Learning Relative Gene Expression Trends from Pathology Images in Spatial Transcriptomics
Authors: Kazuya Nishimura
Haruka Hirose
Ryoma Bise
Kaito Shiku
Yasuhiro Kojima
Venue: NeurIPS 2025 poster ()
Keywords: Spatial Transcriptomics
pathology image
learning to rank
gene expression
Primary area: applications
TL;DR: We tackle gene expression estimation from pathology images by proposing STRank, a novel loss function that captures relative relationships of expression from multiple samples. This approach improves robustness to batch effects and stochastic noise.

Abstract: Gene expression estimation from pathology images has the potential to reduce the RNA sequencing cost.
Point-wise loss functions have been widely used to minimize the discrepancy between predicted and absolute gene expression values. 
However, due to the complexity of the sequencing techniques and intrinsic variability across cells, the observed gene expression contains stochastic noise and batch effects, and estimating the absolute expression values accurately remains a significant challenge.
To mitigate this, we propose a novel objective of learning relative expression patterns rather than absolute levels.
We assume that the relative expression levels of genes exhibit consistent patterns across independent experiments, even when absolute expression values are affected by batch effects and stochastic noise in tissue samples.
Based on the assumption, we model the relation and propose a novel loss function called STRank that is robust to noise and batch effects.
Experiments using synthetic datasets and real datasets demonstrate the effectiveness of the proposed method.
The code is available at https://github.com/naivete5656/STRank.

Learning Relative Gene Expression Trends from Pathology Images in Spatial Transcriptomics
Kazuya Nishimural
Haruka Hirose'
Ryoma Bise²
Kaito Shiku²
Yasuhiro Kojima'
Laboratory of Computational Life Science, National Cancer Center Japan 2 Department of Advanced Information Technology, Kyushu University, Japan
kanishi4@ncc.2 .o.
Abstract
Gene expression estimation from pathology images has the potential to reduce the RNA sequencing cost. Point-wise loss functions have been widely used to minimize the discrepancy between predicted and absolute gene expression values. However, due to the complexity of the sequencing techniques and intrinsic variability across cells, the observed gene expression contains stochastic noise and batch effects, and estimating the absolute expression values accurately remains significant chal- lenge. To mitigate this, propose novel objective of learning relative expression patterns rather than absolute levels. We assume that the relative expression levels of genes exhibit consistent patterns across independent experiments, even when ab- solute expression values are affected by batch effects and stochastic noise tissue samples. Based on the assumption, we model the relation and propose novel loss function called STRank that is robust to noise and batch effects. Experiments using synthetic datasets and real datasets demonstrate the effectiveness of the proposed method. The code is available at https:: //gt githhub... com http://aavveee666//eme STRRnk
Introduction
With the development of spatial transcriptomic techniques (ST), the comprehensive gene expression profile can be captured on small spot with a spatial location corresponding to the pathology image [6]. Due the high cost of acquiring spatial transcriptomies (ST) data, there is growing interest in using computer vision techniques to estimate gene expression from pathology images as more affordable way [19
One of the main difficulties in estimating gene expression from pathology images is the batch effects and stochastic fluctuations in observed data. As shown in Figure I (a). differences reagent batches, equipment, and other technical factors in the measurement process (i.c., batch effects) can cause variations data scaling across tissues [T [8] Additionally, due cellular heterogeneity and temporal dynamics, the observed gene expression level stochastically fluctuates even though the appearance of the pathology image the same as shown in Figure (b).
Although mean squared error (MSE) is commonly used in the previous estimation methods [7] 19 30 4 it is hard to capture variations from the data containing batch effects and stochastic noise. MSE loss focuses on predicting the absolute values of gene expression without correcting for batch effects. Consequently, models trained with MSE loss may inadvertently learn patient-specific biases rather than biologically relevant signals. Additionally, since MSE loss does not model stochastic noise explicitly, it can not account for the significance biological signals from expression count data.
In this paper, we aim to estimate the relative expression relation instead of directly estimating absolute values of gene expression. The key hypothesis of this paper is that relative gene expression trends
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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(a) Batch effects
(b) Stochastic noise
(c) Relative expression trends
Tissue1
Count
Count
Count
Cancer
Patch
Fluctuations
Tissue2
Temporal dynamics
Cancer
Non-cancer
Cancer Non-cancer
Heterogeneity of cell
t
Cancer
Scaling
Follows count dist.
bias
Tissue1
Tissue2
Figure 1: (a) Illustration of scaling bias due to batch effects, (b) stochastic noise, and (c) our hypothesis: learning relative expression trends. Even in the presence of batch effects and stochastic noise, the relative expression trends between patches are preserved.
between image patches preserved, when batch effects or stochastic noise contained in count values. For instance, as illustrated in Figure (cc). we extract cancerous and non-cancerous patches from several tissues, the expression of the cancer cell-specific gene expected to exhibit higher expression cancerous patches for all the tissues. Although the absolute expression values and their scales may vary across tissues, posit that the relative relation of expression between patches remains consistent, In addition, the relative expression relation has been widely used for downstream analysis, such as differential expression analysis, which detects the relative expression difference between clusters. Therefore, capturing relative expression differences between patches within each tissue is more reasonable than directly estimating the absolute value of gene expression.
Learning to rank (i.c., ranking loss) is one of the solutions to learn the relationships between samples 2. 9 10 27 This ranking loss learns which of given pair of samples has higher score, and the pairwise learning approach can mitigate batch effects. However, because signal-to-noiss ratios of lowly expressed genes tend be lower than those of highly expressed genes, stochastic noise can alter the relative ranking between samples when gene expression levels are low. Therefore, it is essential model the relative relationships in manner that reflects the probabilistic characteristics of gene expression data.
To address the challenge of learning relative relationships in gene expression data affected by stochas- tie noise, we propose a novel loss function that models gene expression as a discrete probabilistic assume that the expression distribution conditioned pairwise or listwise input. Specifically, counts paired patches are the consequence of the counting process given relative frequencies among the patches; assume binomial distribution for pairwise and multinomial distribution for listwise scenarios. This formulation enables the model to capture relative relationships in a manner that is consistent with the probabilistic nature of observed count data.
To confirm the characteristics of our proposed loss function, we compared a previous loss function with ours using synthetic dataset. The experiments demonstrated the effectiveness of batch effects and stochastic noise in the low signal situation. Moreover, experiments using real datasets show the generability of our loss function.
Our contributions are highlighted follows:
We redefine the task setup of gene expression estimation from pathology images as a rank score estimation setting. The setting more practical and realistic for the downstream tasks of using gene expression.
We propose a noise-robust loss function designed to handle batch effects and probabilistic noise, which dynamically adjusts its weighting based on the relative magnitude of expression for spatial transcriptomic data (STRank). This allows the model learn more effectively, even when the expressions are sparse.
We demonstrate the effectiveness our loss function for batch effect and stochastic noise using synthetic datasets. In addition, we validated the robustness of the proposed method in expression estimation using real-world data, confirming effectiveness under practical conditions.

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2 Setup and Notation
Let x((m)) = { denote a set of image patches n-th tissue (n 1,.... Ai(iissue) and g(m) = 1= be a set of their corresponding gene expression levels at each patch, where No is the number of patches. The et is N*-dimensional vector and indicates gene expression level for each gene, where No is the number of genes. Unlike previous expression estimation setups that directly estimate expression value e from x²' without considering tissue n, we aim to learn a function f x². + pr that estimates the rank score [3] for each gene which reflects the relative relation of gene expression between the given patches from the same tissue. The ry the scale-invariant, it reflects relative relation among expression of tissue n, where if og > en. then the rank score should be r > rn. Since raw gene expression values have some scaling biases introduced by the complexity of the observation technique and experimental conditions, our setup is more intuitive and practical than directly estimating the raw expression value. For readability, we omit the subscript n in, n. and n These values are referred to xf and e which are samples in tissue n.
