SmartX LabHKUSTstRSC
GitHub

Results

The evaluations of the paper, figure by figure. Each chart is drawn from the source data of its panel, and every file downloads as it is. The sections and saved results behind Figures 2 to 6 open in the data explorers; your own predictions go under Analyze data.

Fig. 1

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

In HER2ST, a class-mean baseline that assigns identical expression to every spot of a 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 observed split-half reliability implies that even an ideal prediction matching the underlying expression would reach a correlation with measured RNA expression of 1.00 at the broadest scale but only 0.44 to 0.57 at the finest, while its RSC stays near 1.

Fig. 1b Pitfall of whole-section correlation

DownloadData (CSV)
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
Whole-section Pearson r across 785 genes in HER2ST (n = 8 patients) for 11 published methods and a class-mean baseline that has no variation within regions. The baseline (gray) scores above the median of the 11 methods (dashed line). Source data: fig1b_whole_section_pearson_HER2ST.csv.

Fig. 1c Noise correction across scales

DownloadData (CSV)
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 1.0000.44–0.570.997Ideal predictionRSCPearson r with measuredRNA expressionThin: P1 CRC, P2 CRC, P3 NATThick: mean of the three
An ideal prediction, equal to the underlying expression, in three colorectal cancer patients (P1 and P2 with colorectal cancer, P3 with normal adjacent tissue) on the 32-µm grid. Pearson r with measured RNA expression (pink) follows from equation (2) with the split-half reliability of the measured counts and drops at fine scales; RSC (teal) stays near 1. Thin lines are patients, thick lines their mean. Source data: fig1c_noise_correction_across_scales.csv.

How it was computed. Fig. 1b, Methods “Whole-section correlation” and “Class-mean baseline”. Fig. 1c, Methods “Expected expression and the mean of the halves”: the measured counts are taken as Poisson rates, the expected expression is scored as the prediction, and Pearson r with measured RNA expression follows from equation (2) with the split-half reliability of the measured counts. 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

Normalized pairwise accuracy of 11 published methods across 785 genes in HER2ST (8 patients) runs from 0% for a majority-order baseline to 100% for split-half agreement. The median 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 stays at 6.6% for matched pairs in the same annotated region. The class-mean baseline scores 6.8% on matched pairs but 1.5% within a region, where each of the 11 methods predicts a positive fraction of the spot-to-spot differences.

Rankings by whole-section correlation agree 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 shifts from EGNv2 to DeepSpaCE. For FASN, Hist2ST predictions correlate with measured RNA at Spearman ρ = 0.534 across all spots of a section but 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 same calculation runs in the browser under Pairwise accuracy.

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

In the Visium HD colorectal cancer sections, 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, and 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 have lower RSC at the finest than at the broadest scale in all nine samples.

Across 70 sections from 45 patients in the nine tasks of HEST-Benchmark, Ridge–Phikon-v2 is lower at the finest scale in 44 of 45 patients (sign-flip P < 10−6). Pathology foundation models raise RSC at every scale, yet the drop from the broadest to the finest scale stays between 0.31 and 0.34 for all five image encoders. Trained on three spatial blocks of a section to predict the fourth, Ridge–Phikon-v2 rises in fine-scale RSC from 0.152 to 0.219.

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

DownloadData (CSV)
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
RSC of Ridge–Phikon predictions of 1,000 genes in 32-µm bins of the Visium HD colorectal cancer sections, from below 128 µm to 4,096 µm and above (1k = 1,024 µm). Gray lines are the three patients (P1 and P2 with colorectal cancer, CRC; P3 with normal adjacent tissue, NAT); the dark line is their mean, with the patient range. Source data: fig3a_rsc_32um_grid_by_patient.csv.

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

DownloadData (CSV)
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
Fraction of the error of predicting each gene by its mean in the training patients that is attributable to tissue composition, which inflates correlations in coarse bins, and to sampling noise, which attenuates correlations in fine bins, across bin sizes of 32 to 512 µm. Signal ≥4k is the share of the reproducible signal at scales of 4,096 µm and above (thin lines, patients; thick, mean). Source data: fig3b_error_fractions_by_bin_size.csv.

Fig. 3c RSC by spatial scale and bin size

DownloadData (CSV)
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
RSC of Ridge–Phikon predictions in P1 CRC at each spatial scale (rows) when the same tissue, genes and 8-µm bins are aggregated to bins of 32 to 512 µm (columns). Hatching marks combinations where the bin size cannot represent the scale. Colors run from 0.5 to 0.9 as in the paper; values below 0.5 take the lightest color, and every value is written in its cell. Source data: fig3c_rsc_scale_by_bin_size.csv.

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

Download
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
RSC at five relative scales of 11 spot-level architectures in nine Xenium samples of breast (IDC), pancreatic (PAAD) and lung cancer, averaged over the samples. Models reach high RSC at the broadest scale and drop at the finest. Right, Broadest − Finest for each sample (points) with the mean and its 95% confidence interval; THItoGene in gray. Source data: fig3d_summary_11_models.csv, fig3d_rsc_11_models_by_sample.csv.

