Compact and Structurally Transparent Cervical Cytology with Geometry-Driven Features and Closed-Form Attention

Conference: ECCV 2026
Paper: ECCV Official
Code: https://github.com/Dichao-Liu/GeoCEAN
Area: Others (Suggested: Medical Imaging)
Keywords: Cervical cytology, Transparent AI, White-box model, Closed-form attention, Free-energy principle

TL;DR

The paper models the clinical cervical cytology screening workflow into an intrinsically transparent network architecture, deriving closed-form spatial attention via free-energy minimization over four diagnostic potential maps and extracting auditable representations through a geometry-driven analytic backbone, achieving SOTA accuracy on DSCC, SIPaKMeD, and Herlev with only 2.2M parameters.

Background & Motivation

Cervical cancer remains a principal cause of cancer-related mortality in women worldwide, yet systematic Pap smear and liquid-based cytological screening can successfully prevent invasive disease through early diagnosis. As massive screening demands surge, automated computer-aided diagnosis systems have become indispensable to relieve the immense manual screening workload of cytotechnologists. However, the majority of contemporary approaches either adapt off-the-shelf vision backbones (such as generic ConvNets or Vision Transformers) or construct complex multi-branch heuristic ensembles. While these deep black-box models attain satisfactory metrics on closed datasets, they lack domain-native inductive biases; staining variations, mucus clutter, and cellular debris frequently cause severe performance degradation when deployed across different clinical centers. Furthermore, high-stakes medical diagnosis strictly demands faithful explainability, whereas popular post-hoc saliency methods (such as Grad-CAM) operate disconnected from the forward decision process, frequently diffusing into irrelevant cytoplasmic regions and staining artifacts without mathematical guarantees.

In actual clinical practice, cytopathologists follow a structured, three-step hierarchy: a screening technologist scans the slide to identify suspicious regions ("where to look"), an attending pathologist scrutinizes nuclear and chromatin abnormalities ("what is present"), and the final diagnostic report accounts for the decision based on explicit clinical criteria ("how to decide"). The core tension is that standard deep neural networks rely on unconstrained dense feature transformations that sever the link between deep representations and biological morphologies; conversely, existing generic white-box architectures lack domain-specific cytological priors, rendering them underperforming and difficult to scale on fine-grained cellular classification benchmarks.

This paper addresses this challenge by translating the three-stage clinical workflow directly into an intrinsically solvable and auditable computational graph: defining a diagnostic potential field from domain-native geometric cues, allocating spatial attention via free-energy minimization, and constraining feature evolution via fixed differential operators and convex updates. The core idea is to frame cervical cytology screening as a free-energy allocation problem over explicit concept potentials alongside a geometry-driven analytic backbone, delivering intrinsic pixel-to-logit accountability and cross-dataset SOTA accuracy with only 2.2M parameters.

Method

Overall Architecture

GeoCEAN (Geometry-driven Concept-Energy-Attention Network) explicitly mirrors the clinical cytology workflow across three stages: locating suspicious areas (Where to look), morphological reading (What to read), and linear decision accounting (How to decide). The input cellular image is first processed by four explicit morphological operators to extract pixelwise diagnostic concepts, which are monotonically calibrated and aggregated onto a probability simplex into a diagnostic potential field \(V(u)\). By treating the negative potential as an energy landscape, spatial attention is derived in closed form via free-energy minimization. In parallel, the image enters an analytic backbone composed of fixed gradient and Laplacian operators, nonnegative near-diagonal channel mixing, and convex residual updates. Finally, a separable probabilistic readout aggregates attention-weighted features into a compact representation, which is mapped into class logits via a linear head.

