arXiv:2605.18576v1 [cs.LG] 18 May 2026
scHelix: Asymmetric Dual-Stream Integration via Explicit Gene-Level Disentanglement Xichen Yan∗
Zelin Zang∗†
Changxi Chi
Jinan University Guangzhou, China
Westlake University Hangzhou, China
Westlake University Hangzhou, China
Jingbo Zhou
Chang Yu
Jinlin Wu
Westlake University Hangzhou, China
Westlake University Hangzhou, China
HKISI Hong Kong, China
Shenghui Cheng
Fuji Yang
Jiebo Luo
Jinan University Guangzhou, China
TIAS Hangzhou, China
HKISI Hong Kong, China
Zhen Lei
Stan Z. Li
HKISI Hong Kong, China
Westlake University Hangzhou, China
Abstract A critical challenge in single-cell RNA sequencing (scRNA-seq) integration is resolving the tension between eliminating batch effects and maintaining biological fidelity. While recent evidence indicates that batch effects manifest heterogeneously across genes, most existing methods process the transcriptome uniformly, frequently resulting in over-correction and loss of subtle biological signals. To address this, we present scHelix, a dataset-adaptive framework that fundamentally changes how features are processed by explicitly partitioning genes into domain-invariant Anchors and domain-sensitive Variants at the input level. scHelix utilizes a dual-stream sparse diffusion encoder equipped with stop-gradient graph caching to efficiently learn multi-scale structural representations. The core of our approach is a novel asymmetric AlignRefine-Fuse protocol: the unstable Variant stream is first aligned to the robust topology of the Anchor stream, followed by a conservative refinement phase where the Anchor stream absorbs denoised details via bounded residual gating. This “divide-and-conquer” architecture prevents shortcut learning and ensures robust batch removal without compromising the integrity of biological clusters. Extensive benchmarking demonstrates that scHelix outperforms state-of-the-art methods.The source code is available at https: //anonymous.4open.science/status/scHelix-E175
Keywords Single-cell integration; disentangled representation learning; graph neural networks; batch effect correction; self-supervised learning
1
Introduction
Single-cell RNA sequencing (scRNA-seq) integration is the cornerstone of constructing unified cell atlases, unlocking the potential to map dynamic trajectories across diverse populations [22, 33]. However, it faces a fundamental trade-off: removing technical batch ∗ Equal contribution. † Corresponding author: [email protected]
effects often comes at the cost of erasing subtle biological heterogeneity [11, 18]. Aggressive correction methods tend to oversmooth data, blurring fine-grained cell states, while conservative approaches fail to align shared populations across domains [22]. This tension persists because most existing methods treat the transcriptome uniformly, processing the entire gene space (e.g., HVGs) as a monolithic feature vector [16, 20, 28]. This ignores a critical reality: batch effects are highly gene-specific [41]. As illustrated in Figure 1, genes governing core cellular programs—such as cell-cycle regulators (e.g., PCNA)—often maintain consistent distributions across platforms, providing a robust scaffold for cell identity. Conversely, context-sensitive genes—such as the interferonstimulated gene ISG15—carry genuine biological signals but are simultaneously confounded by technical artifacts. By forcing these conflicting signals into a single latent space, existing models often settle for a brittle compromise: either residual batch effects or loss of biological fidelity [22]. To address these challenges, we argue that integration methods must move beyond implicit latent space regularization to explicit feature-level disentanglement [21, 26]. Specifically, we answer three core questions: (1) Unsupervised Anchor Discovery: How can we identify a feature scaffold that is biologically discriminative yet technically stable, without relying on external annotations? (2) Structural Disentanglement: How do we prevent domainsensitive noise from dominating the representation learning process (i.e., avoiding shortcut learning)? (3) Safe Interaction: How can we recover fine-grained details from noisy features without reintroducing batch artifacts into the stable topology? We propose scHelix, a "divide-and-conquer" framework that explicitly disentangles features at the input level. Instead of a uniform input, scHelix partitions genes into domain-invariant Anchors and domain-sensitive Variants using a dataset-adaptive discriminability-sensitivity criterion (Section 3.2). This acts as a self-supervised feature selector, creating a hard information barrier:
Batch-Specific Expression Distribution Batch 2 Batch 1
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• Align-Refine-Fuse Protocol: A conservative interaction mechanism that balances topology preservation with detail recovery, preventing anchor contamination. • SOTA Performance: Extensive benchmarks demonstrate that scHelix achieves a superior trade-off between batch mixing and biological conservation compared to state-of-the-art baselines.
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Expression Level UMAP1 (A) Gene-Level Entanglement of Signal and Noise (Dilemma) Anchor Backbone (Teacher)
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Related Work
Batch correction and feature heterogeneity. Single-cell integration seeks to remove technical batch effects while preserving biological structure. Classical methods align datasets via cross-domain neighbor or anchor matching—e.g., MNN, Seurat, and Harmony [11, 17, 28]—while deep generative models such as scVI scale integration by learning batch-conditioned latent spaces [20]. However, most approaches treat the transcriptome as a uniform feature vector and apply global alignment pressure, implicitly assuming batch effects are globally distributed. Recent gene-level analyses challenge this assumption: the Group Technical Effect (GTE) metric reveals that batch shifts are strongly gene-dependent and often dominated by a small subset of highly batch-sensitive genes [42], motivating feature-aware correction strategies.
Alignment Variant Refiner (Student) (B) Asymmetric Disentanglement and Safe Fusion (Strategy)
Figure 1: Motivation and Conceptual framework of scHelix. (A) The Dilemma: Batch effects are gene-specific. Anchor Genes (AG) serve as a stable scaffold, while Variant Genes (VG) are prone to domain noise. (B) The Strategy: scHelix partitions genes into invariant (𝐺 inv ) and variant (𝐺 var ) streams. The Anchor Backbone (Teacher) guides the Variant Refiner (Student) to align and denoise, preserving topology in the fused representation (𝐻 fused ).
the Anchor stream serves as a stable "Teacher" to preserve topology, while the Variant stream acts as a "Student" tasked with denoising. Unlike MLP-based methods that treat cells as independent samples [20, 38], scHelix employs a dual-stream sparse diffusion encoder to capture the non-linear manifold structure of the data [14, 36]. Crucially, we introduce a novel asymmetric Align-RefineFuse protocol. First, the unstable Variant stream aligns to the robust Anchor topology. Second, the Anchor stream conservatively absorbs denoised details via bounded residual gating. Finally, the streams are fused via a hyper-network. This serial, controlled interaction ensures robust batch removal without compromising the integrity of biological clusters. Our contributions are: • Explicit Disentanglement: A dataset-adaptive partition strategy that separates stable anchors from noisy variants, providing an interpretable biological scaffold. • Asymmetric Graph Architecture: A dual-stream design that leverages graph diffusion to learn multi-scale structural representations while strictly isolating noise sources.
Disentanglement, dual-stream architectures, and self-supervised alignment. Disentangled representation learning—via latent regularizers (scGen, biolord) [21, 26] or causal-inspired factorized blocks (CRADLE-VAE, FCR, SCBD) [1, 23, 24]—aims to separate biological from nuisance variation, yet implicit enforcement can be difficult to audit and may still permit leakage. Dual encoders (e.g., BioBatchNet) [19] provide explicit architectural separation, asymmetric selfsupervised objectives (BYOL/SimSiam) [3, 8] offer stable teacher targets, and graph-based encoders (e.g., scGNN) [36] capture singlecell topology. Our method builds on these ideas but makes disentanglement explicit at the input level via Anchor/Variant gene partitioning, coupled with a conservative Align–Refine–Fuse protocol that transfers denoised details while protecting the invariant scaffold.
3 Method 3.1 Problem Setup We formulate multi-domain scRNA-seq integration as representation learning under domain shift [7]. We adopt standard terminology: an instance is a cell, a feature is a gene, and a domain is a batch/technology channel. Given an expression matrix X ∈ R𝑁 ×𝐺 and domain labels 𝑏𝑖 ∈ B for each instance 𝑖 ∈ {1, . . . , 𝑁 }, our goal is to learn an embedding h𝑖 ∈ R𝑑 that preserves biological neighborhood structure while suppressing domain-specific variation. We follow a standard Scanpy-style preprocessing pipeline [37] (Appendix B). Throughout, sg(·) denotes stop-gradient and LN(·) denotes LayerNorm; let 𝜀 > 0 be a small constant, ∥ · ∥ 2 the ℓ2 norm, norm(u) := u/(∥u∥ 2 + 𝜀), and [𝑥] 10 := min{1, max{0, 𝑥 }}.