Fig. 3e Image encoders in HEST-Benchmark

Download
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 models on features of four pathology foundation models (Phikon-v2, UNI, Midnight-12k, Virchow2) and of ResNet50 trained on natural images, in n = 45 HEST-Benchmark patients (70 sections, nine prediction tasks). Left, mean RSC at each scale with 95% confidence intervals. Right, 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

Download
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 trained on other patients (cross-patient) or on three spatial blocks of the same section to predict the fourth (within-section), in 45 HEST-Benchmark patients. Left, mean RSC at each scale with 95% confidence intervals. Right, 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 gives the within-section minus cross-patient differences. 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, Methods “Scales and count transforms” (colorectal cancer bins) and “Aggregation in colorectal cancer”; the toolkit scores physical scales on a regular grid with strsc fourier. Fig. 3d, Methods “Spot-level models in HEST”; strsc hest scores the nine Xenium samples on the 50-gene benchmark panel. Fig. 3e,f, Methods “Evaluation across spatial scales” and “Within-section training”; these HEST-Benchmark analyses belong to the paper and have no toolkit command.

Explore: HEST sample TENX118, spatial scales

Fig. 4

Reproducible-signal correlation (RSC) distinguishes a robust single-cell prediction method

Within malignant cells of breast cancer sections profiled by Xenium (5 patients, nine sections), GHIST has the highest RSC at all five scales. Its fine-scale RSC is 0.242, against 0.042 for DeepSpot2Cell and 0.020 for sCellST, with a fine-scale split-half reliability of 0.173.

Across all cells, a class-mean baseline outscores sCellST (fine-scale RSC 0.081 versus 0.036), and averaging the same predictions into 256-µm bins raises fine-scale RSC by 0.14 to 0.17 (GHIST from 0.285 to 0.435). 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, those of sCellST 0.101 and those of DeepSpot2Cell −0.064.

How it was computed. python -m strsc.cell_score computes RSC within a cell class, across all cells and in bins, and the 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

Eight TLS-associated genes in kidney and lung cancer Visium sections, each section 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, but a class-mean baseline reaches 0.99 to 1.00.

Between regions, the class-mean baseline reaches RSCs of 0.73 to 0.83 and Ridge–Phikon-v2 0.59 to 0.79. Within annotated TLS, Ridge–Phikon-v2 reaches only 0.25 to 0.29.

How it was computed. Methods “Evaluation of TLS-associated genes”: each prediction and each RNA half is divided into the mean of its annotated region and the residual from that mean, and RSC is formed between regions, within regions and within TLS.

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

Fig. 6

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

Across the 11 spot-level models in the nine Xenium samples, the pairwise difference loss raises mean fine-scale RSC from 0.194 to 0.205, and the mean over the models rises in all nine samples. On neighboring spot pairs the loss raises fine-scale RSC by 0.009 more than on the same number of randomly paired non-neighboring spots (exact sign-flip P = 0.0039), with a positive mean gain in 9 of the 11 models.

For Ridge–Phikon-v2 in HEST-Benchmark, the loss raises fine-scale RSC by 0.015, 22% of the 0.067 gain obtained from within-section training. The same 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

Download
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
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 all models rises from 0.194 to 0.205 (+11.3). The full-precision table gives every model, sample and scale before and after. Source data: fig6a_fine_scale_rsc_change_x1000.csv, fig6ab_full_precision_by_model_sample_scale.csv.

Fig. 6b Change in RSC by scale

Download
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
Mean change in RSC (×1,000) over the nine samples at each of the five scales, from Broadest to Finest, with the pairwise difference loss minus 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 strsc.training; predictions after standard training and with the loss are scored as in Fig. 3d (Methods “Training with the pairwise difference loss”). In the browser, Pairwise difference loss trains Ridge with and without the loss on your data.

Fig. 6c,d: the score table 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

With the injected patterns as predictions, RSC is highest at the injected scale in 262 of 264 estimable conditions, and a 90° shift of the spatial phase lowers the mean absolute RSC to 0.0012. When the true underlying expression rates are scored as predictions, RSC stays between 0.956 and 1.000 from the broadest to the finest scales, while the correlation with counts drops by the amount that equation (2) gives.

Downsampling the nine Xenium samples to one-eighth of their molecules lowers the fine-scale split-half reliability from 0.416 to 0.247 and whole-section Pearson r from 0.509 to 0.408, in all nine samples, whereas fine-scale RSC changes from 0.337 to 0.386. With ℓg fixed at its value at full depth, fine-scale RSC changes from 0.337 to 0.358.

Extended Data Fig. 1c Expected expression in three datasets

Download
Extended Data Fig. 1c | Expected 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 expected expression reaches an RSC near 1 in three datasets (colorectal cancer bins, HEST spots, malignant cells), and its correlation with counts follows equation (2), drawn as the curve √(2ρb/(1 + ρb)). Filled points are means over 20 simulated count matrices; 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

DownloadData (CSV)
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 removed at random down to one-eighth, with the same predictions of Ridge–Phikon-v2. Downsampling lowers the split-half reliability and whole-section correlation, whereas fine-scale RSC changes from 0.337 to 0.386. Points are means over the nine samples, error bars 95% bootstrap intervals. Source data: ed_fig1d_downsampled_counts.csv.

How it was computed. Methods “Tests of the reproducible-signal correlation”. Panels a, b, e and f use three colorectal patients with Poisson or negative binomial counts at eight bin sizes; they are in the paper, and their source data are not on this site.

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