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Results

This page shows the evaluations in the paper, figure by figure. Each chart is drawn from the source data of its panel, and the source data files are listed under the chart for download. The sections and saved results behind Figs. 2–6 open in the data explorers, and Analyze data evaluates your own predictions.

Fig. 1

Reproducible-signal correlation (RSC) largely avoids overstating and understating prediction quality

Pearson correlation with measured RNA expression overstates prediction quality across whole sections and understates prediction quality at fine scales. In HER2ST, a class-mean baseline that predicts one value per tissue region reaches a whole-section Pearson r of 0.111, above the median of 11 published methods (0.108; maximum 0.144). In the colorectal cancer data, the split-half reliability of the measured counts implies that the true expression reaches a Pearson r with measured RNA expression of 1.00 at the broadest scale and 0.44 to 0.57 at the finest scale. RSC scores the true expression near 1 across spatial scales.

Fig. 1b Pitfall of whole-section correlation

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Fig. 1b | Pitfall of whole-section correlation0.060.080.100.120.140.16Whole-section Pearson rMedian of 11 methods, 0.108EGNv2EGNv2: whole-section Pearson r 0.1440.144Hist2STHist2ST: whole-section Pearson r 0.1300.130ST-NetST-Net: whole-section Pearson r 0.1250.125DeepPTDeepPT: whole-section Pearson r 0.1220.122TCGNTCGN: whole-section Pearson r 0.1180.118Class-mean baselineClass-mean baseline: whole-section Pearson r 0.1110.111HisToGeneHisToGene: whole-section Pearson r 0.1080.108DeepSpaCEDeepSpaCE: whole-section Pearson r 0.1040.104THItoGeneTHItoGene: whole-section Pearson r 0.1020.102EGNv1EGNv1: whole-section Pearson r 0.0920.092GeneCodeRGeneCodeR: whole-section Pearson r 0.0850.085iStariStar: whole-section Pearson r 0.0640.064Published methodClass-mean baseline
Points show the whole-section Pearson r of 11 published methods and a class-mean baseline over 785 genes in eight HER2ST patients. The class-mean baseline (gray) predicts one value per tissue region and scores above the median of the 11 methods (dashed line). Source data: fig1b_whole_section_pearson_HER2ST.csv.

Fig. 1c Noise correction across scales

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Fig. 1c | Noise correction across scales0.40.50.60.70.80.91.0Correlation<128128–256256–5120.5–1k1–2k2–4k≥4kSpatial scale (µm)RSC, P1 CRCRSC, P2 CRCRSC, P3 NATRSC at <128 µm: mean 0.997; P1 CRC 0.997, P2 CRC 0.997, P3 NAT 0.997RSC at 128–256 µm: mean 0.996; P1 CRC 0.995, P2 CRC 0.997, P3 NAT 0.997RSC at 256–512 µm: mean 0.996; P1 CRC 0.995, P2 CRC 0.997, P3 NAT 0.997RSC at 0.5–1k µm: mean 0.996; P1 CRC 0.995, P2 CRC 0.997, P3 NAT 0.997RSC at 1–2k µm: mean 0.996; P1 CRC 0.995, P2 CRC 0.997, P3 NAT 0.997RSC at 2–4k µm: mean 0.996; P1 CRC 0.994, P2 CRC 0.997, P3 NAT 0.997RSC at ≥4k µm: mean 0.996; P1 CRC 0.994, P2 CRC 0.997, P3 NAT 0.997Pearson r with measured RNA expression, P1 CRCPearson r with measured RNA expression, P2 CRCPearson r with measured RNA expression, P3 NATPearson r with measured RNA expression at <128 µm: mean 0.516; P1 CRC 0.441, P2 CRC 0.569, P3 NAT 0.539Pearson r with measured RNA expression at 128–256 µm: mean 0.780; P1 CRC 0.704, P2 CRC 0.847, P3 NAT 0.791Pearson r with measured RNA expression at 256–512 µm: mean 0.921; P1 CRC 0.875, P2 CRC 0.944, P3 NAT 0.944Pearson r with measured RNA expression at 0.5–1k µm: mean 0.980; P1 CRC 0.965, P2 CRC 0.982, P3 NAT 0.993Pearson r with measured RNA expression at 1–2k µm: mean 0.995; P1 CRC 0.992, P2 CRC 0.996, P3 NAT 0.998Pearson r with measured RNA expression at 2–4k µm: mean 0.999; P1 CRC 0.997, P2 CRC 0.999, P3 NAT 0.999Pearson r with measured RNA expression at ≥4k µm: mean 1.000; P1 CRC 1.000, P2 CRC 1.000, P3 NAT 1.0000.44–0.570.997True expressionRSCPearson r with measuredRNA expressionThin: P1 CRC, P2 CRC, P3 NATThick: mean of patients
Lines show the RSC and the Pearson r with measured RNA expression of the true expression at each spatial scale in three colorectal cancer patients on the 32-µm grid (P1 and P2 with colorectal cancer, P3 with normal adjacent tissue). Pearson r (pink) is computed from the split-half reliability of the measured counts and falls at fine scales, whereas RSC (teal) stays near 1. Thin lines are patients, and thick lines are means over patients. Source data: fig1c_noise_correction_across_scales.csv.

How it was computed. Fig. 1b is described in Methods “Whole-section correlation” and “Class-mean baseline”. For Fig. 1c, the measured counts serve as the true expression, Poisson counts are simulated from the true expression, and the true expression is scored as the prediction. Pearson r with measured RNA expression follows from equation (2) with the split-half reliability of the measured counts (Methods “Expected expression and the mean of the halves”). Panels a and d, an overview of RSC and a summary of Figs. 2–5, are in the figure on the home page.

Fig. 2

Evaluation within tissue regions reveals whole-section correlation overstates prediction quality

Whole-section correlation overstates prediction quality within tissue regions. Normalized pairwise accuracy measures how often a prediction identifies which of two spots has higher measured expression, scaled from 0% for a majority-order baseline to 100% for the agreement between two RNA halves. Over 785 genes in eight HER2ST patients, the median of 11 published methods falls from 28.5% on unmatched spot pairs to 6.7% on pairs matched for total transcript count and expression profile (Holm-adjusted P = 0.023) and to 6.6% on matched pairs within the same annotated region. Matched spots can still lie in different regions, and the class-mean baseline scores 6.8% on matched pairs. Within regions, the baseline scores 1.5%, lower than each of the 11 published methods.

Method rankings by whole-section correlation agree closely with rankings on unmatched pairs (Kendall's τb = 0.818) but are nearly unrelated to rankings within regions (τb = 0.091), and the top-ranked method changes from EGNv2 to DeepSpaCE. The same overstatement appears for single genes. Hist2ST predictions of FASN correlate with measured RNA at Spearman ρ = 0.534 across all spots of a section and at ρ = 0.068 among spots within regions.

How it was computed. strsc her2 computes normalized pairwise accuracy on unmatched, matched and within-region spot pairs (Methods “Evaluation between and within tissue regions”). The browser tool Pairwise accuracy runs the same calculation on your data.

Explore: HER2ST cohort (Fig. 2a–c, g–i) · HER2ST section B1 (Fig. 2f)

Fig. 3

Reproducible-signal correlation (RSC) reveals spot-level methods mainly capture coarse tissue structure

Spot-level predictions generally capture broad regional expression patterns but miss most fine-scale differences between nearby spots. In the Visium HD colorectal cancer sections, the mean RSC of Ridge–Phikon predictions of 1,000 genes in 32-µm bins falls from 0.800 at 4,096 µm and above to 0.298 below 128 µm. The decline persists in 22 of 24 combinations of patient and bin size from 32 to 512 µm. In nine Xenium samples of breast, pancreatic and lung cancer, 10 of the 11 spot-level models that we trained have lower RSC at the finest than at the broadest scale in all nine samples.

The decline largely holds across the tested patient cohorts and image encoders. Across 70 sections from 45 patients in the nine tasks of HEST-Benchmark, Ridge–Phikon-v2 has lower RSC at the finest than at the broadest scale in 44 of 45 patients (sign-flip P < 10−6). Features from pathology foundation models raise mean RSC at all scales compared with ResNet50 features, yet the drop from the broadest to the finest scale stays between 0.31 and 0.34 for all five image encoders. Models trained on other patients miss part of the fine-scale differences that the same image features can predict within a section. When Ridge–Phikon-v2 is trained on three spatial blocks of a section and predicts the fourth block, fine-scale RSC rises from 0.152 to 0.219.

Fig. 3a RSC across spatial scales, 32-µm grid

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Fig. 3a | RSC across spatial scales, 32-µm grid0.20.30.40.50.60.70.80.9Reproducible-signal correlation (RSC)<128128–256256–5120.5–1k1–2k2–4k≥4kSpatial scale (µm)P1 CRCP1 CRC, <128 µm: RSC 0.331P1 CRC, 128–256 µm: RSC 0.563P1 CRC, 256–512 µm: RSC 0.651P1 CRC, 0.5–1k µm: RSC 0.662P1 CRC, 1–2k µm: RSC 0.749P1 CRC, 2–4k µm: RSC 0.652P1 CRC, ≥4k µm: RSC 0.805P1 CRCP2 CRCP2 CRC, <128 µm: RSC 0.350P2 CRC, 128–256 µm: RSC 0.636P2 CRC, 256–512 µm: RSC 0.713P2 CRC, 0.5–1k µm: RSC 0.741P2 CRC, 1–2k µm: RSC 0.778P2 CRC, 2–4k µm: RSC 0.755P2 CRC, ≥4k µm: RSC 0.870P2 CRCP3 NATP3 NAT, <128 µm: RSC 0.214P3 NAT, 128–256 µm: RSC 0.448P3 NAT, 256–512 µm: RSC 0.594P3 NAT, 0.5–1k µm: RSC 0.763P3 NAT, 1–2k µm: RSC 0.708P3 NAT, 2–4k µm: RSC 0.750P3 NAT, ≥4k µm: RSC 0.727P3 NATMean of three patients, <128 µm: RSC 0.298 (range 0.214 to 0.350)Mean of three patients, 128–256 µm: RSC 0.549 (range 0.448 to 0.636)Mean of three patients, 256–512 µm: RSC 0.653 (range 0.594 to 0.713)Mean of three patients, 0.5–1k µm: RSC 0.722 (range 0.662 to 0.763)Mean of three patients, 1–2k µm: RSC 0.745 (range 0.708 to 0.778)Mean of three patients, 2–4k µm: RSC 0.719 (range 0.652 to 0.755)Mean of three patients, ≥4k µm: RSC 0.800 (range 0.727 to 0.870)0.2980.800
Lines show the RSC of Ridge–Phikon predictions of 1,000 genes in 32-µm bins of the Visium HD colorectal cancer sections at spatial scales from below 128 µm to 4,096 µm and above (1k = 1,024 µm). Gray lines are patients P1 and P2 with colorectal cancer (CRC) and P3 with normal adjacent tissue (NAT). The dark line is the mean of the three patients, shown with the range across patients. Source data: fig3a_rsc_32um_grid_by_patient.csv.