%%{init: {'flowchart': {'rankSpacing': 24, 'nodeSpacing': 28, 'padding': 6, 'wrappingWidth': 400}}}%%
flowchart TD
    IN["Input Cervical Cell Image x"] --> C1["Explicit Concept Extraction & Calibration<br/>Roughness / Orientation / N:C / Heterogeneity"]
    IN --> ST["Lightweight Stem Downsampling"]
    C1 --> POT["Diagnostic Potential & Energy Landscape<br/>V(u) and E(u) = -V(u)"]
    POT --> FEA["Free-Energy Allocation & Closed-Form Attention<br/>A* = softmax(-E/tau)"]
    ST --> BB["Analytic Geometric Backbone<br/>Fixed Operators + Nonnegative Mixing + Convex Updates"]
    FEA --> RO["Separable Probabilistic Readout & Attribution<br/>Weighted Aggregation & Linear Head"]
    BB --> RO
    RO --> OUT["Class Logits y & Explicit Concept Gradients"]

Key Designs

1. Explicit Cytology Concepts and Monotone Potential Field: Grounding Screening in Clinical Priors To prevent attention from being misled by non-diagnostic background artifacts, the model constructs four pixelwise concept maps reflecting clinical hallmarks. Given a binary nucleus mask \(n\) and its boundary \(\partial n\), nuclear envelope irregularity \(z_{\mathrm{rough}}\) is calculated via discrete boundary-normalized Laplacian flux; epithelial orientation disorder \(z_{\mathrm{orient}}\) is quantified via circular variance of gradient orientations in a local window \(W_u\); local nucleus-to-cytoplasm ratio \(z_{\mathrm{nc}}\) computes the ratio of nuclear area to dilated cytoplasmic area; and chromatin heterogeneity \(z_{\mathrm{ent}}\) is captured by the log-variance of local intensities. Each concept undergoes strictly increasing calibration \(f_i(z) = a_i^+ z + b_i\) with \(a_i^+ > 0\), followed by simplex fusion over \(\alpha \in \Delta_3\) (\(\sum \alpha_i = 1, \alpha_i \ge 0\)):

\[V(u) = \sum_{i=1}^4 \alpha_i f_i(z_i(u))\]

The strictly positive calibration slopes and nonnegative simplex weights enforce clinical monotonicity: increasing an abnormality cue (e.g., coarser chromatin or rougher envelope) can never decrease the diagnostic potential \(V(u)\), mathematically eliminating rank inversions.

2. Free-Energy Minimization and Closed-Form Spatial Attention: Analytical Resource Allocation Rather than learning unconstrained attention parameters via dense matrix projections, GeoCEAN models screening attention as thermodynamic equilibrium on a discrete spatial lattice \(\Omega'\). Defining the energy landscape as the negative potential \(E(u) = -V(u)\), regions with severe abnormalities correspond to deep potential wells. Over the probability simplex \(\Delta\), the system minimizes the free-energy functional balancing expected energy against Shannon entropy, \(\Phi(A) = \langle A, E \rangle - \tau H(A)\), where \(\tau > 0\) regulates the temperature trade-off between localized focus and global coverage. Under the Karush-Kuhn-Tucker optimality conditions and strict convexity of \(\Phi\), the unique optimal spatial attention distribution is solved analytically:

\[A^\star = \mathrm{softmax}(-E / \tau) = \mathrm{softmax}(V / \tau)\]

This closed-form formulation completely removes trainable attention parameters while naturally concentrating the screening budget on nuclear rims and peri-nuclear regions where cytological evidence is densest.

3. Geometry-Driven Analytic Backbone: Fixed Differential Operators and Convex Residual Updates To guarantee that deep representations remain anchored to interpretable cellular morphology rather than degrading into uninterpretable high-frequency noise, each backbone stage applies structured geometric constraints. For intermediate feature tensor \(X\), channels are first filtered with fixed gradient filters \(G_x, G_y\) and discrete Laplacian \(\Delta\) to extract first-order gradient magnitude \(M_{\mathrm{gm}}\) and second-order curvature \(M_{\mathrm{lap}}\). Channels then undergo nonnegative near-diagonal \(1 \times 1\) coupling \(\mathcal{M}\):

\[\widehat{X} = \mathrm{BN}\Big(\mathcal{M}\big(a_{\mathrm{gm}} M_{\mathrm{gm}} + a_{\mathrm{lap}} M_{\mathrm{lap}}\big)\Big)\]

Bandwidth-limited mixing ensures that only adjacent channels representing compatible geometric phenomena interact, preventing sign-flipping interference. The residual update is executed via a convex combination step with \(\gamma \in (0, 1)\):

\[X^{\mathrm{out}} = X + \gamma (\widehat{X} - X)\]

When gradient and curvature signals agree, features update coherently along the dominant direction; when signals conflict, \(\gamma < 1\) acts as a local contractive operator, ensuring bounded feature stability across network depth.

