Deterministic Finite-Scale Geometry of RNA Language Model Embeddings Predicts siRNA Efficacy: Gϵ(r) Outperforms LID as a Functional Complexity Measure

Abstract

Motivation. BLAST-based screening of small interfering RNAs (siRNAs) frequently produces false positives in the “grey zone”, where alignment statistics are marginally significant but functional affinity is low. Existing approaches based on local intrinsic dimensionality (LID) of language model embeddings are unstable on small datasets and high-dimensional representations. Results. We introduce a deterministic finite-scale geometric index Gϵ(r), constructed from the volume of hyperbolic balls in the Poincaré ball Bn, and apply it to messenger RNA (mRNA) target embeddings obtained from the RNA foundation model RNA-FM. On a curated dataset of 101 siRNAs targeting the PCSK9 mRNA (NM_174936.4) with experimentally determined IC50 values (1–4200 pM), we show that Gϵ(r) significantly correlates with log10(IC50): Spearman ρ = 0.440, p = 4 × 10−6 (bootstrap 95% CI [0.254, 0.603]). In contrast, LID estimators (TwoNN, MLE) correlate neither with Gϵ(r) nor with IC50. The signal of Gϵ(r) is regional: within a single functional region of the mRNA (cluster 3520–3570 nt), no correlation is observed (ρ = 0.022, p = 0.88), whereas between regions the correlation is strong (ρ = 0.478, p < 0.001). A random-data control yields ρ = −0.016 ± 0.101. Conclusion. Gϵ(r) is a self-contained deterministic metric of the functional geometry of mRNA, distinct from LID. It is robust to noise, does not require local density estimation, and can be used for ranking siRNA candidates and filtering false-positive BLAST hits in the grey zone.