Auxiliary Gene Learning: Spatial Gene Expression Estimation by Auxiliary Gene Selection

AI summary

Authors: Kaito Shiku, Kazuya Nishimura, Shinnosuke Matsuo, Yasuhiro Kojima, Ryoma Bise Affiliations: Kyushu University (Department of Advanced Information Technology) and National Cancer Center Japan (Laboratory of Computational Life Science) arXiv: 2511.18336v1 [cs.LG], 23 Nov 2025 Code: https://github.com/Shiku-Kaito/AGL

Overview

Research area: Machine learning for computational pathology — specifically, predicting spatial gene expression from histopathological spot images, using ideas from auxiliary task learning (ATL) and bi-level optimization.

Technical level: Advanced. The paper assumes familiarity with deep learning training loops, multi-task loss weighting, differentiable relaxations of discrete operators, and bi-level optimization.

One-sentence scope: The paper introduces Auxiliary Gene Learning (AGL), which turns the tens of thousands of low-expression genes that prior spatial transcriptomics (ST) pipelines discard into auxiliary training tasks, and proposes DkGSB, a differentiable top-k selection method that learns how many of those auxiliary genes to keep.

What This Paper Is About

Spatial transcriptomics measures the expression of tens of thousands of genes at individual spots in a tissue section, but the measurements are heavily contaminated by observational and dropout noise. Because most genes have extremely low counts that are statistically unreliable, existing gene-expression-estimation models train and evaluate on only a narrow set of highly variable genes (HVGs), discarding the remaining ~20,000 genes entirely. This paper argues that those discarded genes can still carry useful co-expression and regulatory signal, and it shows how to use them as auxiliary supervision — while selecting, rather than blindly using, which ones to include.

Key Contributions

1. Auxiliary Gene Learning (AGL). A framework that reformulates the expression estimation of previously ignored low-expression genes as auxiliary tasks, trained jointly with the primary (evaluation-target) gene tasks. The authors state this is the first attempt to use low-expressing genes as auxiliary supervision in ST gene expression estimation, and they note it is the first study to make practical use of information earlier work discarded.

2. DkGSB (Prior-Knowledge-Based Differentiable Top-k Gene Selection via Bi-level Optimization). A selection method that ranks all auxiliary-gene candidates once by a highly variable gene (HVG) score, replaces the combinatorial subset search (more than 10^6000 possible subsets) with a single learnable scalar cut-off k, and relaxes the hard top-k operator into a temperature-controlled soft mask so k can be updated by gradient descent alongside the network weights.

3. A model-agnostic, pluggable selection module. The proposed auxiliary gene selection is described as model-agnostic and easily pluggable into existing ST prediction approaches; all experiments fix ST-Net as a common backbone so that only the auxiliary-loss strategy varies.

4. Comprehensive empirical validation and analysis. Experiments on the public Hest-1k dataset across intra-batch (BOWEL A, BOWEL B, OVARY) and inter-batch (HEART) settings, plus analyses of HVG-based versus random selection, the behavior of k during optimization, visualization of selected genes, and robustness to the number of primary genes.

Main Findings

• Auxiliary genes help broadly. On every tissue in Table 1, training with all remaining genes as auxiliary tasks ("AGL + All") outperformed training on the 50 primary genes alone ("PGL"). The PGL average PCC across the four tissues was 0.407 versus 0.418 for AGL + All.

• The proposed method wins overall. "AGL + DkGSB" achieved the best scores in every column of Table 1: 0.551 ± 0.009 (BOWEL A), 0.440 ± 0.008 (BOWEL B), 0.458 ± 0.006 (OVARY), and 0.256 ± 0.039 (HEART), for an average of 0.426. For comparison, AGL + Uncertainty averaged 0.419, AGL + AuxLearn 0.412, and AGL + AMAL 0.411.

• Conventional auxiliary task weighting struggles at this scale. Weighting losses by predictive uncertainty gave only a modest gain, while the adaptive weighting schemes AuxLearn and AMAL offered no consistent improvement, which the authors attribute to the difficulty of optimizing weights for nearly 20,000 tasks without additional guidance.

• Batch effects degrade everything, but the method still holds. All methods performed worse in the inter-batch HEART experiment than in the intra-batch experiments. Even so, AGL outperformed PGL, and DkGSB improved further.