4. Separable Decision and Intrinsic Evidence-to-Logit Accounting: Mathematical Attribution without Post-Hoc Tools The terminal feature map \(F\) and closed-form attention \(A^\star\) are aggregated via an attention-weighted probabilistic readout \(m = \sum_u A_u^\star F_{:, u}\), followed by a linear classification head \(W_{\mathrm{cls}}\) yielding logits \(y_c = \sum_{u \in \Omega'} A_u^\star \langle w_c, F_u \rangle\). Because every forward operation possesses an exact closed-form derivative, the marginal contribution of any concept \(z_i\) at location \(v\) to class logit \(y_c\) can be directly computed via the chain rule:

\[\frac{\partial y_c}{\partial z_i(v)} = \frac{\alpha_i f_i'(z_i(v))}{\tau} \Bigg( A_v^\star \langle w_c, F_v \rangle - \sum_{u \in \Omega'} A_u^\star A_v^\star \langle w_c, F_u \rangle \Bigg)\]

This intrinsic formulation provides an exact analytical sensitivity trace from raw pixels and clinical concepts to the final diagnostic classification, entirely bypassing external, unfaithful post-hoc visualizers like Grad-CAM.

Loss & Training

The entire network is trained end-to-end using standard cross-entropy classification loss \(\mathcal{L}_{\mathrm{cls}}(y, t)\) without requiring auxiliary segmentation masks or multi-task regularizers. The forward pass analytically computes the optimal attention, and backpropagation traces gradients through explicit concept and geometric pathways. The model is trained from scratch for 300 epochs using SGD with momentum 0.9, weight decay \(5 \times 10^{-4}\), batch size 16, and an initial learning rate of 0.004 scheduled by cosine annealing.

Key Experimental Results

Main Results

GeoCEAN was benchmarked under a unified 5-fold cross-validation protocol trained entirely from scratch against five representative model families across DSCC, Herlev, and SIPaKMeD. The results on DSCC (Table 1) are summarized below:

Model Category	Representative Model	ACC (%)	F1-score (%)	AUC (%)	Params (M)	GFLOPs	Latency (ms)
(a) General Backbone	ConvNeXtV2-T (CVPR'23)	84.7 ± 0.6	82.6 ± 1.0	94.6 ± 0.2	49.6	8.7	11.6
(a) General Backbone	InceptionNeXt-S (CVPR'24)	86.7 ± 0.5	85.0 ± 0.5	96.1 ± 0.3	47.1	8.4	11.0
(b) Lightweight	MobileNetV4 (ECCV'24)	85.2 ± 1.5	83.4 ± 1.9	94.1 ± 1.0	2.5	0.2	4.2
(b) Lightweight	SHViT-S1 (CVPR'24)	88.5 ± 1.6	87.0 ± 1.7	96.0 ± 1.4	6.0	0.2	8.8
(c) Medical Domain	MedViT (CIBM'23)	87.2 ± 2.3	85.7 ± 2.6	95.7 ± 1.4	31.2	5.9	17.4
(c) Medical Domain	MedMamba (arXiv'24)	86.3 ± 0.8	84.6 ± 1.0	94.3 ± 0.7	14.0	2.0	10.1
(d) Cervix-Specific	MSCCNet (BIBM'23)	87.8 ± 1.2	86.1 ± 1.1	95.2 ± 0.4	18.7	3.7	4.7
(d) Cervix-Specific	Swin-GMRS (J-BHI'25)	89.5 ± 2.1	91.3 ± 1.8	96.9 ± 1.0	100.8	8.8	60.0
(e) White-box	CRATE (JMLR'24)	84.6 ± 0.5	82.4 ± 0.7	94.5 ± 0.3	15.6	2.9	5.0
(e) White-box	BDD Net (TIM'25)	81.5 ± 0.4	78.8 ± 0.4	92.5 ± 0.2	2.6	1.9	0.2
Ours	GeoCEAN	93.2 ± 0.2	92.6 ± 0.2	98.7 ± 0.1	2.2	0.4	5.4

