AbstractUnderstanding the genetic basis of complex diseases is one of the most important challenges in current precision medicine. To this end, Genome-Wide Association Studies aim to correlate Single Nucleotide Polymorphisms (SNPs) to the presence or absence of certain traits. However, these studies do not consider interactions between several SNPs, known as epistasis, which explain most genetic diseases.

摘要了解复杂疾病的遗传基础是当前精准医学中最重要的挑战之一。为此，全基因组关联研究旨在将单核苷酸多态性（SNP）与某些性状的存在或不存在相关联。但是，这些研究没有考虑几种SNP之间的相互作用，称为上位性，这可以解释大多数遗传疾病。

Analyzing SNP combinations to detect epistasis is a major computational task, due to the enormous search space. A possible solution is to employ deep learning strategies for genomic prediction, but the lack of explainability derived from the black-box nature of neural networks is a challenge yet to be addressed.

由于巨大的搜索空间，分析SNP组合以检测上位性是一项主要的计算任务。。

Herein, a novel, flexible, portable, and scalable framework for network interpretation based on transformers is proposed to tackle any-order epistasis. The results on various epistasis scenarios show that the proposed framework outperforms state-of-the-art methods for explainability, while being scalable to large datasets and portable to various deep learning accelerators.

在此，提出了一种新颖，灵活，可移植且可扩展的基于变压器的网络解释框架，以解决任何阶上位性问题。在各种上位性场景上的结果表明，所提出的框架在解释性方面优于最先进的方法，同时可扩展到大型数据集并可移植到各种深度学习加速器。

The proposed framework is validated on three WTCCC datasets, identifying SNPs related to genes known in the literature that have direct relationships with the studied diseases..

所提出的框架在三个WTCCC数据集上得到了验证，确定了与文献中已知的与所研究疾病直接相关的基因相关的SNP。。

IntroductionAdvancements in DNA sequencing in the past 40 years have paved the way from analyzing small sequences to mapping the entire human genome. This technological breakthrough has allowed for the emergence of Genome-Wide Association Studies (GWAS)1, a research approach that aims to unveil correlations between complex diseases and Single Nucleotide Polymorphisms (SNPs), a common type of genetic variation.

引言过去40年来DNA测序的进步为从分析小序列到绘制整个人类基因组铺平了道路。这项技术突破使得全基因组关联研究（GWAS）1得以出现，该研究方法旨在揭示复杂疾病与单核苷酸多态性（SNP）（一种常见的遗传变异类型）之间的相关性。

GWAS study a phenotype, a set of observable characteristics, such as a disease, and define the individuals of a population by the presence (case) or absence (control) of the studied traits. The rationale for this methodology lies in assuming that common diseases have common underlying influential genetic variants across a population2.

GWAS研究表型，一组可观察到的特征，例如疾病，并通过研究特征的存在（病例）或不存在（对照）来定义人群中的个体。这种方法的基本原理在于假设常见疾病在整个人群中具有共同的潜在影响遗传变异2。

Some examples of the success of GWAS include the association between the IL-12/IL-23 pathway and the development of Crohn’s Disease3, as well as the discovery of the PTPN22 gene’s influence in autoimmune diseases4.The approach for GWAS makes a crucial assumption: SNPs are independently correlated to the studied phenotype.

GWAS成功的一些例子包括IL-12/IL-23途径与克罗恩病发展之间的关联3，以及PTPN22基因在自身免疫性疾病中的影响的发现4。GWAS的方法做出了一个至关重要的假设：SNP与研究的表型独立相关。

Therefore, SNPs can be tested individually for statistical relevance to the disease, while neglecting gene-environment and gene-gene interactions, known as the “missing heritability” problem in the literature5. The combinatorial effect that arises when two or more SNPs interact is known as epistasis and may play a fundamental role on the missing heritability problem.

因此，可以单独测试SNP与疾病的统计相关性，同时忽略基因-环境和基因-基因相互作用，这在文献中被称为“遗传力缺失”问题5。。

Research on epistasis has focused on the detection of SNP interactions to explain complex diseases, such as Late Onset Alzheimer’s Disease6.Finding the optimal interacting SNP combination to explain a disease implies the exhaustive evaluation of all possible cases, which presents a current computational challenge.

上位性研究的重点是检测SNP相互作用以解释复杂疾病，例如迟发性阿尔茨海默氏病6。寻找最佳的相互作用SNP组合来解释疾病意味着对所有可能的病例进行详尽的评估，这是目前的计算挑战。

As an example, on WTCCC datasets, as ma.