3.2
Feature Disentanglement & Variant Gating
Feature partition with a hard information barrier (Figure 2(A)). To operationalize our “divide-and-conquer” strategy, we first split the informative gene pool Gsel (e.g., HVGs) into two disjoint sets: Gsel = Gvar ∪ Ginv . Specifically, Ginv denotes domain-invariant
scHelix : Asymmetric Dual-Stream Integration via Explicit Gene-Level Disentanglement
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Figure 2: scHelix overview. (A) Disentanglement: input-level feature split (Anchors vs. Variants) via a discriminability–sensitivity quadrant, with an instance-wise gate applied only to Variants (Section 3.2). (B) Representation Learning: dual-stream multi-scale graph diffusion encoders on learnable sparse feature graphs, with stop-gradient graph caching for efficiency and stability (Section 3.3). (C) Align-Refine-Fuse: serial Align→Refine interaction establishes a stable Anchor topology before bounded residual transfer, followed by HyperFusion and a Teacher-guided warm-up→fusion schedule (Section 3.4). All protective mechanisms (hard barrier, stop-gradient, bounded residual) prevent anchor contamination while enabling controlled information flow. Anchors (the stable Teacher stream), and Gvar captures domainsensitive Variants (the noisy Student stream). We reorder genes so that Gvar occupies the first 𝐺 var = |Gvar | dimensions; accordingly, each cell input x𝑖 is physically split as x𝑖 = [x𝑖var ∥ x𝑖inv ]. Crucially, this creates a hard information barrier: each stream receives only its specific feature subset, preventing the Variant stream from shortcutcopying stable features and forcing it to learn denoising. Anchor discovery via a discriminability–sensitivity quadrant. We identify these sets using a dataset-adaptive quadrant. For each gene 𝑔 ∈ Gsel , we compute (i) a domain sensitivity score 𝑠𝑔dom (Eq. 1) and (ii) an unsupervised structure separability score 𝑠𝑔str (Eq. 2). For domain sensitivity, let 𝜇𝑔(𝑏 ) be the mean expression in domain 𝑏, and 𝜇𝑔(all) , 𝜎𝑔(all) be the global statistics: 𝑠𝑔dom :=
(𝑏 ) (all) 1 ∑︁ 𝜇𝑔 − 𝜇𝑔 . |B| 𝜎𝑔(all) + 𝜀
(1)
𝑏∈B
We z-score {𝑠𝑔dom } to obtain 𝑧𝑔dom . For structure separability, we generate pseudo-clusters 𝑐 (𝑖) via PCA→kNN→Leiden [32] on X [:,Gsel ] and define: Varbetween (𝑔) 𝑠𝑔str := . (2) Varwithin (𝑔) + 𝜀 After log-transforming and z-scoring to obtain 𝑧𝑔str , we apply the quadrant rule: Ginv := 𝑔 ∈ Gsel : 𝑧𝑔dom ≤ 𝜏dom, 𝑧𝑔str ≥ 𝜏str , (3) Gvar := Gsel \ Ginv . Unless stated otherwise, we use (𝜏dom, 𝜏str ) = (0, 0). Because both scores are z-scored within each dataset, this fixed threshold in standardized space corresponds to a dataset-specific mean-bisection in raw-score space: a gene qualifies as an Anchor if and only if its domain sensitivity falls below the dataset mean and its structure
separability exceeds the dataset mean. This mean-bisection rule provides a statistically natural, parameter-free default that automatically adapts to each dataset’s distributional characteristics; we provide a formal stability analysis (boundary-band argument) in Appendix H. This ensures that genes routed to the Anchor stream are both technically stable and biologically informative. Genes that are biologically relevant but batch-affected are routed to the Variant stream to be rectified, rather than discarded. Variant-only instance-wise domain gate. To handle cell-statedependent batch effects without altering the stable scaffold, we apply an instance-wise gate only to the Variant stream. We estimate a local domain sensitivity 𝛾𝑖 (𝑔) ∈ [0, 1] by mixing domain sensitivity scores from multi-resolution clusterings (details in Appendix F.1). The gated Student input is defined using an indicator function I {·} : 𝑥˜𝑖,𝑔 := 𝑥𝑖,𝑔 1 − I {𝑔∈ Gvar } · 𝜆 · 𝛾𝑖 (𝑔) . (4) where 𝜆 ∈ [0, 1] controls suppression strength. This mechanism precisely attenuates technical noise in the Variant stream while preserving the integrity of the Anchor stream.
3.3
Representation Learning via Dual-Stream Sparse Graph Diffusion
Dual-stream sparse diffusion (Figure 2(B)). To capture the nonlinear manifold structure of cells that is often missed by linear encoders, we employ a dual-stream architecture where each branch learns a structural representation via graph diffusion. Unlike generative diffusion, we use diffusion in the graph-signal-processing sense (feature propagation). For each stream ∗ ∈ {var, inv}, we learn a sparse adjacency matrix P∗ via differentiable query/key attention [35] S∗ = ReLU(Q∗ K⊤ ∗ /𝜏) with Top-𝑘 sparsification. Crucially, these are feature-level (gene–gene) graphs of dimension 𝐺 ∗ × 𝐺 ∗ (where each stream contains at most 𝐺 sel = 2,000 genes),
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Table 1: Main benchmark results across three datasets (mean±std). Bio-conservation includes structure (ASW𝑐𝑡 , GC) and cluster agreement (ARI, NMI). We report BioMean = 14 (ARIbest + NMIbest + ASWct + GC) and Overall = 0.4 ASWbatch + 0.6 BioMean, following the scIB benchmark protocol [22]. All metrics are scaled to [0, 1]; higher is better. Bold: best; underline: second best. The last column (Gain) shows the relative improvement of scHelix over the second-best method in Overall score. Bio-conservation (↑)
Info Structure Method
Year
Cluster
Avg.
Type ASW𝑐𝑡
GC
ARI
NMI
ASW𝑏𝑎𝑡𝑐ℎ (↑)
Overall (↑)
Gain (↑)
BioMean
scVI Harmony INSCT SCALEX sysVI SCEMENT scCobra scHelix
2018 2019 2021 2022 2024 2025 2025 Ours
Deep Learning Traditional Deep Learning Deep Learning Deep Learning Traditional Deep Learning Deep Learning
0.567 ±0.003 0.649 ±0.000 0.663 ±0.002 0.631 ±0.003 0.694 ±0.012 0.617 ±0.000 0.606 ±0.003 0.710 ±0.005
0.856 ±0.012 0.919 ±0.001 0.900 ±0.032 0.901 ±0.009 0.962 ±0.004 0.912 ±0.002 0.903 ±0.013 0.913 ±0.001
Human Pancreas 0.940 ±0.002 0.914 ±0.002 0.946 ±0.000 0.912 ±0.001 0.931 ±0.005 0.885 ±0.014 0.910 ±0.000 0.901 ±0.009 0.946 ±0.003 0.907 ±0.005 0.945 ±0.001 0.915 ±0.001 0.945 ±0.001 0.909 ±0.002 0.950 ±0.001 0.922 ±0.002
0.819 0.857 0.845 0.836 0.877 0.847 0.841 0.874
0.898 ±0.003 0.882 ±0.000 0.796 ±0.006 0.877 ±0.004 0.902 ±0.004 0.890 ±0.000 0.873 ±0.005 0.927 ±0.003
0.851 ±0.003 0.867 ±0.000 0.825 ±0.007 0.857 ±0.000 0.887 ±0.001 0.864 ±0.000 0.854 ±0.000 0.895 ±0.002
+0.90%
scVI Harmony INSCT SCALEX sysVI SCEMENT scCobra scHelix
2018 2019 2021 2022 2024 2025 2025 Ours
Deep Learning Traditional Deep Learning Deep Learning Deep Learning Traditional Deep Learning Deep Learning
0.524 ±0.001 0.720 ±0.000 0.602 ±0.011 0.673 ±0.012 0.759 ±0.023 0.658 ±0.000 0.661 ±0.001 0.756 ±0.014
Failing Human Heart 0.818 ±0.001 0.964 ±0.005 0.953 ±0.006 0.945 ±0.003 0.856 ±0.005 0.965 ±0.000 0.945 ±0.010 0.916 ±0.019 0.910 ±0.005 0.924 ±0.022 0.942 ±0.018 0.928 ±0.014 0.911 ±0.008 0.931 ±0.003 0.925 ±0.011 0.883 ±0.000 0.840 ±0.001 0.909 ±0.002 0.953 ±0.001 0.951 ±0.001 0.937 ±0.001 0.890 ±0.003 0.974 ±0.001 0.963 ±0.002
0.815 0.872 0.843 0.867 0.882 0.823 0.876 0.896
0.873 ±0.005 0.861 ±0.000 0.738 ±0.008 0.878 ±0.002 0.853 ±0.005 0.907 ±0.005 0.877 ±0.006 0.875 ±0.002
0.838 ±0.002 0.867 ±0.001 0.801 ±0.003 0.871 ±0.009 0.870 ±0.003 0.856 ±0.002 0.876 ±0.003 0.887 ±0.003
+1.26%
scVI Harmony INSCT SCALEX sysVI SCEMENT scCobra scHelix
2018 2019 2021 2022 2024 2025 2025 Ours
Deep Learning Traditional Deep Learning Deep Learning Deep Learning Traditional Deep Learning Deep Learning
0.536 ±0.001 0.561 ±0.000 0.561 ±0.011 0.574 ±0.002 0.619 ±0.008 0.558 ±0.000 0.563 ±0.001 0.573 ±0.003
Immune (Human) 0.823 ±0.012 0.799 ±0.020 0.809 ±0.003 0.792 ±0.000 0.814 ±0.015 0.816 ±0.003 0.886 ±0.000 0.581 ±0.030 0.737 ±0.008 0.915 ±0.014 0.736 ±0.025 0.775 ±0.011 0.855 ±0.008 0.779 ±0.010 0.745 ±0.017 0.741 ±0.000 0.763 ±0.012 0.800 ±0.006 0.930 ±0.003 0.730 ±0.022 0.779 ±0.013 0.826 ±0.006 0.816 ±0.002 0.810 ±0.001
0.742 0.746 0.691 0.750 0.750 0.716 0.751 0.756
0.921 ±0.001 0.920 ±0.000 0.813 ±0.009 0.871 ±0.001 0.899 ±0.001 0.881 ±0.000 0.878 ±0.004 0.924 ±0.002
0.814 ±0.005 0.815 ±0.003 0.740 ±0.007 0.798 ±0.006 0.810 ±0.002 0.782 ±0.003 0.801 ±0.006 0.823 ±0.002
+0.98%
not cell-level graphs. This keeps the adjacency computation at O (𝐺 ∗2 )—independent of the number of cells 𝑁 and orders of magnitude cheaper than building 𝑁 × 𝑁 cell graphs. Cell-level computation reduces to the sparse matrix product X∗ P∗ , which scales linearly in 𝑁 (see Appendix E for details). Stop-gradient caching for stability. Differentiating through iterative Top-𝑘 selection and multi-hop powers is unstable and computationally expensive. We therefore adopt a piecewise-constant topology strategy: we periodically rebuild P∗ and cache its powers. During representation learning, we treat the graph structure as fixed (sg(P∗ )), allowing gradients to update feature extractors without high-variance structural noise. Multi-scale extraction. We encode the gated variants Xvar = X̃var and raw anchors Xinv separately. For scale 𝑘 ∈ K, we compute low-pass features (smoothing global structure) and high-pass features (sharpening local details): Z∗(𝑘 ),low := X∗ sg(P∗ )𝑘 , (𝑘 ),high
Z∗
:= 𝜉 1 X∗ − Z∗(𝑘 ),low + 𝜉 2 X∗ I − sg(P∗ )𝑚 .
