What Makes High-Magnification Knowledge Transferable? A Study of Cross-Resolution Distillation in Whole-Slide Imaging

Zhiyuan Yang; Jiahao Cheng; Mahdi S. Hosseini

Dataset	Metric	Slides/images	Group	Train / val. / test
CAM16	AUC	270	Slide	194 / 22 / 54
CAM17	Macro $F_{1}$	499	Challenge group	70 / 10 / 20
Private-CRC	Macro $F_{1}$	837	Slide	604 / 67 / 166
BRACS	Macro $F_{1}$	546	Patient	135 / 17 / 37
PANDA	Quadratic $\kappa$	10,615	Image	7645 / 847 / 2123
TCGA-KIRC	Case C-index	494	Case	337 / 52 / 101

Appendix

Table 5: Included datasets, observation counts and task partitions at seed 42. The Slides/images column gives the number of observations, while training, validation and test counts refer to the grouping unit in the preceding column. Slides or image identifiers do not establish patient independence. Higher values are better for every primary metric.

Figure 7: Token count and feature width jointly determine input size. The middle panel counts task tokens per complete region before recipient padding. The right panel counts their scalar coordinates, with the native base and appended prediction shown separately for augmentation. Individual teacher features

H

and repeated means

M^{16}

each use sixteen 1,536-coordinate tokens. The regional mean

M

and native

5\times

vector

X

each use one. Projected augmentation and augmentation in all feature channels deliver one token of width 3,072 and 8,448, respectively. The four summaries that retain every feature channel are concatenated within that token. These are derived representation dimensions, without measurements of memory use or runtime.

Dataset	Epochs	Learning rate	Decay	Accum.	Selection
CAM16	15	$.0004$	$.05$	16	Macro $F_{1}$
CAM17	15	$.0002$	$.01$	16	Macro $F_{1}$
Private-CRC	15	$.0002$	$.01$	16	Macro $F_{1}$
BRACS	15	$.0002$	$.01$	16	Macro $F_{1}$
PANDA	20	$.0004$	$.05$	16	Quadratic $\kappa$
KIRC	20	$.0001$	$.001$	1	Case C-index

Appendix

Table 6: Task training settings for the primary TransMIL comparisons. Decay is the AdamW weight decay, and accumulation counts slide batches per optimizer update. CAM16 selects checkpoints by validation macro

F_{1}

and reports test AUC. Other task models and encoder adaptation use the exceptions specified in their respective sections.

Figure 8: Broad spatial patterns capture variation beyond the regional mean. Each row summarizes the same 1,000 complete regions from each of ten datasets, with equal dataset weight, giving 10,000 regions and 160,000 patch vectors. The top row uses all 1,536 feature channels and the bottom row their 192-coordinate projection. Axes index horizontal and vertical DCT modes, not tissue positions. Zero is constant and larger indices represent faster changes. From left to right, panels show mean absolute coefficient magnitude, fractions of total squared energy, and fractions of nonconstant energy before and after patch permutation. Brighter colors indicate larger values within each scale. Magnitude colors use a base-ten log while cell labels retain the original values. Gray marks the removed DC component. The retained LF4 modes occupy the upper-left

2\times 2

block. These descriptive feature summaries motivate testing spatial targets for task benefit.

	$5\times$ input	$20\times$ teacher construction
Dataset / metric	Native $5\times$ $X$	Regional mean $M$	Repeated mean $M^{16}$	Individual $20\times$ $H$
Tokens per region	1	1	16	16
CAM16 / AUC	$0.8430\pm 0.0215$	$0.8993\pm 0.0118$	$0.8872\pm 0.0540$	$\mathbf{0.9047}\pm 0.0360$
CAM17 / $F_{1}$	$0.5054\pm 0.0612$	$0.4856\pm 0.0476$	$0.4904\pm 0.0456$	$\mathbf{0.5418}\pm 0.0593$
Private-CRC / $F_{1}$	$0.8273\pm 0.0332$	$0.8146\pm 0.0232$	$0.8290\pm 0.0365$	$\mathbf{0.8456}\pm 0.0419$
PANDA / $\kappa$	$0.8535\pm 0.0125$	$0.8660\pm 0.0159$	$0.8706\pm 0.0069$	$\mathbf{0.8726}\pm 0.0108$

Appendix

Table 7: Teacher content and token count have distinct task effects. TransMIL receives native

5\times

features, a regional

20\times

mean, sixteen copies of that mean, or the sixteen individual features from the same tissue regions. Teacher inputs require

20\times

images at evaluation and cover these regions rather than the full slide. Each score comes from a separate TransMIL fit without distillation. Full results for Table 2 are reported as mean

\pm

sample SD across five realizations.

