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Interpreting cis-regulatory mechanisms from genomic deep neural networks using surrogate models

Nature Machine Intelligence volume 6, pages 701–713 (2024)Cite this article

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A preprint version of the article is available at bioRxiv.

Abstract

Deep neural networks (DNNs) have greatly advanced the ability to predict genome function from sequence. However, elucidating underlying biological mechanisms from genomic DNNs remains challenging. Existing interpretability methods, such as attribution maps, have their origins in non-biological machine learning applications and therefore have the potential to be improved by incorporating domain-specific interpretation strategies. Here we introduce SQUID (Surrogate Quantitative Interpretability for Deepnets), a genomic DNN interpretability framework based on domain-specific surrogate modelling. SQUID approximates genomic DNNs in user-specified regions of sequence space using surrogate models—simpler quantitative models that have inherently interpretable mathematical forms. SQUID leverages domain knowledge to model cis-regulatory mechanisms in genomic DNNs, in particular by removing the confounding effects that nonlinearities and heteroscedastic noise in functional genomics data can have on model interpretation. Benchmarking analysis on multiple genomic DNNs shows that SQUID, when compared to established interpretability methods, identifies motifs that are more consistent across genomic loci and yields improved single-nucleotide variant-effect predictions. SQUID also supports surrogate models that quantify epistatic interactions within and between cis-regulatory elements, as well as global explanations of cis-regulatory mechanisms across sequence contexts. SQUID thus advances the ability to mechanistically interpret genomic DNNs.

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Fig. 1: Overview of SQUID.
Fig. 2: Benchmark analysis of attribution methods.
Fig. 3: Benchmark analysis across TFs, DNNs, and flank sizes.
Fig. 4: Attribution method performance during benign overfitting.
Fig. 5: SQUID captures epistatic interactions.

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Data availability

The datasets, models and computational results used to support the findings in this paper are available on Zenodo at https://doi.org/10.5281/zenodo.10047748 ref. 69. Datasets include the test set sequences held out during the training of ResidualBind-32, DeepSTARR and BPNet; the ChIP–seq peaks and background sequences used to train our three-layer CNN; and the CAGI5 challenge dataset.

Code availability

SQUID is an open-source Python package based on TensorFlow70. SQUID can be installed via pip (https://pypi.org/project/squid-nn) or GitHub (https://github.com/evanseitz/squid-nn). Documentation for SQUID is provided on ReadTheDocs (https://squid-nn.readthedocs.io). The code for performing all analyses in this paper is available on GitHub as well (https://github.com/evanseitz/squid-manuscript, ref. 71), and a static snapshot of this code is available on Zenodo69.

References

  1. Linder, J., Srivastava, D., Yuan, H., Agarwal, V. & Kelley, D. R. Predicting RNA-seq coverage from DNA sequence as a unifying model of gene regulation. Preprint at bioRxiv https://doi.org/10.1101/2023.08.30.555582 (2023).

  2. Avsec, Ž. et al. Effective gene expression prediction from sequence by integrating long-range interactions. Nat. Methods 18, 1196–1203 (2021).

    Google Scholar 

  3. Dudnyk, K., Cai, D., Shi, C., Xu, J. & Zhou, J. Sequence basis of transcription initiation in the human genome. Science 384, 694 (2024).

    Google Scholar 

  4. Jaganathan, K. et al. Predicting splicing from primary sequence with deep learning. Cell 176, 535–548.e24 (2019).

    Google Scholar 

  5. Avsec, Ž. et al. Base-resolution models of transcription-factor binding reveal soft motif syntax. Nat. Genet. 53, 354–366 (2021).

    Google Scholar 

  6. Chen, K. M., Wong, A. K., Troyanskaya, O. G. & Zhou, J. A sequence-based global map of regulatory activity for deciphering human genetics. Nat. Genet. 54, 940–949 (2022).

    Google Scholar 

  7. Zhou, J. Sequence-based modeling of three-dimensional genome architecture from kilobase to chromosome scale. Nat. Genet. 54, 725–734 (2022).

    Google Scholar 

  8. Koo, P. K. & Ploenzke, M. Deep learning for inferring transcription factor binding sites. Curr. Opin. Syst. Biol. 19, 16–23 (2020).