(5)
Scales are aggregated via learnable weights 𝜔 = softmax(𝜃 ) to produce stream embeddings Hvar and Hinv . To prevent collapse before
interaction, each stream is regularized by a decoder reconstructing its own input. We formally prove that this multi-scale diffusion acts as a complementary spectral filter (preserving global structure while isolating local details) in Appendix A.1.
3.4
Align-Refine Interaction & HyperFusion
Design principle (Figure 2(C)). Naive fusion can reintroduce domain artifacts into the clean Anchor scaffold. To prevent this, scHelix enforces a strict Align-Refine-Fuse protocol, designed to prevent noise leakage from the unstable Variant stream back to the stable Anchor topology. The process proceeds as follows: (i) align the Variant stream to the Anchor stream, (ii) conservatively refine the Anchor stream using denoised Variant details, and (iii) fuse via a gated mechanism. Asymmetric Variant–Anchor Alignment. We align the unstable Variant stream to the robust Anchor topology using a BYOL/SimSiamstyle objective [4, 9]. We minimize the negative cosine similarity between the Variant stream’s prediction pS and the Anchor stream’s target zT : Lalign := 2 − 2 E[⟨pS, zT ⟩] .
(6)
scHelix : Asymmetric Dual-Stream Integration via Explicit Gene-Level Disentanglement
Figure 3: Anchor-set diagnostics on Human Pancreas (complexBatch). (a) Metric heatmaps on raw PCA-64 embeddings show Quadrant Anchors provide the best initial biological separation. (b) Performance after Harmony integration. (c) The bio-batch trade-off demonstrates that while Anchors are stable, fusing all genes (Ours/scHelix) achieves the optimal balance. Crucially, the stop-gradient on zT ensures the Anchor manifold acts as a fixed topological guide, preventing it from being pulled toward the noisy Student distribution (i.e., preventing model collapse). Conservative Reverse Refinement. Once aligned, the Student stream contains recovered biological signals. We inject these back into the Teacher stream via a bounded residual update: H̃𝑖inv := H𝑖inv + 𝜶𝑖 ⊙ Δh𝑖 ,
0 ≤ 𝜶𝑖 ≤ 𝛼 max .
(7)
where Δh𝑖 is derived from cross-attention (Anchor queries Variant), and 𝜶𝑖 is an element-wise gating vector. The bound 𝛼 max acts as a safety valve (theoretically guaranteed by Lipschitz continuity, see Appendix A.2), ensuring that while the Anchor stream gains detail, its global structure cannot be destabilized by residual batch noise. HyperFusion. Finally, we synthesize the refined streams using HyperFusion. A HyperNetwork [10] generates instance-conditioned low-rank parameters 𝜽𝑖 from the refined Anchor embedding H̃𝑖inv ; these parameters define a two-layer MLP that transforms the raw Variant embedding h𝑖var into a residual update. An adaptive gate gate g𝑖 = 𝜎 (𝜽𝑖 ) controls the injection magnitude: 𝜽𝑖 := HyperNet H̃𝑖inv , (8) H𝑖,fused := LN H̃𝑖inv + g𝑖 ⊙ 𝜆Δ MLP(H𝑖var ; 𝜽𝑖 ) .
Phase 2: Fusion (Coupled). After 𝑇warm steps, we activate the fusion module. The model minimizes a joint objective that includes fused reconstruction and Confidence-Weighted Distillation [12] (LKD ), which encourages the fused embedding to respect the high-confidence cluster structure found by the refined Teacher: fused fused Lfuse := 𝜆rec ∥ X̂ − X∥ 2𝐹 + 𝜆KD LKD + 𝜆conn Lconn (Hfused ).
(10)
The total objective is L := Lwarm + Ifuse (𝑡) Lfuse , ensuring that fusion only occurs after the Anchor scaffold and Variant alignment are sufficiently mature.
4 Experiments 4.1 Experimental Setup
This adaptive gating allows the model to selectively incorporate Variant information—conditioned on the local Anchor context—only where it is biologically congruent, preventing residual batch noise from contaminating the fused representation.
Task, datasets, baselines, and metrics. We study multi-domain scRNA-seq integration as representation learning under domain shift [7]. We benchmark five public datasets; the main text reports three representative ones (Table 1), with the remaining two deferred to the Appendix (Table 5). Baselines include Harmony, scVI, INSCT, SCALEX, sysVI, SCEMENT, and scCobra (5, 13, 16, 20, 27, 38, 40). All methods share the same QC/HVG pool and a unified training/evaluation pipeline (Appendix B–C). Following scIB conventions [22], all metrics are scaled/flipped to [0, 1] (higher is better). We report the standard scIB Overall score (40/60 batch/bio weighting); detailed metric definitions are provided in Table 1.
3.5
4.2
Optimization & Teacher-Guided Schedule
We employ a two-phase curriculum to ensure stability. Phase 1: Warm-up (Decoupled). Initially, we train the streams with a focus on reconstruction and asymmetric alignment. The objective includes per-stream reconstruction (Lrec ), alignment (Lalign ), and topology preservation (Lconn ), Lwarm := ∑︁ ∗ ∗ 𝜆rec ∥ X̂∗ − X∗ ∥ 2𝐹 + 𝜆conn Lconn (H∗ ) + 𝜆align Lalign . (9) ∗∈ {var,inv}
During this phase, we also maintain Teacher prototypes {c𝑘 } via EMA [29] to generate stable pseudo-labels 𝑦𝑖 for the connectivity loss.
Main Integration Performance
Benchmark results. Table 1 summarizes three representative datasets (full five-dataset results with mean±std over three seeds: Appendix Table 5). Across all three, scHelix achieves the best Overall score, surpassing the second-best baseline by an average of 1.05%. Gains are most pronounced in distinguishing subtle cell states. On the Pancreas dataset, Harmony and scVI tend to over-merge Ductal and Acinar populations (Figure 5, red circles) in pursuit of batch removal, whereas scHelix preserves these local neighborhoods while maintaining comparable batch integration scores. This structural preservation is underpinned by molecular fidelity: scHelix maintains sharp expression boundaries of lineage-specific markers
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Figure 4: Align-Refine-Fuse trajectory on Human Pancreas (complexBatch). (A) Alignment pulls the Variant stream toward the Anchor manifold, mixing batches. (B) Refinement injects denoised details into the Anchor, sharpening cluster boundaries. (C) Fusion yields the final embedding with compact biological clusters and minimal batch stratification. Red circles highlight improved local compactness by scHelix. (e.g., KRT19 for Ductal vs. PRSS1 for Acinar [25]), avoiding the “expression smoothing” common in VAE-based baselines where marker specificity is diluted by the Gaussian latent prior. This confirms that our asymmetric design effectively prevents over-correction, ensuring fine-grained biological identities are not sacrificed for batch removal.
Table 2: Ablation study on Human Pancreas. We compare S0 (Full) with variants: S1 (random anchors), S2 (no gating), S3 (no interaction; S3.1 no align, S3.2 no refine), S4 (simple fusion), S5 (no self-training; S5.1 no KD, S5.2 no connectivity), and S6 (linear encoder). Bio metrics (↑)
Setting
4.3
Clustering
Mechanism Analysis
Ablation study. We validate each component by systematically removing it (Table 2); the most diagnostic dataset (Human Pancreas, complexBatch) [22] is reported here, with Lung results in Appendix L. Three key findings emerge: (i) Anchor choice is most critical: Replacing Quadrant selection with random anchors (S1) causes the sharpest drop (Overall 0.891 → 0.763), confirming that biologically discriminative anchors are essential. (ii) Interaction is necessary: Disabling the Align-Refine protocol (S3) degrades the bio-batch trade-off, with specific drops in batch mixing when Alignment is removed. (iii) Teacher guidance stabilizes fusion: Removing self-distillation (S5) yields a significant drop (Overall 0.891 → 0.788), underscoring the importance of a stable teacher topology. Diagnostic I: Anchor Set Quality. We benchmark the intrinsic quality of candidate gene subsets prior to deep integration. Four subsets drawn from the same HVG pool are compared: (i) GTENHBG (GTE ≥ 0.95 [41]); (ii) Quadrant Anchors (our selection: 𝐵𝑧 (𝑔) ≤ 0, 𝐶𝑧 (𝑔) ≥ 0); (iii) All HVGs; and (iv) Random subsets (size-matched, averaged over 𝑅 repeats). For each set, we derive PCA-64 embeddings from scaled expression and evaluate clustering (ARIbest , NMIbest ) and conservation metrics (ASWct , GC, ASWbatch ) before and after Harmony [16]. As shown in Figure 3, Quadrant Anchors form the most robust biological scaffold in raw space (Panel a), yet post-correction results (Panels b, c) show that incorporating Variants further enhances resolution. This empirically motivates our asymmetric design: Anchors provide topological stability, while controlled fusion recovers the fine-grained detail needed for high-resolution clustering.