Fig. 3b Tissue composition and sampling noise across bin sizes

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Fig. 3b | Tissue composition and sampling noise across bin sizes0.00.10.20.30.40.50.60.7Fraction326496128192256384512Bin size (µm)Signal ≥4k, P1 CRCSignal ≥4k, P2 CRCSignal ≥4k, P3 NATSignal ≥4k at 32 µm: mean 0.227 (P1 CRC 0.303, P2 CRC 0.203, P3 NAT 0.177)Signal ≥4k at 64 µm: mean 0.283 (P1 CRC 0.382, P2 CRC 0.257, P3 NAT 0.211)Signal ≥4k at 96 µm: mean 0.314 (P1 CRC 0.420, P2 CRC 0.293, P3 NAT 0.230)Signal ≥4k at 128 µm: mean 0.336 (P1 CRC 0.441, P2 CRC 0.322, P3 NAT 0.246)Signal ≥4k at 192 µm: mean 0.368 (P1 CRC 0.476, P2 CRC 0.365, P3 NAT 0.263)Signal ≥4k at 256 µm: mean 0.390 (P1 CRC 0.516, P2 CRC 0.385, P3 NAT 0.270)Signal ≥4k at 384 µm: mean 0.432 (P1 CRC 0.551, P2 CRC 0.427, P3 NAT 0.317)Signal ≥4k at 512 µm: mean 0.448 (P1 CRC 0.577, P2 CRC 0.456, P3 NAT 0.311)Composition at 32 µm: 0.273Composition at 64 µm: 0.438Composition at 96 µm: 0.524Composition at 128 µm: 0.573Composition at 192 µm: 0.622Composition at 256 µm: 0.641Composition at 384 µm: 0.649Composition at 512 µm: 0.665Sampling noise at 32 µm: 0.522Sampling noise at 64 µm: 0.327Sampling noise at 96 µm: 0.227Sampling noise at 128 µm: 0.167Sampling noise at 192 µm: 0.101Sampling noise at 256 µm: 0.069Sampling noise at 384 µm: 0.037Sampling noise at 512 µm: 0.024Signal ≥4kCompositionSampling noise0.2270.448
A mean prediction assigns each gene its mean expression in the training patients. Lines show the fraction of the error of this mean prediction attributable to tissue composition and to sampling noise across bin sizes of 32 to 512 µm. Tissue composition inflates correlations in coarse bins, and sampling noise lowers correlations in fine bins. Signal ≥4k is the share of the reproducible signal at scales of 4,096 µm and above. Thin lines are patients, and thick lines are means over patients. Source data: fig3b_error_fractions_by_bin_size.csv.

Fig. 3c RSC by spatial scale and bin size

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Fig. 3c | RSC by spatial scale and bin sizeP1 CRC<128128–256256–5120.5–1k1–2k2–4k≥4kSpatial scale (µm)P1 CRC, <128 µm scale, 32-µm bins: RSC 0.3310.331P1 CRC, <128 µm scale, 64-µm bins: RSC 0.4950.495P1 CRC, <128 µm scale, 96-µm bins: unavailableP1 CRC, <128 µm scale, 128-µm bins: unavailableP1 CRC, <128 µm scale, 192-µm bins: unavailableP1 CRC, <128 µm scale, 256-µm bins: unavailableP1 CRC, <128 µm scale, 384-µm bins: unavailableP1 CRC, <128 µm scale, 512-µm bins: unavailableP1 CRC, 128–256 µm scale, 32-µm bins: RSC 0.5630.563P1 CRC, 128–256 µm scale, 64-µm bins: RSC 0.5890.589P1 CRC, 128–256 µm scale, 96-µm bins: RSC 0.5930.593P1 CRC, 128–256 µm scale, 128-µm bins: RSC 0.5820.582P1 CRC, 128–256 µm scale, 192-µm bins: unavailableP1 CRC, 128–256 µm scale, 256-µm bins: unavailableP1 CRC, 128–256 µm scale, 384-µm bins: unavailableP1 CRC, 128–256 µm scale, 512-µm bins: unavailableP1 CRC, 256–512 µm scale, 32-µm bins: RSC 0.6510.651P1 CRC, 256–512 µm scale, 64-µm bins: RSC 0.6870.687P1 CRC, 256–512 µm scale, 96-µm bins: RSC 0.6880.688P1 CRC, 256–512 µm scale, 128-µm bins: RSC 0.6610.661P1 CRC, 256–512 µm scale, 192-µm bins: RSC 0.6390.639P1 CRC, 256–512 µm scale, 256-µm bins: RSC 0.6310.631P1 CRC, 256–512 µm scale, 384-µm bins: unavailableP1 CRC, 256–512 µm scale, 512-µm bins: unavailableP1 CRC, 0.5–1k µm scale, 32-µm bins: RSC 0.6620.662P1 CRC, 0.5–1k µm scale, 64-µm bins: RSC 0.6910.691P1 CRC, 0.5–1k µm scale, 96-µm bins: RSC 0.6920.692P1 CRC, 0.5–1k µm scale, 128-µm bins: RSC 0.7020.702P1 CRC, 0.5–1k µm scale, 192-µm bins: RSC 0.6800.680P1 CRC, 0.5–1k µm scale, 256-µm bins: RSC 0.6410.641P1 CRC, 0.5–1k µm scale, 384-µm bins: RSC 0.6650.665P1 CRC, 0.5–1k µm scale, 512-µm bins: RSC 0.4610.461P1 CRC, 1–2k µm scale, 32-µm bins: RSC 0.7490.749P1 CRC, 1–2k µm scale, 64-µm bins: RSC 0.7810.781P1 CRC, 1–2k µm scale, 96-µm bins: RSC 0.7690.769P1 CRC, 1–2k µm scale, 128-µm bins: RSC 0.7170.717P1 CRC, 1–2k µm scale, 192-µm bins: RSC 0.7390.739P1 CRC, 1–2k µm scale, 256-µm bins: RSC 0.6950.695P1 CRC, 1–2k µm scale, 384-µm bins: RSC 0.7390.739P1 CRC, 1–2k µm scale, 512-µm bins: RSC 0.7450.745P1 CRC, 2–4k µm scale, 32-µm bins: RSC 0.6520.652P1 CRC, 2–4k µm scale, 64-µm bins: RSC 0.6990.699P1 CRC, 2–4k µm scale, 96-µm bins: RSC 0.6880.688P1 CRC, 2–4k µm scale, 128-µm bins: RSC 0.6870.687P1 CRC, 2–4k µm scale, 192-µm bins: RSC 0.6270.627P1 CRC, 2–4k µm scale, 256-µm bins: RSC 0.6270.627P1 CRC, 2–4k µm scale, 384-µm bins: RSC 0.6060.606P1 CRC, 2–4k µm scale, 512-µm bins: RSC 0.6690.669P1 CRC, ≥4k µm scale, 32-µm bins: RSC 0.8050.805P1 CRC, ≥4k µm scale, 64-µm bins: RSC 0.8410.841P1 CRC, ≥4k µm scale, 96-µm bins: RSC 0.8840.884P1 CRC, ≥4k µm scale, 128-µm bins: RSC 0.8700.870P1 CRC, ≥4k µm scale, 192-µm bins: RSC 0.8770.877P1 CRC, ≥4k µm scale, 256-µm bins: RSC 0.8810.881P1 CRC, ≥4k µm scale, 384-µm bins: RSC 0.8990.899P1 CRC, ≥4k µm scale, 512-µm bins: RSC 0.9040.904326496128192256384512Bin size (µm)0.50.70.9RSC
The heatmap shows the RSC of Ridge–Phikon predictions in P1 CRC at each spatial scale (rows) after the same tissue, genes and 8-µm bins are aggregated to bins of 32 to 512 µm (columns). Hatching marks scales that are too fine for the bin size. The color scale runs from ≤0.5 to 0.9 as in the paper, and each cell is labeled with its value. Source data: fig3c_rsc_scale_by_bin_size.csv.