"g"
To motivate this approach, first summarise the two losses most widely adopted in prior work MSE (pointwise) and Rank (pairwise) - and clarify why they remain vulnerable to either batch effects or stochastic noise.
mean squared error loss between raw expression value et and the estimated expression has been widely used for gene expression estimation from pathology image 77 19 30 The mean squared error (MSE) loss for a sample x² defined as:
LMsE(e' Pt)
No ||e' ||e'-
where || || is the L22 norm, and f is the output of a function f that estimates the expression value, such neural network, fr f(=').
The loss function is calculated based on one patch (i.e., pointwise input). If there are batch effects between g(n) and g(m), the loss function can be influenced by scaling bias due to batch effects because the loss does not consider relations between samples obtained from different tissues. When patient data imbalanced, the model may disproportionately rely on data from certain individuals. This can cause the model to learn spurious patterns, resulting in experimental bias.
To deal with the batch effects in the target data, the pairwise loss, such Rank loss ( listwise loss, such as PCC loss [25] 2 that learn relative relations from multiple inputs, is one of the countermeasures. Ranking loss is designed capture the relative ordering between pairwise samples. Given pairwise samples from the same tissue n, x² and xY, such that their gene expression satisfies e' > e², the loss computed for each pairwise sample in the batch as follows:
CRank (ft, (d) max (0, fr. p g
+ +E),
where is a margin value.
While we could learn pairwise relations in tissue by introducing the Rank loss, since the Rank loss does not consider stochastic fluctuation, it is difficult to capture the signal in low signal conditions. The gene expression profile captured by spatial transcriptomics is very sparse and noisy. Therefore, to capture the signal from such a sparse dataset, we should consider the probabilistic model for the loss function.
3 Spatial Transcriptomics Ranking Loss
The motivation of our Spatial Transcriptomics Ranking Loss (STRank) is to learn the relative relationships of gene expression by considering the stochastic noise effect using the distribution of count data by modeling gene expression counts at multiple spots. Similar to the learning to rank setting, we consider two setups: pairwise and listwise loss functions.
3.1 Pairwise STRank Loss
Let us consider the pairwise situation similar to learning rank [.) Given a pair of patches i, obtained from single tissue, train the model f to predict the rank score y², which reflects
3

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the relation of gene expression e², el between the samples from patch images x².,". In contrast the conventional rank loss function [3] that focuses only on learning ordinal relationships (i.e.. which sample is larger), our proposed loss function captures relative differences by incorporating the magnitude of gene expression level.
We assume that the expression count e' on the spot i, given the pairwise patches x', x and total expression t'v, follows a Binomial distribution.
N
Pr(e"|a", ,0) = II Pr(e x², ,tg),, Pr(e x" ,td)) Binomial( .g), g=1
(3)
where No the number genes, Py is the frequency parameter of Bionomial distribution, which quantify how frequently the gene g is observed at spot i given the expression count is derived from either spot or j. and yg the total expression level of gene across these two spots: ty
eg + eeg- This modeling approach accounts for the unique statistical characteristics of count data. enables adaptive weighting of inter-sample relationships based the observed count levels, thereby improving the ability to learn from count data distributions which has stochastic fluctuations.
Given pairwise patches, x² and x², the model output scores, f and 15, where f*, N EN softmax function is then applied between j and fJ
exp(f*)
exp(fy) exp(fs) + exp(ft))
Pg exp(ft) exp(P!)
P
Pg = P
(4)
Our loss function models the predicted probabilities p and p as parameters of a binomial distribution, and the model trained by minimizing the negative log-likelihood of the binomial distribution, thereby aligning the predicted distributions with the observed count-based outcomes. The negative log-likelihood can be decomposed into the following form:
Na
log Pr(e'Ixt ladcl='"",,, , = log
II
(5)
N
Hi
Σ
eg
log pi + egg log + log
(6)
Since log
is constant value, our final loss function 4STRaak is as follows:
N²
L STR (2' ,e, ed) = Σ 8=1
e'),
(e' log p' + teg log log
To construct sample pairs, we randomly select a sample from within the same tissue for each reference sample. Patch pairs are generated per tissue using grouped permutation, and the total loss for mini-batch M, randomly sampled reference without considering patients, is defined to integrate relative signals across tissues as follows:
N
pair STR (M)
Σ
L pair
ST (x', (1) ee, c
No
where æ denotes permutation index obtained by randomly shuffling the sequential sample indices within each tissue n and (() corresponds to randomly selected sample from the same tissue as x'. After training, the i serves as rank score indicating the relative expression levels across individual spots.
Relation with Ranking Loss Function. Our proposed pairwise loss function can be interpreted as relaxed variant of a traditional ranking loss, enabling flexible optimization by considering count value while preserving the core objective of learning relative sample orderings. The previous ranking loss

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functions focus solely on the relative ordering between pairs of samples, determining whether one is larger than the other. This implicitly assumes that the difference rank scores is sufficiently large to make the ordering unambiguous. Under this assumption, f is sufficiently larger than F3, F > لم and exp(fe)
the pairwise probabilities are treated as follows: vi ear(( exr((t))enp(()) 1,
explet) +exp(()) 2
exp(e)
exp()) exp(F
Then, our loss function can be transformed as follows:
exp(fg) exp(ff))
No Σ g=1
L
Pair ST'Htkk (x', xd, e",, e²) - -
Eg log
-
(Pg
(g)
Introducing a margin term and a max operation to the difference in rank scores recovers the form of conventional ranking loss functions, such as the hinge-based pairwise ranking loss.
3.2 Listwise STRank Loss
Similar to the pairwise approach, listwise estimation over multiple N samples can be formulated by modeling the expression level associated with each sample. This allows the model to handle group-wise comparisons within unified probabilistic framework.
We assume that the relationship between the list of patch images, X [xr [x',,.., x:
extracted
from the same tissue and their associated gene expression values, E(²) je"..., N follows multinomial distribution. This probabilistic formulation enables modeling the joint contribution of individual patches to the overall expression profile in a listwise manner.
No
Pr(E (1)
T(a))=
= II Pr(E X ( Pr(EE X (n), T = Multinomial(? .p)).
(10)
where TT(m) 11 &g is the total number of gene expression count, and E,y" = jey.... g The
probabilities for the multinomial distribution p are obtained using the softmax operation, similar to the pairwise case: p'g
exp(F))
A (xp(
The negative log likelihood of the multinomial distribution is transformed
No II
- log Pr(E(") (") T) = log
Pr(E)))) (n) (()) Tg)
(11)
No
T
e log + log
(12)
elle
!o!
Since the second term is independent of the model parameters, it can be omitted during optimization. The resulting listwise rank loss for spatial transcriptomics, referred to as ListWiseSTRank, is defined as follows:
No N
I Liitt
X (n) E(7)
Σ
c log P'
(13)
Similarly to the pairwise loss, define the total loss for a mini-batch M, which is randomly sampled without considering patients, as follows:
N (isuus))
List LSTRank
(M)
Σ
List LTTRakk
(X (()) (M))
(14)
where (M) and (M) are the lists of x and e derived from tissue n in mini-batch M.
Correction Using Expression for Each Spot. Gene expression levels can vary in detectability across spatial spots, so the total count per spot often normalizes expression data. However, such normaliza- tion converts the inherently discrete count data into continuous values, which may compromise loss
5

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functions that rely on count-based statistical properties. To mitigate this, we introduce a correction based on the total expression level I' at each spot, enabling the model to account for inter-spot exp(F")) where 1' = -gg c/3
variability while preserving the count data structure, P'g -ー exp(fg))
4 Experiments
We evaluated our methods using two types of datasets: synthetic datasets to confirm the hypothesis and characteristics of the proposed loss function, and real datasets to confirm practicality.