• HVG ranking beats random selection when the auxiliary pool is small. In Figure 3 (BOWEL B), HVG score-based selection gave a significantly greater improvement than random selection at 5,000 and 10,000 auxiliary genes; at 5,000, random selection actually decreased performance. When the number of auxiliary genes approached the total (15,000), both methods produced similar improvement.

• The learned cut-off discards most candidates. In Figure 4 (HEART), the bi-level loop lowered k from the full auxiliary pool to k = 2,698 while primary-gene validation PCC rose monotonically for about 15–20 outer steps and then stabilized at approximately 0.305. Since HEART contains roughly 15,000 auxiliary genes, the final threshold retained about 18% of candidates and discarded the remaining 82%.

• Selected genes look biologically plausible; the baseline's do not. Figure 5 shows that AGL + DkGSB tends to select highly expressed genes, whereas AGL + AMAL selects genes that are barely expressed across the entire slide — evidence, the authors argue, that AMAL cannot handle the high-dimensional combinatorial problem.

• Robustness to the number of primary genes. In Table 2 (BOWEL A), AGL + DkGSB was best at every setting of 25, 50, 75, and 100 primary genes (0.487, 0.551, 0.564, 0.579; average 0.545), ahead of AGL + All (average 0.538) and PGL (average 0.516).

Methodology in Plain English

The researchers start from a standard setup: an image of a tissue spot goes into a neural network, and the network outputs predicted expression values for a set of genes. Normally, the network is trained only on the small set of highly variable genes that will also be used for evaluation.

Their change is to give the network extra jobs. Besides predicting the primary genes, it also predicts the expression of many of the genes that were previously thrown away. These extra predictions are never scored as final results — they exist only to shape the network's internal representation, in the hope that co-expression relationships between genes let the extra jobs teach the network something useful about the primary ones.

The hard part is choosing which extra genes to keep. There are roughly 20,000 candidates, and picking the best subset involves more than 10^6000 combinations, which cannot be searched. So the authors instead:

1. Rank once, using prior knowledge. They compute an HVG score for every auxiliary gene — dividing each gene's variance by its mean expression to get a raw dispersion, splitting genes into twenty bins by mean expression, and z-score-normalizing dispersions within each bin. The intuition, drawn from standard single-cell practice, is that genes which vary a lot relative to their mean carry more information.

2. Learn a single cutoff. Rather than choosing a subset, they learn one number, k: keep the top k ranked genes. Because a hard cutoff cannot be differentiated, they replace it with a smooth weighting based on a temperature parameter τ; as τ approaches 0, the soft mask approaches the hard top-k selection.

3. Optimize in two nested loops. An inner loop updates the network weights on training data using both primary and masked auxiliary losses. After a fixed number of inner steps, an outer loop evaluates the primary-gene loss on held-out validation data and takes one gradient step on k. This bi-level scheme reduces a combinatorial search to a one-dimensional optimization learned end-to-end.

The loss for both primary and auxiliary tasks is a Pearson correlation coefficient loss, chosen because it is known to reduce batch-effect-related scaling bias. Evaluation uses the Pearson correlation coefficient (PCC) between predicted and ground-truth expression, averaged over target genes.

Experimental setup at a glance:

• Data: Hest-1k (Jaume et al. 2024), a large-scale public dataset of paired spatial gene expression and pathology images.
• Intra-batch: BOWEL A (4,096 patch images, 18,066 gene types), BOWEL B (4,617 patches, 18,054 gene types), OVARY (5,774 patches, 18,043 gene types), all 224×224 crops centered on spots of 55 µm width, acquired with Visium. Five-fold cross-validation at a 3:1:1 train/validation/test ratio. Top 50 HVGs as prediction targets.
• Inter-batch: HEART with four slides (2,857, 3,400, 3,236, and 3,042 patch images) and 15,904 gene types common across batches, evaluated by leave-one-batch-out cross-validation.
• Backbone: ResNet18 pretrained on ImageNet, ST-Net architecture, PyTorch, Adam optimizer, learning rate 3×10⁻⁵, mini-batch size 128, up to 1,000 epochs with early stopping at 20 epochs, H = 2 inner steps, β = 3×10⁻³, τ = 0.01, trained on an Intel Xeon Gold 5122 CPU and NVIDIA RTX A6000 GPU.