例如，在WTCCC数据集上，作为ma。

(1)

(1)

where D is the embedding size. The inner product \(QY^T\) is a measure of a SNP’s importance to predict the current label. Similar embeddings to represent a SNP t and a label are mapped to similar queries and keys. As a consequence, \(Q{Y_t}^T\) should have a large value. Conversely, different embeddings lead to a small product, denoting a non-existent relationship between the SNP and the label.

其中D是嵌入大小。内积（QY ^ T）是衡量SNP预测当前标签重要性的指标。表示SNP t和标签的类似嵌入被映射到类似的查询和键。因此，\（Q{Y\u t}^ t\）应该有一个大值。相反，不同的嵌入会产生一个小产品，表明SNP和标签之间不存在关系。

In Eq. (1), the softmax function is given by$$\begin{aligned} Softmax(QY_{t}^T /\sqrt{D}) = \frac{exp(QY_{t}^T/\sqrt{D})}{\sum _t exp(QY_{t}^T/\sqrt{D})}, \end{aligned}$$.

在等式（1）中，softmax函数由$$\ begin{aligned}softmax（QY\ut}^ t/\ sqrt{D}）=\ frac{exp（QY\ut}^ t/\ sqrt{D}）}{\ sum \u t exp（QY\ut}^ t/\ sqrt{D}）}、\ end{aligned}$$给出。

(2)

(2)

where exp(.) denotes the exponential function. Applying softmax to \(QY^T/\sqrt{D}\) outputs a probability distribution over the SNPs, known as attention scores, which are used to combine the value vectors. As interacting SNPs should have a large \(Q{Y_t}^T/\sqrt{D}\) value, the corresponding attention score should also be large.

其中exp（.）表示指数函数。。由于相互作用的SNP应该具有较大的\（Q{Y\u t}^ t/\ sqrt{D}\）值，因此相应的注意力得分也应该较大。

Therefore, keeping the SNPs with the highest attention scores after training provides a method to identify potential epistatic interactions. An exhaustive search can be performed afterwards on the chosen SNPs to find the optimal SNP combination.While this approach works, it has some drawbacks. In epistatic datasets, it is unlikely that many SNPs have a true correlation to the label.

因此，在训练后保持注意力得分最高的SNP提供了一种识别潜在上位性相互作用的方法。之后可以对所选SNP进行详尽的搜索，以找到最佳的SNP组合。。在上位性数据集中，许多SNP不太可能与标签真正相关。

Therefore, calculating attention simultaneously between all SNPs and the label may hinder the identification of epistatic interactions if most SNPs are noisy. To overcome this problem and boost the transformer’s prediction power, a possible solution is to split the key vector (which represents the SNPs) into several partitions, \(Y_i\), and calculate attention between the query and a partition (the query cannot be split because it represents a single token, the patient’s label).

因此，如果大多数SNP都有噪音，那么同时计算所有SNP和标签之间的注意力可能会阻碍上位相互作用的识别。为了克服这个问题并提高变压器的预测能力，一个可能的解决方案是将关键向量（代表SNP）分成几个分区\（Y\u i \），并计算查询和分区之间的注意力（查询无法分割，因为它代表一个标记，即患者的标签）。

As each partition has a smaller number of SNPs, noise is reduced, increasing the chances of identifying true epistatic SNPs. However, there is no guarantee that a single partition holds all possible interacting SNPs. Therefore, attention should be calculated between combinations of partitions, allowing for all possible subsets of SNPs to be evaluated together.Figure 4 provides an example of this strategy.

由于每个分区的SNP数量较少，因此噪声会降低，从而增加识别真正上位性SNP的机会。但是，不能保证单个分区包含所有可能的交互SNP。因此，应该在分区的组合之间计算注意力，从而可以一起评估所有可能的SNP子集。图4提供了此策略的示例。

In this example, the key vector is split in three partitions and mixed in combinations of two, resulting in three different options (1 and 2, 1 and 3, 2 and 3). Attention sc.