Dataset	Native $5\times$ $[b_{i};0_{768}]$	Native $5\times$ + mean $[b_{i};\widetilde{m}_{i};0_{576}]$	Native $5\times$ + mean and spatial $[b_{i};\widetilde{m}_{i};s_{i}]$	Native $5\times$ + mean and direction control $[b_{i};\widetilde{m}_{i};s_{i}^{\rm rnd}]$
CAM16	$0.6110\!\pm\!0.1605$	$0.6717\!\pm\!0.3244$	$\mathbf{0.5663}\!\pm\!0.2296$	$0.5702\!\pm\!0.2110$
CAM17	$\mathbf{0.8392}\!\pm\!0.4304$	$0.8605\!\pm\!0.3460$	$1.0058\!\pm\!0.5968$	$0.9509\!\pm\!0.5255$
Private-CRC	$0.6230\!\pm\!0.0551$	$\mathbf{0.5563}\!\pm\!0.0356$	$0.6503\!\pm\!0.1546$	$0.6924\!\pm\!0.2528$
PANDA	$1.4584\!\pm\!0.5817$	$\mathbf{1.1328}\!\pm\!0.4491$	$1.3559\!\pm\!0.6075$	$1.4657\!\pm\!0.6855$
BRACS	$1.8613\!\pm\!0.5405$	$\mathbf{1.7576}\!\pm\!0.5130$	$1.8878\!\pm\!0.6489$	$1.9374\!\pm\!0.4963$
KIRC	$2.0562\!\pm\!0.4878$	$\mathbf{1.6173}\!\pm\!0.4347$	$1.7888\!\pm\!0.5891$	$1.6763\!\pm\!0.4250$

Appendix

Table 8: Task NLL for teacher summaries appended to the same native input. Lower is better. The reference is native

5\times

with zero padding. The direction control retains the teacher mean and component norms.

Dataset	Native $5\times$ $[b_{i};0_{768}]$	Native $5\times$ + mean $[b_{i};\widetilde{m}_{i};0_{576}]$	Native $5\times$ + mean and spatial $[b_{i};\widetilde{m}_{i};s_{i}]$	Native $5\times$ + mean and direction control $[b_{i};\widetilde{m}_{i};s_{i}^{\rm rnd}]$
CAM16	$0.8455\!\pm\!0.0485$	$0.8621\!\pm\!0.0600$	$\mathbf{0.8932}\!\pm\!0.0285$	$0.8662\!\pm\!0.0348$
CAM17	$0.5197\!\pm\!0.0336$	$\mathbf{0.5594}\!\pm\!0.0457$	$0.5198\!\pm\!0.0414$	$0.5297\!\pm\!0.0346$
Private-CRC	$0.8305\!\pm\!0.0276$	$\mathbf{0.8410}\!\pm\!0.0272$	$0.8305\!\pm\!0.0233$	$0.8263\!\pm\!0.0342$
PANDA	$0.8386\!\pm\!0.0067$	$0.8446\!\pm\!0.0124$	$\mathbf{0.8456}\!\pm\!0.0114$	$0.8357\!\pm\!0.0089$
BRACS	$0.4211\!\pm\!0.0710$	$0.4257\!\pm\!0.0783$	$0.4094\!\pm\!0.0704$	$\mathbf{0.4381}\!\pm\!0.0722$
KIRC	$0.6823\!\pm\!0.0548$	$0.6892\!\pm\!0.0470$	$0.6907\!\pm\!0.0435$	$\mathbf{0.6990}\!\pm\!0.0550$

Appendix

Table 9: Primary task scores for teacher summaries and their spatial direction control. Higher is better. The reference is native

5\times

with zero padding. The task metrics follow Table 1 .

Primary metric, higher is better
Dataset	Native $5\times$ $Z$	Teacher mean $M$	Teacher spatial $S$	Predicted mean $\widehat{M}$	Predicted spatial $\widehat{S}$	Initial spatial $I_{S}$
CAM16	$0.8722$ $\pm 0.0275$	$\mathbf{0.8955}$ $\pm 0.0126$	$0.8653$ $\pm 0.0389$	$0.8341$ $\pm 0.0620$	$0.8835$ $\pm 0.0272$	$0.8463$ $\pm 0.0226$
CAM17	$\mathbf{0.5261}$ $\pm 0.0418$	$0.5111$ $\pm 0.0505$	$0.5242$ $\pm 0.0357$	$0.4968$ $\pm 0.0308$	$0.5042$ $\pm 0.0407$	$0.5092$ $\pm 0.0425$
Private-CRC	$0.8284$ $\pm 0.0179$	$0.8097$ $\pm 0.0475$	$0.8313$ $\pm 0.0318$	$0.8209$ $\pm 0.0286$	$0.8258$ $\pm 0.0411$	$\mathbf{0.8345}$ $\pm 0.0274$
PANDA	$0.8467$ $\pm 0.0131$	$0.8566$ $\pm 0.0069$	$\mathbf{0.8608}$ $\pm 0.0089$	$0.8460$ $\pm 0.0119$	$0.8446$ $\pm 0.0139$	$0.8385$ $\pm 0.0160$
BRACS	$0.4276$ $\pm 0.0577$	$0.3966$ $\pm 0.0875$	$\mathbf{0.4414}$ $\pm 0.0755$	$0.4398$ $\pm 0.0827$	$0.4224$ $\pm 0.0871$	$0.4147$ $\pm 0.0525$

Appendix

Table 10: Task performance when all feature channels are retained. Every input contains the native base, with different teacher or neural summaries in the remaining coordinates. The reference is

Z=[b_{i};0_{6144}]

. The upper and lower panels report primary scores and NLL separately.