Why This Matters

Impact on research. The paper challenges a default assumption in computational pathology: that unusable measurements should simply be deleted. It shows that distrusting a measurement as a label is not the same as discarding it as a training signal, and it provides a scalable way to exploit ~20,000 auxiliary tasks when existing ATL methods were designed for at most five to ten tasks (or up to around 300 in large-scale cases). The model-agnostic formulation means the idea can be attached to graph-based, Transformer-based, or multi-scale ST predictors, not just ST-Net.

Real-world applications:

• Cancer diagnostics and tumor characterization — ST is described as playing a crucial role in evaluating disease progression, and better gene expression estimates from routine H&E-stained tissue support molecular-level assessment without the cost of full ST measurement.
• Drug efficacy evaluation — the introduction explicitly frames ST as important for evaluating drug efficacy, so more accurate spatial expression estimates could sharpen how tissue-level drug responses are measured.
• Lowering the cost barrier of spatial transcriptomics — the paper notes ST's high observational cost is what motivates image-based estimation; improving these models reduces how often expensive ST measurement must be performed.
• Biomarker and co-expression discovery — the analysis of which genes are selected as auxiliary targets (e.g., highly expressed genes chosen by DkGSB versus barely expressed genes chosen by AMAL) provides a practical way to surface genes that carry coordinated signal across a slide.

Industry relevance. The work targets the same practical bottleneck as commercial and clinical spatial-omics pipelines: the gap between cheap, ubiquitous histology images and expensive, sparse gene expression measurements. Because the selection module is pluggable and trained on existing public data (Hest-1k) with a publicly released codebase, it is positioned as a drop-in improvement rather than a new end-to-end platform.

Future Directions

1. Incorporate biological function, not just variance. The authors note that relying solely on HVG scores makes it difficult to capture underlying biological functional relationships among genes, and that modeling this would require determining both which genes to select and which biological functions are activated. They propose predicting each gene's contribution from both its expression signal strength and its functional relevance to the primary genes.

2. Make selection spatially adaptive. The contribution of an auxiliary gene may vary by location within the tissue — informative in one region, noise in another. The authors suggest detecting and down-weighting unhelpful image–gene pairs during training, for example by monitoring per-sample losses or using co-teaching strategies from the noisy-label literature.

3. Handle the added complexity of joint data and gene selection. The paper warns that adding data selection alongside gene selection would increase overall problem complexity and may require an alternative framework.

4. Test transfer to other ST architectures. Since the framework is described as model-agnostic and was validated only with ST-Net as a fixed backbone, applying DkGSB on top of the graph neural network, Transformer, and multi-scale ST predictors cited in the related work is an open question.

Target Audience

This paper is most useful to researchers and engineers working at the intersection of computational pathology and machine learning — particularly those building image-to-gene-expression models, those interested in auxiliary task learning and multi-task loss weighting at unusually large task counts, and those working with spatial transcriptomics datasets such as Hest-1k. It will also appeal to readers interested in bi-level optimization and differentiable relaxations of discrete selection operators, since DkGSB is a general pattern for turning a combinatorial subset choice into a learnable scalar. A background in deep learning training procedures is assumed; the biology is presented at a level accessible to non-biologists.

Authors’ abstract

Spatial transcriptomics (ST) is a novel technology that enables the observation of gene expression at the resolution of individual spots within pathological tissues. ST quantifies the expression of tens of thousands of genes in a tissue section; however, heavy observational noise is often introduced during measurement. In prior studies, to ensure meaningful assessment, both training and evaluation have been restricted to only a small subset of highly variable genes, and genes outside this subset have also been excluded from the training process. However, since there are likely co-expression relationships between genes, low-expression genes may still contribute to the estimation of the evaluation target. In this paper, we propose $Auxiliary \ Gene \ Learning$ (AGL) that utilizes the benefit of the ignored genes by reformulating their expression estimation as auxiliary tasks and training them jointly with the primary tasks. To effectively leverage auxiliary genes, we must select a subset of auxiliary genes that positively influence the prediction of the target genes. However, this is a challenging optimization problem due to the vast number of possible combinations. To overcome this challenge, we propose Prior-Knowledge-Based Differentiable Top-$k$ Gene Selection via Bi-level Optimization (DkGSB), a method that ranks genes by leveraging prior knowledge and relaxes the combinatorial selection problem into a differentiable top-$k$ selection problem. The experiments confirm the effectiveness of incorporating auxiliary genes and show that the proposed method outperforms conventional auxiliary task learning approaches.