Single-Cell Analysis¤

Single-cell RNA sequencing (scRNA-seq) measures gene expression in individual cells, revealing cellular heterogeneity hidden in bulk experiments. DiffBio provides 24 differentiable operators covering the full single-cell analysis workflow — from raw count processing to trajectory inference and spatial analysis.

What scRNA-seq Measures¤

A scRNA-seq experiment produces a count matrix of shape \((n_{\text{cells}}, n_{\text{genes}})\), where each entry is the number of mRNA transcripts detected for a given gene in a given cell. Typical scale: 500-50,000 cells, 2,000-30,000 genes.

This matrix is the starting point for all downstream analysis. Its key properties:

Sparse: Most entries are zero (dropout)
Noisy: Poisson/negative-binomial sampling noise
Batch-dependent: Technical variation between experiments
High-dimensional: Thousands of genes per cell

Key Challenges¤

Dropout¤

Low-abundance transcripts are frequently missed during library preparation. A gene may be expressed in a cell but recorded as zero. This is not true absence — it is a sampling artifact.

DiffBio addresses dropout with diffusion imputation (DifferentiableDiffusionImputer), which propagates information between similar cells via a learned affinity graph, and transformer denoising (DifferentiableTransformerDenoiser), which reconstructs missing values from context.

Batch Effects¤

When cells are processed in different experiments, batches, or labs, technical variation introduces systematic shifts that can mask biological signal. Cells from the same type but different batches may appear more different than cells from different types in the same batch.

DiffBio provides three differentiable correction strategies:

Operator	Strategy	When to Use
`DifferentiableHarmony`	Soft clustering + batch-aware centroid updates	Default choice, fast
`DifferentiableMMDBatchCorrection`	Autoencoder with MMD regularization	When batch effects are non-linear
`DifferentiableWGANBatchCorrection`	Adversarial training with gradient reversal	When other methods under-correct

Doublets¤

When two cells are captured in the same droplet, their transcriptomes merge into a single observation that looks like a hybrid cell type. Doublets confuse clustering and annotation.

DifferentiableDoubletScorer (Scrublet-style k-NN scoring) and DifferentiableSoloDetector (VAE latent-space classification) both produce continuous doublet probability scores that can be thresholded or used as soft weights.

Ambient RNA¤

Free-floating mRNA from lysed cells contaminates all droplets, adding a background expression profile to every cell. DifferentiableAmbientRemoval uses a VAE to separate the true cell expression from the ambient profile.

The Analysis Workflow¤

A typical single-cell analysis follows this progression:

graph TB
    A["Raw Counts"] --> B["Quality Control<br/>(ambient removal, doublet detection)"]
    B --> C["Normalization<br/>(VAE normalizer, library size correction)"]
    C --> D["Embedding / Dimensionality Reduction<br/>(UMAP, PHATE)"]
    D --> E["Clustering<br/>(soft k-means, community detection)"]
    E --> F["Annotation<br/>(cell type assignment)"]
    F --> G["Downstream Analysis<br/>(trajectory, communication, GRN, DE)"]

    style A fill:#d1fae5,stroke:#059669,color:#064e3b
    style B fill:#e0e7ff,stroke:#4338ca,color:#312e81
    style C fill:#e0e7ff,stroke:#4338ca,color:#312e81
    style D fill:#e0e7ff,stroke:#4338ca,color:#312e81
    style E fill:#dbeafe,stroke:#2563eb,color:#1e3a5f
    style F fill:#dbeafe,stroke:#2563eb,color:#1e3a5f
    style G fill:#d1fae5,stroke:#059669,color:#064e3b

DiffBio provides differentiable operators for every step. Because each step is differentiable, you can define a loss at any point and optimize upstream parameters.

Trajectory Inference¤

Cells captured at a single time point often represent a continuum of states — differentiation, activation, or disease progression. Trajectory inference orders cells along this continuum.

Pseudotime (DifferentiablePseudotime): Assigns each cell a scalar value representing its position along a trajectory. Uses diffusion maps to capture the manifold structure.

Fate Probability (DifferentiableFateProbability): For branching trajectories, estimates the probability that each cell will reach each terminal state. Uses absorption probabilities on a Markov chain over the cell graph.

OT Trajectory (DifferentiableOTTrajectory): Reconstructs temporal trajectories from snapshots at different time points using optimal transport to match cell distributions across time.

All three are differentiable — gradients flow from trajectory outputs back to the count matrix, enabling joint optimization of normalization and trajectory inference.

Cell Type Annotation¤

Assigning biological identities to clusters. DiffBio's DifferentiableCellAnnotator supports three strategies in one operator:

Mode	Input	Method
`celltypist`	Expression only	MLP classifier on VAE latent space
`cellassign`	Expression + marker gene matrix	Guided Poisson likelihood
`scanvi`	Expression + partial labels	Semi-supervised VAE

The marker-guided mode (cellassign) is useful when known marker genes exist. The semi-supervised mode (scanvi) leverages a small number of labelled cells to improve annotation of the rest.

Spatial Transcriptomics¤

Spatial methods (Visium, MERFISH, Slide-seq) preserve the physical location of cells within tissue. This adds coordinates to the count matrix:

Expression: \((n_{\text{spots}}, n_{\text{genes}})\)
Coordinates: \((n_{\text{spots}}, 2)\)

Spatial Domain Identification (DifferentiableSpatialDomain): Uses a GATv2 autoencoder on a spatial neighborhood graph to identify spatially coherent expression domains. The graph attention learns which neighbors are most informative for each spot.

Slice Alignment (DifferentiablePASTEAlignment): Aligns multiple tissue sections using fused Gromov-Wasserstein optimal transport, matching both expression profiles and spatial geometry.

Gene Regulatory Networks¤

DifferentiableGRN infers regulatory relationships between transcription factors and target genes using GATv2 attention on a bipartite TF-gene graph. The attention weights form a differentiable adjacency matrix that can be thresholded to extract a regulatory network.

This is differentiable end-to-end — gradients from a reconstruction loss update the attention parameters, enabling the network to learn which TF-gene relationships best explain the observed expression patterns.

Why Differentiability Matters for Single-Cell¤

Traditional single-cell tools (scanpy, Seurat) apply each step independently. Normalization does not know what clustering will follow. Clustering does not know what trajectory inference needs.

DiffBio's differentiable operators enable:

Joint normalization-clustering: Learn a normalizer that produces embeddings optimized for downstream clustering quality
End-to-end pipelines: A loss on trajectory accuracy updates the imputer, normalizer, and clustering parameters together
Learnable preprocessing: Quality thresholds, diffusion times, and correction strengths adapt to the specific dataset
Gradient-based benchmarking: Compare operators not just by output quality but by how well gradients propagate through them