    Google Scholar 

  9. Novakovsky, G., Dexter, N., Libbrecht, M. W., Wasserman, W. W. & Mostafavi, S. Obtaining genetics insights from deep learning via explainable artificial intelligence. Nat. Rev. Genet. 24, 125–137 (2022).

    Google Scholar 

  10. Han, T., Srinivas, S. & Lakkaraju, H. Which explanation should I choose? A function approximation perspective to characterizing post hoc explanations. Preprint at https://arxiv.org/abs/2206.01254 (2022).

  11. Hooker, S., Erhan, D., Kindermans, P.-J. & Kim, B. A benchmark for interpretability methods in deep neural networks. In Advances in Neural Information Processing Systems Vol. 32 (2019).

  12. Ancona, M., Ceolini, E., Öztireli, C. & Gross, M. Towards better understanding of gradient-based attribution methods for deep neural networks. Preprint at https://arxiv.org/abs/1711.06104 (2017).

  13. Simonyan, K., Vedaldi, A. & Zisserman, A. Deep inside convolutional networks: visualising image classification models and saliency maps. In Workshop at International Conference on Learning Representations (2014).

  14. Shrikumar, A., Greenside, P. & Kundaje, A. Learning important features through propagating activation differences. In Proc. 34th International Conference on Machine Learning Vol. 70, ICML’17, 3145–3153 (JMLR.org, 2017).

  15. Zhou, J. & Troyanskaya, O. G. Predicting effects of noncoding variants with deep learning-based sequence model. Nat. Methods 12, 931–934 (2015).

    Google Scholar 

  16. Smilkov, D., Thorat, N., Kim, B., Viégas, F. & Wattenberg, M. SmoothGrad: Removing noise by adding noise. Preprint at https://arxiv.org/abs/1706.03825 (2017).

  17. Sundararajan, M., Taly, A. & Yan, Q. Axiomatic attribution for deep networks. Preprint at https://arxiv.org/abs/1703.01365 (2017).

  18. Lundberg, S. M. & Lee, S.-I. A Unified approach to interpreting model predictions. In Advances in Neural Information Processing Systems Vol. 30, 4768–4777 (Curran Associates, 2017).

  19. Starr, T. N. & Thornton, J. W. Epistasis in protein evolution. Protein Sci. 25, 1204–1218 (2016).

    Google Scholar 

  20. Weinreich, D. M., Lan, Y., Wylie, C. S. & Heckendorn, R. B. Should evolutionary geneticists worry about higher-order epistasis? Curr. Opin. Genet. Dev. 23, 700–707 (2013).

    Google Scholar 

  21. Aghazadeh, A. et al. Epistatic net allows the sparse spectral regularization of deep neural networks for inferring fitness functions. Nat. Commun. 12, 5225 (2021).

    Google Scholar 

  22. Zhou, J. et al. Higher-order epistasis and phenotypic prediction. Proc. Natl Acad. Sci. USA 119, e2204233119 (2022).

    Google Scholar 

  23. Domingo, J., Baeza-Centurion, P. & Lehner, B. The causes and consequences of genetic interactions (epistasis). Annu. Rev. Genomics Hum. Genet. 20, 433–460 (2019).

    Google Scholar 

  24. Otwinowski, J., McCandlish, D. M. & Plotkin, J. B. Inferring the shape of global epistasis. Proc. Natl Acad. Sci. USA 115, E7550–E7558 (2018).

    Google Scholar 

  25. Poelwijk, F. J., Krishna, V. & Ranganathan, R. The context-dependence of mutations: a linkage of formalisms. PLOS Comput. Biol. 12, e1004771 (2016).

    Google Scholar 

  26. Tareen, A. et al. MAVE-NN: learning genotype–phenotype maps from multiplex assays of variant effect. Genome Biol. 23, 98 (2022).

    Google Scholar 

  27. Tonner, P. D., Pressman, A. & Ross, D. Interpretable modeling of genotype–phenotype landscapes with state-of-the-art predictive power. Proc. Natl Acad. Sci. USA 119, e2114021119 (2022).