S0 Full S1 RandSplit S2 NoGate S3 NoInteract S3.1 NoAlign S3.2 NoRefine S4 SimpFusion S5 NoSelfTrain S5.1 NoKD S5.2 NoConn S6 LinEncoder
Structure
Batch
Total
(↑)
(↑)
ARI
NMI
ASWct
GC
ASWb
Overall
93.1 53.3 93.0 74.8 90.2 92.5 91.6 52.6 91.8 56.0 91.3
89.1 74.8 88.9 83.6 87.0 88.5 86.8 75.6 86.7 77.8 87.3
74.4 60.7 71.2 68.0 56.1 71.8 54.9 56.4 57.6 58.2 69.7
92.3 82.0 90.4 90.7 92.8 82.3 92.0 93.0 85.5 93.2 89.5
92.0 89.1 90.0 91.0 91.4 91.2 93.6 93.0 91.9 92.2 91.4
89.1 76.3 87.9 84.0 85.4 86.8 86.2 78.8 85.0 79.7 87.2
Diagnostic II: Interaction Mechanism. We quantify biological conservation (BioMean) on intermediate embeddings to dissect the asymmetric protocol. The net gain (ΔBioMean) is measured for: (i) the Variant stream via Align (S3.1 vs. S0), and (ii) the Anchor stream via Refine (S3.2 vs. S0). Table 3 confirms that Align substantially boosts the noisy Variant stream by anchoring it to the stable Teacher topology, while Refine yields large gains on the Anchor branch by injecting bounded residuals without compromising structural integrity. This synergy is visually corroborated in Figure 4: Alignment mitigates batch offsets, Refinement sharpens local structures, and the fused embedding balances rigorous batch removal with high-fidelity biological conservation.
4.4
Extended Capabilities & Robustness
Semi-supervised setting and zero-shot foundation models. We extend evaluation to label-scarce scenarios (10–50% masking).
scHelix : Asymmetric Dual-Stream Integration via Explicit Gene-Level Disentanglement
Figure 5: Comparative UMAP plots of four models on Human Pancreas (complexBatch). Red circles highlight improved local compactness by scHelix; blue circles highlight baseline defects, including diffuse neighborhoods and reduced separation between ductal and beta populations due to over-correction. Table 3: Branch-level diagnostics for Align and Refine. We report BioMean on branch embeddings and the net improvement (Δ) provided by each module. Bold indicates the best performance per setting.
Bio metrics (↑) Setting
Structure
Dataset: Lung_atlas_public HBG (w/o Align) S3.1 (Contrast) HBG (w/ Align)
56.2 73.2 58.9 75.0
NHBG (w/o Refine) 47.2 70.9 NHBG (w/ Refine) 58.9 75.0
55.4 83.9 57.1 84.9 57.1 82.7 57.1 84.9
67.2 69.0
Overall (↑)
64.5 69.0
– +5.7
NHBG (w/o Refine) 92.5 88.5 NHBG (w/ Refine) 93.1 89.1
83.8 87.2
– +3.5
Comparison with scANVI [39] (Table 4) shows that scHelix consistently yields superior integration. Even with just 10% labels, scHelix improves Overall by +0.048 (0.861 → 0.909), driven by substantial ASWct gains (+0.13), confirming that Teacher-guided topology effectively propagates sparse label information. We further investigate whether foundation models (FMs) [2] can replace dataset-adaptive integration, benchmarking Geneformer [31] and scGPT-human [6] on Human Pancreas with both raw and Harmony-integrated embeddings. Figure 8 reveals that scHelix achieves a significantly better biobatch trade-off (Overall: 0.895) than the best FM (scGPT+Harmony: 0.796). Gene vocabulary coverage exceeds 96% for both FMs, so the gap stems not from missing features but from the fact that FMs are pre-trained for reconstruction rather than batch invariance, preserving technical artifacts without explicit adaptation.
Batch
Score
87.6 92.2
88.1 91.7
86.1 90.9
65.3 82.8
87.8 94.6
88.2 91.6
86.2 92.0
92.0 96.9
65.4 84.9
89.0 94.7
88.5 90.8
86.7 92.6
93.4 97.3
65.4 86.9
90.1 94.7
91.1 90.9
89.2 93.1
Method
ARI
NMI
ASW𝑐𝑡
GC
10%
scANVI† scHelix †
95.0 96.8
91.2 93.9
65.3 78.8
20%
scANVI† scHelix †
95.0 97.1
91.7 94.5
50%
scANVI† scHelix †
95.2 98.9
100%
scANVI‡ scHelix ‡
96.1 99.0
– +4.5
81.5 87.2
Structure
Ratio
– +1.8
Dataset: Human Pancreas (complexBatch) HBG (w/o Align) 90.2 87.0 56.1 92.8 S3.1 (Contrast) HBG (w/ Align) 93.1 89.1 74.4 92.3 71.8 82.3 74.4 92.3
Cluster
BioMean Δ
ARI NMI ASW𝑐𝑡 GC
S3.2 (Refine)
Bio metrics (↑)
Overall (↑)
Stream Cluster
S3.2 (Refine)
Table 4: Semi-supervised integration on Human Pancreas. Comparison against scANVI across varying label ratios (10%– 100%). † semi-supervised; ‡ fully supervised. Bold indicates best performance.
Over-correction & Runtime. We employ a rigorous over-correction stress test following scCobra [40]. As shown in Figure 6, scHelix achieves the lowest OC scores among deep baselines, indicating superior local-neighborhood preservation. This performance does not sacrifice efficiency: scHelix scales linearly with cell number, processing the 30k-cell Pancreas dataset in ∼150 s with peak memory under 4 GB on a single A100 GPU—comparable to lightweight Harmony (∼120 s) but significantly faster than scVI (∼600 s) and scGPT (>2000 s). Sensitivity analysis. We vary key hyperparameters on Human Pancreas (complexBatch). scHelix exhibits high stability (Figure 7), with the Overall score fluctuating negligibly (Δ ≤ 0.0065) across a broad range of settings, indicating that the default configuration is near-optimal and no precise tuning is required.
Yan, Zang et al.
Figure 6: Over-correction and runtime. Bars: Over-correction (lower is better) in high-dim vs. 2D space. Lines: Runtime. scHelix consistently achieves the lowest global (A, OC𝑎𝑙𝑙 ) and local (B, OC 𝑓 𝑜𝑐𝑢𝑠 ) over-correction scores while maintaining computational efficiency.
Figure 7: Hyperparameter sensitivity on Pancreas (complexBatch). One knob is varied at a time with all others fixed. Bars: Overall; dashed curves: ASWbatch and ARIbest . Results shown for (a) 𝜆fused_conn , (b) 𝛼 init , and (c) 𝜆align (denoted 𝑤 contrastive in plots). and batch-sensitive Variants. Through a conservative Align-RefineFuse protocol, scHelix achieves precise batch correction while preserving subtle biological signals. Extensive benchmarks confirm its superiority over state-of-the-art methods and foundation models, establishing it as a robust tool for high-fidelity cell atlas construction.
6 Figure 8: Zero-shot FM comparison on Human Pancreas. (a) scIB metrics comparing scHelix against Geneformer and scGPT (with/without Harmony). (b) Vocabulary match ratios indicate high feature coverage.
5
Conclusion
We presented scHelix, a framework that resolves the integration trade-off by explicitly disentangling input genes into stable Anchors
Limitations and Ethical Considerations
Limitations. First, the graph-based architecture incurs higher costs than linear methods, potentially requiring optimization for multi-million cell datasets. Second, our strategy relies on the existence of shared biological signals; extreme non-overlapping batch effects may hinder effective anchor discovery. Ethical Considerations. As an AI tool for science, scHelix warrants careful use: the “refined” expression values are computational imputations and must not substitute for experimentally validated
scHelix : Asymmetric Dual-Stream Integration via Explicit Gene-Level Disentanglement
clinical diagnoses. Users must also adhere to data privacy regulations when processing patient-derived transcriptomics to prevent re-identification risks.
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A
Theoretical Analysis
In this section, we provide rigorous theoretical justifications for the “divide-and-conquer” mechanisms in scHelix. We analyze the spectral properties of the dual-stream graph encoder (Section 3.3) and the stability guarantees of the asymmetric refinement protocol (Section 3.4).
