research-article

Toward Interpretable Graph Tensor Convolution Neural Network for Code Semantics Embedding

Authors:
Jia Yang

Hubei Key Laboratory of Distributed System Security, Hubei EngineeringResearch Center on Big Data Security, School of Cyber Science and Engineering, Huazhong University of Science and Technology, China

Hubei Key Laboratory of Distributed System Security, Hubei EngineeringResearch Center on Big Data Security, School of Cyber Science and Engineering, Huazhong University of Science and Technology, China

0000-0003-1469-0789
View Profile

,
Cai Fu

Hubei Key Laboratory of Distributed System Security, Hubei EngineeringResearch Center on Big Data Security, School of Cyber Science and Engineering, Huazhong University of Science and Technology, China

Hubei Key Laboratory of Distributed System Security, Hubei EngineeringResearch Center on Big Data Security, School of Cyber Science and Engineering, Huazhong University of Science and Technology, China

0000-0003-4536-3537
View Profile

,
Fengyang Deng

Huazhong University of Science and Technology, China

Huazhong University of Science and Technology, China

0000-0003-3352-4065
View Profile

,
Ming Wen

Huazhong University of Science and Technology, China

Huazhong University of Science and Technology, China

0000-0001-5588-9618
View Profile

,
Xiaowei Guo

Huazhong University of Science and Technology

Huazhong University of Science and Technology

0000-0001-7239-7471
View Profile

,
Chuanhao Wan

Huazhong University of Science and Technology

Huazhong University of Science and Technology

0000-0002-5428-290X
View Profile

ACM Transactions on Software Engineering and Methodology Volume 32 Issue 5Article No.: 115pp 1–40https://doi.org/10.1145/3582574

Published:21 July 2023Publication History

ACM Transactions on Software Engineering and Methodology

Abstract

Intelligent deep learning-based models have made significant progress for automated source code semantics embedding, and current research works mainly leverage natural language-based methods and graph-based methods. However, natural language-based methods do not capture the rich semantic structural information of source code, and graph-based methods do not utilize rich distant information of source code due to the high cost of message-passing steps.

In this article, we propose a novel interpretable model, called graph tensor convolution neural network (GTCN), to generate accurate code embedding, which is capable of comprehensively capturing the distant information of code sequences and rich code semantics structural information. First, we propose to utilize a high-dimensional tensor to integrate various heterogeneous code graphs with node sequence features, such as control flow, data flow. Second, inspired by the current advantages of graph-based deep learning and efficient tensor computations, we propose a novel interpretable graph tensor convolution neural network for learning accurate code semantic embedding from the code graph tensor. Finally, we evaluate three popular applications on the GTCN model: variable misuse detection, source code prediction, and vulnerability detection. Compared with current state-of-the-art methods, our model achieves higher scores with respect to the top-1 accuracy while costing less training time.