Fig. 3d 11 spot-level models in nine Xenium samples

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Fig. 3d | 11 spot-level models in nine Xenium samples−0.200.20.40.60.8RSCFinestFineMidBroadBroadestMLP, Finest: RSC 0.310MLP, Fine: RSC 0.366MLP, Mid: RSC 0.403MLP, Broad: RSC 0.500MLP, Broadest: RSC 0.685MLPRidge–Phikon-v2, Finest: RSC 0.310Ridge–Phikon-v2, Fine: RSC 0.363Ridge–Phikon-v2, Mid: RSC 0.402Ridge–Phikon-v2, Broad: RSC 0.498Ridge–Phikon-v2, Broadest: RSC 0.675Ridge–Phikon-v2EGNv1, Finest: RSC 0.197EGNv1, Fine: RSC 0.266EGNv1, Mid: RSC 0.300EGNv1, Broad: RSC 0.409EGNv1, Broadest: RSC 0.604EGNv1EGNv2, Finest: RSC 0.246EGNv2, Fine: RSC 0.312EGNv2, Mid: RSC 0.350EGNv2, Broad: RSC 0.446EGNv2, Broadest: RSC 0.600EGNv2ST-Net, Finest: RSC 0.232ST-Net, Fine: RSC 0.288ST-Net, Mid: RSC 0.312ST-Net, Broad: RSC 0.417ST-Net, Broadest: RSC 0.597ST-NetDeepSpaCE, Finest: RSC 0.205DeepSpaCE, Fine: RSC 0.258DeepSpaCE, Mid: RSC 0.279DeepSpaCE, Broad: RSC 0.369DeepSpaCE, Broadest: RSC 0.540DeepSpaCEDeepSpot, Finest: RSC 0.209DeepSpot, Fine: RSC 0.265DeepSpot, Mid: RSC 0.299DeepSpot, Broad: RSC 0.377DeepSpot, Broadest: RSC 0.500DeepSpotTCGN, Finest: RSC 0.147TCGN, Fine: RSC 0.180TCGN, Mid: RSC 0.196TCGN, Broad: RSC 0.245TCGN, Broadest: RSC 0.372TCGNHisToGene, Finest: RSC 0.076HisToGene, Fine: RSC 0.090HisToGene, Mid: RSC 0.118HisToGene, Broad: RSC 0.169HisToGene, Broadest: RSC 0.243HisToGeneHist2ST, Finest: RSC −0.010Hist2ST, Fine: RSC −0.046Hist2ST, Mid: RSC −0.016Hist2ST, Broad: RSC 0.082Hist2ST, Broadest: RSC 0.230Hist2STTHItoGene, Finest: RSC 0.002THItoGene, Fine: RSC −0.010THItoGene, Mid: RSC −0.022THItoGene, Broad: RSC 0.024THItoGene, Broadest: RSC −0.004THItoGeneMLP, NCBI783 (IDC): Broadest − Finest 0.304MLP, NCBI785 (IDC): Broadest − Finest 0.313MLP, TENX95 (IDC): Broadest − Finest 0.312MLP, TENX99 (IDC): Broadest − Finest 0.423MLP, TENX118 (Lung): Broadest − Finest 0.434MLP, TENX141 (Lung): Broadest − Finest 0.453MLP, TENX116 (PAAD): Broadest − Finest 0.374MLP, TENX126 (PAAD): Broadest − Finest 0.288MLP, TENX140 (PAAD): Broadest − Finest 0.475MLP: mean Broadest − Finest 0.375 (95% CI 0.341 to 0.410; higher at the broadest scale in 9/9 samples)Ridge–Phikon-v2, NCBI783 (IDC): Broadest − Finest 0.325Ridge–Phikon-v2, NCBI785 (IDC): Broadest − Finest 0.315Ridge–Phikon-v2, TENX95 (IDC): Broadest − Finest 0.316Ridge–Phikon-v2, TENX99 (IDC): Broadest − Finest 0.419Ridge–Phikon-v2, TENX118 (Lung): Broadest − Finest 0.429Ridge–Phikon-v2, TENX141 (Lung): Broadest − Finest 0.430Ridge–Phikon-v2, TENX116 (PAAD): Broadest − Finest 0.359Ridge–Phikon-v2, TENX126 (PAAD): Broadest − Finest 0.275Ridge–Phikon-v2, TENX140 (PAAD): Broadest − Finest 0.417Ridge–Phikon-v2: mean Broadest − Finest 0.365 (95% CI 0.338 to 0.394; higher at the broadest scale in 9/9 samples)EGNv1, NCBI783 (IDC): Broadest − Finest 0.447EGNv1, NCBI785 (IDC): Broadest − Finest 0.277EGNv1, TENX95 (IDC): Broadest − Finest 0.352EGNv1, TENX99 (IDC): Broadest − Finest 0.467EGNv1, TENX118 (Lung): Broadest − Finest 0.449EGNv1, TENX141 (Lung): Broadest − Finest 0.490EGNv1, TENX116 (PAAD): Broadest − Finest 0.451EGNv1, TENX126 (PAAD): Broadest − Finest 0.356EGNv1, TENX140 (PAAD): Broadest − Finest 0.378EGNv1: mean Broadest − Finest 0.407 (95% CI 0.370 to 0.444; higher at the broadest scale in 9/9 samples)EGNv2, NCBI783 (IDC): Broadest − Finest 0.303EGNv2, NCBI785 (IDC): Broadest − Finest 0.291EGNv2, TENX95 (IDC): Broadest − Finest 0.281EGNv2, TENX99 (IDC): Broadest − Finest 0.421EGNv2, TENX118 (Lung): Broadest − Finest 0.454EGNv2, TENX141 (Lung): Broadest − Finest 0.449EGNv2, TENX116 (PAAD): Broadest − Finest 0.338EGNv2, TENX126 (PAAD): Broadest − Finest 0.246EGNv2, TENX140 (PAAD): Broadest − Finest 0.403EGNv2: mean Broadest − Finest 0.354 (95% CI 0.322 to 0.388; higher at the broadest scale in 9/9 samples)ST-Net, NCBI783 (IDC): Broadest − Finest 0.342ST-Net, NCBI785 (IDC): Broadest − Finest 0.278ST-Net, TENX95 (IDC): Broadest − Finest 0.310ST-Net, TENX99 (IDC): Broadest − Finest 0.408ST-Net, TENX118 (Lung): Broadest − Finest 0.444ST-Net, TENX141 (Lung): Broadest − Finest 0.487ST-Net, TENX116 (PAAD): Broadest − Finest 0.323ST-Net, TENX126 (PAAD): Broadest − Finest 0.281ST-Net, TENX140 (PAAD): Broadest − Finest 0.408ST-Net: mean Broadest − Finest 0.365 (95% CI 0.336 to 0.395; higher at the broadest scale in 9/9 samples)DeepSpaCE, NCBI783 (IDC): Broadest − Finest 0.383DeepSpaCE, NCBI785 (IDC): Broadest − Finest 0.270DeepSpaCE, TENX95 (IDC): Broadest − Finest 0.283DeepSpaCE, TENX99 (IDC): Broadest − Finest 0.410DeepSpaCE, TENX118 (Lung): Broadest − Finest 0.385DeepSpaCE, TENX141 (Lung): Broadest − Finest 0.261DeepSpaCE, TENX116 (PAAD): Broadest − Finest 0.378DeepSpaCE, TENX126 (PAAD): Broadest − Finest 0.300DeepSpaCE, TENX140 (PAAD): Broadest − Finest 0.342DeepSpaCE: mean Broadest − Finest 0.335 (95% CI 0.301 to 0.368; higher at the broadest scale in 9/9 samples)DeepSpot, NCBI783 (IDC): Broadest − Finest 0.292DeepSpot, NCBI785 (IDC): Broadest − Finest 0.294DeepSpot, TENX95 (IDC): Broadest − Finest 0.250DeepSpot, TENX99 (IDC): Broadest − Finest 0.327DeepSpot, TENX118 (Lung): Broadest − Finest 0.239DeepSpot, TENX141 (Lung): Broadest − Finest 0.449DeepSpot, TENX116 (PAAD): Broadest − Finest 0.336DeepSpot, TENX126 (PAAD): Broadest − Finest 0.208DeepSpot, TENX140 (PAAD): Broadest − Finest 0.222DeepSpot: mean Broadest − Finest 0.291 (95% CI 0.251 to 0.331; higher at the broadest scale in 9/9 samples)TCGN, NCBI783 (IDC): Broadest − Finest 0.147TCGN, NCBI785 (IDC): Broadest − Finest 0.166TCGN, TENX95 (IDC): Broadest − Finest 0.277TCGN, TENX99 (IDC): Broadest − Finest 0.225TCGN, TENX118 (Lung): Broadest − Finest 0.230TCGN, TENX141 (Lung): Broadest − Finest 0.366TCGN, TENX116 (PAAD): Broadest − Finest 0.218TCGN, TENX126 (PAAD): Broadest − Finest 0.175TCGN, TENX140 (PAAD): Broadest − Finest 0.225TCGN: mean Broadest − Finest 0.226 (95% CI 0.195 to 0.257; higher at the broadest scale in 9/9 samples)HisToGene, NCBI783 (IDC): Broadest − Finest 0.000HisToGene, NCBI785 (IDC): Broadest − Finest 0.091HisToGene, TENX95 (IDC): Broadest − Finest 0.142HisToGene, TENX99 (IDC): Broadest − Finest 0.011HisToGene, TENX118 (Lung): Broadest − Finest 0.332HisToGene, TENX141 (Lung): Broadest − Finest 0.381HisToGene, TENX116 (PAAD): Broadest − Finest 0.294HisToGene, TENX126 (PAAD): Broadest − Finest 0.186HisToGene, TENX140 (PAAD): Broadest − Finest 0.070HisToGene: mean Broadest − Finest 0.167 (95% CI 0.124 to 0.211; higher at the broadest scale in 9/9 samples)Hist2ST, NCBI783 (IDC): Broadest − Finest 0.427Hist2ST, NCBI785 (IDC): Broadest − Finest 0.217Hist2ST, TENX95 (IDC): Broadest − Finest 0.282Hist2ST, TENX99 (IDC): Broadest − Finest 0.150Hist2ST, TENX118 (Lung): Broadest − Finest 0.324Hist2ST, TENX141 (Lung): Broadest − Finest 0.205Hist2ST, TENX116 (PAAD): Broadest − Finest 0.229Hist2ST, TENX126 (PAAD): Broadest − Finest 0.223Hist2ST, TENX140 (PAAD): Broadest − Finest 0.104Hist2ST: mean Broadest − Finest 0.240 (95% CI 0.189 to 0.294; higher at the broadest scale in 9/9 samples)THItoGene, NCBI783 (IDC): Broadest − Finest −0.131THItoGene, NCBI785 (IDC): Broadest − Finest −0.024THItoGene, TENX95 (IDC): Broadest − Finest −0.003THItoGene, TENX99 (IDC): Broadest − Finest −0.106THItoGene, TENX118 (Lung): Broadest − Finest −0.075THItoGene, TENX141 (Lung): Broadest − Finest −0.005THItoGene, TENX116 (PAAD): Broadest − Finest 0.076THItoGene, TENX126 (PAAD): Broadest − Finest 0.086THItoGene, TENX140 (PAAD): Broadest − Finest 0.130THItoGene: mean Broadest − Finest −0.006 (95% CI −0.032 to 0.021; higher at the broadest scale in 3/9 samples)−0.200.20.40.6Broadest − Finest
Lines show the RSC of 11 spot-level models at five relative scales, averaged over nine Xenium samples of breast (IDC), pancreatic (PAAD) and lung cancer. Most models reach high RSC at the broadest scale and drop at the finest. The right panel shows Broadest − Finest for each sample (points), with the mean and its 95% confidence interval, and THItoGene is shown in gray. Source data: fig3d_summary_11_models.csv, fig3d_rsc_11_models_by_sample.csv.