在本例中，关键向量被分成三个分区，并以两个分区的组合进行混合，从而产生三个不同的选项（1和2、1和3、2和3）。注意sc。

(3)

(3)

where \(\odot\) represents the Hadamard product (element-wise product), \({h_i}^L\) is the output of the i-th token from the last Transformer layer, L, and \(\nabla {h_i}^L\) is given by$$\begin{aligned} \nabla {h_i}^L = \frac{\partial y^c}{\partial {h_i}^L}, \end{aligned}$$

其中\（\ odot \）表示阿达玛乘积（元素乘积），\（{h\u i}^ L \）是最后一个变压器层L的第i个令牌的输出，并且\（\ nabla{h\u i}^ L \）由$$\ begin{aligned}\ nabla{h\u i}^ L=\ frac{\ partial y ^ c}{\ partial{h\u i}^ L}、\ end{aligned}给出$$

(4)

(4)

where \(y^c\) is the transformer’s final output for class c. Therefore, \(\nabla {h_i}^L\) illustrates a partial linearization from \({h_i}^L\) that captures the importance of the i-th token to a target class c. Attentive CAT is then calculated as$$\begin{aligned} {AttCAT_i}^L = ({\alpha _i}^L \cdot {CAT_i}^L)_H, \end{aligned}$$.

其中\（y ^ c \）是c类变压器的最终输出。因此，\（\nabla{h\u i}^ L \）说明了从\（{h\u i}^ L \）捕获第i个标记对目标c类的重要性的部分线性化。然后，注意猫被计算为$$\ begin{aligned}{AttCAT\u i}^ L=（{\ alpha i}^ L \ cdot{CAT\u i}^ L）\u h，end{aligned}$$。

(5)

(5)

where \({\alpha _i}^L\) denotes the attention scores of the i-th token at the L-th layer. This result is averaged over the attention heads, H.For the proposed framework, only one transformer layer exists, with a single encoder. After training, \(\nabla {h_i}^L\) is calculated for each SNP between the transformer’s final output and the encoder’s output, as well as attention scores.

其中\（{\ alpha}^ L \）表示第L层第i个标记的注意力得分。这个结果在注意头H上取平均值。对于所提出的框架，只有一个变压器层存在，只有一个编码器。训练后，计算变压器最终输出和编码器输出之间的每个SNP的\（\ nabla{h\u i}^ L \），以及注意力得分。

While Attentive CAT suggests a element-wise multiplication between attention scores and gradients, for the proposed framework, element-wise sum is also calculated. Furthermore, for these calculations, both gradients and attention scores are scaled from 0 to 1, to mitigate differences in the order of magnitude of both metrics.For element-wise sum and multiplication, averaging along the attention heads is not necessary, as the proposed network architecture works with a single attention head.

虽然注意力猫建议在注意力得分和梯度之间进行元素乘法，但对于所提出的框架，还计算了元素总和。此外，对于这些计算，梯度和注意力分数都从0缩放到1，以减轻两个指标的数量级差异。对于元素级求和和和乘法，不需要沿注意头求平均，因为所提出的网络体系结构使用单个注意头。

In addition to these two metrics, both attention scores and gradients can also be employed separately, adding to the framework’s flexible configuration. A hyperparameter search is done to analyze the optimal network parameters, as well as which of these four interpretation metrics provides the best detection power.Software and hardwareThe transformer model is implemented and trained using TensorFlow.

除了这两个指标之外，注意力得分和梯度也可以分别使用，从而增加了框架的灵活配置。进行超参数搜索以分析最佳网络参数，以及这四个解释指标中哪一个提供最佳检测能力。软件和硬件使用TensorFlow实现和训练变压器模型。

Depending on the used hardware, different TensorFlow versions are employed. Most of the experiments are devised on the LUMI supercomputer, on nodes with 8 AMD MI250X GPUs (TensorFlow 2.11, 128 GB memory). For scalability and comparison purposes, the model is also trained on systems with Intel PVC (TensorFlow 2.12, 48 GB memory), NVIDIA A100 (TensorFlow 2.12, 80 GB memory), Google TPU V4 (TensorFlow 2.12, 32 GB memory) and GraphCore IPU GC-200 (TensorFlow 2.6.3, 900 MB memory).Dataset generationSy.

根据使用的硬件，使用不同的TensorFlow版本。大多数实验是在LUMI超级计算机上设计的，节点上有8个AMD MI250X GPU（TensorFlow 2.11128 GB内存）。出于可扩展性和比较目的，该模型还可以在具有Intel PVC（TensorFlow 2.12，48 GB内存）、NVIDIA A100（TensorFlow 2.12，80 GB内存）、Google TPU V4（TensorFlow 2.12，32 GB内存）和GraphCore IPU GC-200（TensorFlow 2.6.3900 MB内存）的系统上进行训练。数据集生成。

Data availability

数据可用性

The source code of this work is available on: https://github.com/hiperbio/episdet-transformer.

