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One-Slide Calibration of Pathology Foundation Models
Ming Ren Hou, Tianyi Huang
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Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 92%
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Summary
The paper introduces SlideRuler, a method for calibrating pathology foundation models by using internal regions within a single whole-slide image as controls to estimate and correct scanner-induced acquisition shifts. By learning a transfer map from paired rescans, SlideRuler enables calibration from a single scan at inference without retraining the foundation model. The method demonstrates significant reductions in embedding distance and source-feature displacement across multiple scanners and encoders, particularly when using tissue-defined controls like benign glands and stroma.
Entities (10)
Relation Signals (10)
SlideRuler → evaluatedon → SCORPION
confidence 95% · Across two encoders and five SCORPION scanners, learned transfer reduces mean target-to-source embedding distance
Source-anchored variant → reduces → source-feature displacement
confidence 95% · A source-anchored variant reduces source-feature displacement by 47.7-83.6%
Learned transfer → reduces → embedding distance
confidence 95% · learned transfer reduces mean target-to-source embedding distance by 16.3-38.5%
SlideRuler → uses → Learned transfer
confidence 95% · Learned transfer combines direct control subtraction with an affine ridge map.
SlideRuler → uses → Source-anchored variant
confidence 95% · A source-anchored variant combines a control-modulated global shift with a regularized residual
DistillPath-IS16-HOpt0 → usedwith → SlideRuler
confidence 92% · We extract 384-dimensional embeddings with frozen Prost40M and DistillPath-IS16-HOpt0
Prost40M → usedwith → SlideRuler
confidence 92% · We extract 384-dimensional embeddings with frozen Prost40M... SlideRuler estimates acquisition shifts
SlideRuler → evaluatedon → PAR
confidence 90% · For PAR, a fixed patient ordering selects 20 patients and all their biopsies
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Abstract
Abstract:Scanner variation changes how pathology foundation models represent the same tissue. We introduce SlideRuler, which uses regions within a slide as internal controls to estimate and correct acquisition-induced shifts in other regions. A transfer map learned from paired rescans enables calibration from a single scan at inference while keeping the foundation model fixed. Across two encoders and five SCORPION scanners, learned transfer reduces mean target-to-source embedding distance by 16.3-38.5% relative to raw embeddings. Comparisons with unrelated same-scanner controls reveal a positive same-slide contribution across all four evaluation settings, including scanner holdout. A source-anchored variant reduces source-feature displacement by 47.7-83.6% relative to learned transfer while retaining most of its alignment gain. By drawing calibration information from the slide itself, SlideRuler offers a path toward more consistent use of frozen pathology models across imaging systems.
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- Source: https://arxiv.org/abs/2610.08944v1
- Canonical: https://arxiv.org/abs/2610.08944v1
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AI at Scale for Clinical Impact (ASCI): Cancer Pathology Foundation Models One-Slide Calibration of Pathology Foundation Models Ming Ren Hou Affiliation: App-In Club Email: ming.hou@appinclub.org Tianyi Huang Affiliation: Ryquo Email: tianyi@ryquo.com Abstract Scanner variation changes how pathology foundation models represent the same tissue. We introduce SlideRuler, which uses regions within a slide as internal controls to estimate and correct acquisition-induced shifts in other regions. A transfer map learned from paired rescans enables calibration from a single scan at inference while keeping the foundation model fixed. Across two encoders and five SCORPION scanners, learned transfer reduces mean target-to-source embedding distance by 16.3–38.5% relative to raw embeddings. Comparisons with unrelated same-scanner controls reveal a positive same-slide contribution across all four evaluation settings, including scanner holdout. A source-anchored variant reduces source-feature displacement by 47.7–83.6% relative to learned transfer while retaining most of its alignment gain. By drawing calibration information from the slide itself, SlideRuler offers a path toward more consistent use of frozen pathology models across imaging systems. 