	Regional mean		Nonconstant components
Excluded dataset	Predictor	Constant	Predictor	Constant
CAM16	$\mathbf{0.3538}\!\pm\!0.0079$	$0.6935\!\pm\!0.0160$	$0.0730\!\pm\!0.0018$	$\mathbf{0.0563}\!\pm\!0.0012$
CAM17	$\mathbf{0.3461}\!\pm\!0.0107$	$0.6956\!\pm\!0.0149$	$0.0713\!\pm\!0.0018$	$\mathbf{0.0553}\!\pm\!0.0012$
Private-CRC	$\mathbf{0.3812}\!\pm\!0.0102$	$0.7227\!\pm\!0.0231$	$0.0752\!\pm\!0.0017$	$\mathbf{0.0555}\!\pm\!0.0008$
PANDA	$\mathbf{0.3565}\!\pm\!0.0070$	$0.7000\!\pm\!0.0179$	$0.0694\!\pm\!0.0019$	$\mathbf{0.0508}\!\pm\!0.0017$
BRACS	$\mathbf{0.3450}\!\pm\!0.0070$	$0.6702\!\pm\!0.0130$	$0.0718\!\pm\!0.0020$	$\mathbf{0.0556}\!\pm\!0.0015$

Appendix

Table 11: Reconstruction by the mean and spatial heads used downstream. MSE is evaluated on the groups used for checkpoint selection, with the constant equal to the training target mean for that component. Lower is better. Mean and spatial errors use their own scales.

Dataset	Metric	Repeated mean	Spatial summary	Permuted summary
CAM16	AUC	$\mathbf{0.8820}\!\pm\!0.0287$	$0.8716\!\pm\!0.0170$	$0.8730\!\pm\!0.0563$
CAM17	$F_{1}$	$\mathbf{0.5141}\!\pm\!0.0307$	$0.5038\!\pm\!0.0433$	$0.5126\!\pm\!0.0409$
Private-CRC	$F_{1}$	$\mathbf{0.8575}\!\pm\!0.0194$	$0.8491\!\pm\!0.0396$	$0.8455\!\pm\!0.0264$
PANDA	$\kappa$	$0.8569\!\pm\!0.0082$	$\mathbf{0.8609}\!\pm\!0.0118$	$0.8607\!\pm\!0.0110$
BRACS	$F_{1}$	$\mathbf{0.4319}\!\pm\!0.0873$	$0.4138\!\pm\!0.0936$	$0.4094\!\pm\!0.1125$
KIRC	C-index	$\mathbf{0.7163}\!\pm\!0.0448$	$0.6978\!\pm\!0.0569$	$0.7013\!\pm\!0.0607$

Appendix

Table 12: Task performance with three teacher summaries at a common input width of 8,448. Every input retains the native base and appends four vectors from the same observed

20\times

field. The repeated regional mean is the reference. Higher is better.

	TransMIL		Gated ABMIL		DSMIL		RRT-MIL
Dataset	Native $5\times$	Mean $20\times$	Native $5\times$	Mean $20\times$	Native $5\times$	Mean $20\times$	Native $5\times$	Mean $20\times$
CAM16	$0.9605$ $\pm 0.0240$	$\mathbf{0.9642}$ $\pm 0.0205$	$0.9537$ $\pm 0.0173$	$\mathbf{0.9705}$ $\pm 0.0128$	$0.9580$ $\pm 0.0036$	$\mathbf{0.9759}$ $\pm 0.0097$	$0.9494$ $\pm 0.0229$	$\mathbf{0.9682}$ $\pm 0.0073$
CAM17	$\mathbf{0.6743}$ $\pm 0.0552$	$0.6325$ $\pm 0.0212$	$\mathbf{0.6352}$ $\pm 0.0259$	$0.5690$ $\pm 0.0300$	$\mathbf{0.5522}$ $\pm 0.0537$	$0.5373$ $\pm 0.0712$	$\mathbf{0.6294}$ $\pm 0.0313$	$0.5992$ $\pm 0.0500$
Private-CRC	$0.8010$ $\pm 0.0317$	$\mathbf{0.8497}$ $\pm 0.0134$	$\mathbf{0.8288}$ $\pm 0.0250$	$0.8093$ $\pm 0.0262$	$0.8397$ $\pm 0.0114$	$\mathbf{0.8444}$ $\pm 0.0126$	$\mathbf{0.8443}$ $\pm 0.0123$	$0.8394$ $\pm 0.0347$
PANDA	$0.8509$ $\pm 0.0040$	$\mathbf{0.8630}$ $\pm 0.0089$	$0.8363$ $\pm 0.0038$	$\mathbf{0.8518}$ $\pm 0.0045$	$0.8612$ $\pm 0.0041$	$\mathbf{0.8833}$ $\pm 0.0085$	$0.8488$ $\pm 0.0050$	$\mathbf{0.8832}$ $\pm 0.0044$
BRACS	$0.3709$ $\pm 0.0319$	$\mathbf{0.4035}$ $\pm 0.0246$	$\mathbf{0.4141}$ $\pm 0.0530$	$0.3753$ $\pm 0.0155$	$\mathbf{0.4278}$ $\pm 0.0360$	$0.3490$ $\pm 0.0322$	$\mathbf{0.4603}$ $\pm 0.0303$	$0.4116$ $\pm 0.0282$

Appendix

Table 13: Native

5\times

and regional

20\times

mean inputs across downstream models. Each model uses its own native reference on the same tissue support. Higher is better. Five task initializations share one data split. DSMIL is evaluated only for classification and grading.