On Herlev and SIPaKMeD (Table 2), GeoCEAN further demonstrates consistent superiority: achieving 76.8 ± 2.4% ACC on Herlev (outperforming Swin-GMRS at 73.5% and MedMamba at 73.5%) and 98.5 ± 0.5% ACC / 99.9% AUC on SIPaKMeD (surpassing Swin-GMRS at 98.3%).

Ablation Study

Comprehensive ablation experiments on SIPaKMeD (Table 6) validate each structural component:

Component	Setting / Variation	ACC (%)	F1-score (%)	AUC (%)	Note
Backbone Depth	1 stage	82.4 ± 0.6	82.1 ± 0.5	96.3 ± 0.1	Insufficient representation capacity
Backbone Depth	3 stages	96.5 ± 0.8	96.6 ± 0.7	98.9 ± 0.3	Receptive field expanding
Backbone Depth	4 stages (Default)	98.5 ± 0.5	98.5 ± 0.4	99.9 ± 0.0	Optimal saturation point
Backbone Depth	5 stages	97.1 ± 0.8	97.0 ± 0.7	98.7 ± 0.3	Over-downsampling harms local cues
Attention Stride	stride 4	25.8 ± 0.6	15.3 ± 0.5	83.6 ± 0.1	Optimization collapse; insufficient cellular context
Attention Stride	stride 16	97.0 ± 0.8	97.0 ± 0.7	99.0 ± 0.3	Context becoming sufficient
Attention Stride	stride 32 (Default)	98.5 ± 0.5	98.5 ± 0.4	99.9 ± 0.0	Balanced spatial receptive field
Convex Residual Step \(\gamma\)	\(\gamma = 0.2\)	97.8 ± 0.6	97.7 ± 0.5	99.4 ± 0.1	Conservative update rate
Convex Residual Step \(\gamma\)	\(\gamma = 0.5\) (Default)	98.5 ± 0.5	98.5 ± 0.4	99.9 ± 0.0	Ideal balance of update magnitude and contraction
Convex Residual Step \(\gamma\)	\(\gamma = 0.8\)	97.0 ± 0.7	97.0 ± 0.6	99.1 ± 0.2	Overly large steps induce feature instability
Concepts & Constraints	w/o nonnegativity	95.9 ± 0.7	95.6 ± 0.8	98.7 ± 0.4	Rank inversions degrade attention quality
Concepts & Constraints	w/o N/C ratio	95.3 ± 0.8	94.9 ± 0.9	98.3 ± 0.5	Largest drop (-3.2% ACC); critical clinical biomarker
Concepts & Constraints	w/o roughness	96.4 ± 0.6	96.2 ± 0.7	98.9 ± 0.3	Nuclear boundary irregularities are vital
Concepts & Constraints	w/o orientation	96.9 ± 0.5	96.7 ± 0.6	99.1 ± 0.3	Cellular polar alignment loss degrades accuracy
Concepts & Constraints	w/o chromatin	97.8 ± 0.3	97.6 ± 0.4	99.5 ± 0.2	Texture granularity contributes steady gain