    Google Scholar 

  28. Ribeiro, M. T., Singh, S. & Guestrin, C. “Why should I trust you?": explaining the predictions of any classifier. In Proc. 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining 1135–1144 (ACM, 2016).

  29. Kinney, J. B., Murugan, A., Callan Jr, C. G. & Cox, E. C. Using deep sequencing to characterize the biophysical mechanism of a transcriptional regulatory sequence. Proc. Natl Acad. Sci. USA 107, 9158–9163 (2010).

    Google Scholar 

  30. Jones, M. C. & Faddy, M. J. A skew extension of the t-distribution, with applications. J. R. Stat. Soc. Ser. B 65, 159–174 (2003).

    MathSciNet  Google Scholar 

  31. Tareen, A. & Kinney, J. B. Logomaker: beautiful sequence logos in Python. Bioinformatics 36, 2272–2274 (2019).

    Google Scholar 

  32. Gordân, R. et al. Genomic regions flanking E-box binding sites influence DNA binding specificity of bHLH transcription factors through DNA shape. Cell Rep. 3, 1093–1104 (2013).

    Google Scholar 

  33. Jolma, A. et al. DNA-dependent formation of transcription factor pairs alters their binding specificity. Nature 527, 384–388 (2015).

    Google Scholar 

  34. de Almeida, B. P., Reiter, F., Pagani, M. & Stark, A. DeepSTARR predicts enhancer activity from DNA sequence and enables the de novo design of synthetic enhancers. Nat. Genet. 54, 613–624 (2022).

    Google Scholar 

  35. Toneyan, S., Tang, Z. & Koo, P. Evaluating deep learning for predicting epigenomic profiles. Nat. Mach. Intell. 4, 1088–1100 (2022).

    Google Scholar 

  36. Spitz, F. & Furlong, E. E. M. Transcription factors: from enhancer binding to developmental control. Nat. Rev. Genet. 13, 613–626 (2012).

    Google Scholar 

  37. Bartlett, P. L., Long, P. M., Lugosi, G. & Tsigler, A. Benign overfitting in linear regression. Proc. Natl Acad. Sci. USA 117, 30063–30070 (2020).

    MathSciNet  Google Scholar 

  38. Chatterji, N. S. & Long, P. M. Finite-sample analysis of interpolating linear classifiers in the overparameterized regime. J. Mach. Learn. Res. 22, 5721–5750 (2021).

    MathSciNet  Google Scholar 

  39. Wang, Z. et al. Smoothed geometry for robust attribution. Adv. Neural Inform. Process. Syst. 33, 13623–13634 (2020).

    Google Scholar 

  40. Alvarez-Melis, D. & Jaakkola, T. S. Towards robust interpretability with self-explaining neural networks. In Proc. 32nd International Conference on Neural Information Processing Systems 7786–7795 (Curran Associates Inc., 2018).

  41. Majdandzic, A. et al. Selecting deep neural networks that yield consistent attribution-based interpretations for genomics. In Machine Learning in Computational Biology 131–149 (PMLR, 2022).

  42. Zhang, C., Bengio, S., Hardt, M., Recht, B. & Vinyals, O. Understanding deep learning requires rethinking generalization. Preprint at https://arxiv.org/abs/1611.03530 (2017).

  43. Papagianni, A. et al. Capicua controls Toll/IL-1 signaling targets independently of RTK regulation. Proc. Natl Acad. Sci. USA 115, 1807–1812 (2018).

    Google Scholar 

  44. Crocker, J. et al. Low affinity binding site clusters confer hox specificity and regulatory robustness. Cell 160, 191–203 (2015).

    Google Scholar 

  45. Farley, E. K. et al. Suboptimization of developmental enhancers. Science 350, 325–328 (2015).

    Google Scholar 

  46. Castro-Mondragon, J. A. et al. JASPAR 2022: the 9th release of the open-access database of transcription factor binding profiles. Nucleic Acids Res. 50, D165–D173 (2021).

    Google Scholar 

  47. Kircher, M. et al. Saturation mutagenesis of twenty disease-associated regulatory elements at single base-pair resolution. Nat. Commun. 10, 3583 (2019).