Comparisons. We compared our loss function with five loss functions: 1) Mean Squared Error loss (MSE) measures the squared difference between the predicted value and the ground truth on a per-sample basis (widely used on gene expression estimation), 2) Poisson loss (Poisson) models the output as Poisson-distributes count and minimizes the corresponding negative log-likelihood for each sample, 3) Negatíve Binomial loss (NB) extends Poisson loss by incorporating a dispersion parameter to handle overdispersed count data at the individual sample level, 4) Rank loss (Rank) operates on pairs of samples and penalizes incorrect relative ordering, encouraging proper ranking, 5) Pearson Correlation Coefficient loss (PCC) a listwise loss that maximizes the linear correlation between predicted and true values across the full batch. To examine the effectiveness of our proposed learning relative expression trends strategies, we compare the loss functions of PairSTRank (Section 3.1) and ListSTRank (Section 3.2), which are based on pairwise and listwise learning, respectively.
The Spearman Correlation Coefficient (SCC) was used as a metric to evaluate the performance.
4.1 Hypothesis Analysis on Synthetic Dataset.
We simulated 1D synthetic data to evaluate the effects of batch effects and stochastic noise. The reason for using synthetic data is that it is difficult to obtain ground truth from raw gene expression datasets since the observed data already contains bias and noise.
In these experiments, each input variable x² was defined as a one-dimensional scalar constrained to the interval [0, 1]. The corresponding gene expression level e* was modeled using negative binomial distribution, consistent with prior work transcriptomic data analysis [I]] Specifically, et is also 1D data and was sampled from the distribution NB (au((")) + r, where μux²)) is the mean response function of the input, r is the dispersion parameter, a is scaling parameter, ,3 is bias parameter.
The objective of the experiments is to accurately estimate the mean function jua') from a given dataset D = (((x()) g(m),
N g(r) = {e It corresponds to finding the meaningful signal from observed data. The p(x²)) is nonlinear function: sa(²²) sin(cr*) + +-biin (in(""")) +b, which is the same with [21]. We prepared four types of functions with different parameters (cf.
(n) = {x' 1==1:
Supplementary material A). The mean SCC for the four types of functions is calculated.
We assumed a training dataset comprising two patients (n = 2), and each patient's 's gene expression is affected by experimental batch effects, which stem from sources such as differences in imaging protocols or acquisition equipment. We assumed that gene expression measurements for each patient affected by distinct batch parameters (scaling) and / (offset). For simplicity, we a 1 and = for the first patient, a = 10 and 3 = 10, for the second patient (Other conditions are shown in supplementary material A). For training, 50,000 samples were independently sampled from each patient. The validation and test sets, each consisting of 10,000 samples, are sampled from a uniform distribution over the interval [0,1] in both setups. We compared uniform situation, where input samples are sampled from a uniform distribution (Figure (a)), and an imbalanced situation, where the sample of tissue 2 is sampled in the specific section (Figure 2 (b)). Figure 2 shows an example of synthetic data. The color indicates tissue, the dotted line indicates the mean function, and each plot represents an observed value e', which is sampled with the negative binomial distribution.
simple MLP (multi-layer perceptron) with 3 linear layers ([1 x 128), [128 x 128), [128 x 1)) with ReLU was used for the model. The epoch was 2000 using AdamW W [13] with learning rate le 3 with mini batch size = 256. For the scheduler, we used CosiaeAnnealingg [12]. Details regarding
computational resources and related settings are provided in the supplementary material B.
Table shows the comparative performance of various loss functions used for gene expression estimation. Traditional pointwise losses, including widely used Mean Squared Error (MSE), optimize

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(e) Uniform
Imbelanced
Table 1: Performance comparison across multiple patient conditions. Results are based synthetic data. Bold faces indicate the best performance in
each setting, while underlined values denote the second-best.
Uniform
Imbalanced
MSE
0.748
0.583
List! Pair Point
p(2) 10p(1) 10
1N - 10,100)
Po
0.777
0.603
NB
0.788
0.601
Example of synthetic data for validat- ing the batch effect. Colors indicate patients; the dashed line represents the mean function be learned; and the dots show observations. (a) Uni- form setting: Each patient's 's data is drawn from a uniform distribution. (b) Imbalanced setting: Observed data is skewed.
Figure 2:
Rank
0,835
0.738
PairSTRank
0,907
0.818
PCC
'0.88
0.360
ListSTRank
0.945
0.828
prediction accuracy by minimizing the absolute difference in expression levels across individual samples. In contrast, loss functions based on pairwise and listwise learning paradigms, which capture relative expression relationships between genes or samples, demonstrate superior performance overall. These results demonstrate that learning relative expression is effective in situations where batch effects are present. Notably, the proposed methods- ParsssParsSaaan and ListSTRank- (raank-coosistenttl outperform both conventional pairwise and listwise approaches, indicating their enhanced capacity to model the structured dependencies inherent in gene expression data in both uniform and imbalanced situations. Empirical results show that ListSTRank outperforms its pairwise counterpart. We attribute this improvement to ListSTRank's ability capture global expression patterns across entire batches, as opposed to the localized comparisons used in pairwise learning. This suggests that leveraging broader relational context is advantageous under batch-affected conditions.
4.2 Evaluation on Real Datasets
Dataset. To evaluate the effectiveness of our proposed method, we performed experiments using seven datasets from the benchmark of the HEST-IK dataset [8] IDC, PRAD, PAAD, COAD, READ, ccRCC, and IDC-LymphNode. SKCM and LUAD datasets were excluded from the analysis because they contain only two patients and do not align with the assumptions of our study. Each dataset contains samples from three individual patients. The IDC, PAAD, and COAD datasets were acquired using the Xenium platform, whereas other datasets were obtained via the Visium platform. To avoid train/test patient-level data leakage, we used satient-stratified splits and one patient for validation and testing data, respectively, and the other patients were used for training data. The motivation for the experiment is not to compare models, but to compare loss functions. Therefore, we do not use PCC or regularization, and simply train a regression model with each loss function.
We used 50 genes with highly variable genes. To assess the influence of the loss function, we kept the feature extractor fixed and trained only a single fully connected (fc) layer, as shown Figure 3 The feature extractor was CONCH [14], which is vision and language foundation model for pathology. Model optimization employed the AdamW optimizer with a learning rate of 5e 5 and batch size of 256. We trained the model for up 1000 epochs, with early stopping implemented using a patience threshold of 30 epochs.
Table 2 @ablerssmmarizer summarizes the performance comparison across all datasets. Overall, the proposed method outperforms conventional loss functions on average. Although STRank demonstrated superior performance on synthetic data, STRank did not consistently outperform alternatives across all conditions in real datasets. Because real data evaluations are based on observations that inherently include stochastic and measurement noise, it remains essential to assess whether the evaluations reliably reflect true model performance. Even under such conditions, STRank remained relatively stable and was able to demonstrate superior performance on average.
7

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Table Real dataset which obtained from HEST-Ik [
Bold faces indicate the best performance
in each setting, while underlined values denote the second-best Ave. is average performance.
Loss
IDC
PRAD
PAAD
COAD
READ
ccRCC
IDC-L
Ave.