Key Findings

• Nucleus-to-cytoplasm ratio is the most decisive clinical cue: Removing \(z_{\mathrm{nc}}\) causes the largest performance drop (-3.2% ACC), confirming that nuclear enlargement relative to cytoplasm remains the primary hallmark of malignant transformation in cytology. Omitting the nonnegativity constraint drops accuracy by 2.6%, demonstrating that enforcing monotonic calibration is indispensable to avoid negative cancellation across conflicting cues.
• Attention grid stride exhibits sharp sensitivity: Stride 4 and stride 8 experience severe collapse (25.8% and 46.2% ACC), proving that allocating attention on overly fine spatial grids lacks cell-level contextual support and causes softmax probability dilution, whereas a 1/32 downsampled lattice captures the holistic cellular envelope.
• Domain-invariant potentials enhance cross-dataset generalization: In a zero-shot cross-dataset evaluation (DSCC \(\rightarrow\) Herlev, Table 4), GeoCEAN achieves 74.0 ± 3.8% ACC, outperforming Swin-GMRS (70.2%) and RES_DCGAN (59.8%). Anchoring spatial attention to explicit morphological potential wells provides strong resistance against staining shifts and scanner discrepancies.

Highlights & Insights

• Formulating screening attention as analytical free-energy minimization: Framing spatial allocation as a constrained thermodynamic trade-off between energy minimization and entropy coverage yields an elegant closed-form softmax solution, eliminating unconstrained attention weights and saving millions of parameters.
• Harmonizing fixed geometric operators with near-diagonal mixing: Hardcoding gradient and Laplacian operators while restricting channel mixing to band-limited near-diagonal interactions prevents semantic drift across depth, keeping feature representations interpretable and aligned with biological boundaries.
• Exact closed-form concept-to-logit attribution: Deriving analytical sensitivities from raw morphological concepts to class logits gives clinicians faithful, verifiable reasoning paths without resorting to heuristic post-hoc explainers like Grad-CAM.

Limitations & Future Work

• Dependency on reliable initial morphological binarization: The extraction of the four clinical cues relies on Otsu thresholding and morphological cleanup. Under severe background mucus or poor staining contrast (e.g., in DSCC), nuclear boundary estimation can degrade, as reflected by lower sign consistency (0.425).
• Evaluation restricted to isolated single-cell benchmarks: Validation was performed on cropped single-cell benchmarks (DSCC, SIPaKMeD, Herlev); evaluating the framework on gigapixel Whole-Slide Images (WSI) with dense, overlapping clusters remains unexplored.
• Future directions: Integrating a differentiable, lightweight morphological boundary estimator and extending the free-energy allocation framework to gigapixel WSIs for automated population-level screening.

Related Work & Insights

• vs General & Medical Vision Backbones (ConvNeXtV2 / MedViT / MedMamba): Standard backbones rely on black-box channel interactions and suffer severe performance drops under domain shifts; GeoCEAN incorporates domain-native geometric operators and achieves higher accuracy with only 2.2M parameters.
• vs Cervix-Specific Models (Swin-GMRS / MSCCNet): Existing specialized models depend on massive multi-branch architectures (Swin-GMRS uses 100.8M parameters) and post-hoc Grad-CAM visualizations that diffuse into cytoplasm; GeoCEAN achieves superior accuracy at 2.2M parameters with intrinsic, pixel-level attribution.
• vs White-Box Architectures (CRATE / BDD Net): While CRATE relies on sparse rate reduction as a generic signal processing objective, GeoCEAN embeds clinical cytological semantics into its mathematical formulation, offering stronger performance on fine-grained cellular classification.

Rating

• Novelty: ⭐⭐⭐⭐⭐ Formulates screening attention as closed-form free-energy minimization coupled with a geometry-driven analytic backbone.
• Experimental Thoroughness: ⭐⭐⭐⭐⭐ Thorough 5-fold cross-validation on 3 benchmarks, 5 baseline families, cross-dataset transfer, and detailed ablations.
• Writing Quality: ⭐⭐⭐⭐⭐ Rigorous mathematical derivation, elegant presentation, and seamless integration of clinical workflow with computational design.
• Value: ⭐⭐⭐⭐⭐ Highly valuable for trustworthy medical AI, achieving SOTA accuracy with compact size (2.2M parameters) and intrinsic transparency.

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