    Google Scholar 

  48. Shigaki, D. et al. Integration of multiple epigenomic marks improves prediction of variant impact in saturation mutagenesis reporter assay. Hum. Mutat. 40, 1280–1291 (2019).

    Google Scholar 

  49. Kelley, D. R. et al. Sequential regulatory activity prediction across chromosomes with convolutional neural networks. Genome Res. 28, 739–750 (2018).

    Google Scholar 

  50. Kim, S. & Wysocka, J. Deciphering the multi-scale, quantitative cis-regulatory code. Mol. Cell 83, 373–392 (2023).

    Google Scholar 

  51. Georgakopoulos-Soares, I. et al. Transcription factor binding site orientation and order are major drivers of gene regulatory activity. Nat. Commun. 14, 2333 (2023).

    Google Scholar 

  52. Koo, P. K., Majdandzic, A., Ploenzke, M., Anand, P. & Paul, S. B. Global importance analysis: an interpretability method to quantify importance of genomic features in deep neural networks. PLoS Comput. Biol. 17, e1008925 (2021).

    Google Scholar 

  53. Weinreich, D. M., Lan, Y., Jaffe, J. & Heckendorn, R. B. The influence of higher-order epistasis on biological fitness landscape topography. J. Stat. Phys. 172, 208–225 (2018).

    MathSciNet  Google Scholar 

  54. Ackers, G. K., Johnson, A. D. & Shea, M. A. Quantitative model for gene regulation by lambda phage repressor. Proc. Natl Acad. Sci. USA 79, 1129–1133 (1982).

    Google Scholar 

  55. Bintu, L. et al. Transcriptional regulation by the numbers: models. Curr. Opin. Genet. Dev. 15, 116–124 (2005).

    Google Scholar 

  56. Segal, E. & Widom, J. From DNA sequence to transcriptional behaviour: a quantitative approach. Nat. Rev. Genet. 10, 443–456 (2009).

    Google Scholar 

  57. Sherman, M. S. & Cohen, B. A. Thermodynamic state ensemble models of cis-regulation. PLoS Comput. Biol. 8, e1002407 (2012).

    MathSciNet  Google Scholar 

  58. Faure, A. J. et al. Mapping the energetic and allosteric landscapes of protein binding domains. Nature 604, 175–183 (2022).

    Google Scholar 

  59. Tareen, A. & Kinney, J. B. Biophysical models of cis-regulation as interpretable neural networks. In 14th Conference on Machine Learning in Computational Biology (MLCB 2019); https://doi.org/10.1101/835942

  60. Estrada, J., Wong, F., DePace, A. & Gunawardena, J. Information integration and energy expenditure in gene regulation. Cell 166, 234–244 (2016).

    Google Scholar 

  61. Scholes, C., DePace, A. H. & Sánchez, Á. Combinatorial gene regulation through kinetic control of the transcription cycle. Cell Syst. 4, 97–108.e9 (2017).

    Google Scholar 

  62. Park, J. et al. Dissecting the sharp response of a canonical developmental enhancer reveals multiple sources of cooperativity. eLife 8, e41266 (2019).

    Google Scholar 

  63. Pedregosa, F. et al. Scikit-learn: machine learning in Python. J. Mach. Learn. Res. 12, 2825–2830 (2011).

    MathSciNet  Google Scholar 

  64. Avsec, Z. & Weilert, M. kundajelab/bpnet-manuscript: Publication release of BPNet manuscript code. Zenodo https://zenodo.org/records/4294814 (2020).

  65. Avsec, Z. et al. The Kipoi repository accelerates community exchange and reuse of predictive models for genomics. Nat. Biotechnol. https://doi.org/10.1038/s41587-019-0140-0 (2019).

  66. Srivastava, N., Hinton, G., Krizhevsky, A., Sutskever, I. & Salakhutdinov, R. Dropout: a simple way to prevent neural networks from overfitting. J. Mach. Learn. Res. 15, 1929–1958 (2014).

    MathSciNet  Google Scholar 

  67. Kingma, D. P. & Ba, J. Adam: a method for stochastic optimization. Preprint at https://arxiv.org/abs/1412.6980 (2014).

