Differentiable RNA Secondary Structure Extraction for Deep Learning

Tyler Illman; Max Ward; Marcell Szikszai; Ryan K. Krueger

cs.LGSep 25, 2026

Differentiable RNA Secondary Structure Extraction for Deep Learning

Authors: Tyler Illman, Max Ward, Marcell Szikszai, Ryan K. Krueger

Organizations: School of Physics, Maths and Computing The University of Western Australia · School of Engineering and Applied Sciences Harvard University

Abstract

Many deep learning approaches to RNA secondary structure prediction have recently been proposed. They typically output a weight matrix $W$ where $W_{ij}$ is an arbitrary weight for base $i$ pairing with base $j$ . Converting this matrix to a predicted secondary structure or base-pairing probability matrix typically involves ad hoc and problematic downstream algorithms. Despite the importance of this conversion step, which we refer to as structure extraction, it has received relatively little attention in the literature. In this work, we analyze how the congruence between training and extraction methods affects prediction performance. To do this, we compare four extraction algorithms: a Nussinov-like dynamic programming method, maximum-weight graph matching and the greedy extraction algorithms used by SPOT-RNA and RiNALMo. These are evaluated on outputs from the pretrained RiNALMo model and three toy models trained in this paper: a differentiable Nussinov-like model, a binary cross-entropy (BCE) baseline, and a model that incorporates a novel symmetric doubly stochastic matrix (SDSM) normalization algorithm during training which allows it to output base-pairing probability matrices directly, without a separate extraction step. This SDSM normalization algorithm is differentiable and can be added inline to any deep learning model during training and evaluation. We find that the performance of each extraction method depends strongly on how the corresponding model was trained. Considering the toy models themselves, the SDSM model showed the strongest overall performance: it outperformed the BCE baseline under all four extraction algorithms and produced pre-extraction outputs closest to the ground truth. These results suggest that SDSM normalization is a tractable alternative to traditional structure extraction.

Figures & tables

Family	# Sequences
5S rRNA	1,283
SRP RNA	928
tRNA	557
tmRNA	462
RNase P RNA	454
16S rRNA	110

Table 1: Breakdown of RNA families in the ArchiveII dataset.

RNA Type	Train Set	Test Set
5S rRNA	1,018	265
SRP RNA	411	114
tRNA	461	96
Total	1,890	475

Table 2: Breakdown of RNA structure types in the train and test datasets.

Family	RiNALMo F1	Graph Matching F1	Nussinov F1	SPOT-RNA F1
16S rRNA	0.5690	0.5855	0.5990	0.5787
23S rRNA	0.6337	0.6587	0.6636	0.6515
5S rRNA	0.9275	0.8942	0.9308	0.9224
RNase P RNA	0.8820	0.8851	0.8686	0.8874
Group I Intron	0.8028	0.8055	0.7844	0.8083
SRP RNA	0.7973	0.8015	0.8100	0.7921

Table 3: Mean F1 score by RNA family for each structure extraction method (from pretrained RiNALMo model outputs).

Family	RiNALMo F1	Graph Matching F1	Nussinov F1	SPOT-RNA F1
5S rRNA	0.6944	0.9648	0.8787	0.7151
SRP RNA	0.5587	0.7747	0.7561	0.5551
tRNA	0.6681	0.9500	0.8586	0.7189
Mean	0.6524	0.9163	0.8451	0.6774

Table 4: Mean F1 score by RNA family for each structure extraction method using the Nussinov-like model.

Family	RiNALMo F1	Graph Matching F1	Nussinov F1	SPOT-RNA F1
5S rRNA	0.7615	0.6765	0.8809	0.9302
SRP RNA	0.6152	0.2755	0.7571	0.7099
tRNA	0.7038	0.7783	0.8641	0.8972
Mean	0.7147	0.6008	0.8478	0.8707

Table 5: Mean F1 score by RNA family for each structure extraction method using the class-balanced binary cross-entropy model.

Family	RiNALMo F1	Graph Matching F1	Nussinov F1	SPOT-RNA F1
5S rRNA	0.7631	0.9501	0.8899	0.9577
SRP RNA	0.6151	0.7383	0.7467	0.7489
tRNA	0.7111	0.9215	0.8595	0.9219
Mean	0.7171	0.8935	0.8494	0.9004

Table 6: Mean F1 score by RNA family for each structure extraction method using the SDSM model.

Model	RiNALMo F1	Graph Matching F1	Nussinov F1	SPOT-RNA F1	MSE
Nussinov-like	0.6524	0.9163	0.8451	0.6774	0.1459
BCE (baseline)	0.7147	0.6008	0.8478	0.8707	0.00196
SDSM	0.7171	0.8935	0.8494	0.9004	0.000496

Table 7: Overall mean F1 score for each extraction method, and mean squared error between ground-truth target structure and direct model outputs (prior to structure extraction), across the three models trained in this work.

Figure 1: Predicted matrices for a representative sequence (5S_Erysipelothrix-rhusiopathiae-2, length 114): target structure, Nussinov-like output, CB BCE output, and CB BCE SDSM output. The SDSM output concentrates probability mass onto the true base pairs with little off-target signal.