A.1
Spectral Analysis of Multi-Scale Graph Diffusion
We formally demonstrate that the encoder operations defined in Eq. (5) function as complementary spectral filters on the learned gene-gene graph. Specifically, we show that Zlow extracts the global data manifold (Low-Pass), while Zhigh captures fine-grained local variations (High-Pass). Setup: Graph Fourier Transform. Let G be the learned gene-gene graph with row-normalized adjacency matrix P ∈ R𝐺 ∗ ×𝐺 ∗ . Let P = UΛU−1 be its eigendecomposition, where Λ = diag(𝜆1, . . . , 𝜆𝐺 ∗ ) contains eigenvalues ordered by magnitude 1 = 𝜆1 ≥ |𝜆2 | ≥ · · · ≥ |𝜆𝐺 ∗ | ≥ 0. The eigenvectors U form the graph spectral basis. Any Í feature signal x can be represented as x = 𝑖 𝑐𝑖 u𝑖 . Note that during the forward pass, the graph topology is fixed (via sg(P)), acting as a linear operator. Theorem 1 (Complementary Spectral Filtering). The multi-scale features in Eq. (5) modulate the spectral coefficients 𝑐𝑖 via the following transfer functions ℎ(𝜆): Zlow : ℎ low (𝜆) = 𝜆𝑘 high
Z
(11) 𝑘
𝑚
: ℎ high (𝜆) = 𝜉 1 (1 − 𝜆 ) + 𝜉 2 (1 − 𝜆 )
(12)
Proof. 1. Low-Pass (Global Structure): The low-frequency term is defined as Zlow = XP𝑘 . Applying this operator to a basis vector u𝑖 : P𝑘 u𝑖 = 𝜆𝑖𝑘 u𝑖 . (13) The transfer function is ℎ low (𝜆𝑖 ) = 𝜆𝑖𝑘 . Since |𝜆𝑖 | ≤ 1, as the diffusion scale 𝑘 increases, high-frequency components (where |𝜆𝑖 | < 1) decay exponentially (𝜆𝑖𝑘 → 0). The DC component (𝜆1 = 1) is preserved (1𝑘 = 1). Thus, Zlow effectively smooths out local noise and retains the global topological structure. 2. High-Pass (Local Detail): The high-frequency term in Eq. (5) is: Zhigh = 𝜉 1 (X − Zlow ) + 𝜉 2 X(I − P𝑚 ). (14) Substituting Zlow = XP𝑘 , we have: Zhigh = X 𝜉 1 (I − P𝑘 ) + 𝜉 2 (I − P𝑚 ) .
(15)
The transfer function is the linear combination: ℎ high (𝜆𝑖 ) = 𝜉 1 (1 − 𝜆𝑖𝑘 ) + 𝜉 2 (1 − 𝜆𝑖𝑚 ). Consider the limits: • Low Frequencies (𝜆𝑖 → 1): ℎ high (𝜆𝑖 ) → 𝜉 1 (0) + 𝜉 2 (0) = 0. Global background is suppressed. • High Frequencies (𝜆𝑖 → 0): ℎ high (𝜆𝑖 ) → 𝜉 1 (1) + 𝜉 2 (1) = 𝜉 1 + 𝜉 2 . Local signals are preserved/amplified. This proves that Zhigh acts as a high-pass filter, complementing the smoothing effect of the low-pass stream.
scHelix : Asymmetric Dual-Stream Integration via Explicit Gene-Level Disentanglement
Table 5: Full baseline comparison across benchmark datasets (3 seeds; mean±std). All metrics follow the scIB benchmark protocol [22] and the unified evaluation protocol in Appendix C (including the PCA-64 evaluation cap when needed). Higher is better for all reported scores.
Method
scVI† (’18) Harmony (’19) INSCT† (’21) SCALEX† (’22) sysVI† (’24) SCEMENT (’25) scCobra† (’25) scHelix† (Ours) scVI† (’18) Harmony (’19) INSCT† (’21) SCALEX† (’22) sysVI† (’24) SCEMENT (’25) scCobra† (’25) scHelix† (Ours)
Bio-conservation (↑) Structure Cluster ASW𝑐𝑡 GC ARI NMI Human Lung Atlas 0.530±0.002 0.817±0.006 0.592±0.011 0.749±0.005 0.574±0.005 0.764±0.001 0.586±0.007 0.733±0.000 0.561±0.002 0.904±0.001 0.549±0.014 0.681±0.007 0.562±0.001 0.904±0.006 0.592±0.002 0.712±0.004 0.564±0.007 0.918±0.000 0.596±0.007 0.744±0.000 0.553±0.000 0.758±0.004 0.539±0.018 0.725±0.002 0.555±0.002 0.912±0.003 0.571±0.001 0.718±0.004 0.576±0.003 0.843±0.004 0.593±0.003 0.750±0.001 Tabula Muris Senis 0.723±0.008 0.817±0.004 0.537±0.002 0.767±0.017 0.559±0.012 0.708±0.000 0.721±0.001 0.812±0.000 0.534±0.004 0.672±0.011 0.719±0.021 0.782±0.012 0.528±0.001 0.668±0.005 0.668±0.014 0.770±0.001 0.561±0.004 0.751±0.002 0.725±0.010 0.814±0.003 0.543±0.006 0.746±0.000 0.730±0.004 0.815±0.001 0.532±0.009 0.754±0.003 0.713±0.002 0.803±0.002 0.544±0.002 0.760±0.004 0.755±0.003 0.825±0.002
Intuitive Interpretation. Analogous to image processing, the multiscale graph diffusion acts as a composite filter bank. The low-pass component (Zlow ) functions like a Gaussian blur, smoothing out stochastic gene expression noise to reveal the underlying cellular manifold (topology). The high-pass component (Zhigh ), conversely, acts like an unsharp mask, highlighting sharp local transitions— such as the specific expression of marker genes that define boundaries between subtle subtypes. By explicitly separating these frequency bands, scHelix avoids the common pitfall of “oversmoothing” where fine-grained biological details are lost during batch correction.
A.2
Stability Analysis of Asymmetric Interaction
We analyze the stability of the Align-Refine protocol. A key concern in integration is whether the noisy Variant stream (which may contain severe batch effects) can corrupt the stable Anchor stream during interaction. We prove that the Anchor stream is theoretically protected. Proposition 2 (Boundedness and Continuity). Let H𝑖inv be the stable anchor embedding. The refinement update H̃𝑖inv = H𝑖inv + 𝜶𝑖 ⊙ Δh𝑖 (Eq. (7)) satisfies two stability properties: (1) Global Boundedness: The update magnitude is strictly capped by 𝛼 max , independent of
ASW𝑏𝑎𝑡𝑐ℎ (↑)
Overall (↑)
0.916±0.006 0.905±0.000 0.798±0.002 0.887±0.001 0.889±0.006 0.902±0.000 0.894±0.006 0.914±0.003
0.770±0.004 0.761±0.002 0.724±0.002 0.770±0.002 0.779±0.002 0.747±0.002 0.772±0.001 0.780±0.001
0.882±0.001 0.871±0.006 0.857±0.003 0.860±0.001 0.872±0.005 0.873±0.000 0.866±0.004 0.885±0.001
0.779±0.002 0.768±0.002 0.749±0.005 0.739±0.003 0.776±0.001 0.774±0.001 0.767±0.001 0.787±0.001
the Variant input h𝑖var . (2) Lipschitz Continuity: The update function is Lipschitz continuous with respect to H𝑖var , ensuring smooth gradient flow. Proof. The update is governed by the gating vector 𝜶𝑖 and the residual Δh𝑖 : Δh𝑖 := LN(CrossAttn(H𝑖inv, H𝑖var )). (16) 1. Global Boundedness (Safety Valve). The term Δh𝑖 is the output of a LayerNorm (LN) operation. For any input v ∈ R𝑑 , v−𝜇 LN(v) = ⊙ 𝜸 + 𝜷. 𝜎 Since the normalized √ term (v− 𝜇)/𝜎 has unit √ variance, its Euclidean norm is exactly 𝑑. Thus, ∥ LN(v)∥ 2 ≤ 𝑑 ∥𝜸 ∥ ∞ + ∥𝜷 ∥ 2 =: 𝐶 LN . Combined with the sigmoid gate ∥𝜶𝑖 ∥ ∞ ≤ 𝛼 max , the total perturbation is bounded: 𝜶𝑖 := 𝛼 max ·𝜎 (W𝑔 [H𝑖inv ∥H𝑖var ]),
∥ H̃𝑖inv − H𝑖inv ∥ 2 = ∥𝜶𝑖 ⊙ Δh𝑖 ∥ 2 ≤ 𝛼 max𝐶 LN .
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This bound 𝑅 = 𝛼 max𝐶 LN holds regardless of the magnitude of h𝑖var (e.g., even under severe batch outliers). 2. Lipschitz Continuity (Smoothness). The functions composing the update—Sigmoid, LayerNorm, and Softmax (in Attention)— are all Lipschitz continuous and differentiable almost everywhere. This implies there exists a constant 𝐿 such that: ∥Δh̃𝑖inv (x) − Δh̃𝑖inv (y)∥ 2 ≤ 𝐿∥x − y∥ 2
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Yan, Zang et al.
for any two Variant inputs x, y. Consequently, small perturbations or noise in the Variant stream result in proportionally small changes in the Anchor update, preventing chaotic behavior or gradient explosion during fusion.
Because methods output embeddings with different dimensionalities, we apply a PCA-64 evaluation cap to prevent metric variance caused purely by representation dimension: • If a method outputs an embedding with dimension 𝑑 > 64, we project it to 64 dimensions via PCA before computing kNN/Leiden/metrics. • If a method outputs 𝑑 ≤ 64, we evaluate on its native embedding (no artificial up-projection).
Conclusion. The Anchor stream is doubly protected: it is mathematically confined to a safe 𝜖-ball around the stable manifold (Boundedness), and its deformation within that ball is smooth and controlled (Continuity).
B Preprocessing and Data Augmentation B.1 Shared preprocessing: QC, normalization, and HVG pool We follow a standard Scanpy-style pipeline for all datasets and all methods. We apply the same quality-control (QC) filters across benchmarks: (i) remove cells with fewer than 200 detected genes, (ii) remove genes expressed in fewer than 3 cells, and (iii) remove cells with mitochondrial gene percentage exceeding 5%. After QC, we normalize each cell to a library size of 10,000 and apply log(1+𝑥). We then select 𝐺 sel = 2000 highly variable genes (HVGs) using batch-aware HVG selection. For fair comparison, all methods share the same QC filters and the same HVG pool.