1 Introduction A pathology foundation model sees both tissue and the imaging system that digitized it. Optical response, focus, compression, and color processing can change a representation even when the glass slide is fixed [4, 6]. Scanner robustness is therefore partly a measurement problem: how can a model distinguish acquisition variation from the biological information that its downstream tasks require? This distinction matters for deployment across hospitals and devices, where retraining a foundation model or assembling a target-domain calibration cohort may be impractical. Paired rescans provide a direct way to measure acquisition variation. Comparing the same tissue across devices reduces the biological confounding present in comparisons between unrelated cohorts. Recent methods use this evidence to learn global transformations of frozen embeddings [3, 12]. An additional question remains: does the slide being processed contain information about its own correction beyond the correction shared across slides? Answering it requires a comparison that preserves the scanner while changing the identity of the control tissue. SlideRuler estimates acquisition shifts from other regions of the same slide. Paired training scans define an acquisition subspace and supervise a map from control displacement to query-region displacement. At inference, the model uses source prototypes and controls from the current scan, without requiring a paired rescan, scanner identity, or target-cohort statistics. We study two estimators. Learned transfer combines direct control subtraction with an affine ridge map. A source-anchored variant combines a control-modulated global shift with a regularized residual, using source-feature displacement to guide model selection. Prostate biopsies provide a concrete setting for tissue-defined controls: benign glands and stroma can inform the correction of a candidate tumor region. Our contributions connect three aspects of one-slide calibration. First, same-scanner control replacement measures the additional predictive information supplied by the current slide. Second, a source-anchored residual estimator provides an explicit tradeoff between target alignment and source-feature displacement. Third, patient-held-out tissue selection and a fixed-cohort prostate-biopsy study evaluate the availability of tissue-defined controls. These analyses connect a slide’s calibration signal to the correction it induces and the tissue needed to estimate it. 2 Related work Acquisition harmonization. Color transfer and stain normalization address appearance variation [14, 11]; ComBat and CORAL adjust feature distributions using batch structure or domain statistics [7, 17]. Paired-data approaches such as FEATMAP and post-hoc acquisition shrinkage learn corrections directly in foundation-model embedding spaces [3, 12]. PathoROB evaluates biological representation structure alongside downstream robustness, motivating evaluation of both alignment and information preservation [9]. Our focus is the incremental information available within one test slide. We compare against explicit pooled-mean, scanner-mean, affine-ridge, and subspace-shrinkage implementations. Control tissue and scanner benchmarks. MuSClD uses off-target organs collected at a deployment site for cross-organ calibration [20]; non-tumor regions have also been used to define pseudo-domains for pathology domain generalization [16]. SlideRuler uses within-slide controls to predict a region-specific acquisition shift. SCORPION supplies 480 aligned regions scanned on five devices [15]. PAR contains three scans of each of 339 prostate-biopsy slides from 185 patients [1]. Together, paired-region and whole-slide data support separate measurements of acquisition transfer and control availability. Figure 1: One-slide calibration with learned transfer. Top: paired rescans define the acquisition basis U from residuals centered across scanners within each registered region and train the transfer map. Bottom: a single scan supplies control displacements relative to source prototypes; learned transfer corrects the query while preserving QzjQz_j. Controls exclude the query; training prototype matches exclude its entire slide. The nine-control SCORPION example is schematic. 3 One-slide acquisition calibration 3.1 Paired training and within-slide controls Let ziqj∈ℝdz_iqj ^d be a frozen encoder’s embedding for region j of slide i on scanner q, standardized with source-training statistics. Scanner 00 is the designated source. Registered training regions define shifts Δiqj=ziqj−zi0j _iqj=z_iqj-z_i0j. All scans of a physical slide remain in the same fold. Training permits paired rescans; inference receives only the query scan. Let trQ_ tr contain the permitted training scanners, including source scanner 00. For learned transfer, center each registered region across these scanners and stack the residuals: diqj=ziqj−1|tr|∑q′∈trziq′j,U=[u1,…,ur],Q=Id−UU⊤.d_iqj=z_iqj- 1|Q_ tr| _q _ trz_iq j, U=[u_1,…,u_r], Q=I_d-U . (1) The rows of D are diqj⊤d_iqj , and u1,…,uru_1,…,u_r are its leading right singular vectors. Thus U∈ℝd×rU ^d× r has orthonormal columns. We retain the smallest rank reaching 90% of residual energy, or the rank cap of 16 when that threshold is not reached. The projector Q removes these acquisition coordinates for prototype matching. Let pU(z)p_U(z) be the mean of the k=8k=8 nearest source-bank embeddings to z under distance ‖Q(z−p)‖2\|Q(z-p)\|_2. The control vector for query region j in scan X is aj(X,U)=medℓ≠jU⊤[zℓ−pU(zℓ)].a_j(X;U)= *med_ ≠ jU \! [z_ -p_U(z_ ) ]. (2) The median is coordinate-wise, and aj∈ℝra_j ^r. Training matches exclude every prototype from the query slide; held-out slides use the training bank. On SCORPION, each query has nine other regions as controls. A tissue-defined extension replaces these regions with selected benign-gland and stromal fields, with separate prototype banks and transfer maps (Appendix E). 