REFERENCES

[1] Yaqin Zhou. 2019. Source codes of the paper: Devign: Effective vulnerability identification by learning comprehensive program semantics via graph neural networks. https://github.com/epicosy/devign.Google Scholar
[2] Yu Wang. 2020. Source codes of the paper: Learning semantic program embeddings with graph interval neural network. https://github.com/GINN-Imp/GINN.Google Scholar
[3] Vincent J. Hellendoorn. 2020. Source codes of the paper: Global relational models of source code. https://github.com/VHellendoorn/ICLR20-Great.Google Scholar
[4] Zhangyin Feng. 2021. Source codes of the paper: CodeBERT: A pre-trained model for programming and natural languages. https://github.com/microsoft/CodeBERT.Google Scholar
[5] Jia Yang. 2022. Source codes of this paper. https://gitee.com/cse-sss/GTCN.Google Scholar
[6] Jia Yang. 2022. Source codes of this paper. https://github.com/SmileResearch/GTCN.Google Scholar
[7] Yi Li. 2021. Source codes of the paper: Vulnerability detection with fine-grained interpretations. https://github.com/vulnerabilitydetection/VulnerabilityDetectionResearch.Google Scholar
[8] Allamanis Miltiadis, Brockschmidt Marc, and Khademi Mahmoud. 2018. Learning to represent programs with graphs. In 6th International Conference on Learning Representations.Google Scholar
[9] Aye Gareth Ari and Kaiser Gail E.. 2020. Sequence model design for code completion in the modern IDE. CoRR abs/2004.05249 (2020).Google Scholar
[10] Baraniuk Richard G.. 2011. More is less: Signal processing and the data deluge. Science 331(6018) (2011), 717–719.Google ScholarCross Ref
[11] Bichsel Benjamin, Raychev Veselin, Tsankov Petar, and Vechev Martin T.. 2016. Statistical deobfuscation of Android applications. In ACM SIGSAC Conference on Computer and Communications Security. 343–355.Google ScholarDigital Library
[12] Bielik Pavol, Raychev Veselin, and Vechev Martin T.. 2016. PHOG: Probabilistic model for code. In 33rd International Conference on Machine Learning. 2933–2942.Google Scholar
[13] Cai Tianle, Luo Shengjie, and Xu Keyulu. 2021. GraphNorm: A principled approach to accelerating graph neural network training. In 38th International Conference on Machine Learning. 1204–1215.Google Scholar
[14] Cao Sicong, Sun Xiaobing, Bo Lilial. et2022. MVD: Memory-related vulnerability detection based on flow-sensitive graph neural networks. In 44th IEEE/ACM 44th International Conference on Software Engineering. ACM, 1456–1468.Google ScholarDigital Library
[15] Cheng Lei and Shi Qingjiang. 2021. Towards overfitting avoidance: Tuning-free tensor-aided multi-user channel estimation for 3D massive MIMO communications. IEEE J. Sel. Top. Sig. Process. 15, 3 (2021), 832–846.Google ScholarCross Ref
[16] Cheng Xiao, Wang Haoyu, Hua Jiayial. et2021. DeepWukong: Statically detecting software vulnerabilities using deep graph neural network. ACM Trans. Softw. Eng. Methodol. 30, 3 (2021), 38:1–38:33.Google ScholarDigital Library
[17] Cherkassky Vladimir. 1997. The nature of statistical learning theory. IEEE Trans. Neural Netw. 8, 6 (1997), 1564.Google ScholarDigital Library
[18] Cichocki Andrzej and Mandic Danilo P.. 2015. Tensor decompositions for signal processing applications: From two-way to multiway component analysis. IEEE Sig. Process. Mag. 32, 2 (2015), 145–163.Google ScholarCross Ref
[19] Feng Zhangyin, Guo Daya, Tang Duyual. et2020. CodeBERT: A pre-trained model for programming and natural languages. In Findings of the Association for Computational Linguistics: EMNLP 2020, Online Event, 16–20 November 2020 (Findings of ACL), Vol. EMNLP 2020. Association for Computational Linguistics, 1536–1547.Google Scholar
[20] Fernandes Patrick, Allamanis Miltiadis, and Brockschmidt Marc. 2019. Structured neural summarization. In 7th International Conference on Learning Representations. OpenReview.net.Google Scholar
