Contrastive Learning

The core mechanism relies on creating positive pairs—two views of the same biological sample that share identical biology but differ in batch-specific noise. Augmentations simulate batch effects through:

• Gaussian noise injection mimicking technical variation
• Dropout-based masking of gene expression values
• Poisson sampling to model count-based technical noise

The encoder is trained to pull these augmented views together in latent space, forcing it to ignore the simulated batch variation while retaining the underlying biological identity.

The push-apart mechanism requires careful negative pair selection to avoid collapsing representations. Effective strategies include:

• Batch-stratified sampling: negatives drawn from different batches to explicitly penalize batch-specific features
• Hard negative mining: selecting samples from the same cell type but different batches, forcing the model to disentangle biology from batch
• Temperature-scaled contrastive loss (NT-Xent) to control the concentration of the distribution

Poor negative selection leads to overcorrection, where distinct biological states are erroneously merged.

The objective is to learn a batch-invariant latent space where:

• Cells of the same type cluster together regardless of their batch of origin
• Batch identity becomes unpredictable from the learned features
• Biological variance is maximally preserved

This is measured by domain classification accuracy—a well-trained encoder should yield features from which a classifier cannot determine batch membership, indicating successful removal of technical artifacts while maintaining cell-type separability.

Several loss formulations drive the learning process:

• InfoNCE Loss: maximizes mutual information between positive pairs while minimizing it for negatives
• Triplet Loss: ensures the anchor-positive distance is smaller than anchor-negative distance by a margin
• SupCon Loss: leverages known cell-type labels to create a supervised contrastive objective that explicitly groups same-type cells across batches

The choice of loss function directly impacts the tightness of biological clusters and the degree of batch mixing achieved in the final embedding.

Contrastive methods are evaluated on two competing axes:

• Batch mixing metrics: kBET acceptance rate, batch LISI, and entropy of batch mixing quantify how well batches are intermingled
• Biological preservation metrics: cell-type LISI, average silhouette width for cell types, and kNN classification accuracy verify that biological distinctions remain intact

The Pareto frontier of these metrics reveals the optimal correction strength—excessive contrastive pressure can erase rare cell populations, while insufficient pressure leaves residual batch effects that confound differential expression analysis.

The typical architecture employs:

• A shared-weight encoder (Siamese network) processing both augmented views to ensure consistent feature extraction
• A projection head (2-3 layer MLP) that maps encoder outputs to the space where contrastive loss is applied
• Batch normalization layers strategically placed or removed to control information leakage

After training, the projection head is discarded—the encoder outputs serve as the batch-corrected representations for downstream tasks like clustering, trajectory inference, or differential expression testing.

Contrastive learning frames batch correction as a representation learning problem. The model is trained to pull together positive pairs—augmented views of the same biological sample or cells of the same type across batches—while pushing apart negative pairs from different batches. This forces the encoder to learn features that are invariant to batch identity but sensitive to true biological variation. The resulting latent space is free of technical artifacts and can be used directly for downstream tasks like clustering or differential expression analysis.

Effective contrastive learning depends on designing meaningful data augmentations that preserve biological identity while simulating batch effects. Common strategies include:

• Gene expression masking: Randomly dropping out a subset of genes to simulate technical dropout
• Gaussian noise injection: Adding small perturbations to expression values
• Library size scaling: Artificially varying sequencing depth
• Subsampling reads: Downsampling to simulate different capture efficiencies These augmentations teach the model that these technical variations should not change the learned representation.

Adaptations of the SimCLR framework have proven effective for single-cell batch correction. The architecture uses a siamese encoder network with a projection head, trained with the NT-Xent loss (normalized temperature-scaled cross-entropy). Key design choices include:

• Encoder backbone: Typically a multi-layer perceptron or graph neural network
• Projection head: A small MLP that maps representations to the space where contrastive loss is applied
• Temperature parameter: Controls the concentration of the distribution over negative samples After training, the projection head is discarded and the encoder outputs serve as batch-corrected embeddings.

The construction of negative pairs is critical for batch correction. Rather than random sampling, effective strategies include:

• Batch-aware hard negative mining: Selecting negatives from different batches that are close in the current embedding space
• Cross-batch pairing: Ensuring each positive pair is contrasted against negatives drawn uniformly from all other batches
• Memory bank approaches: Maintaining a queue of representations from previous mini-batches to increase the effective number of negatives without large batch sizes This ensures the model learns to separate samples by batch identity rather than biological differences.

The success of contrastive batch correction is quantified using batch mixing metrics:

• kBET (k-nearest neighbor Batch Effect Test): Tests whether the local batch label distribution matches the global distribution. An acceptance rate near 1.0 indicates perfect mixing.
• LISI (Local Inverse Simpson's Index): Measures the effective number of batches in each cell's neighborhood. A high iLISI score indicates good batch mixing, while a high cLISI score confirms biological signal preservation.
• ASW (Average Silhouette Width): Evaluates the trade-off between batch mixing and cell-type separation in the integrated embedding.

Contrastive methods offer distinct advantages over MNN-based correction:

• Scalability: Contrastive models learn a parametric mapping function, enabling correction of new query data without re-running the full integration
• Stochasticity handling: The probabilistic nature of augmentation-based training provides robustness to noise
• No explicit pairing: Unlike MNN which requires identifying cross-batch cell pairs, contrastive learning works with batch-level labels However, contrastive methods require careful hyperparameter tuning of temperature and augmentation strength, and may need larger training datasets to learn robust invariances.