	Native $5\times$ $x_{i}$	Constant $\bar{m}_{\mathrm{train}}$	Direct $f_{\theta}(B)_{i}$		Residual $x_{i}+r_{\phi}(B)_{i}$
Dataset			Zero	Random	Zero	Random
CAM16	$0.1759$ $\pm 0.0103$	$0.0875$ $\pm 0.0079$	$\mathbf{0.0667}$ $\pm 0.0067$	$0.0686$ $\pm 0.0066$	$0.0935$ $\pm 0.0061$	$0.0972$ $\pm 0.0076$
CAM17	$0.1939$ $\pm 0.0044$	$0.0912$ $\pm 0.0038$	$\mathbf{0.0776}$ $\pm 0.0049$	$0.0801$ $\pm 0.0053$	$0.1064$ $\pm 0.0048$	$0.1100$ $\pm 0.0045$
Private-CRC	$0.1876$ $\pm 0.0162$	$\mathbf{0.1051}$ $\pm 0.0034$	$0.1331$ $\pm 0.0040$	$0.1551$ $\pm 0.0085$	$0.1675$ $\pm 0.0171$	$0.2017$ $\pm 0.0235$
PANDA	$0.1554$ $\pm 0.0067$	$\mathbf{0.0837}$ $\pm 0.0071$	$0.0988$ $\pm 0.0120$	$0.1088$ $\pm 0.0112$	$0.1231$ $\pm 0.0107$	$0.1364$ $\pm 0.0106$
BRACS	$0.1882$ $\pm 0.0094$	$0.1099$ $\pm 0.0080$	$\mathbf{0.0936}$ $\pm 0.0082$	$0.0941$ $\pm 0.0089$	$0.1102$ $\pm 0.0065$	$0.1175$ $\pm 0.0074$

Appendix

Table 14: Raw regional mean MSE on independent test fields from the excluded dataset. Native

5\times

is the reference. Zero and random identify final-layer initialization. The constant

\bar{m}_{\mathrm{train}}

is estimated from distillation training targets.

Zero final-layer initialization
	Direct		Residual
Dataset	Permuted	Aligned	Permuted	Aligned
CAM16	$0.1205\!\pm\!0.0136$	$\mathbf{0.0667}\!\pm\!0.0067$	$0.1652\!\pm\!0.0131$	$\mathbf{0.0935}\!\pm\!0.0061$
CAM17	$0.1216\!\pm\!0.0037$	$\mathbf{0.0776}\!\pm\!0.0049$	$0.1733\!\pm\!0.0039$	$\mathbf{0.1064}\!\pm\!0.0048$
Private-CRC	$0.1496\!\pm\!0.0041$	$\mathbf{0.1331}\!\pm\!0.0040$	$0.2475\!\pm\!0.0130$	$\mathbf{0.1675}\!\pm\!0.0171$
PANDA	$0.1145\!\pm\!0.0105$	$\mathbf{0.0988}\!\pm\!0.0120$	$0.1769\!\pm\!0.0123$	$\mathbf{0.1231}\!\pm\!0.0107$

Appendix

Table 15: Raw regional mean MSE with aligned or permuted input tuples. The native vector, slide context and residual skip are permuted together. Permuted input is the reference within each prediction form.

MSE $\downarrow$
	Native $5\times$	Direct		Residual
Dataset	$x_{i}$	Initial	Trained	Initial	Trained
CAM16	$0.1759\!\pm\!0.0103$	$0.1206\!\pm\!0.0108$	$\mathbf{0.0686}\!\pm\!0.0066$	$0.1998\!\pm\!0.0116$	$0.0972\!\pm\!0.0076$
CAM17	$0.1939\!\pm\!0.0044$	$0.1231\!\pm\!0.0032$	$\mathbf{0.0801}\!\pm\!0.0053$	$0.2183\!\pm\!0.0045$	$0.1100\!\pm\!0.0045$
Private-CRC	$0.1876\!\pm\!0.0162$	$0.1574\!\pm\!0.0042$	$\mathbf{0.1551}\!\pm\!0.0085$	$0.2322\!\pm\!0.0128$	$0.2017\!\pm\!0.0235$
PANDA	$0.1554\!\pm\!0.0067$	$0.1183\!\pm\!0.0069$	$\mathbf{0.1088}\!\pm\!0.0112$	$0.1855\!\pm\!0.0056$	$0.1364\!\pm\!0.0106$

Appendix

Table 16: Feature matching before and after distillation in the original 1,536 coordinates. Both predictors use random final-layer initialization. Native

5\times

is the reference for MSE and correlation of pairwise distances. Variance ratios are descriptive, with teacher variation equal to one.