Fig. 3e Image encoders in HEST-Benchmark

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Fig. 3e | Image encoders in HEST-Benchmark00.20.40.6RSCFinestFineMidBroadBroadestResNet50, Finest: RSC 0.098 (95% CI 0.074 to 0.123)ResNet50, Fine: RSC 0.132 (95% CI 0.102 to 0.162)ResNet50, Mid: RSC 0.151 (95% CI 0.120 to 0.184)ResNet50, Broad: RSC 0.215 (95% CI 0.181 to 0.251)ResNet50, Broadest: RSC 0.407 (95% CI 0.355 to 0.459)Phikon-v2, Finest: RSC 0.138 (95% CI 0.105 to 0.172)Phikon-v2, Fine: RSC 0.168 (95% CI 0.131 to 0.207)Phikon-v2, Mid: RSC 0.191 (95% CI 0.151 to 0.233)Phikon-v2, Broad: RSC 0.253 (95% CI 0.208 to 0.300)Phikon-v2, Broadest: RSC 0.465 (95% CI 0.406 to 0.520)UNI, Finest: RSC 0.142 (95% CI 0.106 to 0.180)UNI, Fine: RSC 0.171 (95% CI 0.130 to 0.216)UNI, Mid: RSC 0.202 (95% CI 0.159 to 0.248)UNI, Broad: RSC 0.262 (95% CI 0.212 to 0.314)UNI, Broadest: RSC 0.480 (95% CI 0.422 to 0.536)Midnight-12k, Finest: RSC 0.164 (95% CI 0.124 to 0.207)Midnight-12k, Fine: RSC 0.202 (95% CI 0.158 to 0.248)Midnight-12k, Mid: RSC 0.231 (95% CI 0.185 to 0.281)Midnight-12k, Broad: RSC 0.291 (95% CI 0.240 to 0.345)Midnight-12k, Broadest: RSC 0.498 (95% CI 0.439 to 0.555)Virchow2, Finest: RSC 0.167 (95% CI 0.129 to 0.208)Virchow2, Fine: RSC 0.201 (95% CI 0.156 to 0.250)Virchow2, Mid: RSC 0.236 (95% CI 0.191 to 0.284)Virchow2, Broad: RSC 0.291 (95% CI 0.240 to 0.344)Virchow2, Broadest: RSC 0.499 (95% CI 0.440 to 0.556)ResNet50ResNet50, CCRCC-01 (CCRCC): Broadest − Finest 0.303ResNet50, CCRCC-02 (CCRCC): Broadest − Finest 0.283ResNet50, CCRCC-03 (CCRCC): Broadest − Finest 0.130ResNet50, CCRCC-04 (CCRCC): Broadest − Finest 0.206ResNet50, CCRCC-05 (CCRCC): Broadest − Finest 0.111ResNet50, CCRCC-06 (CCRCC): Broadest − Finest 0.063ResNet50, CCRCC-07 (CCRCC): Broadest − Finest 0.680ResNet50, CCRCC-08 (CCRCC): Broadest − Finest 0.672ResNet50, CCRCC-09 (CCRCC): Broadest − Finest 0.135ResNet50, CCRCC-10 (CCRCC): Broadest − Finest −0.054ResNet50, CCRCC-11 (CCRCC): Broadest − Finest 0.378ResNet50, CCRCC-12 (CCRCC): Broadest − Finest 0.134ResNet50, CCRCC-13 (CCRCC): Broadest − Finest 0.390ResNet50, CCRCC-14 (CCRCC): Broadest − Finest 0.315ResNet50, CCRCC-15 (CCRCC): Broadest − Finest 0.320ResNet50, CCRCC-16 (CCRCC): Broadest − Finest 0.426ResNet50, CCRCC-17 (CCRCC): Broadest − Finest 0.336ResNet50, CCRCC-18 (CCRCC): Broadest − Finest 0.346ResNet50, CCRCC-19 (CCRCC): Broadest − Finest 0.400ResNet50, CCRCC-20 (CCRCC): Broadest − Finest 0.155ResNet50, CCRCC-21 (CCRCC): Broadest − Finest 0.334ResNet50, CCRCC-22 (CCRCC): Broadest − Finest 0.479ResNet50, CCRCC-23 (CCRCC): Broadest − Finest 0.161ResNet50, CCRCC-24 (CCRCC): Broadest − Finest 0.392ResNet50, COAD-01 (COAD): Broadest − Finest 0.259ResNet50, COAD-02 (COAD): Broadest − Finest 0.372ResNet50, IDC-01 (IDC): Broadest − Finest 0.438ResNet50, IDC-02 (IDC): Broadest − Finest 0.308ResNet50, IDC-03 (IDC): Broadest − Finest 0.336ResNet50, IDC-04 (IDC): Broadest − Finest 0.425ResNet50, LUNG-01 (LUNG): Broadest − Finest 0.339ResNet50, LUNG-02 (LUNG): Broadest − Finest 0.406ResNet50, LYMPH_IDC-01 (LYMPH_IDC): Broadest − Finest 0.517ResNet50, LYMPH_IDC-02 (LYMPH_IDC): Broadest − Finest 0.416ResNet50, LYMPH_IDC-03 (LYMPH_IDC): Broadest − Finest 0.202ResNet50, LYMPH_IDC-04 (LYMPH_IDC): Broadest − Finest 0.283ResNet50, PAAD-01 (PAAD): Broadest − Finest 0.312ResNet50, PAAD-02 (PAAD): Broadest − Finest 0.434ResNet50, PAAD-03 (PAAD): Broadest − Finest 0.345ResNet50, PRAD-01 (PRAD): Broadest − Finest 0.132ResNet50, PRAD-02 (PRAD): Broadest − Finest 0.164ResNet50, READ-01 (READ): Broadest − Finest 0.302ResNet50, READ-02 (READ): Broadest − Finest 0.044ResNet50, SKCM-01 (SKCM): Broadest − Finest 0.536ResNet50, SKCM-02 (SKCM): Broadest − Finest 0.243ResNet50: mean Broadest − Finest 0.309 (95% CI 0.265 to 0.353); higher at the broadest scale in 44 of 45 patientsPhikon-v2Phikon-v2, CCRCC-01 (CCRCC): Broadest − Finest 0.505Phikon-v2, CCRCC-02 (CCRCC): Broadest − Finest 0.343Phikon-v2, CCRCC-03 (CCRCC): Broadest − Finest 0.111Phikon-v2, CCRCC-04 (CCRCC): Broadest − Finest 0.149Phikon-v2, CCRCC-05 (CCRCC): Broadest − Finest 0.139Phikon-v2, CCRCC-06 (CCRCC): Broadest − Finest 0.136Phikon-v2, CCRCC-07 (CCRCC): Broadest − Finest 0.682Phikon-v2, CCRCC-08 (CCRCC): Broadest − Finest 0.743Phikon-v2, CCRCC-09 (CCRCC): Broadest − Finest 0.143Phikon-v2, CCRCC-10 (CCRCC): Broadest − Finest −0.116Phikon-v2, CCRCC-11 (CCRCC): Broadest − Finest 0.483Phikon-v2, CCRCC-12 (CCRCC): Broadest − Finest 0.285Phikon-v2, CCRCC-13 (CCRCC): Broadest − Finest 0.299Phikon-v2, CCRCC-14 (CCRCC): Broadest − Finest 0.447Phikon-v2, CCRCC-15 (CCRCC): Broadest − Finest 0.330Phikon-v2, CCRCC-16 (CCRCC): Broadest − Finest 0.248Phikon-v2, CCRCC-17 (CCRCC): Broadest − Finest 0.235Phikon-v2, CCRCC-18 (CCRCC): Broadest − Finest 0.359Phikon-v2, CCRCC-19 (CCRCC): Broadest − Finest 0.387Phikon-v2, CCRCC-20 (CCRCC): Broadest − Finest 0.252Phikon-v2, CCRCC-21 (CCRCC): Broadest − Finest 0.524Phikon-v2, CCRCC-22 (CCRCC): Broadest − Finest 0.495Phikon-v2, CCRCC-23 (CCRCC): Broadest − Finest 0.244Phikon-v2, CCRCC-24 (CCRCC): Broadest − Finest 0.332Phikon-v2, COAD-01 (COAD): Broadest − Finest 0.194Phikon-v2, COAD-02 (COAD): Broadest − Finest 0.361Phikon-v2, IDC-01 (IDC): Broadest − Finest 0.416Phikon-v2, IDC-02 (IDC): Broadest − Finest 0.293Phikon-v2, IDC-03 (IDC): Broadest − Finest 0.358Phikon-v2, IDC-04 (IDC): Broadest − Finest 0.375Phikon-v2, LUNG-01 (LUNG): Broadest − Finest 0.347Phikon-v2, LUNG-02 (LUNG): Broadest − Finest 0.369Phikon-v2, LYMPH_IDC-01 (LYMPH_IDC): Broadest − Finest 0.517Phikon-v2, LYMPH_IDC-02 (LYMPH_IDC): Broadest − Finest 0.392Phikon-v2, LYMPH_IDC-03 (LYMPH_IDC): Broadest − Finest 0.144Phikon-v2, LYMPH_IDC-04 (LYMPH_IDC): Broadest − Finest 0.230Phikon-v2, PAAD-01 (PAAD): Broadest − Finest 0.261Phikon-v2, PAAD-02 (PAAD): Broadest − Finest 0.431Phikon-v2, PAAD-03 (PAAD): Broadest − Finest 0.355Phikon-v2, PRAD-01 (PRAD): Broadest − Finest 0.143Phikon-v2, PRAD-02 (PRAD): Broadest − Finest 0.247Phikon-v2, READ-01 (READ): Broadest − Finest 0.506Phikon-v2, READ-02 (READ): Broadest − Finest 0.194Phikon-v2, SKCM-01 (SKCM): Broadest − Finest 0.464Phikon-v2, SKCM-02 (SKCM): Broadest − Finest 0.368Phikon-v2: mean Broadest − Finest 0.327 (95% CI 0.281 to 0.373); higher at the broadest scale in 44 of 45 patientsUNIUNI, CCRCC-01 (CCRCC): Broadest − Finest 0.481UNI, CCRCC-02 (CCRCC): Broadest − Finest 0.370UNI, CCRCC-03 (CCRCC): Broadest − Finest 0.073UNI, CCRCC-04 (CCRCC): Broadest − Finest 0.198UNI, CCRCC-05 (CCRCC): Broadest − Finest 0.132UNI, CCRCC-06 (CCRCC): Broadest − Finest 0.041UNI, CCRCC-07 (CCRCC): Broadest − Finest 0.705UNI, CCRCC-08 (CCRCC): Broadest − Finest 0.689UNI, CCRCC-09 (CCRCC): Broadest − Finest 0.043UNI, CCRCC-10 (CCRCC): Broadest − Finest 0.097UNI, CCRCC-11 (CCRCC): Broadest − Finest 0.377UNI, CCRCC-12 (CCRCC): Broadest − Finest 0.211UNI, CCRCC-13 (CCRCC): Broadest − Finest 0.336UNI, CCRCC-14 (CCRCC): Broadest − Finest 0.537UNI, CCRCC-15 (CCRCC): Broadest − Finest 0.385UNI, CCRCC-16 (CCRCC): Broadest − Finest 0.439UNI, CCRCC-17 (CCRCC): Broadest − Finest 0.319UNI, CCRCC-18 (CCRCC): Broadest − Finest 0.441UNI, CCRCC-19 (CCRCC): Broadest − Finest 0.483UNI, CCRCC-20 (CCRCC): Broadest − Finest 0.202UNI, CCRCC-21 (CCRCC): Broadest − Finest 0.549UNI, CCRCC-22 (CCRCC): Broadest − Finest 0.480UNI, CCRCC-23 (CCRCC): Broadest − Finest 0.188UNI, CCRCC-24 (CCRCC): Broadest − Finest 0.383UNI, COAD-01 (COAD): Broadest − Finest 0.228UNI, COAD-02 (COAD): Broadest − Finest 0.362UNI, IDC-01 (IDC): Broadest − Finest 0.393UNI, IDC-02 (IDC): Broadest − Finest 0.315UNI, IDC-03 (IDC): Broadest − Finest 0.373UNI, IDC-04 (IDC): Broadest − Finest 0.387UNI, LUNG-01 (LUNG): Broadest − Finest 0.328UNI, LUNG-02 (LUNG): Broadest − Finest 0.322UNI, LYMPH_IDC-01 (LYMPH_IDC): Broadest − Finest 0.479UNI, LYMPH_IDC-02 (LYMPH_IDC): Broadest − Finest 0.436UNI, LYMPH_IDC-03 (LYMPH_IDC): Broadest − Finest 0.200UNI, LYMPH_IDC-04 (LYMPH_IDC): Broadest − Finest 0.219UNI, PAAD-01 (PAAD): Broadest − Finest 0.290UNI, PAAD-02 (PAAD): Broadest − Finest 0.438UNI, PAAD-03 (PAAD): Broadest − Finest 0.359UNI, PRAD-01 (PRAD): Broadest − Finest 0.187UNI, PRAD-02 (PRAD): Broadest − Finest 0.127UNI, READ-01 (READ): Broadest − Finest 0.505UNI, READ-02 (READ): Broadest − Finest 0.219UNI, SKCM-01 (SKCM): Broadest − Finest 0.468UNI, SKCM-02 (SKCM): Broadest − Finest 0.394UNI: mean Broadest − Finest 0.338 (95% CI 0.292 to 0.383); higher at the broadest scale in 45 of 45 patientsMidnight-12kMidnight-12k, CCRCC-01 (CCRCC): Broadest − Finest 0.355Midnight-12k, CCRCC-02 (CCRCC): Broadest − Finest 0.342Midnight-12k, CCRCC-03 (CCRCC): Broadest − Finest 0.191Midnight-12k, CCRCC-04 (CCRCC): Broadest − Finest 0.251Midnight-12k, CCRCC-05 (CCRCC): Broadest − Finest 0.146Midnight-12k, CCRCC-06 (CCRCC): Broadest − Finest 0.004Midnight-12k, CCRCC-07 (CCRCC): Broadest − Finest 0.621Midnight-12k, CCRCC-08 (CCRCC): Broadest − Finest 0.631Midnight-12k, CCRCC-09 (CCRCC): Broadest − Finest 0.205Midnight-12k, CCRCC-10 (CCRCC): Broadest − Finest 0.124Midnight-12k, CCRCC-11 (CCRCC): Broadest − Finest 0.358Midnight-12k, CCRCC-12 (CCRCC): Broadest − Finest 0.291Midnight-12k, CCRCC-13 (CCRCC): Broadest − Finest 0.336Midnight-12k, CCRCC-14 (CCRCC): Broadest − Finest 0.531Midnight-12k, CCRCC-15 (CCRCC): Broadest − Finest 0.465Midnight-12k, CCRCC-16 (CCRCC): Broadest − Finest 0.397Midnight-12k, CCRCC-17 (CCRCC): Broadest − Finest 0.185Midnight-12k, CCRCC-18 (CCRCC): Broadest − Finest 0.272Midnight-12k, CCRCC-19 (CCRCC): Broadest − Finest 0.462Midnight-12k, CCRCC-20 (CCRCC): Broadest − Finest 0.238Midnight-12k, CCRCC-21 (CCRCC): Broadest − Finest 0.503Midnight-12k, CCRCC-22 (CCRCC): Broadest − Finest 0.561Midnight-12k, CCRCC-23 (CCRCC): Broadest − Finest 0.161Midnight-12k, CCRCC-24 (CCRCC): Broadest − Finest 0.323Midnight-12k, COAD-01 (COAD): Broadest − Finest 0.254Midnight-12k, COAD-02 (COAD): Broadest − Finest 0.369Midnight-12k, IDC-01 (IDC): Broadest − Finest 0.369Midnight-12k, IDC-02 (IDC): Broadest − Finest 0.239Midnight-12k, IDC-03 (IDC): Broadest − Finest 0.291Midnight-12k, IDC-04 (IDC): Broadest − Finest 0.337Midnight-12k, LUNG-01 (LUNG): Broadest − Finest 0.334Midnight-12k, LUNG-02 (LUNG): Broadest − Finest 0.335Midnight-12k, LYMPH_IDC-01 (LYMPH_IDC): Broadest − Finest 0.535Midnight-12k, LYMPH_IDC-02 (LYMPH_IDC): Broadest − Finest 0.460Midnight-12k, LYMPH_IDC-03 (LYMPH_IDC): Broadest − Finest 0.246Midnight-12k, LYMPH_IDC-04 (LYMPH_IDC): Broadest − Finest 0.223Midnight-12k, PAAD-01 (PAAD): Broadest − Finest 0.344Midnight-12k, PAAD-02 (PAAD): Broadest − Finest 0.428Midnight-12k, PAAD-03 (PAAD): Broadest − Finest 0.345Midnight-12k, PRAD-01 (PRAD): Broadest − Finest 0.177Midnight-12k, PRAD-02 (PRAD): Broadest − Finest 0.230Midnight-12k, READ-01 (READ): Broadest − Finest 0.502Midnight-12k, READ-02 (READ): Broadest − Finest 0.232Midnight-12k, SKCM-01 (SKCM): Broadest − Finest 0.451Midnight-12k, SKCM-02 (SKCM): Broadest − Finest 0.381Midnight-12k: mean Broadest − Finest 0.334 (95% CI 0.295 to 0.374); higher at the broadest scale in 45 of 45 patientsVirchow2Virchow2, CCRCC-01 (CCRCC): Broadest − Finest 0.507Virchow2, CCRCC-02 (CCRCC): Broadest − Finest 0.307Virchow2, CCRCC-03 (CCRCC): Broadest − Finest 0.236Virchow2, CCRCC-04 (CCRCC): Broadest − Finest 0.152Virchow2, CCRCC-05 (CCRCC): Broadest − Finest 0.150Virchow2, CCRCC-06 (CCRCC): Broadest − Finest −0.002Virchow2, CCRCC-07 (CCRCC): Broadest − Finest 0.656Virchow2, CCRCC-08 (CCRCC): Broadest − Finest 0.656Virchow2, CCRCC-09 (CCRCC): Broadest − Finest 0.119Virchow2, CCRCC-10 (CCRCC): Broadest − Finest 0.027Virchow2, CCRCC-11 (CCRCC): Broadest − Finest 0.473Virchow2, CCRCC-12 (CCRCC): Broadest − Finest 0.234Virchow2, CCRCC-13 (CCRCC): Broadest − Finest 0.424Virchow2, CCRCC-14 (CCRCC): Broadest − Finest 0.459Virchow2, CCRCC-15 (CCRCC): Broadest − Finest 0.380Virchow2, CCRCC-16 (CCRCC): Broadest − Finest 0.437Virchow2, CCRCC-17 (CCRCC): Broadest − Finest 0.301Virchow2, CCRCC-18 (CCRCC): Broadest − Finest 0.382Virchow2, CCRCC-19 (CCRCC): Broadest − Finest 0.404Virchow2, CCRCC-20 (CCRCC): Broadest − Finest 0.189Virchow2, CCRCC-21 (CCRCC): Broadest − Finest 0.582Virchow2, CCRCC-22 (CCRCC): Broadest − Finest 0.525Virchow2, CCRCC-23 (CCRCC): Broadest − Finest 0.203Virchow2, CCRCC-24 (CCRCC): Broadest − Finest 0.360Virchow2, COAD-01 (COAD): Broadest − Finest 0.114Virchow2, COAD-02 (COAD): Broadest − Finest 0.321Virchow2, IDC-01 (IDC): Broadest − Finest 0.350Virchow2, IDC-02 (IDC): Broadest − Finest 0.272Virchow2, IDC-03 (IDC): Broadest − Finest 0.281Virchow2, IDC-04 (IDC): Broadest − Finest 0.344Virchow2, LUNG-01 (LUNG): Broadest − Finest 0.356Virchow2, LUNG-02 (LUNG): Broadest − Finest 0.331Virchow2, LYMPH_IDC-01 (LYMPH_IDC): Broadest − Finest 0.503Virchow2, LYMPH_IDC-02 (LYMPH_IDC): Broadest − Finest 0.401Virchow2, LYMPH_IDC-03 (LYMPH_IDC): Broadest − Finest 0.224Virchow2, LYMPH_IDC-04 (LYMPH_IDC): Broadest − Finest 0.288Virchow2, PAAD-01 (PAAD): Broadest − Finest 0.345Virchow2, PAAD-02 (PAAD): Broadest − Finest 0.429Virchow2, PAAD-03 (PAAD): Broadest − Finest 0.368Virchow2, PRAD-01 (PRAD): Broadest − Finest 0.155Virchow2, PRAD-02 (PRAD): Broadest − Finest 0.215Virchow2, READ-01 (READ): Broadest − Finest 0.484Virchow2, READ-02 (READ): Broadest − Finest 0.189Virchow2, SKCM-01 (SKCM): Broadest − Finest 0.419Virchow2, SKCM-02 (SKCM): Broadest − Finest 0.392Virchow2: mean Broadest − Finest 0.332 (95% CI 0.288 to 0.376); higher at the broadest scale in 44 of 45 patients−0.2500.250.500.751.00Broadest − Finest
Ridge regression models are trained on features from four pathology foundation models (Phikon-v2, UNI, Midnight-12k and Virchow2) and from ResNet50, which was trained on natural images, in 45 HEST-Benchmark patients (70 sections, nine prediction tasks). The left panel shows the mean RSC at each scale with 95% confidence intervals. The right panel shows Broadest − Finest for each patient (gray points), with the mean and its 95% confidence interval. Source data: fig3e_encoders_rsc_by_scale.csv, fig3e_encoders_summary.csv, fig3e_encoders_broadest_minus_finest_per_patient.csv.