这项工作的源代码位于：https://github.com/hiperbio/episdet-transformer.

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Download referencesAcknowledgementsThis work was supported by European Union HE Research and Innovation programme under grant agreement No 101092877 (SYCLOPS), and FCT (Fundação para a Ciência e a Tecnologia, Portugal) through the UIDB/50021/2020 project and the UI/BD/154603/2022 research grant.

下载参考文献致谢这项工作得到了欧盟HE研究与创新计划（第101092877号赠款协议（SYCLOPS））和FCT（葡萄牙技术基金会）通过UIDB/50021/2020项目和UI/BD/154603/2022研究资助的支持。

The research presented in this paper has benefited from the Experimental Infrastructure for Exploration of Exascale Computing (eX3), which is financially supported by the Research Council of Norway under contract 270053, and the FCT+Google Advanced Computing Project (CPCA-IAC/AV/478750/2022). Finally, we acknowledge the EuroHPC Joint Undertaking for awarding this project access to the EuroHPC supercomputer LUMI, hosted by CSC (Finland) and the LUMI consortium through a EuroHPC Benchmark Access call (EHPC-BEN-2023B01-002).Author informationAuthor notesThese authors contributed equally: Miguel Graça, Ricardo Nobre, Leonel Sousa and Aleksandar Ilic.Authors and AffiliationsINESC-ID, Instituto Superior Técnico, 1000-029, Lisbon, PortugalMiguel Graça, Ricardo Nobre, Leonel Sousa & Aleksandar IlicAuthorsMiguel GraçaView author publicationsYou can also search for this author in.

本文介绍的研究受益于挪威研究委员会根据合同270053提供的Exascale计算探索实验基础设施（eX3）和FCT+谷歌高级计算项目（CPCA-IAC/AV/478750/2022）。最后，我们感谢EuroHPC联合承诺授予该项目访问EuroHPC超级计算机LUMI的权限，该超级计算机由CSC（芬兰）和LUMI财团通过EuroHPC基准访问呼叫（EHPC-BEN-2023B01-002）托管。作者信息作者注意到这些作者做出了同样的贡献：米格尔·格拉萨（MiguelGraça），里卡多·诺布雷（RicardoNobre），莱昂内尔·索萨（LeonelSousa）和亚历山达尔·艾里克（AleksandarIlic）。作者和附属机构ID，Instituto Superior Técnico，1000-029，里斯本，PortugalMiguel Graça，Ricardo Nobre，Leonel Sousa＆Aleksandar Ilicauthors Miguel GraçaView作者出版物您也可以在中搜索这位作者。

PubMed Google ScholarRicardo NobreView author publicationsYou can also search for this author in

PubMed谷歌学术评论作者出版物您也可以在

PubMed Google ScholarLeonel SousaView author publicationsYou can also search for this author in

PubMed Google ScholarLeonel SousaView作者出版物您也可以在

PubMed Google ScholarAleksandar IlicView author publicationsYou can also search for this author in

PubMed Google ScholarAleksandar IlicView作者出版物您也可以在

PubMed Google ScholarContributionsAll authors contributed equally to this work: M.G., A.L., and L.S. designed the experiments; M.G., R.N., L.S., and A.L. performed the experiments and analyzed the data; M.G., R.N., L.S., and A.L. wrote the manuscript. All authors reviewed the manuscript.Corresponding authorCorrespondence to.

PubMed谷歌学术贡献所有作者都对这项工作做出了同样的贡献：M.G.，A.L。和L.S.设计了实验；M、 G.，R.N.，L.S。和A.L.进行了实验并分析了数据；M、 G.，R.N.，L.S。和A.L.撰写了手稿。所有作者都审阅了手稿。对应作者对应。

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Reprints and permissionsAbout this articleCite this articleGraça, M., Nobre, R., Sousa, L. et al. Distributed transformer for high order epistasis detection in large-scale datasets.

转载和许可本文引用本文Graça，M.，Nobre，R.，Sousa，L。等人。分布式变压器，用于大规模数据集中的高阶上位性检测。

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KeywordsBioinformaticsMachine learningHigh performance computing

关键词信息机器学习高性能计算

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