Most Colon Grading Mistakes Are Neighbors: Adjacent-Grade Error Shares and Grade-3 Recall on Public Histopathology Embeddings

1. Introduction

Histological grade for colorectal adenocarcinoma is not a balanced three-way quiz. Well-, moderately, and poorly differentiated tumors sit on a morphological continuum, Grade 3 is usually the minority class on curated patch sets, and missing poorly differentiated disease is not clinically interchangeable with confusing Grade 1 and Grade 2 [1,2,3]. Yet grading CAD abstracts still often lead with a single accuracy or macro-F1 number that pools those events.

Public patch corpora such as LC25000 made binary colon detection easy to reproduce [4]. Fine-grained grading is harder: class imbalance, adjacent morphology, and frozen-embedding limits all show up once the task leaves the binary table [5,6]. Reporting guidance for early AI decision support already asks authors to name the error that matters and the intended use [7,8]. The gap this paper fills is narrower. It takes a fixed public embedding bank for 560 graded colon patches, recomputes stratified five-fold classification, and writes down how many mistakes are neighbors versus Grade 3→Grade 1 jumps.

No new slides were scanned here. The contribution is a checkable error anatomy: adjacent-grade share, Grade 3 recall, and a short argument that those two statistics should travel with pooled accuracy. A published two-stage colon pipeline supplies the embedding protocol and an ensemble confusion-matrix anchor [9]; the calculations below concern the grading stage only.

2. Materials and Methods

We use 560 colorectal adenocarcinoma patches with pathologist-assigned grades stored with 2,048-dimensional ResNet50 (ImageNet) penultimate activations [4,10]. Class counts are Grade 1 $n=251$ (44.8%), Grade 2 $n=210$ (37.5%), and Grade 3 $n=99$ (17.7%). Filenames in the embedding table correspond to 20× tiles; multi-magnification stratification is out of scope for this reanalysis. Binary detection results on the larger LC25000-derived colon set are not recomputed here; prior work already shows near-ceiling detection on that corpus [9,11,12].

Features were standardized inside each training fold. An RBF-kernel support vector machine (SVM) was trained under stratified five-fold cross-validation (shuffle seed 42). Metrics are accuracy, macro-F1, and per-grade precision, recall, and F1. Out-of-fold predictions supply one confusion matrix for adjacent-error accounting. Adjacent errors are defined as $|\mathrm{true}-\mathrm{pred}|=1$ on the ordered labels $\{1,2,3\}$; non-adjacent errors are Grade 1↔Grade 3 swaps. As an external published reference—not re-trained here—we also decompose the soft-voting ensemble confusion matrix reported for the same 560-patch grading task [9]. That matrix is used only to test whether adjacent dominance is an SVM-only artifact.

We treat Grade 3 recall and adjacent-error share as primary reporting statistics. Pooled accuracy remains in the tables because readers expect it; it is not treated as a release summary. An illustrative relative-cost scale (adjacent G1↔G2 $=1$, adjacent G2↔G3 $=2$, non-adjacent G3→G1 $=5$) is used only in discussion to make asymmetry concrete. Those weights are author-chosen discussion devices, not surveyed clinical utilities [3,8].

3. Results

3.1. Per-Grade Recall Under Cross-Validation

Five-fold CV accuracy is $73.6\%\pm 2.9\%$ with macro-F1 $0.705$. Per-grade recall is 0.865 (Grade 1), 0.705 (Grade 2), and 0.475 (Grade 3). Grade 3 precision is high (0.887) because the model rarely predicts Grade 3; when it does, it is often correct, but it misses more than half of true Grade 3 patches (52 of 99). Figure 1 shows the class imbalance next to those recalls. Table 1 records the full per-grade profile.

Table 1. Per-grade SVM performance under stratified five-fold cross-validation on 560 public embeddings.

Grade	Support	Precision	Recall	F1
Grade 1	251	0.719	0.865	0.785
Grade 2	210	0.722	0.705	0.713
Grade 3	99	0.887	0.475	0.618
Macro avg	560	0.776	0.682	0.705

Table 1. Per-grade SVM performance under stratified five-fold cross-validation on 560 public embeddings.