	Centered variance ratio		Pearson correlation of pairwise distances $\uparrow$
Dataset	Direct	Residual	Native $5\times$	Direct	Residual
CAM16	$0.6997$ $\pm 0.0473$	$1.4150$ $\pm 0.0391$	$0.7720$ $\pm 0.0334$	$\mathbf{0.8896}$ $\pm 0.0140$	$0.8530$ $\pm 0.0245$
CAM17	$0.4978$ $\pm 0.0326$	$1.1662$ $\pm 0.0634$	$0.5915$ $\pm 0.0561$	$\mathbf{0.7465}$ $\pm 0.0289$	$0.6338$ $\pm 0.0564$
Private-CRC	$0.6253$ $\pm 0.0463$	$2.3830$ $\pm 0.1137$	$0.6855$ $\pm 0.0434$	$\mathbf{0.8169}$ $\pm 0.0282$	$0.6917$ $\pm 0.0423$
PANDA	$0.4742$ $\pm 0.0388$	$1.6700$ $\pm 0.1179$	$0.5973$ $\pm 0.0506$	$\mathbf{0.7908}$ $\pm 0.0294$	$0.6611$ $\pm 0.0397$
BRACS	$0.4876$ $\pm 0.0291$	$1.3241$ $\pm 0.0862$	$0.6206$ $\pm 0.0424$	$\mathbf{0.7543}$ $\pm 0.0411$	$0.6962$ $\pm 0.0524$

Appendix

Table 17: Variation and target geometry after training from a zero output layer. Centered variance is divided by teacher variance, with one indicating equal total variation rather than an optimum. Pearson correlation compares pairwise distances between regions in the output and target spaces. Native

5\times

is its reference. The five realizations use independent test fields from the excluded dataset, whereas the feature maps illustrate one slide and one realization.

Dataset	Regions	Native $x_{i}$	Direct $f_{\theta}(B)_{i}$	Residual $x_{i}+r_{\phi}(B)_{i}$
CAM16	128	$0.1571$	$\mathbf{0.0516}$	$0.0821$
CAM17	135	$0.2518$	$\mathbf{0.1360}$	$0.1641$
Private-CRC	149	$0.2346$	$\mathbf{0.1278}$	$0.1978$
PANDA	52	$0.1463$	$\mathbf{0.1044}$	$0.1232$
BRACS	134	$0.1429$	$\mathbf{0.0761}$	$0.0889$
KIRC	128	$0.1697$	$\mathbf{0.0902}$	$0.0942$

Appendix

Table 18: Reconstruction error for the exact regions in the feature maps. Native features are the reference. Each entry is MSE over one displayed test slide and one trained model with zero final-layer initialization. Errors use the original 1,536 coordinates and equal weight per region. These are individual illustrative cases, without aggregation across training seeds. Lower is better.

Figure 9: Teacher correspondence in Private-CRC. Direct and residual predictions for all 149 cached regions of one test slide. Some residual outputs remain near the native reference distribution while their corresponding teacher targets occupy different neighborhoods. Colors and connections follow Figure 4 . Table 18 reports errors for these exact regions.

Figure 10: Teacher correspondence in PANDA. Direct and residual predictions for all 52 cached regions of one test slide. Direct outputs form a compact group near teacher means, while residual outputs also extend toward native neighborhoods. Colors and connections follow Figure 4 . Table 18 reports errors for these exact regions.

Figure 11: Teacher correspondence in BRACS. Direct and residual predictions for all 134 cached regions of one test slide. Direct outputs concentrate near central teacher neighborhoods, while residual outputs extend across more of the displayed target distribution. Colors and connections follow Figure 4 . Table 18 reports errors for these exact regions.

Figure 12: Teacher correspondence in TCGA-LUAD. Direct and residual predictions for all 128 cached regions of one test slide. Both prediction forms overlap teacher neighborhoods, but the residual outputs show a broader spread in this view. Colors and connections follow Figure 4 . Table 18 reports errors for these exact regions.

Figure 13: Teacher correspondence in TCGA-STAD. Direct and residual predictions for all 154 cached regions of one test slide. Both prediction forms approach the lower teacher neighborhoods, while direct outputs retain less variation in the original coordinates. Colors and connections follow Figure 4 . Table 18 reports errors for these exact regions.

Figure 14: Teacher correspondence in TCGA-UCEC. Direct and residual predictions for all 160 cached regions of one test slide. Residual outputs extend across the right teacher neighborhoods more broadly than direct outputs, yet direct prediction has lower target MSE. Colors and connections follow Figure 4 . Table 18 reports errors for these exact regions.

A. Independent evaluation within distillation datasets
	Regional mean		Spatial components
Excluded dataset	Constant	Network	Constant	Network
CAM16	$0.6361\!\pm\!0.0305$	$\mathbf{0.3648}\!\pm\!0.0173$	$\mathbf{0.0524}\!\pm\!0.0022$	$0.0697\!\pm\!0.0031$
CAM17	$0.6665\!\pm\!0.0335$	$\mathbf{0.3702}\!\pm\!0.0219$	$\mathbf{0.0527}\!\pm\!0.0025$	$0.0676\!\pm\!0.0021$
Private-CRC	$0.6851\!\pm\!0.0567$	$\mathbf{0.4007}\!\pm\!0.0191$	$\mathbf{0.0527}\!\pm\!0.0010$	$0.0698\!\pm\!0.0019$
PANDA	$0.6592\!\pm\!0.0310$	$\mathbf{0.3775}\!\pm\!0.0188$	$\mathbf{0.0487}\!\pm\!0.0011$	$0.0662\!\pm\!0.0023$

Appendix

Table 19: MSE for regional mean and spatial components. The constant is the reference within each component. Panel A evaluates independent groups from the distillation datasets, and Panel B evaluates the excluded dataset. Neither population selects predictors.