List Pair Point
MSE
0.393
0.484
0.307
0.556
0.140
0.093
0.168
0.306
Po
0,314
0.485
0.336
0.524
0.172
0.091
0.134
0.293
NB
0.199
0.491
0.119
0.538
0.160
0.075
0.126
0.244
Rank
0.317
00.17
0.181
0.366
0.047
0.059
0.1
0.222
PairSTRank
0.494
0.458
0.346
0.613
0.136
0.127
0.228
0.343
PCC
0.472
0.459
0.307
0.640
0.105
0.102
0.198
0.326
ListSTRank
0.510
0.459
0.343
0.597
0.140
0.125
0.238
0.345
0.5
0.4
fruas
0.2
Avg
fac:
Fazk
0.1
PuiSTRank
PCC
Figure 3: Illustration of our framework for the real dataset. To assess the loss function, we only update the classifier head for this evaluation.
0.01
0.1
Down sampling rate
Figure Effectiveness for sparsity. The x- axis is log scale.
4.3 Effectiveness for Sparcity
To further assess the robustness of STRank for the sparsity, conducted performance variability for varying sparsities in modified real dataset. One way to assess robustness for the sparsity is by assessing the performance low-expressed genes. However, as discussed in [17), sparsity evaluation becomes challenging in low-expression data due to the lack of known ground-trui signals. To address this, simulated the pparsity-enhance mean expression levels. For a count of each gene in each cell, we conducted binomial sampling using specified down-sampling rate acquire down-sampled count data. We varied levels of expression by downsampling each gene expression count using probabilities p = 0.01, 0.05, 0.1, 0.2, 0.5, 0.8, 1.
expression data for genes with the top 50 highest
Figure E shows the performance of the pairwise and listwise loss functions on each downsampling rate. Our Pair and List STRank loss outperforms Rank and PCC on each fown-sampling rate. The difference becomes significant when the rate is 0.01, effectiveness Since gene expression is inherently sparse, these results suggest that the STRank well-suited for capturing gene expression signals.
highly sparse and weak signals.
4.4 Effect for Parameter & of Our Loss Function
We varied & and assessed the effect of N which is the number of samples to calculate our ListSTRank. A larger & is expected to be generally preferable, it facilitates the capture of global trends. However, in the presence of noise or distortion in the global structure, pairwise learning may offer improved performance.
Table 3 shows the performance on each N The results indicate that increasing beyond 4 leads to improved performance. However, in practice, increasing N is not always beneficial due to numerical instability and computational overhead in both situations. For 2 4, the model demonstrates robustness, with stable performance observed at k = 8 and k 16.

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Table 3: Performance of STRank for N on three conditions.
N²
Uniform
Imbalanced
B Xenium
2
0,907
0.818
0,447
4
0,938
0.837
0,462
8
0.958
0.839
0,455
16
0,943
0.833
0.458
32
0,938
0.818
0.463
64
0,926
0.827
0,462
128
0,941
0,845
0,457
256
0.945
0.828
0.459
5
Related work
Gene expression estimation from pathological image. Estimating gene expression from pathology images has the potential reduce sequencing costs and help understand diseases. Deep learning has been introduced this field, and the deep learning models are trained with patch and gene expression pairs captured by spatial transcriptomics. ST-Neet [7] has introduced transfer learning approach and estimates gene expression by a convolutional neural network pre-trained on ImageNet [5]. To utilize global information of patches, graph convolution neural networks and transformers have been introduced Hist2gene [19 and Hist2st [30]. To effectively combine local and global information, M2OST [24] and TRIPLEX 4 effectively combined multiple features that are extracted from multiple resolutions. By focusing on the difficulty of directly estimating multiple-dimensional gene expression, exemplar-guided estimation 26
28 29 which utilizes retrieved gene expression,
has been proposed. BLEEP [26] has trained model with image and gene expression in a contrastive learning manner and retrieves gene expression based on the image. EGN (29 has refined the retrieved gene expression with a transformer block.
MSE loss has been mainly used the loss function for these methods. In contrast, focus the relative relation among tissues and propose a novel noise-robust loss function with pairwise learning.
Learning to rank. Learning to rank is the field that learns the ranking function from ground-truth rankings (3] Sculley has adapted the Stochastic Gradient Descent method for learning to rank [22]. allowing models to be trained on large datasets. The ranking loss has been integrated with neural networks, which have been widely utilized in applications including Image Quality Assessment 9 and crowd counting [7 10].
In contrast to these works, which only consider ranking, our loss function considers the size of the count value and adaptively weights depending on the relation of input samples. Since the gene expression sparse and has a low signal, taking into account the count value helps learn the relation in the low signal situation.
Conclusion
In this paper, tackled gene expression estimation from pathology images by reconsidering the objective. In contrast to the previous method, which estimates the absolute expression value, we aim learn the relative gene expression relation. In addition, we propose novel loss function (STRank) designed to capture the relative gene expression across spatial patches by modeling the relative expression relation. Through comprehensive experiments on both synthetic and real-world datasets, we demonstrated that our method achieves more stable and reliable performance compared traditional point-wise approaches. These results suggest that exploiting relative gene expression patterns is promising strategy for enhancing robustness in gene expression prediction.
7 Limitations
We hypothesized that STRank would perform well under sparse conditions, and we evaluated its performance by varying the number of target genes from 50 to all possible genes. As shown in Supplementary D, we could not confirm the effectiveness STRank a sparse situation of a real dataset. Furthermore, shown in Table 2, rigorous evaluation real data remains open challenge,

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and the fundamental reasons why STRank fails to outperform conventional loss functions in some datasets have yet to be elucidated.
Although STRank shows effectiveness across multiple patients, it converges more slowly than PCC when evaluated data from single patient. This behavior is likely due STRank's conservative weight updates under low-sample conditions. As a result, PCC may offer better convergence performance on simpler datasets with limited observations.
Another challenge is performance multi-cohort settings, where the sample obtained from different experimental conditions (e.g., different hospitals and procedures). As detailed in Supplementary D, our proposed loss functions exhibit limitations when applied to such large number of genes. In such cases, batch effects in gene expression amplified, and pathology images are likewise influenced by experimental batch effects due to variations in imaging conditions. While addressing this issue is beyond the scope of our study, it represents open question for this field. Future research should aim to develop more robust and generalizable approaches to mitigate these effects.
datasets with a
Acknowledgments and Disclosure of Funding
Funding in direct support of this work: JSPS KAKEN JP24KJ2205, JPMJBS2406, JP23K18509, and JP25K22846, Development (AMED) grant
(to YK). National Cancer Center Research and Development Fund 2024-A-6 (to YK). We used ABCI 3.0 provided by AIST and AIST Solutions.
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A
Details of Experiments on Synthetic Dataset
MW
100
a-0.4, b=0.6, 2- d-7
0.5, b-0.5, c-3, d-50
a=0.5, b-0.5, c-15, d-32
a=0.5 b-0.5, o= 10, d-10
Figure Visualization of p(z).
Figure shows four types of mean functions for our synthetic data. A nonlinear function was chosen to generate waveforms characterized by varying frequencies and slope gradients. This property allows the function to model complex, non-uniform signal behavior, which is relevant in representing heterogeneous patterns observed
gene expression data.
Figure 6 shows the performance of each loss function under various parameters in the synthetic dataset. We changed scale a. bias B, dispersion parameter r. scale for tissue a, bias for tissue B. Overall, our loss function outperforms all comparisons on each condition. The proposed loss function demonstrates robustness under low-scale conditions. Furthermore, its effectiveness improves as the variability in intensity scales across patients increases.
SCC
SCC
SCC
16
Scale
Bius B
Dispersion r
Rank
PainSTRank
PCC
ListSTRank
SCC
SCC
MSE
Poisson
NB
33
Scale for tissuc2 6
Bias for tissue2
Figure 6: Visualization of p(z).
B Computer Resources
We used the Cloud Environment 23 for the experiment on synthetic data, and an internal desktop computer for Experiment 2.