Fig. 3f Cross-patient and within-section training

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Fig. 3f | Cross-patient and within-section training00.20.40.6RSCFinestFineMidBroadBroadestCross-patient training, Finest: RSC 0.138 (95% CI 0.104 to 0.172)Cross-patient training, Fine: RSC 0.167 (95% CI 0.130 to 0.206)Cross-patient training, Mid: RSC 0.192 (95% CI 0.153 to 0.234)Cross-patient training, Broad: RSC 0.257 (95% CI 0.212 to 0.302)Cross-patient training, Broadest: RSC 0.444 (95% CI 0.394 to 0.494)Within-section training, Finest: RSC 0.207 (95% CI 0.165 to 0.251)Within-section training, Fine: RSC 0.231 (95% CI 0.181 to 0.283)Within-section training, Mid: RSC 0.280 (95% CI 0.231 to 0.333)Within-section training, Broad: RSC 0.350 (95% CI 0.294 to 0.408)Within-section training, Broadest: RSC 0.632 (95% CI 0.585 to 0.678)CCRCC-01: 0.399 cross-patient, 0.557 within-sectionCCRCC-02: 0.254 cross-patient, 0.327 within-sectionCCRCC-03: 0.093 cross-patient, 0.452 within-sectionCCRCC-04: 0.284 cross-patient, 0.285 within-sectionCCRCC-05: 0.174 cross-patient, 0.292 within-sectionCCRCC-06: 0.248 cross-patient, 0.359 within-sectionCCRCC-07: 0.513 cross-patient, 0.704 within-sectionCCRCC-08: 0.516 cross-patient, 0.439 within-sectionCCRCC-09: 0.011 cross-patient, 0.312 within-sectionCCRCC-10: 0.021 cross-patient, 0.273 within-sectionCCRCC-11: 0.362 cross-patient, 0.583 within-sectionCCRCC-12: 0.297 cross-patient, 0.344 within-sectionCCRCC-13: 0.248 cross-patient, 0.416 within-sectionCCRCC-14: 0.401 cross-patient, 0.503 within-sectionCCRCC-15: 0.270 cross-patient, 0.354 within-sectionCCRCC-16: 0.283 cross-patient, 0.497 within-sectionCCRCC-17: 0.224 cross-patient, 0.220 within-sectionCCRCC-18: 0.240 cross-patient, 0.478 within-sectionCCRCC-19: 0.418 cross-patient, 0.492 within-sectionCCRCC-20: 0.233 cross-patient, 0.367 within-sectionCCRCC-21: 0.482 cross-patient, 0.514 within-sectionCCRCC-22: 0.500 cross-patient, 0.570 within-sectionCCRCC-23: 0.200 cross-patient, 0.351 within-sectionCCRCC-24: 0.298 cross-patient, 0.350 within-sectionCOAD-01: 0.133 cross-patient, 0.540 within-sectionCOAD-02: 0.366 cross-patient, 0.512 within-sectionIDC-01: 0.422 cross-patient, 0.457 within-sectionIDC-02: 0.296 cross-patient, 0.352 within-sectionIDC-03: 0.374 cross-patient, 0.416 within-sectionIDC-04: 0.381 cross-patient, 0.387 within-sectionLUNG-01: 0.321 cross-patient, 0.368 within-sectionLUNG-02: 0.290 cross-patient, 0.338 within-sectionLYMPH_IDC-01: 0.518 cross-patient, 0.573 within-sectionLYMPH_IDC-02: 0.373 cross-patient, 0.452 within-sectionLYMPH_IDC-03: 0.194 cross-patient, 0.377 within-sectionLYMPH_IDC-04: 0.282 cross-patient, 0.431 within-sectionPAAD-01: 0.296 cross-patient, 0.413 within-sectionPAAD-02: 0.432 cross-patient, 0.473 within-sectionPAAD-03: 0.362 cross-patient, 0.443 within-sectionPRAD-01: 0.126 cross-patient, 0.259 within-sectionPRAD-02: 0.231 cross-patient, 0.357 within-sectionREAD-01: 0.475 cross-patient, 0.574 within-sectionREAD-02: 0.153 cross-patient, 0.312 within-sectionSKCM-01: 0.451 cross-patient, 0.557 within-sectionSKCM-02: 0.364 cross-patient, 0.481 within-sectionCross-patient training, CCRCC-01 (CCRCC): Broadest − Finest 0.399Cross-patient training, CCRCC-02 (CCRCC): Broadest − Finest 0.254Cross-patient training, CCRCC-03 (CCRCC): Broadest − Finest 0.093Cross-patient training, CCRCC-04 (CCRCC): Broadest − Finest 0.284Cross-patient training, CCRCC-05 (CCRCC): Broadest − Finest 0.174Cross-patient training, CCRCC-06 (CCRCC): Broadest − Finest 0.248Cross-patient training, CCRCC-07 (CCRCC): Broadest − Finest 0.513Cross-patient training, CCRCC-08 (CCRCC): Broadest − Finest 0.516Cross-patient training, CCRCC-09 (CCRCC): Broadest − Finest 0.011Cross-patient training, CCRCC-10 (CCRCC): Broadest − Finest 0.021Cross-patient training, CCRCC-11 (CCRCC): Broadest − Finest 0.362Cross-patient training, CCRCC-12 (CCRCC): Broadest − Finest 0.297Cross-patient training, CCRCC-13 (CCRCC): Broadest − Finest 0.248Cross-patient training, CCRCC-14 (CCRCC): Broadest − Finest 0.401Cross-patient training, CCRCC-15 (CCRCC): Broadest − Finest 0.270Cross-patient training, CCRCC-16 (CCRCC): Broadest − Finest 0.283Cross-patient training, CCRCC-17 (CCRCC): Broadest − Finest 0.224Cross-patient training, CCRCC-18 (CCRCC): Broadest − Finest 0.240Cross-patient training, CCRCC-19 (CCRCC): Broadest − Finest 0.418Cross-patient training, CCRCC-20 (CCRCC): Broadest − Finest 0.233Cross-patient training, CCRCC-21 (CCRCC): Broadest − Finest 0.482Cross-patient training, CCRCC-22 (CCRCC): Broadest − Finest 0.500Cross-patient training, CCRCC-23 (CCRCC): Broadest − Finest 0.200Cross-patient training, CCRCC-24 (CCRCC): Broadest − Finest 0.298Cross-patient training, COAD-01 (COAD): Broadest − Finest 0.133Cross-patient training, COAD-02 (COAD): Broadest − Finest 0.366Cross-patient training, IDC-01 (IDC): Broadest − Finest 0.422Cross-patient training, IDC-02 (IDC): Broadest − Finest 0.296Cross-patient training, IDC-03 (IDC): Broadest − Finest 0.374Cross-patient training, IDC-04 (IDC): Broadest − Finest 0.381Cross-patient training, LUNG-01 (LUNG): Broadest − Finest 0.321Cross-patient training, LUNG-02 (LUNG): Broadest − Finest 0.290Cross-patient training, LYMPH_IDC-01 (LYMPH_IDC): Broadest − Finest 0.518Cross-patient training, LYMPH_IDC-02 (LYMPH_IDC): Broadest − Finest 0.373Cross-patient training, LYMPH_IDC-03 (LYMPH_IDC): Broadest − Finest 0.194Cross-patient training, LYMPH_IDC-04 (LYMPH_IDC): Broadest − Finest 0.282Cross-patient training, PAAD-01 (PAAD): Broadest − Finest 0.296Cross-patient training, PAAD-02 (PAAD): Broadest − Finest 0.432Cross-patient training, PAAD-03 (PAAD): Broadest − Finest 0.362Cross-patient training, PRAD-01 (PRAD): Broadest − Finest 0.126Cross-patient training, PRAD-02 (PRAD): Broadest − Finest 0.231Cross-patient training, READ-01 (READ): Broadest − Finest 0.475Cross-patient training, READ-02 (READ): Broadest − Finest 0.153Cross-patient training, SKCM-01 (SKCM): Broadest − Finest 0.451Cross-patient training, SKCM-02 (SKCM): Broadest − Finest 0.364Cross-patient training: mean Broadest − Finest 0.307 (95% CI 0.270 to 0.344); positive in 45 of 45 patientsCross-patient trainingWithin-section training, CCRCC-01 (CCRCC): Broadest − Finest 0.557Within-section training, CCRCC-02 (CCRCC): Broadest − Finest 0.327Within-section training, CCRCC-03 (CCRCC): Broadest − Finest 0.452Within-section training, CCRCC-04 (CCRCC): Broadest − Finest 0.285Within-section training, CCRCC-05 (CCRCC): Broadest − Finest 0.292Within-section training, CCRCC-06 (CCRCC): Broadest − Finest 0.359Within-section training, CCRCC-07 (CCRCC): Broadest − Finest 0.704Within-section training, CCRCC-08 (CCRCC): Broadest − Finest 0.439Within-section training, CCRCC-09 (CCRCC): Broadest − Finest 0.312Within-section training, CCRCC-10 (CCRCC): Broadest − Finest 0.273Within-section training, CCRCC-11 (CCRCC): Broadest − Finest 0.583Within-section training, CCRCC-12 (CCRCC): Broadest − Finest 0.344Within-section training, CCRCC-13 (CCRCC): Broadest − Finest 0.416Within-section training, CCRCC-14 (CCRCC): Broadest − Finest 0.503Within-section training, CCRCC-15 (CCRCC): Broadest − Finest 0.354Within-section training, CCRCC-16 (CCRCC): Broadest − Finest 0.497Within-section training, CCRCC-17 (CCRCC): Broadest − Finest 0.220Within-section training, CCRCC-18 (CCRCC): Broadest − Finest 0.478Within-section training, CCRCC-19 (CCRCC): Broadest − Finest 0.492Within-section training, CCRCC-20 (CCRCC): Broadest − Finest 0.367Within-section training, CCRCC-21 (CCRCC): Broadest − Finest 0.514Within-section training, CCRCC-22 (CCRCC): Broadest − Finest 0.570Within-section training, CCRCC-23 (CCRCC): Broadest − Finest 0.351Within-section training, CCRCC-24 (CCRCC): Broadest − Finest 0.350Within-section training, COAD-01 (COAD): Broadest − Finest 0.540Within-section training, COAD-02 (COAD): Broadest − Finest 0.512Within-section training, IDC-01 (IDC): Broadest − Finest 0.457Within-section training, IDC-02 (IDC): Broadest − Finest 0.352Within-section training, IDC-03 (IDC): Broadest − Finest 0.416Within-section training, IDC-04 (IDC): Broadest − Finest 0.387Within-section training, LUNG-01 (LUNG): Broadest − Finest 0.368Within-section training, LUNG-02 (LUNG): Broadest − Finest 0.338Within-section training, LYMPH_IDC-01 (LYMPH_IDC): Broadest − Finest 0.573Within-section training, LYMPH_IDC-02 (LYMPH_IDC): Broadest − Finest 0.452Within-section training, LYMPH_IDC-03 (LYMPH_IDC): Broadest − Finest 0.377Within-section training, LYMPH_IDC-04 (LYMPH_IDC): Broadest − Finest 0.431Within-section training, PAAD-01 (PAAD): Broadest − Finest 0.413Within-section training, PAAD-02 (PAAD): Broadest − Finest 0.473Within-section training, PAAD-03 (PAAD): Broadest − Finest 0.443Within-section training, PRAD-01 (PRAD): Broadest − Finest 0.259Within-section training, PRAD-02 (PRAD): Broadest − Finest 0.357Within-section training, READ-01 (READ): Broadest − Finest 0.574Within-section training, READ-02 (READ): Broadest − Finest 0.312Within-section training, SKCM-01 (SKCM): Broadest − Finest 0.557Within-section training, SKCM-02 (SKCM): Broadest − Finest 0.481Within-section training: mean Broadest − Finest 0.425 (95% CI 0.395 to 0.455); positive in 45 of 45 patientsWithin-section training00.20.40.60.8Broadest − Finest
Ridge–Phikon-v2 is trained on other patients (cross-patient training) or on three spatial blocks of the same section to predict the fourth (within-section training) in 45 HEST-Benchmark patients. The left panel shows the mean RSC at each scale with 95% confidence intervals. The right panel shows Broadest − Finest for each patient, with gray lines joining the two trainings of a patient, and the means with 95% confidence intervals. The table below lists the differences between within-section and cross-patient training. Source data: fig3f_training_rsc_by_scale.csv, fig3f_training_broadest_minus_finest_summary.csv, fig3f_training_broadest_minus_finest_per_patient.csv, fig3f_within_minus_cross_differences.csv.
Within-section minus cross-patient training (fig3f_within_minus_cross_differences.csv)
ReadoutWithin-sectionCross-patientDifference (95% CI)Patients higherSign-flip P
Broadest0.6320.4440.187 (0.161 to 0.215)44 of 455 × 10⁻⁷
Broad0.3500.2570.094 (0.070 to 0.118)41 of 455 × 10⁻⁷
Mid0.2800.1920.088 (0.066 to 0.111)39 of 455 × 10⁻⁷
Fine0.2310.1670.064 (0.041 to 0.088)33 of 454 × 10⁻⁶
Finest0.2070.1380.070 (0.050 to 0.090)41 of 455 × 10⁻⁷
Fine scale (mean of Fine and Finest)0.2190.1520.067 (0.047 to 0.088)38 of 455 × 10⁻⁷
Broad scale (mean of Broadest and Broad)0.4910.3500.141 (0.119 to 0.163)44 of 455 × 10⁻⁷
Whole-section Pearson r0.3230.2420.081 (0.063 to 0.101)44 of 455 × 10⁻⁷

How it was computed. Fig. 3a–c is described in Methods “Scales and count transforms” and “Aggregation in colorectal cancer”, and the toolkit command strsc fourier scores physical scales on a regular grid. Fig. 3d is described in Methods “Spot-level models in HEST”, and strsc hest scores the nine Xenium samples on the 50-gene benchmark panel. Fig. 3e,f is described in Methods “Evaluation across spatial scales” and “Within-section training”, and the toolkit has no command for these HEST-Benchmark analyses.

Explore: HEST sample TENX118, spatial scales

Fig. 4

Reproducible-signal correlation (RSC) distinguishes the most robust of three single-cell prediction methods

RSC within a cell class identifies single-cell methods that maintain fine-scale prediction quality. Within malignant cells of breast cancer sections profiled by Xenium (5 patients, nine sections), GHIST has the highest RSC of the three methods at all five scales. At the fine scale, GHIST reaches an RSC of 0.242, compared with 0.042 for DeepSpot2Cell and 0.020 for sCellST, and the split-half reliability is 0.173.

Scores across all cells or in bins are inflated by cell-type composition. Across all cells, a class-mean baseline outscores sCellST (fine-scale RSC 0.081 versus 0.036). Averaging the same predictions into 256-µm bins raises fine-scale RSC across all cells by 0.14 to 0.17 for the three methods (GHIST from 0.285 to 0.435).

Among the three methods, GHIST also locates proliferation hotspots best. Hotspots defined in one RNA half and scored in the other reach a mean enrichment of 0.976. Hotspots predicted by GHIST reach 0.335, compared with 0.101 for sCellST and −0.064 for DeepSpot2Cell.

How it was computed. python -m strsc.cell_score computes RSC within a cell class, across all cells and in bins, and the enrichment of proliferation hotspots (Methods “Evaluation within cell classes”).

Explore: Xenium breast cancer cells · all cells in bins · proliferation hotspots

Fig. 5

Reproducible-signal correlation (RSC) reveals models locate tertiary lymphoid structures (TLS) yet poorly predict internal expression

A high AUROC for locating tertiary lymphoid structures (TLS) can overstate how well a method predicts expression inside the structures. For eight TLS-associated genes in kidney and lung cancer Visium sections, each section is predicted by Ridge–Phikon-v2 trained on the remaining sections. The predictions separate annotated TLS from immune-infiltrated, tumor and normal spots with an AUROC of 0.93 to 0.99 across sections, above the 0.61 to 0.71 of single-spot measured RNA. A class-mean baseline that predicts one value per annotated region reaches an AUROC of 0.99 to 1.00.

Between regions, the class-mean baseline reaches RSCs of 0.73 to 0.83 and Ridge–Phikon-v2 reaches 0.59 to 0.79. Within annotated TLS, the RSC of Ridge–Phikon-v2 is 0.25 to 0.29, far below the between-region values.

How it was computed. Each prediction and each RNA half is decomposed into the mean of the annotated region and the residual from the mean, and RSC is computed between regions, within regions and within TLS (Methods “Evaluation of TLS-associated genes”).

Explore: External TLS sections (Fig. 5a–f)

Fig. 6

Training guided by reproducible-signal correlation (RSC) generally improves method performance

A pairwise difference loss that supervises expression differences between neighboring spots raises fine-scale RSC on average across models. Across the 11 spot-level models in the nine Xenium samples, the loss raises mean fine-scale RSC from 0.194 to 0.205, and the mean over the models rises in all nine samples. For Ridge–Phikon-v2 in HEST-Benchmark, the loss raises fine-scale RSC by 0.015, which is 22% of the 0.067 gain from within-section training.