[21] Gauthier Gidel, Tony Jebara, and Simon Lacoste-Julien. 2017. Frank-Wolfe algorithms for Saddle point problems. In 20th International Conference on Artificial Intelligence and Statistics AISTATS. 362–371.Google Scholar
[22] Grohe Martin. 2020. word2vec, node2vec, graph2vec, X2vec: Towards a theory of vector embeddings of structured data. In 39th ACM Symposium on Principles of Database Systems. 1–16.Google Scholar
[23] Guo Daya, Ren Shuo, and Lu Shuai. 2021. GraphCodeBERT: Pre-training code representations with data flow. In 9th International Conference on Learning Representations. OpenReview.net.Google Scholar
[24] Guo Xiawei, Yao Quanming, and Kwok James Tin-Yau. 2017. Efficient Sparse low-rank tensor completion using the Frank-Wolfe algorithm. In 31st AAAI Conference on Artificial Intelligence. 1948–1954.Google ScholarCross Ref
[25] Hanayama Kaisei, Matsumoto Shinsuke, and Kusumoto Shinji. 2020. Humpback: Code completion system for Dockerfile based on language models (short paper). In Joint Proceedings of SEED & NLPaSE co-located with 27th Asia Pacific Software Engineering Conference. 67–73.Google Scholar
[26] Hawkins Douglas M.. 2004. The problem of overfitting. J. Chem. Inf. Model. 44, 1 (2004), 1–12.Google Scholar
[27] Hellendoorn Vincent J., Sutton Charles, Singh Rishabh, Maniatis Petros, and Bieber David. 2020. Global relational models of source code. In 8th International Conference on Learning Representations. OpenReview.net.Google Scholar
[28] Hindle Abram, Barr Earl T., Su Zhendongal. et2012. On the naturalness of software. In 34th International Conference on Software Engineering. 837–847.Google ScholarDigital Library
[29] Horenko Illia. 2020. On a scalable entropic breaching of the overfitting barrier for small data problems in machine learning. Neural Comput. 32, 8 (2020), 1563–1579.Google ScholarDigital Library
[30] Huang Ruizhe, Li Ke, and Arora Ashish. 2020. Efficient MDI adaptation for n-gram language models. In 21st Annual Conference of the International Speech Communication Association. 4916–4920.Google ScholarCross Ref
[31] Huang Zhichao, Li Xutao, Ye Yunming, and Ng Michael K.. 2020. MR-GCN: Multi-relational graph convolutional networks based on generalized tensor product. In 29th International Joint Conference on Artificial Intelligence. 1258–1264.Google ScholarCross Ref
[32] Jaggi Martin. 2013. Revisiting Frank-Wolfe: Projection-free sparse convex optimization. In 30th International Conference on Machine Learning. 427–435.Google Scholar
[33] Jain Prateek, Thakkar Om, and Thakurta Abhradeep. 2017. Differentially private matrix completion, revisited. CoRR abs/1712.09765 (2017).Google Scholar
[34] Jayadeva, Sharma Mayank, Soman Sumit, and Pant Himanshu. 2018. Ultra-sparse classifiers through minimizing the VC dimension in the empirical feature space—submitted to the special issue on “off the mainstream: Advances in neural networks and machine learning for pattern recognition.” Neural Process. Lett. 48, 2 (2018), 881–913.Google ScholarCross Ref
[35] Jukic Ante and Filipovic Marko. 2013. Supervised feature extraction for tensor objects based on maximization of mutual information. Pattern Recognit. Lett. 34, 13 (2013), 1476–1484.Google ScholarDigital Library
[36] Kajo Ibrahim, Kamel Nidal S., and Ruichek Yassine. 2020. Self-motion-assisted tensor completion method for background initialization in complex video sequences. IEEE Trans. Image Process. 29 (2020), 1915–1928.Google ScholarDigital Library
[37] Karampatsis Rafael-Michael, Babii Hlib, Robbes Romain, Sutton Charles, and Janes Andrea. 2020. Big code != big vocabulary: Open-vocabulary models for source code. In 42nd International Conference on Software Engineering. 1073–1085.Google ScholarDigital Library
[38] Kempf Dominic, Heß René, Müthing Steffen, and Bastian Peter. 2021. Automatic code generation for high-performance discontinuous Galerkin methods on modern architectures. ACM Trans. Math. Softw. 47, 1 (2021), 6:1–6:31.Google ScholarDigital Library