Experiment 1 (Cloud environment)
CPU: 16 assigned physical CPU cores
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Table Performance on HER2ST dataset with 50 90-9385 gene sets.
Method
50
250
1000
5000
9385
MSE
0.193
0.181
0.172
0.162
0.132
NB
0.020
0.154
0.098
0.083
0.074
Po
0.009
0.150
0.095
0.076
0.069
Rank
0.095
0.052
0.041
00.02
0.011
PairSTRank
0.244
0.194
0.176
0.177
0.173
PCC
0.189
0.173
0.165
0.171
0.152
ListSTRank
0.260
0.175
0.110
0.085
0.087
Table 5: Performance on COAD Visium dataset with 50-2000 gene sets.
Method
50
250
1000
2000
MSE
0.2712
0.2090
0.2125
0.2084
NB
0.3043
0.1682
0.0899
0.0868
Po
0.2572
0.1440
0.0858
0.0829
Rank
0.1118
0.0714
0.0260
0.0599
PairSTRank
0.3456
0.1957
0.1383
0.1319
PĆC
0.2615
0.2000
0.2035
0.195I
ListSTRank
0.3398
0.1973
0.1404
0.1375
GPU: None
Memory: 320 GB
Experiment 2 (Internal desktop environment)
CPU: 12th Gen Intel(R) Core(TM) 19-12900KS, Physical Cores: 16
GPU: NVIDIA RTX A6000
Memory: 128 GB
C Licenses for Existing Assets
We implemented our method with Pytorch (00 with modified BSD LICENSE, PytorchLightning with Apache-2.0 LICENSE. For the feature extraction from whole slide images, we modified the
CLAM implementation
[15]. We used Hest 1k 8 with CC BY-NC-SA 4.0 for the real datasets.
D Experiments on More Realistic Scenarios
We conducted experiments using the HER2ST datasets 1 and the COAD Visium (multi-cohort) with large gene sets evaluate the robustness of our loss function more realistic gene expression estimation scenarios. For HER2ST, we used gene sets of size 50, 250, 1000, 5000, and the full set of 9,385 genes. For COAD, we evaluated the loss functions on gene sets of size 50, 250, 1000, and 2000.
The results shown in Tables and Our loss function demonstrated robustness the HER2ST dataset, which is highly sparse spatial transcriptomics dataset, outperforming other loss functions. This suggests that the proposed loss function is effective for sparse real-world data and for mit- igating batch effects within the same cohort. However, for the COAD dataset, our loss function underperformed MSE and PCC when using multi-cohort data with large gene sets (250-2000 genes).
In multi-cohort settings (e.g. COAD setting in Table with many target genes, we assume that distribution of stochastic noise varies substantially across cohorts; therefore, for low-signal genes where the noise component dominant, further extensions that account for cohort-specifie noise characteristies needed. To effectively handle multi-cohort data, additional factors beyond batch
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Table Results of different methods on Hest2gene
Method
Hest2gene
MSE
0.039
NB
0.005
Po
-0,014
Rank
0.042
PairSTrank
0.052
PCC
0.039
ListSTrank
0.046
effects should be considered, including potential differences in biological signals and domain shifts in image features. This one of the open problems and is essential for the practical application of gene expression prediction.
E
Integration with Previous Method
To evaluate the generalizability of the proposed loss function, we examined its performance when integrated into existing gene expression estimation methods. We evaluated the Spearman correlation coefficient (SCC) for predicting 250 genes using the HER2ST dataset [[] In contrast to the original study, adopted a patient-level data split evaluate generalizability. We then assessed the performance of HisToGeen [19] trained with various loss functions. As summarized the Table 6 the proposed PairSTrank loss achieved the highest performance. In conclusion, loss functions demonstrated effectiveness on this setup.
F Exploring the Impact of Mini-Batch Sampling Strategies
To investigate the effect of a mini-batch sampling strategy, we compared three settings: the original implementation (Default), setting where the mini-batch contains samples from only one tissue (Intra-tissue), and setting where samples are evenly sampled from all tissues (Inter-tissue).
Table 7 shows the results of these experiments on the 250 and 1000 gene sets. Even when we use different mini-batch strategies, the performance of ListSTRank is not improved. PairSTRank loss also does not consider the intra-tissue and inter-tissue, but it still outperforms ListSTRank loss. This suggests that the performance degradation of ListSTRank on these results, we suspect that the performance degradation of ListSTRank may be due to numerical effects.
due to the mini-batch setting. Based
Table 7: Effect of mini-batch sampling on 250 and 1000. We compare three settings: Default, Intra-tissue (mini-batch contains samples from only one tissue), and Inter-tissue (samples are evenly sampled from all tissues).
Method
250
1000
Default
0.175
0.110
Intra-tissue
0.177
0.105
Inter-tissue
0.173
0.105
22


Reviews:
[{"review_id": "TmHNF4cTh5", "reviewer": "Reviewer_o7H2", "summary": "The authors study the problem of predicting spatially resolved gene-expression from histopathology images.\n\nInstead of directly predicting the absolute expression levels, they aim to predict the _relative_ expression relationships. To this end, they propose a loss function called STRank which models the gene-expression as a discrete distribution conditioned on pair-wise or list-wise inputs.\n\nThe proposed STRank is compared to five other loss functions on a synthetic 1D dataset, and on 7/9 tasks from the HEST-1k dataset.", "questions": "Questions/Suggestions:\n- Could you please clarify what you mean by \"Learning to Relative Expression\" in the title and \"learning to relative expression strategies\"?\n- As a practitioner, how do I know which one of PairSTRank or ListSTRank to use for a given problem? In what type of scenarios is e.g. PairSTRank preferable? Why? \n- Given that your models don't output predictions for the absolute gene-expression levels, how should it actually be used in practice? Given a WSI for e.g. a new breast cancer patient, for whom I want to analyze the gene-expression of the PAM50 genes, how do you apply your model? What clinically relevant tasks can your models be used for? How?\n- In Table 2 you only report results in terms of the Spearman correlation, while the HEST-1k benchmark uses the Pearson correlation (see e.g. https://github.com/mahmoodlab/HEST?tab=readme-ov-file#hest-benchmark-results-083024). Your results and the results for CONCH in the benchmark are quite different (and perhaps this is just because you report Spearman and they Pearson), could you report Pearson correlation results for Table 2 as well, to enable a direct comparison with the benchmark?\n\n\n\n\nMinor things:\n- Inconsistent use of capitalization in section headings, e.g. \"2 Setup and notation\" and \"5 Related work\" vs \"3 Spatial Transcriptomics Ranking Loss\", and \"4.1 Hypothesis analysis on synthetic dataset\" vs \"3.1 Pairwise ST Rank Loss\".\n- Line 27 - 29: MSE is defined twice. And then again on line 93. And then yet again on line 225.\n- Line 45: \"While learning to rank (i.e., ranking loss) is one of the solutions to learn the relationships between samples. This ranking loss...\" --> \"Learning to rank (i.e., ranking loss) is one possible solution to learn the relationships between samples. This ranking loss...\", perhaps? \n- Line 46: \"This ranking loss learns which of a given pairwise of samples has a higher\" --> \"This ranking loss learns which of a given pair of samples has a higher\"?\n- Line 80: \"without consider tissue n\" --> \"without considering tissue n\"?\n- Line 115: \"Similar to learning to rank setting\" --> \"Similar to the learning to rank setting\"?\n- \"3.1 Pairwise ST Rank Loss\" --> \"3.1 Pairwise STRank Loss\", \"3.2 Listwise ST Rank Loss\" --> \"3.2 Listwise STRank Loss\"?\n- Line 118: \"Let me consider\" --> \"Let us consider\"?\n- End of equation 8: The period should be replaced with a comma?\n- Line 151: Inconsistent indices, r^{i} but r_{j}.\n- \"SCC\" should probably be defined on line 193, before being used on Line 207 etc.\n- Line 222: Not sure what \"ConeAnnealing\" is? Cosine?\n- Line 245: \"We train simple regression.\"?\n- Throughout the paper, a bit inconsistent use of \"STrank\" vs \"STRank\".\n- \"HEST 1k\" and \"Hest 1k\" should instead be \"HEST-1k\"?\n- In Figure 3, both WSIs are marked as X_{(n)}, should the indices perhaps different?\n- Line 273: \"Since gene expression is sparse, our loss is suit. Since gene expression is inherently sparse, these results suggest that the STRank is well-suited for capturing gene expression signals\", probably forgot to remove the first short sentence \"Since gene expression is sparse, our loss is suit\"?