Independent evaluation within distillation datasets
	Regional mean		Spatial components
Excluded dataset	Base	Corrected	Base	Corrected
CAM16	$0.3648\!\pm\!0.0173$	$\mathbf{0.3401}\!\pm\!0.0199$	$0.0697\!\pm\!0.0031$	$\mathbf{0.0696}\!\pm\!0.0034$
CAM17	$0.3702\!\pm\!0.0219$	$\mathbf{0.3361}\!\pm\!0.0156$	$0.0676\!\pm\!0.0021$	$\mathbf{0.0665}\!\pm\!0.0019$
Private-CRC	$0.4007\!\pm\!0.0191$	$\mathbf{0.3748}\!\pm\!0.0152$	$0.0698\!\pm\!0.0019$	$\mathbf{0.0694}\!\pm\!0.0023$
PANDA	$0.3775\!\pm\!0.0188$	$\mathbf{0.3532}\!\pm\!0.0097$	$0.0662\!\pm\!0.0023$	$\mathbf{0.0659}\!\pm\!0.0031$

Appendix

Table 20: Absolute component MSE before and after neural error correction. The base predictor is the reference within each component. Spatial MSE averages three equally sized components. Neither evaluation population determines the selected predictors.

Dataset	Metric	$[B;0]$	$[B;M]$	Global input	Spatial input
CAM16	AUC	$0.8455\!\pm\!0.0485$	$\mathbf{0.8935}\!\pm\!0.0635$	$0.8729\!\pm\!0.0384$	$0.8516\!\pm\!0.0515$
CAM17	$F_{1}$	$0.5197\!\pm\!0.0336$	$0.5158\!\pm\!0.0700$	$0.5144\!\pm\!0.0381$	$\mathbf{0.5275}\!\pm\!0.0310$
Private-CRC	$F_{1}$	$0.8305\!\pm\!0.0276$	$\mathbf{0.8378}\!\pm\!0.0267$	$0.8277\!\pm\!0.0228$	$0.8276\!\pm\!0.0367$
PANDA	$\kappa$	$0.8386\!\pm\!0.0067$	$\mathbf{0.8601}\!\pm\!0.0137$	$0.8387\!\pm\!0.0124$	$0.8330\!\pm\!0.0062$
BRACS	$F_{1}$	$\mathbf{0.4211}\!\pm\!0.0710$	$0.4168\!\pm\!0.0542$	$0.4178\!\pm\!0.0575$	$0.4125\!\pm\!0.0856$
KIRC	C-index	$0.6823\!\pm\!0.0548$	$0.6879\!\pm\!0.0586$	$0.6876\!\pm\!0.0718$	$\mathbf{0.7186}\!\pm\!0.0538$

Appendix

Table 21: Task performance when a common native

5\times

base receives zeros, the teacher mean or a prediction from global or spatial input. Zero augmentation is the reference. The teacher mean requires

20\times

features during evaluation.

Figure 15: Spatial and global input for a common regional mean target. Horizontal position is

100(\mathrm{MSE}_{\rm global}-\mathrm{MSE}_{\rm spatial})/\mathrm{MSE}_{\rm global}

. Vertical position is the spatial minus global task score. Circles show individual realizations and diamonds show their mean. Positive values favor spatial input on each axis.

Dataset / metric	Native $5\times$ Zero augmentation	Native $5\times$ Initial prediction	Native $5\times$ Trained mean + spatial	Native $5\times$ Same trained mean
CAM16 / AUC	$\mathbf{0.9770}\!\pm\!0.0129$	$0.9625\!\pm\!0.0308$	$0.9589\!\pm\!0.0293$	$0.9487\!\pm\!0.0315$
CAM17 / $F_{1}$	$0.6300\!\pm\!0.0294$	$0.6397\!\pm\!0.0262$	$\mathbf{0.6462}\!\pm\!0.0445$	$0.6079\!\pm\!0.0719$
Private-CRC / $F_{1}$	$0.8244\!\pm\!0.0482$	$\mathbf{0.8462}\!\pm\!0.0154$	$0.8426\!\pm\!0.0312$	$0.8238\!\pm\!0.0383$
PANDA / $\kappa$	$0.8425\!\pm\!0.0121$	$0.8489\!\pm\!0.0149$	$0.8430\!\pm\!0.0103$	$\mathbf{0.8508}\!\pm\!0.0132$
BRACS / $F_{1}$	$0.4141\!\pm\!0.0340$	$0.4336\!\pm\!0.0714$	$0.4321\!\pm\!0.0780$	$\mathbf{0.4570}\!\pm\!0.0587$
KIRC / C-index	$0.7017\!\pm\!0.0456$	$0.7104\!\pm\!0.0127$	$\mathbf{0.7151}\!\pm\!0.0277$	$0.7026\!\pm\!0.0395$

Appendix

Table 22: Task scores after omitting projected spatial predictions on unrestricted native bags. Every input retains the native UNI2-h and DINOv3 base and has 3,072 coordinates. Native input with zero augmentation is the reference. Higher is better.