[39] Khaire Utkarsh Mahadeo and Dhanalakshmi R.. 2020. High-dimensional microarray dataset classification using an improved adam optimizer (iAdam). J. Amb. Intell. Humaniz. Comput. 11, 11 (2020), 5187–5204.Google ScholarCross Ref
[40] Khavari Behnoush and Rabusseau Guillaume. 2021. Lower and upper bounds on the VC-dimension of tensor network models. CoRR abs/2106.11827 (2021).Google Scholar
[41] Kilmer Misha E. and Martin Carla D.. 2011. Factorization strategies for third-order tensors. Linear Algeb. Applic. 435, 3 (2011), 641–658.Google ScholarCross Ref
[42] Kim Seohyun, Zhao Jinman, Tian Yuchi, and Chandra Satish. 2021. Code prediction by feeding trees to transformers. In 43rd IEEE/ACM International Conference on Software Engineering. 150–162.Google ScholarDigital Library
[43] Kipf Thomas N. and Welling Max. 2017. Semi-supervised classification with graph convolutional networks. In 5th International Conference on Learning Representations. OpenReview.net.Google Scholar
[44] Kuo Bor-Chen and Landgrebe David A.. 2002. A covariance estimator for small sample size classification problems and its application to feature extraction. IEEE Trans. Geosci. Rem. Sensor 40, 4 (2002), 814–819.Google ScholarCross Ref
[45] Li Jian, Wang Yue, Lyu Michael R., and King Irwin. 2018. Code completion with neural attention and pointer networks. In 27th International Joint Conference on Artificial Intelligence. 4159–4165.Google ScholarDigital Library
[46] Li Xiang, Qiu Kefan, Qian Cheng, and Zhao Gang. 2020. An adversarial machine learning method based on OpCode N-grams feature in malware detection. In 5th IEEE International Conference on Data Science in Cyberspace. 380–387.Google ScholarCross Ref
[47] Li Yujia, Tarlow Daniel, Brockschmidt Marc, and Zemel Richard S.. 2016. Gated graph sequence neural networks. In 4th International Conference on Learning Representations.Google Scholar
[48] Li Yi, Wang Shaohua, and Nguyen Tien N.. 2021. Vulnerability detection with fine-grained interpretations. In 29th ACM Joint European Software Engineering Conference and Symposium on the Foundations of Software Engineering. ACM, 292–303.Google ScholarDigital Library
[49] Li Zhao, Xing Yuying, Huang Jiamingal. et2021. Large-scale online multi-view graph neural network and applications. Fut. Gen. Comput. Syst. 116 (2021), 145–155.Google ScholarCross Ref
[50] Li-mei Zhang, Li-shan Qiao, and Song-can Chen. 2009. A survey of feature extraction and classifier design based on tensor pattern. J. Shandong Univ. (Eng. Sci.) 39, 1 (2009), 6–14.Google Scholar
[51] Liu Fang, Li Ge, and Wei Bolin. 2020. A self-attentional neural architecture for code completion with multi-task learning. In 28th International Conference on Program Comprehension. 37–47.Google ScholarDigital Library
[52] Liu Fang, Li Ge, Zhao Yunfei, and Jin Zhi. 2020. Multi-task learning based pre-trained language model for code completion. In 35th IEEE/ACM International Conference on Automated Software Engineering. 473–485.Google ScholarDigital Library
[53] Liu Risheng, Lin Zhouchen, Su Zhixun, and Tang Kewei. 2010. Feature extraction by learning Lorentzian metric tensor and its extensions. Pattern Recognit. 43, 10 (2010), 3298–3306.Google ScholarDigital Library
[54] Liu Xien, You Xinxin, and Zhang Xiao. 2020. Tensor graph convolutional networks for text classification. In 34th AAAI Conference on Artificial Intelligence. 8409–8416.Google ScholarCross Ref
[55] Myburgh Johannes C., Mouton Coenraad, and Davel Marelie H.. 2021. Tracking translation invariance in CNNs. CoRR abs/2104.05997 (2021).Google Scholar
[56] Nguyen Anh Tuan and Nguyen Tien N.. 2015. Graph-based statistical language model for code. In 37th IEEE/ACM International Conference on Software Engineering. IEEE Computer Society, 858–868.Google ScholarCross Ref
[57] Nguyen Anh Tuan, Nguyen Tung Thanh, and Nguyen Hoan Anh. 2012. Graph-based pattern-oriented, context-sensitive source code completion. In 34th International Conference on Software Engineering. IEEE Computer Society, 69–79.Google ScholarDigital Library
