🧬 biology

SOLAR: Fixed orthogonal label anchors for single-cell reference mapping

SOLAR is a supervised contrastive method that assigns fixed orthogonal label anchors to reference cells to learn an encoder mapping expression profiles into a structured space, achieving high annotation accuracy and improved label separation for single-cell reference mapping without requiring further optimization on query data.

Original authors: Minqi Chen, Guanjie Zou, Minrui Chen, Hiroto Saigo, Koji Tsuda, Lunxu Liu

Published 2026-10-19

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CC BY 4.0

Original authors: Minqi Chen, Guanjie Zou, Minrui Chen, Hiroto Saigo, Koji Tsuda, Lunxu Liu

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

Imagine a library where millions of books have been carefully sorted into sections by genre, author, and era. Now imagine a new shipment of books arrives, unsorted and mixed up, and you need to place each one on the correct shelf without reading every single page. This is the daily challenge for scientists working with single-cell data. They have vast collections of genetic profiles from individual cells, already labeled with their biological identities, such as "immune cell" or "lung cell." When a new experiment produces a fresh batch of cells, researchers need a way to quickly and accurately match these new cells to the existing, well-organized library. The goal is to understand what these new cells are and how they relate to the known ones, even if the new data was collected in a different lab or at a different time, which often introduces subtle, confusing variations.

For years, scientists have tried to build digital maps to solve this sorting problem. They use computer programs to translate complex genetic patterns into simpler coordinates, hoping that cells of the same type will naturally cluster together on the map. However, these maps often struggle to keep the different cell types clearly separated while also mixing out the technical noise from different experiments. If the map is too messy, a new cell might be placed in the wrong section, leading to incorrect conclusions about its function. The core difficulty lies in teaching the computer to recognize the true biological identity of a cell while ignoring the irrelevant differences caused by how the data was collected.

A team of researchers has now introduced a new method called SOLAR to tackle this sorting challenge with greater precision. Instead of letting the computer figure out where each cell type should sit on the map during the learning process, the researchers decided to define those locations in advance. They assigned each known cell type a fixed, distinct direction in the digital space, ensuring that every category has its own unique, non-overlapping path. Think of it as setting up permanent, immovable signposts for every section of the library before the new books even arrive. The computer's job then becomes simply to learn how to guide each new cell toward its correct signpost, rather than trying to invent the layout of the library itself.

The researchers tested this approach using data from human immune cells, lungs, and pancreas tissue, comparing their method against several existing tools. They found that by fixing these directional signposts, the system became much better at organizing the cells. When they mapped new cells from different experimental batches, the method successfully identified the correct cell types more often than the previous standard approaches. Specifically, the new method correctly labeled about 81.1% of the cells on average, a noticeable improvement over the older technique which managed about 77.4%. More importantly, the resulting map showed much clearer separation between the different cell groups, making it easier to distinguish one type from another without confusion.

The study also explored what happens when the researchers change how these signposts are used. They discovered that repeating the signposts in the training process—essentially giving the computer multiple reminders of where each cell type belongs—helped create a map where the different groups were even more distinct from one another. However, this extra repetition did not significantly change the accuracy of the final labels for the new cells. It turned out that the most important factor was simply having those fixed, orthogonal directions established from the start. This construction allows the computer to learn the position of every cell based on its genetic profile while keeping the relationships between the different cell types rigid and clear.

In the end, this work provides a reliable way to transfer knowledge from a well-studied reference set to new, unexplored data. By fixing the target locations before training begins, the method ensures that the relationships between cell types remain explicit and consistent. This means that once the system is trained, it can be reused to map new cells from future experiments without needing to be retrained or adjusted. The result is a more stable and interpretable map of cellular life, helping scientists navigate the complex landscape of human biology with greater confidence and clarity.

Technical Summary: SOLAR – Fixed Orthogonal Label Anchors for Single-Cell Reference Mapping

Problem Statement
Annotated single-cell atlases serve as references for mapping and annotating new query experiments. However, existing methods face challenges in balancing label-guided representation learning with the preservation of local data structure and batch diversity. Traditional supervised contrastive approaches, such as Supervised Contrastive Learning on Cells and their Types (SCLSC), construct class representatives from mean expression profiles. These representatives are passed through a trainable encoder, meaning their positions in the learned space shift during optimization. This dynamic nature can obscure the explicit geometric relationships between labels. Furthermore, reference mapping methods must effectively handle batch effects while ensuring that query cells are accurately assigned to known reference labels without introducing spurious structure.

Methodology
The authors introduce SOLAR (Supervised Orthogonal Label-Anchor Representation), a supervised contrastive learning framework designed for single-cell reference mapping. The core innovation lies in decoupling the definition of label relationships from the learning of cell embeddings.