3.2 Learned transfer Write m for a training slide/scanner/query example, ama_m for its control vector, and em=U⊤Δme_m=U _m. Fit an affine ridge map with R∈ℝr×rR ^r× r and b∈ℝrb ^r, then blend its prediction with direct subtraction: (R,b) (R,b) =argmin∑mR,b‖em−Ram−b‖22+λ‖R‖F2, = _R,b _m\|e_m-Ra_m-b\|_2^2+λ\|R\|_F^2, (3) e^(a) e(a) =(1−α)a+α(Ra+b),zj⋆=zj−Ue^(aj). =(1-α)a+α(Ra+b), z_j =z_j-U e(a_j). Source examples have Δm=0 _m=0. The original region-transfer estimator uses λ=1λ=1. Five inner physical-slide folds rebuild standardization, basis, prototypes, and regression. The shared blend α∈0,.01,…,1α∈\0,.01,…,1\ minimizes a worst-scanner score based on slide-mean projected residual distance (Appendix A). The direct-control baseline uses α=0α=0. 3.3 Source-anchored global and residual correction The second estimator balances target alignment against source-feature displacement. Its basis UAU_A is fitted to group-weighted, source-referenced shifts Δ , and g=w[Δ]∈ℝdg=E_w[ ] ^d is their pooled mean over non-source scanners. Each training group receives equal total mass. Define the centered control vector and global activation by a~j=aj(X,UA)−μ0,v=UA⊤g,t(a)=clip(a⊤v⊤v,0,2), a_j=a_j(X;U_A)- _0, v=U_A g, t(a)=clip\! ( a vv v,0,2 ), (4) where μ0 _0 is the group-weighted mean of source control vectors computed with own-group prototypes excluded. Set t=0t=0 if v⊤v≤10−8v v≤ 10^-8. The global prediction t(a)gt(a)g retains the full embedding dimension. A zero-intercept ridge map predicts the remaining acquisition coordinates: Bλ B_λ =argmin∑mBwm‖UA⊤[Δm−t(a~m)g]−Ba~m‖22+λ‖B‖F2, = _B _mw_m \|U_A \! [ _m-t( a_m)g ]-B a_m \|_2^2+λ\|B\|_F^2, (5) r(a) r(a) =βBλamin1,‖a‖2max(‖βBλa‖2,10−8),Δ^A(a)=t(a)g+UAr(a). =β B_λa\, \! \1, \|a\|_2 (\|β B_λa\|_2,10^-8) \, _A(a)=t(a)g+U_Ar(a). (6) The fitted correction is zj⋆=zj−Δ^A(a~j)z_j =z_j- _A( a_j). Source examples again have zero target shift. The residual cap bounds its acquisition-coordinate norm by the control norm. At the learned anchor a~=0 a=0, the correction is exactly zero. Four penalties λ∈.1,1,10,100λ∈\.1,1,10,100\ and three residual weights β∈.25,.5,1β∈\.25,.5,1\, plus global-only and identity, give 14 candidates. Five inner grouped folds select M⋆=argminM∈ℳ[maxq∈tr∖0‖Δ−Δ^M‖2¯q+‖Δ^M‖2¯ 0].M = _M [ _q _ tr \0\ \| - _M\|_2_\,q+ \| _M\|_2_\,0 ]. (7) Each mean averages regions within a slide, slides within a group, and then groups equally. Every learned component, including μ0 _0 and g, is rebuilt inside each fold. The selected candidate is refitted on the outer training set. The global-only candidate retains control-dependent activation. 3.4 Tissue-defined controls For prostate biopsies, we train a three-class linear selector on frozen Prost40M embeddings from an external annotated dataset [2]. Its classes are benign gland, residual stroma, and tumor. A field is retained when its largest predicted class probability is at least 0.8; otherwise it is unassigned. The cutoff is fixed before evaluation and applies to uncalibrated probability estimates. Five outer patient-grouped folds evaluate the selector; three inner folds select logistic-regression regularization by class- and patient-balanced out-of-fold log loss. Both levels use stratified group splits. The final selector is fitted on all external patients and then frozen for PAR, where fields in each scanner image are selected independently from their uncorrected embeddings. 4 Experimental design Paired scanner evaluation. SCORPION contains 48 physical slides, ten registered regions per slide, and five scanners [15]. We extract 384-dimensional embeddings with frozen Prost40M and DistillPath-IS16-HOpt0 [18, 5, 8, 13]. Leica AT2 is the source. Six outer splits use 32 training, eight reserved validation, and eight test slides. The calibrated protocol permits training pairs from all scanners; scanner holdout excludes the evaluated device from all fitting and selection. Each encoder/protocol condition contains 1,920 held-out target-region comparisons. Comparisons and endpoints. We evaluate raw embeddings, pooled-mean and scanner-mean correction, affine ridge, subspace shrinkage, direct controls, learned transfer, and the anchored variant. All SCORPION alignment comparisons apply the estimators without the optional strict gate. We measure mean target-to-source Euclidean distance in source-standardized coordinates, source-feature displacement ‖z⋆−z‖2\|z -z\|_2 on source scans, and top-1 same-region retrieval accuracy among the 80 source regions in an outer test fold. Material distance worsening means an increase exceeding 2% of the median raw non-source distance on the eight reserved validation slides. The anchored variant does not use those slides for fitting or candidate selection. Isolating slide identity. Thirty-two seeded derangements replace only the control regions with those of another slide on the same scanner and in the same test fold. The query embedding remains fixed. We average the paired effects across permutations before computing pointwise 95% intervals from 5,000 physical-slide bootstrap resamples. The comparison measures the benefit of same-slide controls while holding the query, scanner, and learned estimator fixed. The donor pool and seeded assignments remain fixed during resampling. External