Comparing neighboring spots contributes to the gain. The loss on neighboring spot pairs raises fine-scale RSC by 0.009 more than the same loss on an equal number of random non-neighboring pairs (exact sign-flip P = 0.0039), with a positive mean gain in 9 of the 11 models.

The effect of the loss depends on the analysis and the model type. The loss lowers the RSC of Ridge–Phikon-v2 between regions and within TLS and changes fine-scale RSC little for sCellST and DeepSpot2Cell.

Fig. 6a Pairwise difference loss versus standard training

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Fig. 6a | Pairwise difference loss versus standard trainingChange in fine-scale RSC (×1,000)IDCPAADLungDeepSpotDeepSpot, NCBI783: +34.5 (×1,000)+34.5DeepSpot, NCBI785: +15.7 (×1,000)+15.7DeepSpot, TENX95: +33.9 (×1,000)+33.9DeepSpot, TENX99: +11.9 (×1,000)+11.9DeepSpot, TENX116: +58.0 (×1,000)+58.0DeepSpot, TENX126: +20.6 (×1,000)+20.6DeepSpot, TENX140: +6.4 (×1,000)+6.4DeepSpot, TENX118: +8.3 (×1,000)+8.3DeepSpot, TENX141: +43.6 (×1,000)+43.6DeepSpot, Mean: +25.9 (×1,000)+25.9DeepSpaCEDeepSpaCE, NCBI783: −31.8 (×1,000)−31.8DeepSpaCE, NCBI785: −6.9 (×1,000)−6.9DeepSpaCE, TENX95: +15.9 (×1,000)+15.9DeepSpaCE, TENX99: −9.7 (×1,000)−9.7DeepSpaCE, TENX116: +18.2 (×1,000)+18.2DeepSpaCE, TENX126: +3.4 (×1,000)+3.4DeepSpaCE, TENX140: 0.0 (×1,000)0.0DeepSpaCE, TENX118: −31.7 (×1,000)−31.7DeepSpaCE, TENX141: −12.1 (×1,000)−12.1DeepSpaCE, Mean: −6.1 (×1,000)−6.1EGNv1EGNv1, NCBI783: +53.8 (×1,000)+53.8EGNv1, NCBI785: −1.0 (×1,000)−1.0EGNv1, TENX95: −18.0 (×1,000)−18.0EGNv1, TENX99: +35.7 (×1,000)+35.7EGNv1, TENX116: +13.3 (×1,000)+13.3EGNv1, TENX126: −7.4 (×1,000)−7.4EGNv1, TENX140: +4.8 (×1,000)+4.8EGNv1, TENX118: −61.5 (×1,000)−61.5EGNv1, TENX141: −6.0 (×1,000)−6.0EGNv1, Mean: +1.5 (×1,000)+1.5EGNv2EGNv2, NCBI783: −20.4 (×1,000)−20.4EGNv2, NCBI785: −7.3 (×1,000)−7.3EGNv2, TENX95: −0.6 (×1,000)−0.6EGNv2, TENX99: +2.1 (×1,000)+2.1EGNv2, TENX116: +80.0 (×1,000)+80.0EGNv2, TENX126: +3.6 (×1,000)+3.6EGNv2, TENX140: −15.3 (×1,000)−15.3EGNv2, TENX118: +0.5 (×1,000)+0.5EGNv2, TENX141: +1.2 (×1,000)+1.2EGNv2, Mean: +4.9 (×1,000)+4.9Hist2STHist2ST, NCBI783: −4.1 (×1,000)−4.1Hist2ST, NCBI785: +27.1 (×1,000)+27.1Hist2ST, TENX95: +22.6 (×1,000)+22.6Hist2ST, TENX99: −16.0 (×1,000)−16.0Hist2ST, TENX116: +1.8 (×1,000)+1.8Hist2ST, TENX126: −14.6 (×1,000)−14.6Hist2ST, TENX140: +11.6 (×1,000)+11.6Hist2ST, TENX118: +9.0 (×1,000)+9.0Hist2ST, TENX141: −9.7 (×1,000)−9.7Hist2ST, Mean: +3.1 (×1,000)+3.1HisToGeneHisToGene, NCBI783: +0.3 (×1,000)+0.3HisToGene, NCBI785: +39.8 (×1,000)+39.8HisToGene, TENX95: +23.4 (×1,000)+23.4HisToGene, TENX99: +22.1 (×1,000)+22.1HisToGene, TENX116: +27.4 (×1,000)+27.4HisToGene, TENX126: +17.2 (×1,000)+17.2HisToGene, TENX140: +50.1 (×1,000)+50.1HisToGene, TENX118: +55.9 (×1,000)+55.9HisToGene, TENX141: +5.2 (×1,000)+5.2HisToGene, Mean: +26.8 (×1,000)+26.8MLPMLP, NCBI783: +0.7 (×1,000)+0.7MLP, NCBI785: +8.8 (×1,000)+8.8MLP, TENX95: +6.4 (×1,000)+6.4MLP, TENX99: −1.1 (×1,000)−1.1MLP, TENX116: +7.0 (×1,000)+7.0MLP, TENX126: +16.0 (×1,000)+16.0MLP, TENX140: +3.0 (×1,000)+3.0MLP, TENX118: +14.1 (×1,000)+14.1MLP, TENX141: +0.2 (×1,000)+0.2MLP, Mean: +6.1 (×1,000)+6.1Ridge–Phikon-v2Ridge–Phikon-v2, NCBI783: +26.2 (×1,000)+26.2Ridge–Phikon-v2, NCBI785: +19.1 (×1,000)+19.1Ridge–Phikon-v2, TENX95: +23.4 (×1,000)+23.4Ridge–Phikon-v2, TENX99: +20.5 (×1,000)+20.5Ridge–Phikon-v2, TENX116: +16.0 (×1,000)+16.0Ridge–Phikon-v2, TENX126: +30.3 (×1,000)+30.3Ridge–Phikon-v2, TENX140: +13.0 (×1,000)+13.0Ridge–Phikon-v2, TENX118: +15.3 (×1,000)+15.3Ridge–Phikon-v2, TENX141: +10.0 (×1,000)+10.0Ridge–Phikon-v2, Mean: +19.3 (×1,000)+19.3ST-NetST-Net, NCBI783: +9.7 (×1,000)+9.7ST-Net, NCBI785: +19.7 (×1,000)+19.7ST-Net, TENX95: +31.3 (×1,000)+31.3ST-Net, TENX99: +17.0 (×1,000)+17.0ST-Net, TENX116: +24.5 (×1,000)+24.5ST-Net, TENX126: +21.3 (×1,000)+21.3ST-Net, TENX140: +26.1 (×1,000)+26.1ST-Net, TENX118: +30.8 (×1,000)+30.8ST-Net, TENX141: +17.7 (×1,000)+17.7ST-Net, Mean: +22.0 (×1,000)+22.0THItoGeneTHItoGene, NCBI783: −1.0 (×1,000)−1.0THItoGene, NCBI785: −1.8 (×1,000)−1.8THItoGene, TENX95: −1.7 (×1,000)−1.7THItoGene, TENX99: −0.7 (×1,000)−0.7THItoGene, TENX116: +2.1 (×1,000)+2.1THItoGene, TENX126: +2.5 (×1,000)+2.5THItoGene, TENX140: +1.8 (×1,000)+1.8THItoGene, TENX118: +3.6 (×1,000)+3.6THItoGene, TENX141: −0.1 (×1,000)−0.1THItoGene, Mean: +0.5 (×1,000)+0.5TCGNTCGN, NCBI783: +67.0 (×1,000)+67.0TCGN, NCBI785: +30.4 (×1,000)+30.4TCGN, TENX95: +11.9 (×1,000)+11.9TCGN, TENX99: +10.4 (×1,000)+10.4TCGN, TENX116: +6.5 (×1,000)+6.5TCGN, TENX126: +26.6 (×1,000)+26.6TCGN, TENX140: +19.8 (×1,000)+19.8TCGN, TENX118: +5.1 (×1,000)+5.1TCGN, TENX141: +9.1 (×1,000)+9.1TCGN, Mean: +20.7 (×1,000)+20.7Mean of 11 modelsMean of 11 models, NCBI783: +12.3 (×1,000)+12.3Mean of 11 models, NCBI785: +13.1 (×1,000)+13.1Mean of 11 models, TENX95: +13.5 (×1,000)+13.5Mean of 11 models, TENX99: +8.4 (×1,000)+8.4Mean of 11 models, TENX116: +23.2 (×1,000)+23.2Mean of 11 models, TENX126: +10.9 (×1,000)+10.9Mean of 11 models, TENX140: +11.0 (×1,000)+11.0Mean of 11 models, TENX118: +4.5 (×1,000)+4.5Mean of 11 models, TENX141: +5.4 (×1,000)+5.4Mean of 11 models, Mean: +11.3 (×1,000)+11.3NCBI783NCBI785TENX95TENX99TENX116TENX126TENX140TENX118TENX141Mean−750+75Change ×1,000
The heatmap shows the change in fine-scale RSC (×1,000) when the pairwise difference loss is added to the standard training of 11 spot-level models in nine samples of invasive ductal carcinoma (IDC), pancreatic adenocarcinoma (PAAD) and lung cancer. Mean fine-scale RSC over the 11 models rises from 0.194 to 0.205 (+11.3). The full-precision table lists the RSC of each model, sample and scale with and without the loss. Source data: fig6a_fine_scale_rsc_change_x1000.csv, fig6ab_full_precision_by_model_sample_scale.csv.