Fixed Orthogonal Label Anchors: Before training begins, SOLAR assigns each reference cell type a fixed, orthogonal direction in the output embedding space. These anchors are derived from a Gaussian matrix via QR factorization to ensure they are orthonormal ( $u_k^\top u_l = 0$ for $k \neq l$ ). Unlike methods that learn class centroids, these anchor vectors remain static throughout training.
Encoder Architecture: The method employs a three-layer multilayer perceptron (MLP) with batch normalization, ReLU activations, dropout, and layer normalization. The encoder maps expression profiles (preprocessed via reference-only gene selection and PCA) into a normalized embedding space where the output vectors share the unit sphere with the fixed anchors.
Anchor-Augmented Contrastive Objective: SOLAR extends supervised contrastive learning by creating a shared pool of views for each mini-batch. This pool includes:
- Expression embeddings of the cells.
- Indexed copies of the fixed label anchors corresponding to the cells' labels.
  The loss function encourages expression embeddings to align with their corresponding fixed anchors while remaining distinct from other anchors and non-matching cells. The objective includes a margin term to separate same-label logits from different-label logits.
Reference-Only Training and Direct Mapping: The model is trained exclusively on reference data. Once trained, the encoder is frozen. Query cells are mapped using the same reference-fitted preprocessing (gene selection and PCA transform) and the frozen encoder, without further optimization or query-specific fine-tuning.

Key Contributions

Fixed Geometric Constraints: SOLAR explicitly prescribes label relationships (orthogonality) in the output space prior to training, contrasting with methods that learn these relationships dynamically from data-dependent representatives.
Reusable Encoder: The method produces a reusable encoder that maps new query cells into a space where label relationships are structurally defined by the fixed anchors, facilitating direct label transfer.
Controlled Anchor Multiplicity: The study investigates the impact of anchor presence and multiplicity (repeated anchors per cell vs. unique anchors per label vs. no anchors) on the learned representation, isolating the effects of anchor geometry on label separation and batch diversity.

Results
The method was evaluated on nine held-out batches across human immune, lung, and pancreas datasets, comparing SOLAR against Matched PCA, SCLSC, scVI, and scANVI at a common output dimension of 30.

Query Label Recovery: SOLAR achieved a mean query macro-F1 of 0.811 and balanced accuracy of 0.837. This outperformed Matched PCA (0.774 macro-F1), while SCLSC produced a similar mean macro-F1 of 0.815. scANVI achieved the highest macro-F1 (0.838) and balanced accuracy (0.882) among the compared methods.
Label Separation: SOLAR demonstrated superior label organization, achieving a Label Average Silhouette Width (ASW) of 0.873, significantly higher than Matched PCA (0.574), scVI (0.578), and scANVI (0.657). Only SCLSC (0.948) exceeded SOLAR in label separation.
Batch Diversity and Local Structure:
- SOLAR showed higher Batch ASW (0.836) than SCLSC (0.743), indicating better mixing of batches within cell types.
- However, SOLAR had lower Integration Local Inverse Simpson's Index (iLISI) compared to scVI and scANVI, suggesting slightly less local batch diversity in the immediate neighborhood.
- In terms of local structure preservation (Trustworthiness) and pseudotime smoothness, SOLAR retained more query-neighbourhood structure than SCLSC but slightly less than Matched PCA, scVI, and scANVI.
Anchor Multiplicity Effects: Experiments at 128 dimensions revealed that using repeated anchors (one per cell) increased label separation and local batch diversity compared to unique anchors or no anchors, but resulted in a slight reduction in local structure scores and query-label recovery metrics.

Significance and Claims
The paper claims that SOLAR provides a concrete mechanism for prescribing label relationships before training while learning data-driven cell positions. By fixing orthogonal anchors, the method makes label relationships explicit in the output space, producing a reusable encoder for mapping new cells.

The authors position SOLAR as a method that improves query-label recovery and label separation over standard PCA baselines and SCLSC, while offering a distinct trade-off profile compared to variational models like scANVI. The study emphasizes that while anchor repetition enhances label separation and batch diversity, it does not necessarily improve query-label prediction accuracy, highlighting that different evaluation metrics capture complementary aspects of the learned representation. The work is presented as a specific contribution to the field of supervised contrastive learning for single-cell integration, focusing on the structural role of fixed anchors rather than proposing new biological applications or future algorithmic extensions beyond the scope of the reported experiments.

Technical Summary: SOLAR – Fixed Orthogonal Label Anchors for Single-Cell Reference Mapping

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