selection and PAR sampling. The external selector study uses 8,325 fields from 37 slides and 32 patients. Evaluation gives each patient total weight one; 95% intervals use 2,000 patient bootstrap resamples of saved out-of-fold predictions. For PAR, a fixed patient ordering selects 20 patients and all their biopsies, yielding 35 slides and 105 scans. Reference and dense policies request 512 and 2,048 fields per scan, respectively, sampled independently on each scanner image at a nominal 112 μ field size, with up to 128 and 512 registered fields. The policies use non-nested sampled locations and otherwise fixed extraction, selection, and registration settings. Control-count eligibility requires at least 16 benign-gland and 16 stromal fields per scan. All assigned scans remain in the denominators. Controlled compartment experiment. A 64-run synthetic suite combines eight regimes and eight seeds, with known acquisition shifts and separate benign, stromal, and lesion compartments. It evaluates the two-compartment transfer and selective-correction implementation. All seeds contribute to the reported means; a failed outer screen returns the uncorrected embeddings. The suite tests acquisition-sensitive and already robust ordinal heads, tissue-response differences, scanner extrapolation, and calibration-set size. 5 Results Figure 2: Slide-specific acquisition information across scanners. Same-slide distance advantage over unrelated same-scanner controls, disaggregated by target device. Positive values favor same-slide controls. Points and bars show mean differences and pointwise 95% physical-slide bootstrap intervals over 48 slides, after averaging 32 within-fold donor permutations. The query embedding is unchanged. Limits are shared within encoder rows; distances use each encoder’s source-training scale. 5.1 Same-slide controls improve acquisition correction Learned transfer reduces paired distance relative to raw embeddings in every encoder/protocol setting, by 16.3–38.5% (Table 1). Same-slide controls improve on unrelated same-scanner controls by 0.535 and 0.303 for Prost40M, and by 0.330 and 0.249 for DistillPath, in calibrated and held-out settings respectively. All four pooled intervals exclude zero, as do all 16 learned-transfer scanner-specific intervals; the pooled effect is positive under each of the 32 permutations. Figure 2 disaggregates the effect by device. These results show that same-slide controls improve prediction of paired acquisition shifts beyond unrelated controls from the same device. Table 1: Paired embedding alignment on SCORPION. Mean target-to-source distance; lower is better. All corrections are ungated. Bold denotes the lowest point estimate in each row. Scanner mean falls back to pooled mean for a held-out scanner. Distances use each encoder’s source-training scale. Encoder Protocol Raw Scanner mean Affine ridge Shrinkage Learned Anchored Prost40M Calibrated 18.654 11.328 9.640 13.181 11.470 12.030 Holdout 18.654 15.940 13.294 14.801 13.871 14.196 DistillPath Calibrated 17.551 13.805 14.447 13.808 13.843 14.591 Holdout 17.551 15.840 15.420 14.690 14.682 14.973 Global baselines remain competitive in mean distance: affine ridge attains the lowest Prost40M values, while scanner mean and subspace shrinkage perform well for DistillPath. Retrieval and distance-worsening rates provide complementary comparisons. Under Prost40M scanner holdout, learned transfer achieves 99.74% retrieval accuracy versus 98.18% for affine ridge, a paired advantage of 1.56 percentage points (95% CI 0.83–2.34), with material distance worsening of 3.07% versus 19.58%. Under DistillPath holdout, learned transfer and shrinkage have similar mean distance, with worsening rates of 2.40% and 6.77%, respectively. 5.2 Source anchoring changes the operating point The anchored estimator reduces mean source-feature displacement by 47.7–83.6% across the four settings. Figure 3 shows the joint alignment–displacement comparison and its physical-slide variation; source displacement decreases on all 48 slides in every setting. This reduction accompanies an increase of 0.291–0.749 in mean target distance relative to learned transfer; all four paired intervals exclude zero. Pooled material distance-worsening rates also decrease in every setting (Appendix C). Anchoring retains 79.8–93.2% of learned transfer’s distance reduction over raw embeddings, providing a way to reduce source displacement while preserving most of the target alignment gain. Training-only model selection retains a residual component in 42 of 60 unique fits and selects the control-modulated global correction in the remaining 18. All Prost40M fits retain a residual, whereas all six calibrated DistillPath fits select the global correction. This variation shows how model selection adjusts correction complexity across encoders. The anchored estimator retains positive pooled same-slide advantages of 0.031–0.249 (Appendix B). Figure 3: Alignment and source displacement form distinct evaluation axes. Large markers are method means; faint blue/orange points show learned/anchored results for each of 48 physical slides, joined within slide. Lower values on both axes are preferable. Target values average ten regions and four target scanners; source values average ten regions and one fitted model per slide when calibrated, or four models under scanner holdout. Axis limits are shared within encoder rows; distances use source-standardized coordinates. Figure 4: Control availability across sampling policies. (a–c) Empirical cumulative distributions of benign-gland counts for 35 reference and 34 dense scans per scanner. The horizontal coordinate is log2(n+1) _2(n+1), with ticks labeled by count n; dashed lines mark 16 fields. (d) Availability requires at least 16 benign-gland and 16 stromal fields per scan. Columns represent all 35 slides, with unavailable preparations marked. G/H/L denote Grundium/Hamamatsu/Leica. Sampling locations are non-nested. 