B.2
Two synchronized data views (fairness & method compliance)
MixUp-style augmentation (training only)
During training, we optionally apply a 𝑘 mix -nearest-neighbor MixUp strategy (e.g., 𝑘 mix = 300). For each cell x𝑖 , we sample a neighbor x 𝑗 and construct an augmented sample: xaug := 𝛼 x𝑖 + (1 − 𝛼) x 𝑗 ,
𝛼 ∼ U (0, 1).
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We do not use augmentation in validation/evaluation.
C Optimization Details and Evaluation Protocol C.1 Optimization details We optimize parameters using AdamW and apply gradient clipping for stability. For the learnable sparse feature graphs, cached graph topologies and cached multi-scale diffusion powers are rebuilt periodically every 𝑇 steps to reduce overhead.
C.2
C.3
Unified evaluation representation: PCA-64 as a robust cap
Raw baseline used in OC normalization
For normalized over-correction (OC) in Appendix G, the Raw baseline refers to the uncorrected representation computed from the log-normalized HVG expression (Appendix B.2): • HD Raw space (pre-UMAP): log-normalized HVGs → (Scanpy/scIB-style scaling if applicable) → PCA-64. • UMAP Raw space: 2D UMAP computed from the above Raw PCA-64 representation.
C.4
To respect method-specific input assumptions without giving any method extra information, we maintain two synchronized views after QC, always restricted to the same HVG pool when a method requires it: • Raw counts view: the integer count matrix (after QC). Used by count-based generative models (e.g., scVI-style pipelines). • Log-normalized view: library-size normalized to 10,000, then log(1 + 𝑥). Used by PCA/distance-based methods (e.g., Harmony) and preprocessing-dependent components.
B.3
Why 64? scIB-style pipelines commonly use a moderate PCA dimensionality (often ∼50 PCs) to build neighbor graphs. We use 64 as a slightly higher but still moderate, stable setting for kNN-based metrics.
Clustering protocol for ARIbest /NMIbest
Following the scIB benchmarking protocol [22], we compute a kNN graph on the evaluation representation and run Leiden clustering over a fixed resolution grid. We report ARIbest /NMIbest using the best result over the sweep.
C.5 Metric definitions (scIB-style; scaled to [0, 1] when applicable) All metrics are computed on the unified evaluation representation described in Appendix C.2. When a metric is naturally defined on [−1, 1], we linearly rescale it to [0, 1] for consistent aggregation. All metric definitions and the overall aggregation scheme follow the scIB benchmark [22]. Adjusted Rand Index (ARI).. Let 𝑈 be the ground-truth labels (cell types) and 𝑉 be the predicted clusters. Let 𝑛𝑖 𝑗 denote contingency Í Í Í table counts, 𝑎𝑖 = 𝑗 𝑛𝑖 𝑗 , 𝑏 𝑗 = 𝑖 𝑛𝑖 𝑗 , and 𝑁 = 𝑖 𝑗 𝑛𝑖 𝑗 . We use the standard ARI: (𝑎2𝑖 ) 𝑗 (𝑏2𝑗 ) ( 𝑁2 ) ARI(𝑈 , 𝑉 ) := Í 𝑎𝑖 Í 𝑏 𝑗 . Í 𝑏𝑗 𝑖 (2) 𝑗 ( 2) 1 Í 𝑎𝑖 − 𝑖 2 + 𝑗 2 2 ( 𝑁2 ) Í
𝑖𝑗
𝑛𝑖 𝑗 − 2
Í
𝑖
Normalized Mutual Information (NMI).. NMI(𝑈 , 𝑉 ) :=
2 𝐼 (𝑈 ; 𝑉 ) . 𝐻 (𝑈 ) + 𝐻 (𝑉 )
Cell-type ASW (reported as ASWct ∈ [0, 1]). Let 𝑠 (𝑖) ∈ [−1, 1] be the standard silhouette score for cell 𝑖 under cell-type labels. We define 𝑁
Many scIB-style metrics [22] (e.g., ASW, GC, and Leiden-based ARI/NMI) are computed from a kNN graph in an embedding space.
Í
[ −1,1] := ASWct
1 ∑︁ 𝑠 (𝑖), 𝑁 𝑖=1
ASWct :=
[ −1,1] ASWct +1 . 2
scHelix : Asymmetric Dual-Stream Integration via Explicit Gene-Level Disentanglement
Batch ASW.. 1 ∑︁ 1 ∑︁ (1 − |𝑠 batch (𝑖)|) . ASWbatch := |𝐶 | 𝑐 ∈𝐶 |𝐶𝑐 | 𝑖 ∈𝐶 𝑐
Graph Connectivity (GC).. GC :=
1 ∑︁ |LCC(𝐺𝑐 )| . |𝐶 | 𝑐 ∈𝐶 |𝐶𝑐 |
BioMean (unweighted biological summary). BioMean :=
ASWct + ARIbest + NMIbest + GC . 4
Overall score. Overall := 0.4 · ASWbatch + 0.6 ·
D
datasets with hundreds of thousands of cells on a single GPU (Table 9), and the architecture itself does not impose a fundamental barrier to million-cell datasets—scaling to such regimes would primarily require standard engineering optimizations (e.g., mini-batch sampling) rather than architectural changes.
F
Deferred Definitions for Gating and Objectives F.1 Instance-wise domain gate (details) Within each cluster 𝑐 (with at least 𝑁 min instances and at least two domains), we compute a composite local domain sensitivity score for feature 𝑔 ∈ Gvar : (𝑐 ) 𝑠 dom (𝑔) := 𝑤 𝜇 Δ𝜇 (𝑐 ) (𝑔) + 𝑤 𝜎 Δ𝜎 (𝑐 ) (𝑔)
ASWct + ARIbest + NMIbest + GC . 4 (20)
Hyperparameter Settings and Sensitivity
What we tune. We group hyperparameters by modules following the Method sections: (i) anchor selection and gating (Section 3.2), (ii) graph learning and multi-scale diffusion (Section 3.3), (iii) serial interaction and fusion (Section 3.4), and (iv) prototypes and confidence-weighted distillation (Section 3.5).
Intuitively, Δ𝜇 (𝑐 ) (𝑔), Δ𝜎 (𝑐 ) (𝑔), and ΔVar (𝑐 ) (𝑔) measure cross-domain dispersion of gene 𝑔 within cluster 𝑐, computed from cluster-wise sufficient statistics. (𝑐 ) Let 𝑠 +(𝑐 ) (𝑔) := max{𝑠 dom (𝑔), 0}. We normalize it and combine low/high-resolution gates to obtain the per-instance gate: 𝛾 (𝑐 ) (𝑔) :=
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0
F.2
E
𝑠 +(𝑐 ) (𝑔)
, maxℎ∈ Gvar 𝑠 +(𝑐 ) (ℎ) + 𝜀 h i1 low high 𝛾𝑖 (𝑔) := 𝑤 low𝛾 (𝑐 (𝑖 ) ) (𝑔) + 𝑤 high𝛾 (𝑐 (𝑖 ) ) (𝑔) .
Default settings (Pancreas; complexBatch). Unless stated otherwise, all datasets use the same defaults; we list the full configuration used in the Human Pancreas (complexBatch) experiment. Sensitivity analysis. We report one-at-a-time sensitivity sweeps in the main text (with corresponding tables/figures). To avoid redundancy, we omit additional discussion here.
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+ 𝑤 𝑣 ΔVar (𝑐 ) (𝑔).
Warm-up objective (full expression)
The warm-up objective used in Section 3.5 is var inv Lwarm := 𝜆rec ∥ X̂var − Xvar ∥ 2𝐹 + 𝜆rec ∥ X̂inv − Xinv ∥ 2𝐹 ∑︁ ∗ + 𝜆align Lalign + 𝜆conn Lconn (H∗ ).
Computational Efficiency
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∗∈ {var,inv}
Hardware. All experiments are run on a single NVIDIA GeForce RTX 2080 Ti GPU (11 GB). Why the method scales. The method avoids dense 𝐺 × 𝐺 feature interactions by learning sparse feature graphs (Top-𝑘 per gene). Graph topology is rebuilt periodically and reused via stop-gradient caching, and multi-scale diffusion powers are cached for reuse. Gene-level graphs, not cell-level graphs. A key design choice is that the learnable sparse graphs in scHelix are feature-level (gene– gene) adjacency matrices of size 𝐺 ∗ × 𝐺 ∗ (where 𝐺 ∗ ≤ 𝐺 sel = 2,000), not cell-level (𝑁 × 𝑁 ) graphs. We emphasize this distinction because cell-level graph construction would incur O (𝑁 2 ) cost, which is prohibitive for large atlases (𝑁 > 105 ). In contrast, the adjacency construction cost in scHelix is O (𝐺 ∗2 · 𝑑𝑎 ) per rebuild (with 𝑑𝑎 being the attention dimension), which is negligible: for 𝐺 ∗ ≈ 1,000 and 𝑑𝑎 = 64, a single rebuild involves ∼6.4 × 107 operations—orders of magnitude smaller than a single forward pass over the data. Cell-level computation involves only the sparse matrix product X∗ ∈ R𝑁 ×𝐺 ∗ multiplied by P∗ ∈ R𝐺 ∗ ×𝐺 ∗ , scaling as O (𝑁 · 𝐺 ∗ · 𝑘) where 𝑘 is the Top-𝑘 sparsity level—linear in the number of cells 𝑁 . The graph P∗ is a global gene–gene relation graph shared across all cells; it is not constructed per mini-batch but rebuilt periodically (every 𝑇 steps) and cached. Combined with stop-gradient caching of multi-hop powers, this ensures that scHelix scales to
G
Over-correction (OC) Metric: Definitions and Implementation Details
Setup and notation. Let Z ∈ R𝑁 ×𝑑 denote the representation on which kNN neighborhoods are computed. We compute OC both in (i) the high-dimensional pre-UMAP space and (ii) the 2D UMAP space. kNN neighborhood. Let N𝑘 (𝑖; Z) be the index set of the 𝑘 nearest neighbors of cell 𝑖 in Z (excluding 𝑖). Pseudo labels (two variants). We use two variants: OCall (global) and OCfocus (within a focus cell type), following the controlled perturbation setup in the main text: • OCall treats the perturbed subset as an additional pseudo “cell type” label. • OCfocus restricts evaluation to the focus cell type only, comparing perturbed vs. unperturbed within that type. Neighborhood label inconsistency (OC).. 1 ∑︁ 1 ∑︁ I 𝑦 𝑗 ≠ 𝑦𝑖 , OC(Z, y) := |I| 𝑘 𝑖∈I
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𝑗 ∈ N𝑘 (𝑖;Z)
where I is the evaluation index set: I = {1, . . . , 𝑁 } for OCall , and I is the focus-cell-type subset for OCfocus .