\n- Line 290: \"To utilize global information of patch, graph convolution neural network, and transformer have been introduced on Hist2gene [15 ] and Hist2st [24]\" --> \"To utilize global information of patches, graph convolution neural networks and transformers have been introduced in Hist2gene [15 ] and Hist2st [24]\" or similar?\n- Line 300: \"Learning to rank is the field that learn the\" --> \"Learning to rank is the field that learns the\"?\n- Line 301: \"Sculley has adapted\" --> \"Sculley et al. have adapted\"?\n\n\n\n\nJustification of rating:\n- Quite interesting paper, I like the proposed approach overall. But the paper could definitely be more well written overall, and some things need to be clarified. I'm borderline on this paper, but currently leaning slightly towards accept (I _want to_ be able to recommend accept at least, I hope that my remaining concerns will be addressed by a solid rebuttal).", "limitations": "Yes.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n- The studied problem and the proposed approach are quite interesting, the approach makes intuitive sense overall.\n- The proposed loss functions seem to perform quite well compared to the MSE and rank-based losses. \n\n\n\n\nWeaknesses:\n- The paper could be more well written overall and would definitely benefit from more careful proofreading.\n- - Moreover, the \"Learning to Relative Expression\" part of the title doesn't quite make sense to me, I'm not entirely sure what this is meant to say. Same with \"To examine the effectiveness of our proposed learning to relative expression strategies\" on line 190, \"our proposed learning to relative expression strategies\" doesn't quite make sense.\n- The authors propose two variants of their STRank loss function, PairSTRank and ListSTRank, but it's not entirely clear when/why one should be preferred over the other in practice.\n- At least to me, it's not clear how the proposed approach actually should be used in practice, given that their models don't output predictions for the absolute gene-expression levels.", "was_revised": true, "final_justification": "The authors have provided a very solid rebuttal. I think they responded well to Reviewer NEgj, I'm quite happy with their response to me, and Reviewer XD8s's concerns have been addressed.\n\nTherefore, I have raised my score from \"4: Borderline accept\" to \"5: Accept\".", "rebuttal": "We appreciate your careful review and insightful comments. We are encouraged that you found our experimental setup and model of interest. We address reviewer comments below and will incorporate all feedback.\n\n### Q1: What is the meaning of \"Learning to Relative Expression\" in the title?\nThe phrase was originally intended to describe the concept of learning relative gene expression trends, inspired by the “learning to rank” [1]. Since our goal is not to predict absolute expression values but to capture relative expression trends, we coined the term “learning to relative expression” as a catchy way to convey this idea. However, as you rightly noted, the phrase causes some confusion. Accordingly, we will revise it to “learning relative gene expression trends” for clarity and precision.\n\n[1] Burges+, Learning to Rank using Gradient Descent, 2015\n\n### Q2: From a practical perspective, which loss function should we use in practice: pairSTRank or ListSTRank? \nAs described in Sec. 4.4, we prefer ListSTRank with N_k = 8 or 16 on the 50 gene set condition because it demonstrated stable performance on multiple datasets. Assuming no significant numerical instability due to floating-point precision, the list-wise approach is generally preferable. \nHowever, the PairSTRank loss outperforms ListSTRank in situations where the number of target genes is large, as shown below.\n\nThe PairSTRank has advantages in terms of implementation simplicity, low computational cost, and numerical stability, as it has been widely used for application tasks, such as crowd counting [2]. Particularly, ListSTRank has a numerical issue that vanishes gradients due to floating-point.  When the number of target genes is large and their expression values are nearly the same, and softmax produces very small values, the PairSTRank loss function may outperform the ListSTRank. \n\nIndeed, as shown in Table 1 of the supplementary material and below, the performance of the listwise loss function declines when the number of genes is large. This finding suggests that additional methodological improvements are required for listwise approaches to maintain robustness across a broader range of targets. However, since the listwise loss function performs well on synthetic data, we hypothesize that the observed performance degradation is not attributable to stochastic noise or batch effects. We will include the discussion of this issue in the supplementary material.\n\nWe will revise the description to be clearer in the camera-ready version.\n\nTable 1: Performance across different numbers of target genes (50, 250, 1000) on HER2ST dataset [3]. \n| Method       | 50  | 250 | 1000 |\n|--------------|--------|--------|--------|\n| MSE          | 0.193  | *0.181*  | *0.172*  |\n| NB           | 0.020  | 0.154  | 0.098  |\n| Po           | 0.009  | 0.150  | 0.095  |\n| Rank         | 0.095  | 0.052  | 0.041  |\n| PairSTrank   | *0.244*  | **0.194**  | **0.176**  |\n| PCC          | 0.189  | 0.173  | 0.165  |\n| ListSTrank   | **0.260**  | 0.175  | 0.110  |\n\n[2] Yan Yang+, “Exemplar guided deep neural network for spatial transcriptomics analysis of gene expression prediction”, In WACV 2023.\n\n[3] Andersson+, Spatial deconvolution of HER2-positive breast tumors reveals novel intercellular relationships, 2020.\n\n### Q3: How to use the estimation result of our model in practice?\nAs described in L42-43, we assume differential gene expression (DEG) analysis as a downstream task that is the main application using spatial transcriptomics. In the DEG analysis procedure, we begin by identifying clusters that we want to focus on (normally, it is determined by clustering or segmentation), such as tumor versus normal tissue. Differential gene expression is then calculated between these clusters to characterize expression level differences associated with the distinct regions. Then, the gene sets that are significantly different are used for other analyses, such as pathway or enrichment analysis. The important thing about the analysis procedure is to capture the difference in expression level between clusters, not to capture the absolute value. Our estimation result can be directly utilized for this DEG analysis.\n\nWhen we use observed gene expression levels instead of estimated results, the level of expression intensity of the gene expression level is changed depending on the capturing technique and the sequence length of RNA. Therefore, normally, absolute gene expression level is also not utilized for analysis. The absolute expression level is definitely not important for gene expression analysis.\n\nWhen focusing on PAM50, the analysis framework of using spatial transcriptomics is similar. In spatial transcriptomics, the initial step typically involves performing differential expression analysis to identify genes whose expression trends vary in association with PAM50 profiles. These genes are then subjected to pathway and enrichment analyses to explore potential links to relevant biological functions. Importantly, even in this context, the emphasis is placed on relative expression dynamics associated with PAM50, rather than on absolute expression levels, which are generally not utilized.\n\n\n### Q4: The difference from the HEST 1k benchmark.\nOur evaluation setting is different from the HEST 1k benchmark. Unlike benchmarks that use ridge regression with dimension reduction with PCA, our model only uses a linear layer. In addition, we split the data into train, validation, and test by patient. The number of patients used for training is not the same as the benchmark. While the setup is not the same as the benchmark, we evaluated loss functions on the same setup. Therefore, we believe our evaluation is valid.\n\n\n| Method       | IDC   | PRAD  | PAAD  | COAD  | READ  | ccRCC | IDC-L | Ave.  |\n|--------------|-------|-------|-------|-------|--------|--------|--------|--------|\n| MSE          | 0.373 | 0.449 | 0.301 | 0.567 | 0.147  | 0.136  | 0.144  | 0.302  |\n| NB           | 0.183 | 0.459 | 0.110 | 0.547 | 0.157  | 0.090  | 0.109  | 0.236  |\n| Po           | 0.468 | 0.443 | 0.306 | 0.663 | 0.103  | 0.121  | 0.179  | 0.326  |\n| Rank         | 0.309 | 0.298 | 0.167 | 0.570 | 0.050  | 0.056  | 0.103  | 0.222  |\n| PairSTRank   | 0.479 | 0.421 | 0.319 | 0.636 | 0.129  | 0.134  | 0.211  | 0.333  |\n| PCC          | 0.291 | 0.452 | 0.311 | 0.531 | 0.175  | 0.107  | 0.118  | 0.283  |\n| ListSTRank   | 0.495 | 0.420 | 0.323 | 0.620 | 0.132  | 0.128  | 0.216  | 0.333  |"}, {"review_id": "AKnKmJZqd0", "reviewer": "Reviewer_NEgj", "summary": "The manuscript introduces STRank, a pair-wise/list-wise loss designed to predict relative gene-expression ranks from pathology image patches rather than absolute counts, with the aim of being inherently robust to batch effects and stochastic noise in spatial-transcriptomics (ST) measurements. The authors motivate the method, derive binomial/multinomial likelihoods for pair-wise and list-wise settings, and benchmark STRank against point-wise (MSE, Poisson, NB), pair-wise (Rank) and list-wise (PCC) objectives on synthetic toy data and the HEST-1k benchmark. On average, STRank outperforms the baselines on synthetic data and shows modest gains on real datasets.", "questions": "Could you discuss the computational complexity of the proposed model and compare with SOTA models?", "limitations": "The paper presents an elegant loss tailored to batch/noise robustness and shows promise on synthetic data. However, the experimental evidence on real ST tasks is limited, and, critically, the method omits spatial context—the defining feature of spatial transcriptomics. Incorporating (or justifying the exclusion of) spatial information and benchmarking against modern ST foundation models would greatly improve the paper.", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\n- Framing expression estimation as a ranking task is intuitive given scaling biases across batches and low S/N ratios in ST counts.\n- The proposed loss function, STRank can be attached to any differentiable backbone without architectural changes, making it easy to adopt\n\nWeaknesses:\n- Despite being framed as a spatial transcriptomics problem, STRank neither models spot coordinates nor uses tissue-level spatial graphs/priors. Spatial context is critical in ST. The spatial information can be used to select samples in list wise ranking. \n- Baselines do not include current ST foundation models such as cGPT-spatial. Simple linear heads on frozen CONCH features are compared instead, leaving open whether STRank still helps when stronger domain-specific encoders are used.\n- The authors do not evaluate by fine-tuning scGPT-spatial with STRank loss, which would be crucial in knowing if the loss actually boosts an existing ST foundation models.", "was_revised": true, "final_justification": "I increased score to 3 based on the additional experimental evidence.", "rebuttal": "We thank the reviewer for taking the time to review our manuscript. We are encouraged by your assessment of our setup as intuitive and by your recognition of the method’s general applicability. We address your comments and concerns below.\n\n\n### Q1: Why does the proposed method omit the use of spatial contextual information?\nThe objective of our method is to propose a loss function which are robust to stochastic noise and batch effect: it is not to propose a new architecture designed to capture spatial context, as done in prior work. As discussed in [1, 2], methods that use spatial context may introduce estimation biases, which can obscure the isolated effect of the proposed loss function. To enable a clearer evaluation of our loss function, we therefore opted to use a simple gene expression estimation model. To the best of our understanding, this is a common practice when evaluating target functions.\n\n[1] Mejia+, SpaRED benchmark: Enhancing Gene Expression Prediction from Histology Images with Spatial Transcriptomics Completion, MICCAI 2024\n\n[2] Ganguly+, MERGE: Multi-faceted Hierarchical Graph-based GNN for Gene Expression Prediction from Whole Slide Histopathology Images, CVPR 2025\n\n### Q2: Why do we not use scGPT-spatial for feature extraction?\nThank you for your suggestion regarding scGPT-spatial. Does reference [3] correctly refer to your suggested scGPT-spatial? If [3] indeed corresponds to scGPT-spatial, the method seems to be designed for feature extraction for gene expression and is difficult to use it for image feature extraction. Therefore, we could not apply scGPT-spatial for gene expression estimation from a pathology image. However, if you indicate a different study, we would appreciate it if the formal title of the correct publication could be provided for clarification.\n\n[3] Wang+, scGPT-spatial: Continual Pretraining of Single-Cell Foundation Model for Spatial Transcriptomics\n\n### Q3: Could you discuss the computational complexity of the proposed model and compare it with SOTA models?\nSince our proposed model consists only of a classification head, it contains fewer parameters compared to existing methods. We provide a table summarizing the number of parameters for each method. However, we emphasize that our primary contribution lies not in architectural design, but in the task formulation and the proposed loss function. Therefore, model complexity is not the central focus of our work.\n\n| Method    | Number of Parameters |\n|-----------|----------------------|\n| Ours      | 128,000              |\n| HE2GENE   | 73,281,512           |\n| TRIPLEX   | 29,294,296           |"}, {"review_id": "e6PMqEwvIe", "reviewer": "Reviewer_XD8s", "summary": "This paper introduces a new loss/objective function to train regression models for Spatial gene-expression estimation from histology images. While the application of the objective function is on spatial transcriptomics data, the objective function seems to be quite generalizable for any kind of data with stochastic noise and/or batch effects. The authors suggest, due to the fairly assumed nature of spatial gene expressions where the relative values of the genes between two biologically different regions (eg. Cancerous & non-cancerous), exhibit a pattern across multiple experiments, this pattern can be exploited to make the gene-expression prediction models more robust to such batch effects and stochastic noise. The paper elaborates on certain decisions of the loss function, and shows performance of the objective function using synthetic data experiments, real world spatial xenium/visium data experiments and further ablation studies. The paper also shows effectiveness of the loss function in relation to sparsity of the data. The motivation of the paper is to compare the loss function to other established loss functions and their effectiveness on the downstream task and not to compare different models.", "questions": "Scalable comparisons: Can the authors compare the performance of the STRank loss function against other losses for a larger dataset? This will make the paper even stronger. For example, the main purpose of HEST to use a small set of samples was to compare different histology foundation models, irrespective of the inherent noise in the spatial dataset. Since your work is to compare loss functions with the main motivation to train models robust to batch effects, it will be highly valuable to see the effectiveness of the model on a larger distribution of batch effects and stochastic noise. This can be achieved by including more samples in the mentioned 7 tissue tasks from the HEST dataset. \n\nNumber of genes > 50 in real world data (Can be combined with previous question):  Can the authors show the effectiveness of the loss function on a larger set of genes? As suggested, the experiment can be scaled to ~1000 HVG genes for Visium and the complete gene-panel for Xenium which ranges between 280 - 480 genes in the HEST dataset. \n\nApplication of loss function on other possible architectures: Since the loss function can be used instead of conventional regression based losses like MSE, can the authors show the results of the loss function when applied to other feasible methods like ST-net to see whether it improves the gene-expression prediction performance of the method? \n\nSynthetic experiment val and test splitting confusion: In the synthetic data setting, the validation and test set is sampled from the same distribution as the training set for both the Uniform and Imbalanced setting. For the imbalanced setting, it’s confusing whether the validation and test sets were sampled from the same section of Tissue 2 or a different section. If it’s sampled from the same section of Tissue 2, one could say the model has seen the test samples. Please clarify about the same.\n\nResults for the above questions can highly boost the impact of the paper.", "limitations": "The limitations were addressed based on the real-world data experiments performed which aren’t rigorous. The overall suggestion for improving this paper is to show results for larger datasets and comparisons with other models.