5.3 Denser sampling increases tissue-control availability Table 2: External patient-held-out tissue selection. Precision and recall are percentages with 95% patient bootstrap intervals. Counts denote reference-class fields and patients containing that class. Residual stroma is the dataset’s postprocessed remaining-tissue class. Reference class Fields Patients Precision Recall Benign gland 337 21 89.37 [80.05, 95.72] 89.51 [82.19, 94.40] Residual stroma 7,028 32 99.98 [99.93, 100.00] 98.16 [96.78, 99.18] Tumor 960 20 96.32 [91.85, 98.69] 81.40 [71.34, 89.38] The external selector achieves patient-weighted precision of 89.37% for benign glands, 99.98% for residual stroma, and 96.32% for tumor (Table 2). Coverage is 96.75%. Four additional patient partitions give benign precision of 90.81–93.05% at the same cutoff. On PAR, dense sampling doubles the number of scans meeting both control-count requirements from 29/105 to 58/105 (Table 3). Among the 102 scans available under both policies, 27 pass under both, 31 pass only under dense sampling, and none pass only under reference sampling. Hamamatsu shows the largest absolute increase, from 3 to 17 eligible scans out of 35. Every available dense scan meets the stromal count threshold, identifying benign-gland sampling as the remaining constraint on control availability. The full distributions and paired scanner outcomes appear in Figure 4. At slide level, all three scanners meet the control requirements on 3/35 reference slides and 16/35 dense slides. Table 3: PAR control-count availability. Scans with at least 16 selected benign-gland and 16 stromal fields. Each scanner has 35 assigned scans. The three unavailable dense scans remain in the denominator. Policy Grundium Hamamatsu Leica Overall Reference (512 fields) 12/35 3/35 14/35 29/105 (27.6%) Dense (2,048 fields) 21/35 17/35 20/35 58/105 (55.2%) 5.4 Controlled tests explain when transfer helps In the acquisition-sensitive synthetic regime, the two-compartment method reduces shift root-mean-square error (RMSE) from 4.014 to 1.894, with paired reduction 2.120 (95% CI 1.468–2.512), and increases worst-target quadratically weighted kappa (QWK) from 0.828 to 0.949. Grade flips fall from 56.7% to 15.7% across all eight seeds. Source embeddings remain unchanged in this regime. The corresponding kappa gain is smaller for an already robust head, 0.009 versus 0.121. When lesion and control responses differ strongly, learned ungated transfer improves RMSE from 3.766 for direct subtraction to 1.662. These comparisons link the benefit of learned transfer to tissue-response differences and the downstream head’s sensitivity to acquisition shifts. 6 Scope and limitations Our evidence concerns embedding calibration and tissue-control availability. SCORPION provides aligned regions and physical-slide groups, but no patient identifiers, compartment annotations, or clinical grades. Its bootstrap intervals condition on the fitted models and development choices; public metadata also do not permit a complete audit of pretraining overlap. Acquisition coordinates may contain biological variation, and reduced source-feature displacement does not establish preservation of downstream predictions. The optional strict gate accepts no SCORPION corrections at this sample size; the reported real-scanner results therefore concern the ungated estimators. PAR control counts are an intermediate endpoint. Registration and matched-tumor requirements leave at most six eligible training patients, below the fixed ten-patient minimum, so no end-to-end PAR calibration or grading comparison was run. Control purity on PAR requires expert validation, and denser sampling yields spatially clustered fields. Synthetic stress tests show that agreement between control compartments does not protect against shared control drift or altered lesion responses. These findings identify the next validation priorities: expert-verified controls, patient-separated downstream evaluation, and assessment of correction decisions under broader acquisition changes. The method is intended for research use; its statistical screens do not provide clinical risk guarantees. 7 Conclusion A slide can supply information about how its own acquisition has changed its representation. 