Yan, Zang et al.
Table 6: Default data-level hyperparameters (Pancreas; complexBatch). Here 𝐵𝑧 and 𝐶𝑧 denote the standardized domainsensitivity and structure-separability scores used in the quadrant split. The gate is applied only to the Variant/HBG subset, while the Anchor/NHBG subset remains untouched. Category
Parameter (code name)
Quadrant split (NHBG anchors)
Threshold on 𝐵𝑧 (selector_b_thresh) Threshold on 𝐶𝑧 (selector_c_thresh)
Pseudo-type separability (for 𝐶𝑧 )
PCA comps (selector_n_pcs) kNN neighbors (selector_n_neighbors) Leiden resolution (selector_leiden_res)
Layered variant-only domain gate (HBG only)
Gate enabled (layered_gate) Low-resolution Leiden (layered_low_res) High-resolution Leiden (layered_high_res) Gate strength 𝜆 (layered_gate_strength) 𝑤low / 𝑤high (layered_low/high_weight) Min cluster size 𝑁 min (layered_min_cells)
Table 7: Default model/training hyperparameters (Pancreas; complexBatch). Using a wide table layout to prevent column overlap. Category
Parameter (code name)
Value
Graph learning + diffusion
Top-𝑘 sparsity (lg_k_top) Graph temperature 𝜏 (lg_temp) Diffusion scales 𝑆 (scales) HP mixing 𝜉 1 / 𝜉 2 (hp_alpha, hp_beta) Rebuild period 𝑇 (graph_rebuild_every)
22 0.1 {1, 2, . . . , 5} 0.8 / 0.2 25 steps
Align / Refine
Align weight 𝜆align (w_contrastive) Refinement init 𝛼 init (refinement_init_alpha) Refinement bound 𝛼 max (clamp in refiner) Refinement temperature (refinement_temperature)
1.0 0.3 1.5 0.3
Fusion
Residual scaling 𝜆Δ (delta_init_scale) Fusion gate mode (gate_mode)
0.6 Gated
Connectivity / self-training
HBG connectivity weight (conn_weight_hbg) NHBG connectivity weight (conn_weight_nhbg) Fused connectivity weight (fused_conn_weight) KD clusters 𝐾 (kd_clusters) KD weight 𝜆KD (kd_weight)
0.08 0.2 0.2 24 0.5
Schedule / confidence filter
Align-only steps (align_only_steps) Confidence threshold (conf_threshold) Confidence exponent 𝑝 (conf_pow)
3000 0.75 1.0
Space-specific OC and UMAP seed averaging. Let ZHD be the evaluation representation in the high-dimensional space (PCA-64 if needed; Appendix C.2). We define
HD • := OCHD OC Z , y , •
• ∈ {all, focus}.
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For 2D UMAP, for each seed 𝑠 ∈ {1, . . . , 𝑆 }, let Z𝑠UMAP ∈ R𝑁 ×2 be the UMAP embedding computed from ZHD . We report mean±std
over seeds.
𝑆 1 ∑︁ OC Z𝑠UMAP, y• , 𝑆 𝑠=1 # " 𝑆 2 1/2 1 ∑︁ UMAP • UMAP := UMAP Std OC• OC Z𝑠 , y − OC• . 𝑆 −1 𝑠=1 (26)
:= OCUMAP •
scHelix : Asymmetric Dual-Stream Integration via Explicit Gene-Level Disentanglement
Table 8: Baseline Implementation Details. Key hyperparameters and software versions used for reproducibility.
Algorithm 1 Dataset-adaptive anchor discovery (quadrant rule) 𝑁 , 1: Input: Expression matrix X ∈ R𝑁 ×𝐺 , domain labels {𝑏𝑖 }𝑖=1
selected genes Gsel , thresholds (𝜏dom, 𝜏str ). Method
Version
scVI
v1.0.4 v0.0.9
Harmony
v2.0.1
SCALEX
sysVI
v1.0.4
scCobra
v1.0.0
scHelix (Ours)
-
Key Hyperparameters
2: Output: Anchor genes Ginv and variant genes Gvar .
n_hidden=128, n_latent=10, n_layers=2, dispersion=’gene’, gene_likelihood=’nb’, max_epochs=400 theta=2, lambda=1, sigma=0.1, nclust=50, max_iter=10, epsilon=1e-5 min_features=600, min_cells=3, n_domain=batch_size, seed=1234, hidden_layer=[256, 64] n_hidden=128, n_latent=10, n_layers=2, loss_weights=[1, 1], prior=’standard_normal’ contrastive_weight=0.1, temperature=0.07, proj_dim=128 See Tables 6 and 7
3: Compute domain sensitivity 𝑠 dom,z (𝑔) for all 𝑔 ∈ Gsel according
to Eq. (1). 4: Compute pseudo-clusters 𝑐 (𝑖) on X [:,Gsel ] (PCA → kNN graph
→ Leiden). 5: Compute structure separability 𝑠 str,z (𝑔) for all 𝑔 ∈ Gsel accord-
ing to Eq. (2). 6: Ginv ← {𝑔 ∈ Gsel : 𝑠 dom,z (𝑔) ≤ 𝜏dom ∧ 𝑠 str,z (𝑔) ≥ 𝜏str }. 7: Gvar ← Gsel \ Ginv .
Algorithm 2 Teacher-guided warm-up → fusion schedule 1: Input: Warm-up steps 𝑇warm , total steps 𝑇 . 2: Output: Trained parameters (and EMA teacher prototypes, if
used). Table 9: Computational Efficiency Benchmarks. Peak GPU memory usage and total runtime (training + inference) on a single NVIDIA RTX 2080 Ti. scHelix is consistently more efficient than deep generative baselines (scVI, SCALEX, scGPT) and comparable to the lightweight Harmony.
Method
Pancreas (16k)
Immune (33k)
Heart (270k)
Mem
Mem
Mem
Time
210s 6.5GB 950s 4.2GB 1,100s 5.1GB 4,500s OOM 280s 3.8GB
1,450s 4,800s 5,200s >24h 1,900s
Harmony 0.8GB scVI 1.4GB SCALEX 1.6GB scGPT 8.5GB scHelix 1.1GB
Time
120s 1.2GB 600s 1.8GB 750s 2.1GB 2,100s 10.8GB 150s 1.5GB
Time
Normalized OC (relative to Raw). We report normalized OC by subtracting the Raw baseline computed in the same space (Appendix C.3):
3: for 𝑡 = 1, 2, . . . ,𝑇 do 4:
if 𝑡 < 𝑇warm then Set 𝐼 fuse ← 0. 6: else 7: Set 𝐼 fuse ← 1. 8: end if 9: Compute warm-up losses Lwarm . 10: Compute fusion losses Lfuse if 𝐼 fuse = 1. 11: Update parameters by optimizing L = Lwarm + 𝐼 fuse Lfuse . 12: end for 5:
H.2
Proposition (Only boundary-near genes can flip). Consider perturbing the thresholds by (𝛿 dom, 𝛿 str ). Define the symmetric difference ΔGinv := Ginv (𝜏dom, 𝜏str ) △ Ginv (𝜏dom + 𝛿 dom, 𝜏str + 𝛿 str ).
space
OCnorm,• (method) := space
OC•
space
(method) − OC•
(Raw),
space ∈ {HD, UMAP}. (27)
By construction, smaller (more negative) values indicate less overcorrection relative to Raw.
H
(28)
Then any gene whose membership changes must lie in a narrow band around at least one boundary: n o ΔGinv ⊆ 𝑔 : 𝑧𝑔dom − 𝜏dom ≤ |𝛿 dom | (29) n o ∪ 𝑔 : 𝑧𝑔str − 𝜏str ≤ |𝛿 str | .
Threshold Selection for Anchor Discovery
Recap: quadrant rule in z-space. For each gene 𝑔 ∈ Gsel , we compute a domain-sensitivity score 𝑠𝑔dom (Eq. (1)) and a structureseparability score 𝑠𝑔str (Eq. (2)), then standardize them within Gsel to obtain 𝑧𝑔dom and 𝑧𝑔str . Anchors are selected by Eq. (3).