  68. Majdandzic, A., Rajesh, C. & Koo, P. K. Correcting gradient-based interpretations of deep neural networks for genomics. Genome Biol. 24, 1–13 (2023).

    Google Scholar 

  69. Seitz, E. evanseitz/squid-manuscript: SQUID manuscript workflow with outputs. Zenodo https://doi.org/10.5281/zenodo.10047747 (2023).

  70. Abadi, M. et al. TensorFlow: large-scale machine learning on heterogeneous systems. Software available from tensorflow.org (2015).

  71. Seitz, E. & Koo, P. evanseitz/squid-nn: surrogate quantitative interpretability for deepnets. Zenodo https://doi.org/10.5281/zenodo.11060672 (2023).

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Acknowledgements

We thank Z. Tang, S. Toneyan, M. Kooshkbaghi, C. Rajesh, J. Kaczmarzyk and C. Martí-Gómez for helpful discussions. This work was supported in part by: the Simons Center for Quantitative Biology at Cold Spring Harbor Laboratory; NIH grants R01HG012131 (P.K.K., E.E.S., J.B.K. and D.M.M.), R01HG011787 (J.B.K., E.E.S. and D.M.M.), R01GM149921 (P.K.K.), R35GM133777 (J.B.K.) and R35GM133613 (D.M.M.); and an Alfred P. Sloan Foundation Research Fellowship (D.M.M.). Computations were performed using equipment supported by NIH grant S10OD028632.

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  1. Simons Center for Quantitative Biology, Cold Spring Harbor Laboratory, Cold Spring Harbor, NY, USA

    Evan E. Seitz, David M. McCandlish, Justin B. Kinney & Peter K. Koo

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Contributions

E.E.S., D.M.M., J.B.K. and P.K.K. conceived of the study. E.E.S. wrote the software and performed the analysis. E.E.S. designed the analysis with help from D.M.M., J.B.K. and P.K.K. J.B.K. and P.K.K. supervised the study. E.E.S., D.M.M., J.B.K. and P.K.K. wrote the paper.

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Correspondence to Justin B. Kinney or Peter K. Koo.

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Extended data

Extended Data Fig. 1 Additional comparisons of K-Lasso LIME to SQUID.

Shown are the results of analyses, performed as in Fig. 2b for n = 50 genomic sequences, comparing the performance of SQUID to the performance of the K-Lasso implementation of LIME for four different values of K. P values were computed using a one-sided Mann-Whitney U test; ***, p < 0.001. We note that the attribution variation values obtained for SQUID in these tests varied systematically with the choice of K. The reason is as follows. The K-Lasso LIME algorithm produces sparse attribution maps that have only K nonzero parameters. Consequently, the variation observed in K-Lasso LIME attribution maps systematically decreases as K decreases. This gives K-Lasso LIME an unfair advantage in the attribution variation test described in Main Text and in Methods. To fairly compare K-Lasso LIME to SQUID in this figure, we therefore modified this test. In the analysis of each in silico MAVE, the attribution map elements inferred by SQUID were first set to zero at the same positions where all K-Lasso LIME attribution map elements were exactly zero. Attribution variation values were then calculated as described in Main Text and in Methods.

Extended Data Fig. 2 Influence of mutation rate and library size on SQUID attribution maps.

a,b, attribution variation (left) and average attribution maps (right) found for 50 SQUID attribution maps computed for the TF AP-1 as in Fig. 2 but using in silico MAVE libraries having (a) variable mutation rate (r) and fixed number of mutagenized sequences N = 100, 000, or (b) fixed mutation rate r = 10% and variable number of mutagenized sequences (N). All SQUID attribution maps were computed using additive models with GE nonlinearities, followed by cropping these maps using a flank size of nf = 50 nt.

Extended Data Fig. 3 Nonlinearities and noise across DNNs and TFs.

Examples of the GE nonlinearities and heteroscedastic noise models inferred in the SQUID (GE) analyses performed for Fig. 3. Each plot shows results for a representative sequence among the n = 50 sequences analyzed for each combination of DNN and TF.