Figure 16: Reconstruction error need not rank task performance. Small marks show five realizations and large marks their means. Positive differences favor residual prediction in both panels. Reconstruction uses direct minus residual MSE on historical downstream training fields from datasets excluded from distillation. Task performance uses residual minus direct test score multiplied by 100 in each named metric. Table 23 reports absolute task scores.

Dataset / metric	Native $5\times$	Direct Zero init.	Residual Zero init.	Direct Random init.	Residual Random init.
CAM16 / AUC	$0.9494\!\pm\!0.0198$	$0.9142\!\pm\!0.0422$	$\mathbf{0.9638}\!\pm\!0.0244$	$0.9224\!\pm\!0.0464$	$0.9440\!\pm\!0.0417$
CAM17 / $F_{1}$	$0.6093\!\pm\!0.0556$	$0.6116\!\pm\!0.0857$	$0.6081\!\pm\!0.0385$	$0.6069\!\pm\!0.0683$	$\mathbf{0.6231}\!\pm\!0.0494$
Private-CRC / $F_{1}$	$0.8432\!\pm\!0.0198$	$0.8249\!\pm\!0.0179$	$\mathbf{0.8504}\!\pm\!0.0142$	$0.8412\!\pm\!0.0258$	$0.8499\!\pm\!0.0239$
PANDA / $\kappa$	$0.8496\!\pm\!0.0089$	$0.8281\!\pm\!0.0203$	$\mathbf{0.8542}\!\pm\!0.0116$	$0.8154\!\pm\!0.0175$	$0.8486\!\pm\!0.0104$
BRACS / $F_{1}$	$0.4170\!\pm\!0.0527$	$0.4337\!\pm\!0.0907$	$\mathbf{0.4493}\!\pm\!0.0443$	$0.4068\!\pm\!0.0790$	$0.3620\!\pm\!0.0708$
KIRC / C-index	$0.7007\!\pm\!0.0279$	$\mathbf{0.7082}\!\pm\!0.0250$	$0.6906\!\pm\!0.0407$	$0.6909\!\pm\!0.0458$	$0.7047\!\pm\!0.0423$

Appendix

Table 23: Task scores for native

5\times

features and standalone predictions of the regional

20\times

mean. Each input has 1,536 coordinates. Zero and random specify final-layer initialization before distillation. Native

5\times

input is the reference. Higher is better.

Figure 17: Native retention changes task results for unchanged predictions. Upper panels show 100 times the primary score for

[x_{i};q_{i}]

minus

[0;q_{i}]

. Lower panels show NLL for

[0;q_{i}]

minus

[x_{i};q_{i}]

. Positive values favor retention. Columns distinguish prediction forms, while circles and triangles distinguish zero and random final-layer initialization. All predictors are trained. Small marks show five corresponding task differences and large marks their means. Appendix E.5 reports absolute scores.

Zero final-layer initialization before distillation
Dataset / metric	Native $5\times$ $[x_{i};0_{d}]$	Direct $[0_{d};q_{i}^{D}]$	Direct + native $[x_{i};q_{i}^{D}]$	Residual $[0_{d};q_{i}^{R}]$	Residual + native $[x_{i};q_{i}^{R}]$
CAM16 / AUC	$0.9669\!\pm\!0.0183$	$0.9415\!\pm\!0.0306$	$0.9450\!\pm\!0.0290$	$0.9486\!\pm\!0.0556$	$\mathbf{0.9672}\!\pm\!0.0146$
CAM17 / $F_{1}$	$0.6080\!\pm\!0.0327$	$0.5934\!\pm\!0.0464$	$\mathbf{0.6248}\!\pm\!0.0339$	$0.5852\!\pm\!0.0608$	$0.6161\!\pm\!0.0505$
Private-CRC / $F_{1}$	$\mathbf{0.8391}\!\pm\!0.0337$	$0.8159\!\pm\!0.0438$	$0.8063\!\pm\!0.0511$	$0.8370\!\pm\!0.0227$	$0.8346\!\pm\!0.0326$
PANDA / $\kappa$	$\mathbf{0.8517}\!\pm\!0.0221$	$0.8251\!\pm\!0.0155$	$0.8496\!\pm\!0.0122$	$0.8445\!\pm\!0.0122$	$0.8471\!\pm\!0.0184$
BRACS / $F_{1}$	$0.3809\!\pm\!0.1116$	$0.3987\!\pm\!0.0517$	$\mathbf{0.4323}\!\pm\!0.1115$	$0.4268\!\pm\!0.0741$	$0.4118\!\pm\!0.0515$

Appendix

Table 24: Task scores with the same trained prediction and either a zero or retained native block. All inputs have 3,072 coordinates. The matched native

5\times

reference

[x_{i};0_{d}]

is reused across panels. Higher is better.