H.1
Stability to threshold perturbations (boundary-band argument)
Why fixed 𝜏 = 0 is still dataset-adaptive
Mean-bisection equivalence in raw-score space. By definition of z-scoring, 𝑧𝑔dom ≤ 0 is equivalent to 𝑠𝑔dom ≤ 𝜇 dom , and 𝑧𝑔str ≥ 0 is equivalent to 𝑠𝑔str ≥ 𝜇 str , where 𝜇 dom and 𝜇 str are empirical means computed within each dataset over Gsel . Thus fixed thresholds in zspace correspond to dataset-specific boundaries in raw-score space.
Proof (sketch). A membership flip requires at least one of the two inequalities to change truth value after shifting its threshold. This can only occur if the corresponding z-score lies within the shifted margin of that boundary. □
H.3
Optional unsupervised auto-thresholding (not used by default)
Quantile- and Otsu-style variants can be used when desired; our paper keeps (0, 0) as a stable, parameter-free default.
I
Algorithms (Deferred)
Yan, Zang et al.
J
Algorithm 3 Graph Learning with Cached Topology (per stream)
Graph Learning with Cached Topology
We clarify the gradient flow in our learnable sparse feature graph construction, addressing the interaction between trainable parameters and stop-gradient caching. What is learned vs. what is cached. For each stream ∗ ∈ {var, inv}, we maintain trainable query/key matrices Q∗, K∗ ∈ R𝐺 ∗ ×𝑑𝑎 . The similarity matrix is computed as: S∗ := ReLU(Q∗ K⊤ ∗ /𝜏),
S∗ [𝑖, 𝑖] = 0.
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We then apply top-𝑘 sparsification per row, symmetrize, add selfloops, and normalize to obtain P∗ . Selective gradient flow (single-hop differentiable; multi-hop cached). • Rebuild step: we compute a fresh P∗ without detaching. For 1-hop propagation, we use this differentiable P∗ so gradients flow to Q∗, K∗ . • Multi-hop: for 𝑠 > 1, we use cached powers sg(P𝑠∗ ) (precomputed at rebuild time), where sg(·) denotes stop_gradient. • Between rebuilds: we store a detached copy Pcached and reuse ∗ it for subsequent steps until the next rebuild. Why this design? Fully differentiable sparse graph learning with multi-hop powers is computationally prohibitive for 𝐺 ∼ 103 and tends to introduce gradient instability due to discrete top-𝑘 selection and matrix power compositions. Our piecewise-constant topology strategy balances (i) learnability (via the 1-hop path), (ii) stability (stop-gradient for multi-hop), and (iii) efficiency (reuse cached powers). Empirical validation. Ablation S6 (LinearEncoder) removes graph diffusion entirely and yields consistent performance drops (e.g., −0.022 Overall on Lung; −0.019 on Pancreas), supporting the utility of diffusion even with cached topology.
K
Dataset Descriptions and Benchmark Coverage
We evaluate scHelix on five public scRNA-seq benchmarking datasets spanning diverse tissue types, technologies, and integration challenges. For dataset scale and domain counts, see Table 9. Table 10 provides an at-a-glance dataset profile. Human Pancreas (complexBatch). This dataset aggregates human pancreatic islet scRNA-seq data from six independent studies [22] spanning multiple sequencing technologies, including CEL-seq, CEL-seq2, Smart-seq2, inDrop, Fluidigm C1, and SMARTER-seq. It comprises 16,382 cells across 9 technology-defined batches, with cell type annotations covering major endocrine populations and supporting cell types. It presents a challenging integration scenario due to substantial technical variation introduced by diverse library preparation protocols. Human Lung Atlas. The Human Lung Cell Atlas dataset [34] contains droplet- and plate-based scRNA-seq measurements of human lung tissue and circulating blood. For benchmarking, we use a subset of 32,472 cells with 16 batch labels and 58 annotated populations spanning epithelial, endothelial, stromal, and immune compartments.
Require: Trainable Q, K ∈ R𝐺 ×𝑑𝑎 ; rebuild period 𝑅; scales S = {1, 𝑠 2, . . . , 𝑠𝑆 } 1: Initialize Pcached ← None; cached_powers ← {}; step ← 0 2: for each training step do 3: if Pcached = None or step mod 𝑅 = 0 then 4: // Rebuild step: compute differentiable P 5: S ← ReLU(QK⊤ /𝜏); S[𝑖, 𝑖] ← 0 6: A ← top_k_sparsify(S); symmetrize; add self-loops 7: Pgrad ← sym_normalize(A) {Differentiable, for 1-hop} 8: Pcached ← Pgrad .detach() {For subsequent steps} 9: cached_powers ← {P𝑠 .detach() : 𝑠 ∈ S, 𝑠 > 1} {Multihop, stop-grad} 10: Use Pgrad for 1-hop; cached_powers for multi-hop 11: else 12: // Non-rebuild step: use cached (no gradient to Q,K) 13: Use Pcached for 1-hop; cached_powers for multi-hop 14: end if 15: Encode: Z (1) ← XP; Z (𝑠 ) ← X · cached_powers[𝑠] for 𝑠 > 1 16:
step ← step +1
17: end for
Table 10: Dataset profile and integration challenges. “Domains” denotes the integration domain channel (batch IDs for most datasets; technology for Human Pancreas). All datasets use 𝐺 sel =2000 HVGs (Appendix B). Dataset Pancreas Lung Atlas Immune Tabula Muris Heart
#Cells #Dom. Species Challenge 16K 32K 34K 111K 270K
9 16 10 21 45
Human Human Human Mouse Human
Technology Donor/cond. Trajectory Multi-tissue Disease
Challenge key. Technology: cross-platform library-prep artifacts; Donor/cond.: donor and condition variation with fine-grained populations; Trajectory: continuous developmental trajectories mixed with discrete types; Multi-tissue: large-scale heterogeneity across 23 tissues; Disease: disease-associated confounding overlaid on donor/technical shifts.
Immune (Human). Derived from scIB-style benchmarks [22], this dataset contains 33,506 human immune cells from peripheral blood and bone marrow across 10 batches. Cell types include major immune lineages and an erythrocyte developmental trajectory, making trajectory preservation important. Tabula Muris Senis. A mouse aging atlas [30]; we use a subset of 110,824 cells from 21 tissue-defined batches (FACS-sorted Smartseq2), with expert-curated cell types across 23 tissues. Failing Human Heart. This dataset integrates single-cell and single-nucleus RNA sequencing from healthy donors and dilated cardiomyopathy patients [15]. We use a subset of 269,794 cells across 45 batches, with annotations including cardiomyocytes, fibroblasts, endothelial cells, pericytes, and immune populations.
scHelix : Asymmetric Dual-Stream Integration via Explicit Gene-Level Disentanglement
Table 11: Additional end-to-end ablations on Lung atlas public. Higher is better for all metrics. (S0: Full model; S1–S6: Ablation variants defined in main text). Bio metrics (↑)
Batch (↑)
Overall (↑)
ASWbatch
Score
Lung atlas public (label: cell type; batch: batch) S0 Full 0.589 0.750 0.571 0.849 0.917 S1 RandomSplit 0.497 0.723 0.499 0.821 0.916 S2 NoGate 0.575 0.740 0.561 0.832 0.909 S3 NoInteraction 0.512 0.729 0.574 0.809 0.910 S3.1 NoAlign 0.562 0.732 0.554 0.839 0.912 S3.2 NoRefine 0.472 0.709 0.571 0.827 0.920 S4 SimpleFusion 0.518 0.693 0.418 0.812 0.728 S5 NoSelfTraining 0.535 0.720 0.551 0.866 0.921 S5.1 NoKD 0.492 0.723 0.560 0.797 0.944 S5.2 NoConn 0.504 0.717 0.555 0.773 0.943 S6 LinearEncoder 0.508 0.719 0.551 0.771 0.942
0.781 0.748 0.770 0.758 0.768 0.752 0.650 0.763 0.765 0.759 0.759
Setting ARI
NMI
ASWct
GC
Dataset selection rationale. These datasets cover: (i) technologydriven batch effects, (ii) donor-driven variation, (iii) tissue heterogeneity, (iv) disease-associated confounding, and (v) scale (from ∼16K to ∼270K cells).
L Additional Supplementary Results L.1 Detailed Ablation Settings In the main text (Table 2), we summarized the ablation settings S1–S6. Here we provide the precise definitions:
• S0 (Full Model): The complete scHelix architecture with all components enabled. • S1 (RandomSplit): Replaces the quadrant-based anchor selection with a random selection of anchors, matching the size of the original anchor set. This tests the necessity of our disentanglement strategy. • S2 (NoGate): Sets the gating regularization weight 𝜆 = 0, removing the instance-wise domain gate mechanism. • S3 (NoInteraction): Disables the dual-stream interaction by setting 𝜆align = 0 and 𝛼 max = 0. – S3.1 (NoAlign): Removes only the alignment loss (𝜆align = 0). – S3.2 (NoRefine): Removes the refinement stage (𝛼 max = 0), defaulting to simple additive fusion. • S4 (SimpleFusion): Replaces the HyperFusion module with a fixed additive fusion (i.e., simple summation of features). • S5 (NoSelfTraining): Disables all self-supervised learning signals by setting 𝜆KD = 𝜆fused_conn = 0. – S5.1 (NoKD): Disables only the knowledge distillation loss (𝜆KD = 0). – S5.2 (NoConn): Disables only the connectivity preservation loss (𝜆fused_conn = 0). • S6 (LinearEncoder): Replaces the graph diffusion encoder with a linear projection layer, testing the benefit of structural modeling. Additional ablations. We include extra end-to-end ablations not shown in the main text to provide fuller component-level diagnostics.