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The affine ridge in Equation 3 includes an unpenalized intercept. Its source examples use zero paired shift. Inner-fold transfer errors are projected Euclidean residuals ‖U⊤Δ−e^‖2\|U - e\|_2, averaged over regions within slide. For each permitted non-source scanner q, write the slide-mean error as E¯q E_q with sample standard deviation sqs_q over nqn_q slides. The training selection score is maxq(E¯q+1.6448536sq/nq), _q ( E_q+1.6448536\,s_q/ n_q ), with ties resolved by mean scanner error, worst-scanner material-worsening fraction, and smaller blend weight. Standardization and all fitted geometric components are rebuilt in each inner fold. Anchored estimator. Let G be the number of independent training groups, D the number of permitted domains including source, and J the number of regions per slide. Residual-regression weights give each group/domain equal total mass and sum to GDJGDJ. This fixes the normalization of the ridge penalties. For groups with several biopsies, each biopsy receives equal weight within its group; prototype matching retains all source regions. The source mean and scale, source-referenced basis, prototype bank, mean source-control anchor, pooled shift, and residual map are refitted in every inner split. Exact ties follow a fixed candidate ordering: identity, anchored global-only, then residual candidates in penalty-major order. The global shift is full-dimensional; only the residual is constrained to the acquisition subspace. The basis and source centering therefore differ from the original estimator. Global comparators. Pooled mean subtracts the mean paired shift over permitted non-source training scanners. Scanner mean uses a target scanner’s own training pairs when available and otherwise returns pooled mean. Affine ridge learns a regularized map from a query embedding to its source counterpart. Subspace shrinkage attenuates coordinates in a paired acquisition basis. Their hyperparameters are selected within training-only grouped folds. Paired source test regions provide evaluation references; all corrections use training-derived parameters and the query scan. Appendix B Complete scanner comparisons The same-slide increment accounts for 6.3–8.9% of learned transfer’s total distance reduction over raw embeddings. Unrelated same-scanner controls retain the remaining gain, separating the shared acquisition correction from the contribution of the current slide. Table 4: Additional baseline distances, completing Table 1. Encoder Protocol Pooled mean Direct controls Prost40M Calibrated 14.131 12.215 Holdout 15.940 13.837 DistillPath Calibrated 14.985 14.051 Holdout 15.840 14.770 Table 5: Learned transfer compared with global alternatives. Positive paired distance reductions favor learned transfer. Intervals use 5,000 paired physical-slide bootstrap resamples. Encoder Protocol Versus affine ridge Versus scanner mean Versus shrinkage Prost40M Calibrated −1.830-1.830 [−2.007,−1.649-2.007,-1.649] −.142-.142 [−.251,−.035-.251,-.035] 1.711 [1.565,1.865] Holdout −.576-.576 [−.739,−.411-.739,-.411] 2.069 [1.979,2.158] .930 [.792,1.082] DistillPath Calibrated .604 [.411,.798] −.038-.038 [−.091,.018-.091,.018] −.035-.035 [−.121,.052-.121,.052] Holdout .738 [.553,.922] 1.158 [1.101,1.219] .008 [−.064,.079-.064,.079] Table 6: Same-slide distance advantage over 32 wrong-slide assignments. Permutations are averaged before physical-slide resampling; the gain range describes variation across the 32 assignments. Encoder Protocol Learned, 95% CI Anchored, 95% CI Learned gain range Prost40M Calibrated .535 [.427,.641] .249 [.169,.325] .472–.591 Holdout .303 [.238,.369] .156 [.099,.213] .261–.348 DistillPath Calibrated .330 [.270,.392] .031 [.015,.047] .298–.367 Holdout .249 [.201,.299] .058 [.041,.075] .220–.277 Table 7: Top-1 retrieval accuracy (%) and material distance worsening (%). The worsening threshold is defined in Section 4. Top-1 retrieval accuracy Distance worsening Encoder Protocol Raw Learned Anchored Learned Anchored Prost40M Calibrated 93.91 99.74 99.84 1.77 1.15 Holdout 93.91 99.74 99.58 3.07 2.45 DistillPath Calibrated 99.79 100.00 99.95 1.77 1.35 Holdout 99.79 99.95 99.90 2.40 1.35 Appendix C Source-anchored refinement Table 8: Paired anchored-minus-learned changes. Positive target-distance change means less alignment; negative worsening-rate change is favorable. Rate changes are percentage points. Encoder Protocol Target distance, 95% CI Retrieval change, 95% CI Worsening change, 95% CI Prost40M Calibrated .560 [.466,.652] .104 [.000,.260] −.625-.625 [−1.094,−.260-1.094,-.260] Holdout .326 [.264,.389] −.156-.156 [−.521,.156-.521,.156] −.625-.625 [−1.302,.000-1.302,.000] DistillPath Calibrated .749 [.677,.822] −.052-.052 [−.156,.000-.156,.000] −.417-.417 [−.833,−.052-.833,-.052] Holdout .291 [.241,.344] −.052-.052 [−.156,.000-.156,.000] −1.042-1.042 [−1.562,−.573-1.562,-.573] Figure 5: External tissue-selector validation. Each patient’s complete field set has total weight one. (a) Row-normalized primary out-of-fold selection outcomes, including unassigned fields at the fixed 0.8 cutoff. (b) Precision and recall with 95% intervals from 2,000 patient bootstrap resamples; recall includes unassigned reference fields. (c) Benign precision and recall for the primary partition and all four post-result randomized partitions of the same 32 patients. The four additional partitions assess sensitivity to patient allocation. Table 9: Source-feature displacement and model selection. Counts refer to six unique fits per calibrated setting and 24 per holdout setting. Source