Zero final-layer initialization before distillation
Dataset	Native $5\times$ $[x_{i};0_{d}]$	Direct $[0_{d};q_{i}^{D}]$	Direct + native $[x_{i};q_{i}^{D}]$	Residual $[0_{d};q_{i}^{R}]$	Residual + native $[x_{i};q_{i}^{R}]$
CAM16	$\mathbf{0.2610}\!\pm\!0.0953$	$0.3580\!\pm\!0.1922$	$0.2924\!\pm\!0.1396$	$0.3253\!\pm\!0.1347$	$0.3048\!\pm\!0.1512$
CAM17	$0.6529\!\pm\!0.2769$	$0.9189\!\pm\!0.3316$	$\mathbf{0.6241}\!\pm\!0.3428$	$0.7350\!\pm\!0.4200$	$0.6791\!\pm\!0.2495$
Private-CRC	$0.6192\!\pm\!0.0378$	$0.5823\!\pm\!0.1906$	$0.5690\!\pm\!0.0727$	$0.5371\!\pm\!0.0869$	$\mathbf{0.5297}\!\pm\!0.1282$
PANDA	$1.2043\!\pm\!0.4426$	$1.0014\!\pm\!0.0692$	$\mathbf{0.9764}\!\pm\!0.0898$	$1.5970\!\pm\!0.7405$	$1.1580\!\pm\!0.2178$
BRACS	$1.5287\!\pm\!0.6716$	$1.5428\!\pm\!0.3129$	$1.4855\!\pm\!0.5011$	$1.5966\!\pm\!0.4032$	$\mathbf{1.4386}\!\pm\!0.3485$

Appendix

Table 25: Task NLL with the same trained prediction and either a zero or retained native block. All inputs have 3,072 coordinates. The matched native

5\times

reference

[x_{i};0_{d}]

is reused across panels. Lower is better.

Dataset / metric	Frozen UNI2-h	Mean KD Encoder	Mean KD Mean head	Mean KD + flow Regional mean	Mean KD + flow Individual feature
CAM16 / AUC	$0.8808\!\pm\!0.0568$	$0.8734\!\pm\!0.0787$	$\mathbf{0.8982}\!\pm\!0.0548$	$0.8827\!\pm\!0.0775$	$0.8749\!\pm\!0.0768$
CAM17 / $F_{1}$	$0.5025\!\pm\!0.0435$	$0.5115\!\pm\!0.0539$	$\mathbf{0.5403}\!\pm\!0.0355$	$0.5077\!\pm\!0.0423$	$0.5211\!\pm\!0.0606$
Private-CRC / $F_{1}$	$0.8411\!\pm\!0.0262$	$0.8353\!\pm\!0.0509$	$0.8353\!\pm\!0.0408$	$0.8225\!\pm\!0.0434$	$\mathbf{0.8492}\!\pm\!0.0282$
PANDA / $\kappa$	$0.8499\!\pm\!0.0155$	$\mathbf{0.8519}\!\pm\!0.0131$	$0.8458\!\pm\!0.0117$	$0.8496\!\pm\!0.0122$	$0.8495\!\pm\!0.0067$
BRACS / $F_{1}$	$0.4589\!\pm\!0.0541$	$0.4331\!\pm\!0.0477$	$\mathbf{0.4608}\!\pm\!0.0606$	$0.4204\!\pm\!0.0339$	$0.4347\!\pm\!0.0363$
KIRC / C-index	$0.7321\!\pm\!0.0407$	$0.7206\!\pm\!0.0176$	$0.7186\!\pm\!0.0451$	$\mathbf{0.7378}\!\pm\!0.0176$	$0.7069\!\pm\!0.0332$

Appendix

Table 26: Task scores from frozen UNI2-h, the mean-KD encoder and its prediction head, and encoders trained with mean KD plus flow supervision. Every readout has 1,536 coordinates on the same sampled

5\times

patches. Published frozen UNI2-h is the reference. Higher is better.

Dataset / metric	Flow toward regional mean	Flow toward individual feature
CAM16 / AUC	$\mathbf{0.8598}\!\pm\!0.0900$	$0.8538\!\pm\!0.0921$
CAM17 / $F_{1}$	$0.5468\!\pm\!0.0535$	$\mathbf{0.5549}\!\pm\!0.1129$
Private-CRC / $F_{1}$	$\mathbf{0.8889}\!\pm\!0.0303$	$0.8800\!\pm\!0.0367$
PANDA / $\kappa$	$\mathbf{0.8709}\!\pm\!0.0114$	$0.8691\!\pm\!0.0136$
BRACS / $F_{1}$	$0.4201\!\pm\!0.0934$	$\mathbf{0.4333}\!\pm\!0.0992$
KIRC / C-index	$0.6957\!\pm\!0.0499$	$\mathbf{0.6965}\!\pm\!0.0566$

Appendix

Table 27: Validation task scores at the selected downstream checkpoints. Both encoders retain mean KD. Regional-mean flow is the reference for individual-feature flow. Higher is better.

What Makes High-Magnification Knowledge Transferable? A Study of Cross-Resolution Distillation in Whole-Slide Imaging

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