Extended Data Fig. 4 Average and example binding motifs for Oct4 and Sox2.

a, Oct4 motifs, centered on the putative binding site TTTGCAT. b, Sox2 motifs, centered on the putative binding site GAACAATAG. TF binding motifs are from attribution maps computed for BPNet and plotted as in Fig. 3c.

Extended Data Fig. 5 Benchmark analysis of attribution variation for putative weak TF binding sites.

a, ISM attribution map given by BPNet for a representative genomic sequence containing multiple putative weak binding sites for the mouse TF Nanog (top). Blue represents the wild-type nucleotides while gray represents other nucleotides. PWM scores (given by PWM for Nanog motif) are displayed across the genomic sequence (bottom). Only positive PWM scores are shown. b, For each TF and DNN, plots show attribution variation values for 150 putative TF binding sites plotted against putative binding site strength. Bold lines indicate signals smoothed with a sliding window of 20 nt. Stars indicate P values computed using the one-sided Mann-Whitney U test: **, 0.001≤ p < 0.01; ***, p < 0.001. PWM scores for each of the 150 putative sites are shown above, along with a logo representation of the PWM used. Each site is represented by a gray bar shaded according to the number of mutations (0, 1, or 2) in the core of the putative site.

Extended Data Fig. 6 Attribution maps computed for strong and weak TF binding sites.

a,b, Top row shows the average of 50 attribution maps in the 0-mutation ensemble computed for IRF1 using ResidualBind-32 (a), and for Ohler using DeepSTARR (b). Remaining rows show attribution maps for four representative genomic loci with the central putative binding site having varying numbers of mutations from the consensus binding site.

Extended Data Fig. 7 Occlusion analysis of AP-1 binding site effects.

Occlusion study based on the wild-type sequence investigated in Figures 6d and 6e. Occlusions were performed for every combination of one, two, or three occluded motifs, with the DNN prediction taken independently for each instance (n = 100 for each boxplot). In each occluded sequence, the corresponding AP-1 core (7-mer) sites were scrambled using a uniform probability of nucleotides at each position. The baseline score (CTRL) was calculated from the median of predictions corresponding to n = 100 instances of a dinucleotide shuffle over the full (2048 nt) sequence. The DNN prediction rapidly approaches the genomic baseline as additional binding sites are occluded. Boxplot lines represent median, upper quartile, and lower quartile; whiskers represent 1.5 × the inter-quartile range.

Extended Data Fig. 8 SQUID supports global DNN interpretations.

a, In silico MAVE libraries used by SQUID to infer surrogate models of global TF specificity. Each sequence in the library contains a partially-mutagenized version of a consensus TF binding site embedded within random DNA. b, Additive surrogate models for BPNet inferred by SQUID using libraries of the form in panel a for the mouse TFs Oct4, Sox2, Klf4, and Nanog. Gray bars indicate 10.5 nt periodicity on either side of the inferred Nanog motif. c, Format of the in silico MAVE libraries used to study global TF-TF epistatic interactions. Each sequence in the library contains two partially mutagenized consensus TF binding sites embedded a fixed distance apart (0 nt to 32 nt) within random DNA. d, Pairwise surrogate model inferred for BPNet by SQUID using a library of the form in c and putative binding sites for Nanog and Sox2. e, Distance-dependence of inter-site interactions between Nanog and Sox2. Dots show the Frobenius norm of inter-site pairwise interactions, inferred as in d, using libraries having different distances between the embedded Nanog and Sox2 sites. The occurrence of periodic inter-site interaction minima occurred at distances where the central nucleotides in Sox2 (that is, AA) overlapped with the periodic Nanog-associated flanking signals. Black line is from a least-squares fit of a polynomial of degree 10. d,e, Libraries comprised of 500,000 sequences. BPNet profiles were projected to scalars using PCA, which yielded substantially lower background noise than obtained using profile contribution scores.

Extended Data Table 1 SQUID computation times
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Extended Data Table 2 GE modelling is robust to the number of hidden nodes
Full size table

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Seitz, E.E., McCandlish, D.M., Kinney, J.B. et al. Interpreting cis-regulatory mechanisms from genomic deep neural networks using surrogate models. Nat Mach Intell 6, 701–713 (2024). https://doi.org/10.1038/s42256-024-00851-5

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