means average 48 physical slides, each evaluated under one calibrated model or four holdout models. Source displacement Selected models Encoder Protocol Learned Anchored Global-only Residual Identity Prost40M Calibrated 3.562 1.861 0 6 0 Holdout 3.306 1.683 0 24 0 DistillPath Calibrated 2.365 .388 6 0 0 Holdout 2.248 .555 12 12 0 Every selected residual uses ridge penalty 100 and weight 0.25 or 0.5. The source-displacement means and physical-slide distributions in Figure 3 use the same evaluation units. Appendix D Tissue selection and PAR preparation External annotations and fitting. The external release contains 37 slides from 32 patients [2]. Benign labels cover whole glands, including lumen; the residual-stroma class is assigned by postprocessing remaining tissue. The selector uses 224-pixel inputs at 0.5 μ /pixel and adapts the native crop to each image’s recorded resolution. Training balances classes and patients within class; evaluation weights each patient’s complete field set to total one. Inner folds choose the inverse regularization strength C∈.01,.1,1,10C∈\.01,.1,1,10\ by minimizing out-of-fold log loss with equal class weight and equal patient weight within class. Scaling and all fitting are restricted to training patients. All five primary outer folds select C=1C=1. Among 327 out-of-fold benign selections, 301 have benign reference labels, 24 tumor labels, and two residual-stroma labels. Patient-weighted accuracy, counting unassigned fields as errors, is 95.96%. Four additional randomized patient partitions, specified after the primary results, assess sensitivity to patient allocation at the same cutoff. Their benign precision is 90.81–93.05% and recall is 84.62–88.37%. PAR uses the selector fitted under the primary protocol. Cohort and acquisition. The PAR cohort uses a deterministic patient ordering, excludes the two patients used to develop tissue-compartment extraction, and retains all biopsies and all three scanners for the selected 20 patients. Cohort selection uses no grading outcomes. Reference and dense sampling share the encoder, selector, cutoff, physical scale, and seed, with non-nested sampled locations. Thumbnail tissue fraction must be at least 0.55. Reference preparations are available for all 35 slides and dense preparations for 34; the unavailable dense preparation remains in all assigned-cohort denominators. Registration and joint eligibility. Registration uses 448 μ context, 12 local probes, normalized cross-correlation at least 0.45, maximum local shift 64 μ , common support at least 0.5, and cycle-consistency median/95th-percentile limits of 96/192 μ . Automated registration quality control approves 22 reference trios and 21 dense trios, with 13 rejected under each policy and one dense preparation unavailable. The 34 matched-policy slides have identical decisions. Among approved dense trios, four Grundium–Hamamatsu and eight each Grundium–Leica and Hamamatsu–Leica pairs lack four jointly selected tumor fields. These restrictions can overlap with missing controls. Table 10: Direction-specific calibration eligibility. Each fold assigns 16 training and four held-out patients. Eligibility requires both scans’ controls, approved registration, and four matched tumor fields. G: Grundium; H: Hamamatsu; L: Leica. Policy Direction Slides /35 Patients /20 Training patients, folds 0–4 Reference G→ 0 0 0, 0, 0, 0, 0 G→ 2 2 2, 2, 0, 2, 2 H→ 0 0 0, 0, 0, 0, 0 H→ 0 0 0, 0, 0, 0, 0 L→ 2 2 2, 2, 0, 2, 2 L→ 0 0 0, 0, 0, 0, 0 Dense G→ 5 4 3, 3, 2, 4, 4 G→ 5 5 4, 4, 3, 4, 5 H→ 5 4 3, 3, 2, 4, 4 H→ 3 3 2, 2, 2, 3, 3 L→ 5 5 4, 4, 3, 4, 5 L→ 3 3 2, 2, 2, 3, 3 Pooling at least one eligible target direction gives reference patient totals G/H/L of 2/0/2 and dense totals of 6/4/5. Dense pooled training counts in folds 0–4 are G: 5,5,3,5,6; H: 3,3,2,4,4; L: 4,4,3,4,5. Multiple biopsies from one patient contribute one patient to these counts. Table 11: Spatial clustering of selected controls. A nearby center is another selected center of the same class within 112 μ . The fraction measures spatial clustering of sampled fields. Policy Class Selected fields With nearby center Fraction Reference Benign gland 1,667 459 27.5% Residual stroma 25,729 12,213 47.5% Dense Benign gland 6,251 4,016 64.2% Residual stroma 100,660 86,688 86.1% Appendix E Two-compartment selective estimator The synthetic study uses a compartment-specific instantiation. For controls c∈b,sc∈\b,s\, compute aca_c by taking the coordinate-wise median over selected control tiles using a compartment-specific source bank. Subtract the coordinate-wise median source-control vector μc _c to obtain dc=ac−μcd_c=a_c- _c. The lesion target eme_m is the coordinate-wise median of projected registered lesion shifts. Two zero-intercept ridge maps predict eme_m: Rc=argmin∑mR‖em−Rdcm‖22+λ‖R‖F2,e^=12∑c∈b,s[(1−α)dc+αRcdc].R_c= _R _m\|e_m-Rd_cm\|_2^2+λ\|R\|_F^2, e= 12 _c∈\b,s\ [(1-α)d_c+α R_cd_c ]. The basis is constructed by centering each registered region across the permitted scanners, as in Equation 1. This experiment uses ridge penalty λ=0.5λ=0.5 and 21 blend weights α∈0,.05,…,1α∈\0,.05,…,1\. Patient-grouped out-of-fold selection minimizes non-source mean residual norm, then any-worsening rate, then blend weight. The two compartments, source-median centering, and zero-intercept maps define the instantiation used in these synthetic experiments. Write e^c=(1−α)dc+αRcdc e_c=(1-α)d_c+α R_cd_c for each compartment prediction. Selective correction requires sufficient controls; bounded dispersion and prototype-matching radius; supported joint control coordinates under Ledoit–Wolf covariance shrinkage [10]; and bounded disagreement ρ=‖e^b−e^s‖2‖e^b‖2+‖e^s‖2+ϵρ.