ManifoldRNA · M-CIM Framework · TCGA BRCA

Finding the cancer genes
that variance
cannot see.

AI has narrowed millions of candidates to hundreds. ManifoldRNA determines which of those hundreds are real — applying geometry-aware manifold analysis to reveal structurally influential genes systematically missed by PCA and variance-based methods.

Explore Interactive Findings Read Preprint ↗
0.0048
M-CIM log-rank p-value
0.157
PCA baseline p-value
17K
genes analyzed
526
TCGA BRCA patients
32×
Better survival stratification
vs PCA baseline
128
Latent dimensions
manifold embedding
<0.01
p-value under 20% masking
topological resilience
25
Experimental steps
full trajectory
Interactive Findings

Three figures.
One geometric argument.

Hover the highlighted points on each figure for detailed annotations. Figure panels use bundled SVG demo assets under manifoldRNA/fig/ (swap filenames to your publication PNGs when ready). M-CIM trajectory: TCGA BRCA (N=526, G=17,800).

Figure 1 — Geometric Leverage Index (GLI) vs. Variance-Based Rank
17,800 genes · ASCL2 and NAPRT1 exhibit high GLI despite low variance rank · Hover highlighted genes
Hover to explore
Figure 1: GLI vs Variance
ASCL2 and NAPRT1 ranked beyond top 15,000 genes by variance yet exhibit GLI > 0.88 — invisible to PCA, critical to manifold geometry.
Figure 2 — ASCL2 as Master Topological Switch
Latent space z1/z2 · Virtual intervention → Manifold Shift · Hover points
Hover to explore
Figure 2: ASCL2 Manifold
Small ASCL2 perturbation propagates globally — confirming structural control rather than marginal correlation.
Figure 3 — Topological Resilience under Feature Masking
Log-rank p-value · 0% vs 20% random feature masking stress test
Hover to explore
Figure 3: Topological Resilience
M-CIM maintains p < 0.01 under 20% feature masking — while Vanilla NN degrades to p = 0.12.
M-CIM Architecture

Mechanism-Grounded Science.

Generation creates possibilities. Verification creates confidence. ManifoldRNA is the verification layer — applying physics-informed geometric analysis to determine which AI-generated candidates are structurally defensible.

01 · Embedding
Nonlinear Manifold Construction
Autoencoder with manifold regularization (λ=0.5) maps 17,800 genes into 128-dimensional latent space. No variance pre-filtering — preserves structurally important low-variance signals.
02 · Perturbation
Local Gene Perturbation Probe
Controlled perturbations along individual gene dimensions measure how small changes propagate through the latent geometry — Jacobian norm aggregated across all N samples.
03 · GLI
Geometric Leverage Index
S(g) captures global structural response to local gene perturbation. High GLI genes exert disproportionate control regardless of marginal expression magnitude or variance rank.
04 · Taxonomy
Structural Role Classification
Genes classified as SL-Drivers, Anchor Nodes, Singularity Indicators, or Morphogenetic Drivers based on regime-dependent behavior across the λ regularization sweep.
Structural Gene Taxonomy

Beyond variance.
Structural roles.

Key genes identified by M-CIM. None were prioritized by variance-based filtering. Biological context from literature — not causal claims, but structural vocabulary.

M-CIM Structural Role Table · TCGA BRCA · N=526
Gene M-CIM Role GLI Score Variance Rank Biological Context
ASCL2 SL-Driver
0.92
 > 15,000 Wnt signaling · Cancer stem cell self-renewal · Primary Topological Control Node
NAPRT1 SL-Driver
0.88
 > 14,000 NAD+ biosynthesis · Metabolic stability under hypoxia · Metabolic Anchor Node
OR10AG1 Singularity
0.72
 > 16,000 Ectopic OR expression · Invasive phenotype · Geometric Singularity Indicator
ANKRD30A Anchor
0.21
 ~ 8,500 Breast-specific expression · Local manifold anchoring
HOXD10 Morphogenetic
0.19
 ~ 9,000 EMT · Cellular polarity · Spatial Morphogenetic Regulator
Publication

Open access preprint.
CC BY 4.0.

Posted January 2026 on Research Square. Full methodology, 25-step experimental trajectory, ablation studies, and masking stress tests available.

Geometric Prognostic Singularities and Structural Leverage Drivers: A Manifold-Based Framework (M-CIM) for Cancer Gene Prioritization Chi-Hsing Wu¹  ·  Kai-Siang Chen²
¹ TaiScience Institution  ·  ² Chia Nan University of Pharmacy and Science
Keywords: gene prioritization · manifold learning · gradient sensitivity · transcriptomics · feature selection
Posted: January 8, 2026  ·  License: CC BY 4.0
DOI: https://doi.org/10.21203/rs.3.rs-8537800/v1
Contact

Interested in licensing
or collaboration?

ManifoldRNA is available for research licensing and commercial partnership through TaiScience / Fu Jen Catholic University tech transfer. Full technical data room under NDA.

Request Licensing Info jcwu@taiscience.org