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Layer	Type	Neurons	Activation
1	Input	800 ( $200\times 4$ )	–
2	Dense	1024	ReLU
3	Dense	512	ReLU
4	Dense	256	ReLU
5	Dense	40,000 ( $200\times 200$ )	∗

Appendix

Table 8: Architecture for the fully connected MLP models used in this work. All models share the same base structure, consisting of three ReLU-activated hidden layers followed by a dense output layer of size

200\times 200

Row $>$ Column	Graph Matching	Nussinov	RiNALMo	SPOT-RNA
Graph Matching	–	$p=1.000$	$p=0.999$	$p=1.000$
Nussinov	$<0.001$	–	$p=0.127$	$<0.001$
RiNALMo	$<0.001$	$p=0.873$	–	$<0.001$
SPOT-RNA	$<0.001$	$p=0.999$	$p=0.999$	–

Appendix

Table 9: Pairwise permutation test

p

-values for the pre-trained RiNALMo model outputs on the full ArchiveII dataset (

n=3{,}975

; 10,000 permutations). Each cell gives the

p

-value for the hypothesis that the row method outperforms the column method. Significant results (

p<0.05

) are shown in bold.

Row $>$ Column	Graph Matching	Nussinov	RiNALMo	SPOT-RNA
Graph Matching	–	$<0.001$	$<0.001$	$<0.001$
Nussinov	$p=1.000$	–	$<0.001$	$<0.001$
RiNALMo	$p=1.000$	$p=1.000$	–	$p=0.999$
SPOT-RNA	$p=1.000$	$p=1.000$	$p=0.001$	–

Appendix

Table 10: Pairwise permutation test

p

-values for the Nussinov-like model (10,000 permutations). Each cell gives the

p

-value for the hypothesis that the row method outperforms the column method. Significant results (

p<0.05

) are shown in bold.

Row $>$ Column	Graph Matching	Nussinov	RiNALMo	SPOT-RNA
Graph Matching	–	$p=1.000$	$p=0.999$	$p=1.000$
Nussinov	$<0.001$	–	$<0.001$	$p=1.000$
RiNALMo	$p=0.001$	$p=1.000$	–	$p=1.000$
SPOT-RNA	$<0.001$	$<0.001$	$<0.001$	–

Appendix

Table 11: Pairwise permutation test

p

-values for the CB BCE baseline model (10,000 permutations). Each cell gives the

p

-value for the hypothesis that the row method outperforms the column method. Significant results (

p<0.05

) are shown in bold.

Row $>$ Column	Graph Matching	Nussinov	RiNALMo	SPOT-RNA
Graph Matching	–	$<0.001$	$<0.001$	$p=1.000$
Nussinov	$p=1.000$	–	$<0.001$	$p=1.000$
RiNALMo	$p=1.000$	$p=1.000$	–	$p=1.000$
SPOT-RNA	$p=0.0002$	$<0.001$	$<0.001$	–

Appendix

Table 12: Pairwise permutation test

p

-values for the SDSM model (10,000 permutations). Each cell gives the

p

-value for the hypothesis that the row method outperforms the column method. Significant results (

p<0.05

) are shown in bold.

Extraction Method	Mean Nussinov F1	Mean CB BCE F1	Nussinov $>$ CB BCE	CB BCE $>$ Nussinov
Graph Matching	0.9163	0.6008	$<0.001$	$p=1.000$
Nussinov	0.8451	0.8478	$p=1.000$	$<0.001$
RiNALMo	0.6524	0.7147	$p=1.000$	$<0.001$
SPOT-RNA	0.6774	0.8707	$p=1.000$	$<0.001$

Appendix

Table 13: Model-vs-model permutation test

p

-values comparing the Nussinov-like model against the CB BCE baseline, per extraction method. Significant results (

p<0.05

) are shown in bold.

Extraction Method	Mean SDSM F1	Mean CB BCE F1	SDSM $>$ CB BCE	CB BCE $>$ SDSM
Graph Matching	0.8935	0.6008	$<0.001$	$p=1.000$
Nussinov	0.8494	0.8478	$<0.001$	$p=1.000$
RiNALMo	0.7171	0.7147	$p=0.001$	$p=1.000$
SPOT-RNA	0.9004	0.8707	$<0.001$	$p=1.000$

Appendix

Table 14: Model-vs-model permutation test

p

-values comparing the SDSM model against the CB BCE baseline, per extraction method. Significant results (

p<0.05

) are shown in bold.

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Accurate prediction of RNA secondary structure underpins transcriptome annotation, mechanistic analysis of non-coding RNAs, and RNA therapeutic design. Recent gains from deep learning and RNA foundation models are difficult to interpret because current benchmarks may overestimate generalization across RNA families. We present the Comprehensive Hierarchical Annotation of Non-coding RNA Groups (CHANRG), a benchmark of 170{,}083 structurally non-redundant RNAs curated from more than 10 million sequences in Rfam~15.0 using structure-aware deduplication, genome-aware split design and multiscale structural evaluation. Across 29 predictors, foundation-model methods achieved the highest held-out accuracy but lost most of that advantage out of distribution, whereas structured decoders and direct neural predictors remained markedly more robust. This gap persisted after controlling for sequence length and reflected both loss of structural coverage and incorrect higher-order wiring. Together, CHANRG and a padding-free, symmetry-aware evaluation stack provide a stricter and batch-invariant framework for developing RNA structure predictors with demonstrable out-of-distribution robustness.

Abstract

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