ρ= \| e_b- e_s\|_2\| e_b\|_2+\| e_s\|_2+ _ρ. The denominator stabilizer is 0.1 times the median non-source target-shift norm, with a numerical lower bound. Prediction norms must exceed the maximum source prediction norm, computed out of fold during threshold selection and recomputed after refitting the transfer maps. Candidate thresholds maximize eligible non-source coverage subject to grouped gain and event-rate screens. An outer patient cross-fit repeats the complete procedure from supplied embeddings. If it fails, the fitted model returns identity for every slide; otherwise rejected slides return identity individually. Accepted candidate lesion tiles receive zj⋆=zj−Ue^z_j =z_j-U e. For gate selection, material worsening is an increase in projected residual norm exceeding 2% of the fitting set’s median non-source projected target norm. For binary group indicators HiH_i, let n be the number of evaluated groups and p^=n−1∑iHi p=n^-1 _iH_i. The one-sided 95% Wilson upper bound is [19] UW(p^,n)=p^+z2/(2n)+zp^(1−p^)/n+z2/(4n2)1+z2/n,z=1.6448536.U_ W( p,n)= p+z^2/(2n)+z p(1- p)/n+z^2/(4n^2)1+z^2/n, z=1.6448536. (8) The worsening screen uses patients with at least one accepted target scan; the source-correction screen uses all control-count-eligible source patients. The screens require the Wilson upper bounds for patient-any material worsening and patient-any source correction to be at most 5% and 2%, respectively, alongside nonnegative grouped lower alignment gain. Pooled and supplied domain-specific constraints are checked. At zero events, UW=z2/(n+z2)U_ W=z^2/(n+z^2) requires at least 52 groups for 5% and 133 for 2%. The separate SCORPION gate evaluates eight reserved validation slides using one region-control summary and a training-source prediction threshold, without the two-compartment disagreement test. Appendix F Controlled synthetic results The generator uses 48-dimensional embeddings, a rank-six acquisition process, three tissue compartments, and ordinal labels 0–5. Each scenario has eight seeds and 300 patients with a patient-disjoint 70/30 train/test split and 24 tiles per compartment; the 60- and 170-patient scenarios restrict paired calibration while source scaling, prototype banks, and ordinal-head fitting retain all 210 source-training patients. Let δm _m be the coordinate-wise median full-dimensional lesion target-minus-source difference for non-source scan m. Shift RMSE is M−1∑m=1M‖δm−δ^m‖22 M^-1 _m=1^M\| _m- δ_m\|_2^2, where δ^m δ_m is the applied correction. Worst-target QWK is the minimum over non-source scanners, computed over all simulated labels 0–5. Grade flips average disagreement over all unordered scanner pairs and all test slides, including the source scanner. Paired inference uses 10,000 seed-level percentile bootstrap replicates and exact two-sided sign-flip tests, with Holm adjustment over three comparisons. In the acquisition-sensitive regime, RMSE reduction and QWK gain each have adjusted p=0.03125p=0.03125. Source QWK is unchanged at 0.9976. Table 12: Complete synthetic regimes. Means include all eight seeds; rejection by the outer screen returns the raw embeddings. Cov.: mean correction coverage. Audit: seeds passing the outer screen. Shift RMSE Worst QWK Grade flip Regime Audit Raw Corrected Raw Corrected Raw Corrected Cov. Acquisition-sensitive 7/8 4.014 1.894 .828 .949 .567 .157 .804 Already robust head 7/8 4.031 1.893 .983 .993 .098 .038 .807 Unseen scanner 7/8 4.449 2.513 .790 .932 .617 .185 .753 Unseen, 1.5× range 7/8 6.673 5.925 .643 .729 .714 .479 .365 Matched tissue response 7/8 3.504 1.630 .865 .961 .555 .150 .813 Strong response gap 6/8 5.371 2.985 .739 .908 .624 .275 .686 60 calibration patients 0/8 4.014 4.014 .828 .828 .567 .567 .000 170 calibration patients 5/8 4.014 2.535 .828 .911 .567 .289 .565 With matched tissue response, direct and learned ungated transfer have similar RMSE, 0.964 and 0.962. With a strong response gap, their RMSEs are 3.766 and 1.662. In the acquisition-sensitive regime, learned transfer improves on direct subtraction by 0.794 (95% CI 0.627–1.002; adjusted p=0.0234p=0.0234). This isolates the benefit of learning tissue-dependent transfer in the controlled generator. Table 13: Synthetic stress tests in the acquisition-sensitive regime. Material worsening exceeds 2% of the corresponding clean test regime’s median raw non-source shift norm. Accepted worsening is conditional on acceptance and undefined at zero coverage. Means of conditional rates omit seeds with undefined rates. Stress Ungated worsening Coverage Accepted worsening One-control conflict .738 .000 – Concordant control drift .964 .037 .990 Morphology out of support .003 .000 – Novel acquisition direction .001 .000 – Insufficient controls .000 .000 – 25% selector contamination .001 .415 .000 Wrong-slide controls .697 .804 .692 Lesion-response mismatch .266 .804 .272