Fig. 6b Change in RSC by scale

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Fig. 6b | Change in RSC by scaleChange in RSC (×1,000)DeepSpotDeepSpot, Broadest: +12.8 (×1,000)+12.8DeepSpot, Broad: +23.3 (×1,000)+23.3DeepSpot, Mid: +26.1 (×1,000)+26.1DeepSpot, Fine: +27.2 (×1,000)+27.2DeepSpot, Finest: +24.6 (×1,000)+24.6DeepSpaCEDeepSpaCE, Broadest: +1.7 (×1,000)+1.7DeepSpaCE, Broad: −2.4 (×1,000)−2.4DeepSpaCE, Mid: −8.8 (×1,000)−8.8DeepSpaCE, Fine: −8.2 (×1,000)−8.2DeepSpaCE, Finest: −3.9 (×1,000)−3.9EGNv1EGNv1, Broadest: +14.3 (×1,000)+14.3EGNv1, Broad: +6.8 (×1,000)+6.8EGNv1, Mid: +5.0 (×1,000)+5.0EGNv1, Fine: +1.1 (×1,000)+1.1EGNv1, Finest: +2.0 (×1,000)+2.0EGNv2EGNv2, Broadest: +7.3 (×1,000)+7.3EGNv2, Broad: +4.9 (×1,000)+4.9EGNv2, Mid: +5.7 (×1,000)+5.7EGNv2, Fine: +6.5 (×1,000)+6.5EGNv2, Finest: +3.3 (×1,000)+3.3Hist2STHist2ST, Broadest: +42.6 (×1,000)+42.6Hist2ST, Broad: −2.5 (×1,000)−2.5Hist2ST, Mid: +5.0 (×1,000)+5.0Hist2ST, Fine: +7.8 (×1,000)+7.8Hist2ST, Finest: −1.6 (×1,000)−1.6HisToGeneHisToGene, Broadest: +32.0 (×1,000)+32.0HisToGene, Broad: +33.6 (×1,000)+33.6HisToGene, Mid: +29.5 (×1,000)+29.5HisToGene, Fine: +27.9 (×1,000)+27.9HisToGene, Finest: +25.8 (×1,000)+25.8MLPMLP, Broadest: +1.6 (×1,000)+1.6MLP, Broad: +3.9 (×1,000)+3.9MLP, Mid: +5.7 (×1,000)+5.7MLP, Fine: +6.0 (×1,000)+6.0MLP, Finest: +6.3 (×1,000)+6.3Ridge–Phikon-v2Ridge–Phikon-v2, Broadest: +9.1 (×1,000)+9.1Ridge–Phikon-v2, Broad: +17.8 (×1,000)+17.8Ridge–Phikon-v2, Mid: +18.9 (×1,000)+18.9Ridge–Phikon-v2, Fine: +20.2 (×1,000)+20.2Ridge–Phikon-v2, Finest: +18.5 (×1,000)+18.5ST-NetST-Net, Broadest: +14.4 (×1,000)+14.4ST-Net, Broad: +17.6 (×1,000)+17.6ST-Net, Mid: +20.3 (×1,000)+20.3ST-Net, Fine: +22.4 (×1,000)+22.4ST-Net, Finest: +21.6 (×1,000)+21.6THItoGeneTHItoGene, Broadest: +8.8 (×1,000)+8.8THItoGene, Broad: −6.0 (×1,000)−6.0THItoGene, Mid: −7.2 (×1,000)−7.2THItoGene, Fine: −1.2 (×1,000)−1.2THItoGene, Finest: +2.2 (×1,000)+2.2TCGNTCGN, Broadest: +24.9 (×1,000)+24.9TCGN, Broad: +28.4 (×1,000)+28.4TCGN, Mid: +22.0 (×1,000)+22.0TCGN, Fine: +22.1 (×1,000)+22.1TCGN, Finest: +19.4 (×1,000)+19.4Mean of 11 modelsMean of 11 models, Broadest: +15.4 (×1,000)+15.4Mean of 11 models, Broad: +11.4 (×1,000)+11.4Mean of 11 models, Mid: +11.1 (×1,000)+11.1Mean of 11 models, Fine: +12.0 (×1,000)+12.0Mean of 11 models, Finest: +10.7 (×1,000)+10.7BroadestBroadMidFineFinest−750+75Change ×1,000
The heatmap shows the mean change in RSC (×1,000) over the nine samples at each of five scales, from Broadest to Finest, computed as the RSC with the pairwise difference loss minus the RSC with standard training. Source data: fig6b_rsc_change_by_scale_x1000.csv, fig6ab_full_precision_by_model_sample_scale.csv.

How it was computed. The loss and the model adapters are in the toolkit module strsc.training. Predictions after standard training and with the loss are scored as in Fig. 3d (Methods “Training with the pairwise difference loss”). The browser tool Pairwise difference loss trains ridge regression with and without the loss on your data.

The score table of Fig. 6c,d opens under Computed results (Score table) and downloads as neighboring-pairs-scores.csv.

Extended Data Fig. 1

Validation of reproducible-signal correlation with simulated and downsampled counts

RSC resolves individual spatial scales and separates prediction quality from sampling noise. When synthetic patterns of known scale are scored as predictions, RSC is highest at the scale of the pattern in 262 of 264 evaluable conditions, and a 90° shift of the spatial phase lowers the mean absolute RSC to 0.0012. When the true expression is scored as the prediction, RSC stays between 0.956 and 1.000 from the broadest to the finest scales, whereas the correlation with counts falls by the amount given by equation (2).

RSC stays largely stable when sampling noise increases. Downsampling the nine Xenium samples to one-eighth of the molecules lowers the fine-scale split-half reliability from 0.416 to 0.247, and whole-section Pearson r falls in all nine samples, from a mean of 0.509 to 0.408. Fine-scale RSC changes from 0.337 to 0.386. With ℓg fixed at the full-depth value, fine-scale RSC changes from 0.337 to 0.358.

Extended Data Fig. 1c True expression in three datasets

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Extended Data Fig. 1c | True expression in three datasets0.40.50.60.70.80.91.0Correlation0.20.40.60.81.0Split-half reliability (ρb)√(2ρb / (1 + ρb))Colorectal cancer bins, <128: correlation with counts 0.779 at split-half reliability 0.440 (simulated counts)Colorectal cancer bins, <128: RSC 0.997 at split-half reliability 0.440 (simulated counts)Colorectal cancer bins, 128–256: correlation with counts 0.866 at split-half reliability 0.610 (simulated counts)Colorectal cancer bins, 128–256: RSC 0.996 at split-half reliability 0.610 (simulated counts)Colorectal cancer bins, 256–512: correlation with counts 0.940 at split-half reliability 0.805 (simulated counts)Colorectal cancer bins, 256–512: RSC 0.996 at split-half reliability 0.805 (simulated counts)Colorectal cancer bins, 0.5–1k: correlation with counts 0.980 at split-half reliability 0.940 (simulated counts)Colorectal cancer bins, 0.5–1k: RSC 0.996 at split-half reliability 0.940 (simulated counts)Colorectal cancer bins, 1–2k: correlation with counts 0.993 at split-half reliability 0.985 (simulated counts)Colorectal cancer bins, 1–2k: RSC 0.996 at split-half reliability 0.985 (simulated counts)Colorectal cancer bins, 2–4k: correlation with counts 0.995 at split-half reliability 0.995 (simulated counts)Colorectal cancer bins, 2–4k: RSC 0.996 at split-half reliability 0.995 (simulated counts)Colorectal cancer bins, ≥4k: correlation with counts 0.996 at split-half reliability 0.999 (simulated counts)Colorectal cancer bins, ≥4k: RSC 0.996 at split-half reliability 0.999 (simulated counts)HEST spots, Finest: correlation with counts 0.843 at split-half reliability 0.561 (simulated counts)HEST spots, Finest: RSC 0.995 at split-half reliability 0.561 (simulated counts)HEST spots, Fine: correlation with counts 0.866 at split-half reliability 0.610 (simulated counts)HEST spots, Fine: RSC 0.996 at split-half reliability 0.610 (simulated counts)HEST spots, Mid: correlation with counts 0.881 at split-half reliability 0.645 (simulated counts)HEST spots, Mid: RSC 0.996 at split-half reliability 0.645 (simulated counts)HEST spots, Broad: correlation with counts 0.914 at split-half reliability 0.727 (simulated counts)HEST spots, Broad: RSC 0.997 at split-half reliability 0.727 (simulated counts)HEST spots, Broadest: correlation with counts 0.985 at split-half reliability 0.947 (simulated counts)HEST spots, Broadest: RSC 0.999 at split-half reliability 0.947 (simulated counts)Malignant cells, Finest: correlation with counts 0.787 at split-half reliability 0.454 (simulated counts)Malignant cells, Finest: RSC 0.997 at split-half reliability 0.454 (simulated counts)Malignant cells, Fine: correlation with counts 0.797 at split-half reliability 0.470 (simulated counts)Malignant cells, Fine: RSC 0.997 at split-half reliability 0.470 (simulated counts)Malignant cells, Mid: correlation with counts 0.814 at split-half reliability 0.502 (simulated counts)Malignant cells, Mid: RSC 0.997 at split-half reliability 0.502 (simulated counts)Malignant cells, Broad: correlation with counts 0.835 at split-half reliability 0.544 (simulated counts)Malignant cells, Broad: RSC 0.996 at split-half reliability 0.544 (simulated counts)Malignant cells, Broadest: correlation with counts 0.880 at split-half reliability 0.649 (simulated counts)Malignant cells, Broadest: RSC 0.996 at split-half reliability 0.649 (simulated counts)HEST spots, Fine+Finest, NCBI783: correlation with counts 0.836 at split-half reliability 0.537 (measured counts, equation 2)HEST spots, Fine+Finest, NCBI785: correlation with counts 0.803 at split-half reliability 0.476 (measured counts, equation 2)HEST spots, Fine+Finest, TENX116: correlation with counts 0.695 at split-half reliability 0.319 (measured counts, equation 2)HEST spots, Fine+Finest, TENX118: correlation with counts 0.775 at split-half reliability 0.429 (measured counts, equation 2)HEST spots, Fine+Finest, TENX126: correlation with counts 0.709 at split-half reliability 0.336 (measured counts, equation 2)HEST spots, Fine+Finest, TENX140: correlation with counts 0.679 at split-half reliability 0.299 (measured counts, equation 2)HEST spots, Fine+Finest, TENX141: correlation with counts 0.764 at split-half reliability 0.412 (measured counts, equation 2)HEST spots, Fine+Finest, TENX95: correlation with counts 0.825 at split-half reliability 0.515 (measured counts, equation 2)HEST spots, Fine+Finest, TENX99: correlation with counts 0.769 at split-half reliability 0.420 (measured counts, equation 2)Malignant cells, Fine+Finest: correlation with counts 0.543 at split-half reliability 0.173 (measured counts, equation 2)ScoreRSCCorrelation with countsfrom the measured reliabilityDatasetColorectal cancer binsHEST spotsMalignant cells
The true expression reaches an RSC near 1 in three datasets (colorectal cancer bins, HEST spots and malignant cells). The correlation of the true expression with counts follows equation (2), drawn as the curve √(2ρb/(1 + ρb)). Filled points are means over 20 simulated count matrices, and open points apply equation (2) to the split-half reliability of the measured counts at fine scales. Source data: ed_fig1c_expected_expression_points.csv, ed_fig1c_theory_curve.csv.

Extended Data Fig. 1d Downsampled counts in HEST

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Extended Data Fig. 1d | Downsampled counts in HEST0.20.30.40.50.6Correlation11/21/41/8Fraction of molecules keptWhole-section Pearson r, 1 of the molecules: 0.509 (95% interval 0.459 to 0.561)Whole-section Pearson r, 1/2 of the molecules: 0.481 (95% interval 0.431 to 0.534)Whole-section Pearson r, 1/4 of the molecules: 0.448 (95% interval 0.396 to 0.500)Whole-section Pearson r, 1/8 of the molecules: 0.408 (95% interval 0.354 to 0.462)Whole-section Pearson rFine-scale RSC, 1 of the molecules: 0.337 (95% interval 0.303 to 0.377)Fine-scale RSC, 1/2 of the molecules: 0.354 (95% interval 0.320 to 0.394)Fine-scale RSC, 1/4 of the molecules: 0.369 (95% interval 0.334 to 0.408)Fine-scale RSC, 1/8 of the molecules: 0.386 (95% interval 0.347 to 0.425)Fine-scale RSCFine-scale split-half reliability, 1 of the molecules: 0.416 (95% interval 0.366 to 0.466)Fine-scale split-half reliability, 1/2 of the molecules: 0.360 (95% interval 0.307 to 0.411)Fine-scale split-half reliability, 1/4 of the molecules: 0.305 (95% interval 0.254 to 0.355)Fine-scale split-half reliability, 1/8 of the molecules: 0.247 (95% interval 0.200 to 0.293)Fine-scale split-half reliability
Molecules of the nine Xenium samples of breast, pancreatic and lung cancer are removed at random down to one-eighth, and the same predictions of Ridge–Phikon-v2 are scored at each depth. Downsampling lowers the split-half reliability and whole-section Pearson r, whereas fine-scale RSC changes from 0.337 to 0.386. Points are means over the nine samples, and error bars are 95% bootstrap intervals. Source data: ed_fig1d_downsampled_counts.csv.

How it was computed. Extended Data Fig. 1 is described in Methods “Tests of the reproducible-signal correlation”. Panels a, b, e and f simulate Poisson or negative binomial counts in three colorectal cancer patients at eight bin sizes, and the paper contains these panels with the source data.

The source and license of each dataset are listed with the data explorers and in Supplementary Table 7 of the paper.