Grade	Support	Precision	Recall	F1
Grade 1	251	0.719	0.865	0.785
Grade 2	210	0.722	0.705	0.713
Grade 3	99	0.887	0.475	0.618
Macro avg	560	0.776	0.682	0.705

Figure 1. Grade distribution on the 560-patch set (left) and per-grade recall under five-fold CV SVM (right). The dashed line marks an arbitrary 0.70 discussion bar for Grade 3 recall.

Figure 1. Grade distribution on the 560-patch set (left) and per-grade recall under five-fold CV SVM (right). The dashed line marks an arbitrary 0.70 discussion bar for Grade 3 recall.

3.2. Adjacent-Grade Dominance

The out-of-fold confusion matrix is shown in Figure 2 and Table 2. Of 148 errors, 119 ($80.4\%$) are adjacent-grade swaps and 29 ($19.6\%$) are non-adjacent Grade 3→Grade 1 calls. No Grade 1 patch was predicted as Grade 3 in the CV predictions. Most Grade 3 misses land on Grade 1 (29) or Grade 2 (23).

Table 2. Out-of-fold SVM confusion counts (rows: true grade; columns: predicted).

True \ Pred	G1	G2	G3
G1	217	34	0
G2	56	148	6
G3	29	23	47

Table 2. Out-of-fold SVM confusion counts (rows: true grade; columns: predicted).

True \ Pred	G1	G2	G3
G1	217	34	0
G2	56	148	6
G3	29	23	47

Figure 2. Five-fold CV SVM confusion matrix on 560 graded colon patches.

Figure 2. Five-fold CV SVM confusion matrix on 560 graded colon patches.

The published ensemble confusion matrix for the same patch set shows 107 total errors, of which 92 ($86.0\%$) are adjacent and 15 ($14.0\%$) are non-adjacent [9]. Figure 3 compares those shares. Soft voting improves Grade 3 recall in the source report, but it does not erase adjacent-grade structure: residual mistakes remain mostly neighbors on the differentiation spectrum [1,2].

3.3. What Pooled Accuracy Hides

A 73.6% accuracy headline is compatible with Grade 3 recall below 0.50. Macro-F1 (0.705) softens the minority miss but still does not separate adjacent swaps from Grade 3→Grade 1 jumps. Under the illustrative cost scale in Figure 4, the 29 non-adjacent CV misses receive five times the weight of a G1↔G2 swap; those 29 events alone outweigh dozens of adjacent mistakes if the weighted sum is the decision statistic. Committees need not adopt these particular weights, but they should choose some Grade 3-aware accounting rather than treating every off-diagonal cell as equal [3,8].

4. Discussion

Adjacent-grade dominance is expected under a continuous differentiation spectrum, and it is still useful to quantify. An 80–86% adjacent share means most residual CAD mistakes look like disagreements pathologists already negotiate along the Grade 2 boundary, while the non-adjacent remainder is the sharper safety signal [1,13]. Reporting only pooled accuracy hides both facts: how often the model is “almost right,” and how often it is wrong in the costly direction.

The Grade 3 recall of 0.475 under CV SVM fails any reasonably strict minority gate near 0.70. That failure is not rescued by Grade 3 precision of 0.887. A model that rarely predicts Grade 3 can look precise while still missing poorly differentiated tiles. Binary colon detectors on LC25000-style data can approach ceiling performance [11,12]; grading does not inherit that ease. Foundation-model embeddings and weakly supervised whole-slide methods may change the absolute numbers [14,15], but they do not remove the need to publish minority recall and adjacency structure.

Limits are straightforward. The 560 patches are public research tiles, not a multi-site whole-slide cohort; all graded embeddings used here are 20×; the SVM and fold seed are specific; and the cost weights in Figure 4 are illustrative. The ensemble matrix is cited from a published source and was not re-fit in this notebook [9]. Replication should keep the adjacent/non-adjacent split visible even if a stronger backbone raises Grade 3 recall.

5. Conclusions

On these public embeddings, colon grading errors are mostly neighbors: $80.4\%$ of CV SVM mistakes and $86.0\%$ of published ensemble mistakes are adjacent-grade swaps, while Grade 3 recall under cross-validation is only 0.475. Pooled accuracy of 73.6% does not communicate either fact. Before a colon grading CAD number is treated as operational, report Grade 3 recall and the adjacent versus non-adjacent error split alongside accuracy.