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 4, "originality": 3, "strengths_and_weaknesses": "The paper is well written and focuses on the problem statement clearly. It addresses a well known problem of batch-ridden data and devises a well thought and justified solution for the same. The authors clearly explain certain assumptions and decisions taken when developing the loss function. Most of the experiments performed indicate the benefits gained from the suggested solution i.e new loss function.The approach of modelling pair-wise or list-wise gene expression inputs in a probabilistic distribution and estimating the relative rank of the genes based on this objective is novel, and the synthetic dataset experiments adds value to show the effectiveness of using the loss during training. The overall effectiveness of the loss function is modest and well put.\n\nWhile the synthetic experiments are well thought and show clear effectiveness of the approach, the real world data experiments are limited. The authors show the gene expression prediction experiment on merely 50 HVGs similar to the HEST paper, which is not enough to show the difference in performance of different loss functions. As mentioned in related works, several methods for gene-expression prediction have been developed over time (Hist2Gene, BLEEP, Hist2st) showing efficacy of their approaches on a much larger set of genes. The authors miss an opportunity to test their loss function on a larger set of genes where MSE can be lacking in performance. This experiment can easily be scaled to ~1000 HVG genes for Visium (with sparsity in high-expressed genes) and the complete gene-panel for Xenium which ranges between 280 - 480 genes in the HEST benchmark dataset. It would be curious to see the effectiveness of the STRank loss function in this range of genes. Additionally, the experiment of sparsity is ambiguous in showing the effectiveness of the approach. The experiments in the main text show the loss function performs robustly in case of sparse data, but as mentioned in the supplements and limitations, the hypothesis doesn’t hold true for a larger set of genes which negates the claims in the results section 4.3. \n\nThe limitations of the loss function are addressed, based on the experiments performed. But the concern about the true effectiveness of the loss function still remains when scaled up to larger datasets which is possible by utilising other samples in the HEST dataset.", "was_revised": true, "final_justification": "The authors addressed my concerns in a strong rebuttal, I especially appreciate the additional results.", "rebuttal": "We thank your careful review and insightful comments. We appreciate your recognition of the clarity of our problem formulation, the justification of our proposed loss function, and the novelty of modeling gene expression in a probabilistic ranking framework. We address reviewer comments below and will incorporate all feedback.\n### Q1: Can the authors compare the performance of the STRank loss function against other losses for a larger dataset?\nTo demonstrate the scalability of the proposed method, we conducted experiments on the HER2ST [1] dataset, which contained 6 patients with 36 whole slide images. The number of target genes for prediction was varied across three settings: 50, 250, and 1000. \n\nTable 1 shows the result of the comparisons. Among all evaluated loss functions, PairSTRank consistently achieved the best performance on average. While ListSTRank demonstrated good performance on synthetic data and the 50-gene set condition, the performance of ListSTRank deteriorated as the number of target genes increased.\n\nListSTRank exhibited best performance across both the synthetic dataset and the experiments described in Section 4.3, suggesting robustness to noise and batch effects. In addition, PairSTRank maintained consistently high performance even as the number of target genes increased. These observations support the hypothesis that the observed degradation in ListSTRank's performance stems from numerical instability, rather than from noise or batch-related artifacts.\nThis issue lies beyond the scope of this study, which addresses stochastic noise and batch effect. We will include these results and the discussion in the supplementary material of the camera-ready version.\n\nTable 1: Performance across different numbers of target genes (50, 250, 1000) on HER2ST dataset [1]. \n| Method       | 50  | 250 | 1000 |\n|--------------|--------|--------|--------|\n| MSE          | 0.193  | *0.181*  | *0.172*  |\n| NB           | 0.020  | 0.154  | 0.098  |\n| Po           | 0.009  | 0.150  | 0.095  |\n| Rank         | 0.095  | 0.052  | 0.041  |\n| PairSTrank   | *0.244*  | **0.194**  | **0.176**  |\n| PCC          | 0.189  | 0.173  | 0.165  |\n| ListSTrank   | **0.260**  | 0.175  | 0.110  |\n\n[1] Andersson+, Spatial deconvolution of HER2-positive breast tumors reveals novel intercellular relationships, 2020.\n\n### The validity of our original experiments.\nAs noted by you, our proposed loss function is expected to demonstrate effectiveness in settings with a large number of patient samples. However, many existing gene expression datasets, such as Her2ST [1], are based on earlier spatial transcriptomics technologies, which contain more observation noise than the Xenium platform employed in our study. \nReal-world gene expression data includes significant observational noise, and the ground truth signal is typically unknown. Reliable evaluation thus requires data in which the underlying biological signal is at least partially preserved. Therefore, we believe the dataset captured by Xenium is better than the dataset captured by Spatial Transcriptomics. Furthermore, as discussed in [2, 3], evaluation procedures such as the use of smoothing introduce additional methodological variability, raising concerns about reproducibility and trustworthiness.\n\nTo mitigate these issues, we adopt the hest 1k benchmark, which is constructed primarily from Xenium-based data. This platform offers more stable and accurate measurements compared to earlier spatial transcriptomics techniques, making it more suitable for evaluating the effectiveness of our loss function.\n\nFor these reasons, we consider our experimental design using real-world Xenium data to be valid and appropriate for demonstrating the strengths of our proposed method.\n\n[2] Mejia+, SpaRED benchmark: Enhancing Gene Expression Prediction from Histology Images with Spatial Transcriptomics Completion, MICCAI 2024\n\n[3] Ganguly+, MERGE: Multi-faceted Hierarchical Graph-based GNN for Gene Expression Prediction from Whole Slide Histopathology Images, CVPR 2025\n\n### Q3: Can the authors show the results of the loss function when applied to other feasible methods?\nWe evaluated the Spearman correlation coefficient (SCC) for predicting 250 genes using the HER2ST dataset. In contrast to the original study, we adopted a patient-level data split to better reflect generalization across individuals. We then assessed the performance of HisToGene[4] trained with various loss functions. (Since STnet is almost the same as our architecture, we selected HisToGene) As summarized in the table, the model incorporating the proposed PairSTrank loss achieved the highest performance. In conclusion, while we do not perform cross-validation, our loss functions demonstrated effectiveness on this setup.\nTable 2: Performance of loss function on HisTogene\n| Method        | Hest2gene   |\n|---------------|---------|\n| MSE           | 0.039   |\n| NB            | 0.005   |\n| Po            | -0.014  |\n| Rank          | 0.042   |\n| PairSTrank    | 0.052   |\n| PCC           | 0.039   |\n| ListSTrank    | 0.046   |\n\n[4] Pang+, Leveraging information in spatial transcriptomics to predict super-resolution gene expression from histology images in tumors, 2021\n\n### Q4: Synthetic experiment, val and test splitting confusion.\nIn both settings, validation and test data are sampled from a uniform distribution over the interval [0,1]. Thank you for pointing that out. As you pointed out, the term “generated from the same distribution” lacked clarity, and we will revise it in the camera-ready version."}]

Author rebuttal:

Meta-review: Two of the reviewers were supportive of this submission after a strong rebuttal and a thorough discussion with the authors. The third reviewer, who provided a negative recommendation but increased their final score, chose not to engage in the discussions. The AC agrees with the positive reviewers that the merits of the paper outweigh its limitations. The final version should carefully include reviewer feedback and clarifications from the discussion.
Decision: Accept (poster)