_{ij}\) indicates the assignment probability of sample \(i\) to discrete variable \(j\). This soft partitioning retains gradient flow while allowing multiple latent vectors to share semantic clusters, improving representational stability and generalization. Building on this, a contrastive objective based on joint mutual information maximization is designed to measure the alignment of latent variables across different views. Let the discrete variable sets from two views be \(v_{i}^{\prime}\) and \(v_{j}^{\prime\prime}\), respectively; then, the cross-view joint mutual information loss is defined as  
\[\mathcal{L}\text{info}=-\sum i=1^{m}\sum_{j=1}^{m}P(v_{i}^{\prime},v_{j}^{ \prime\prime})\log\frac{P(v_{i^{\prime}}^{\prime},v_{j}^{\prime\prime})}{P(v_ {i}^{\prime})P(v_{j}^{\prime\prime})}, \tag{15}\]  
where \(P(v_{i}^{\prime},v_{j}^{\prime\prime})\) is the estimated joint distribution from a sample co-occurrence matrix and \(P(v_{i}^{\prime})\), \(P(v_{j}^{\prime\prime})\) denote the corresponding marginal probabilities. This loss essentially represents the negative mutual information, and its optimization encourages the latent variables from different views to exhibit stronger semantic dependency and structural consistency.