[58] Nguyen Son, Phan Hung, Le Trinh, and Nguyen Tien N.. 2020. Suggesting natural method names to check name consistencies. In 42nd International Conference on Software Engineering. 1372–1384.Google ScholarDigital Library
[59] Pandey Vijay. 2020. Overcoming overfitting and large weight update problem in linear rectifiers: Thresholded exponential rectified linear units. CoRR abs/2006.02797 (2020).Google Scholar
[60] Pham Nam H., Nguyen Tung Thanh, Nguyen Hoan Anh, and Nguyen Tien N.. 2010. Detection of recurring software vulnerabilities. In 25th IEEE/ACM International Conference on Automated Software Engineering. ACM, 447–456.Google ScholarDigital Library
[61] Quoc Do Le, Gregor Franz, Arnautov Sergei, Kunkel Roland, Bhatotia Pramod, and Fetzer Christof. 2021. secureTF: A secure TensorFlow framework. CoRR abs/2101.08204 (2021).Google Scholar
[62] Md. Mostafizer Rahman, Yutaka Watanobe, and Keita Nakamura. 2020. A neural network based intelligent support model for program code completion. Sci. Program. 2020, 7426461 (2020), 1–18.Google Scholar
[63] Ratre Avinash and Pankajakshan Vinod. 2018. Tucker tensor decomposition-based tracking and Gaussian mixture model for anomaly localisation and detection in surveillance videos. IET Comput. Vis. 12, 6 (2018), 933–940.Google ScholarCross Ref
[64] Romaniuk Myroslava. 2020. N-gram models for code completion in Pharo. In 4th International Conference on the Art, Science, and Engineering of Programming. 227–228.Google ScholarDigital Library
[65] Russell Rebecca L., Kim Louis Y., Hamilton Lei H.al. et2018. Automated vulnerability detection in source code using deep representation learning. In 17th IEEE International Conference on Machine Learning and Applications. IEEE, 757–762.Google ScholarCross Ref
[66] Schlichtkrull Michael Sejr, Kipf Thomas N., Bloem Peteral. et2018. Modeling relational data with graph convolutional networks. In The Semantic Web—15th International Conference, ESWC 2018, Heraklion, Crete, Greece (Lecture Notes in Computer Science), Vol. 10843. Springer, 593–607.Google ScholarDigital Library
[67] Sennrich Rico, Haddow Barry, and Birch Alexandra. 2016. Neural machine translation of rare words with subword units. In 54th Annual Meeting of the Association for Computational Linguistics, ACL.Google Scholar
[68] Sun Penghao, Lan Julong, Li Junfeial. et2021. Combining deep reinforcement learning with graph neural networks for optimal VNF placement. IEEE Commun. Lett. 25, 1 (2021), 176–180.Google ScholarCross Ref
[69] Svyatkovskiy Alexey, Zhao Ying, Fu Shengyu, and Sundaresan Neel. 2019. In 25th ACM International Conference on Knowledge Discovery & Data Mining. 2727–2735.Google Scholar
[70] Tjandra Andros, Sakti Sakriani, and Manurung Ruli. 2016. Gated recurrent neural tensor network. In International Joint Conference on Neural Networks. 448–455.Google Scholar
[71] S. Waner. 1986. Introduction to differential geometry and general relativity. Lecture Notes by Stefan Waner, with a Special Guest Lecture by Gregory C. Levine, Department of Mathematics, Hofstra University, https://medusa.teodesian.net/docs/mathematics/Intro%20to%20Differential%20Geometry%20and%20General%20Relativity%20-%20S.%20Warner%20(2002)%20WW.pdf.Google Scholar
[72] Wang Huanting, Ye Guixin, and Tang Zhanyong. 2021. Combining graph-based learning with automated data collection for code vulnerability detection. IEEE Trans. Inf. Forens. Secur. 16 (2021), 1943–1958.Google ScholarDigital Library
[73] Wang Wenhan, Zhang Kechi, Li Ge, and Jin Zhi. 2020. Learning to Represent Programs with Heterogeneous Graphs. (2020). arxiv:cs.SE/2012.04188Google Scholar
[74] Wang Yu, Wang Ke, Gao Fengjuanal. et2020. Learning semantic program embeddings with graph interval neural network. Proc. ACM Program. Lang. 4, OOPSLA (2020), 137:1–137:27.Google ScholarDigital Library
[75] Wu Yingxin, Wang Xiang, Zhang An, He Xiangnan, and Chua Tat-Seng. 2022. Discovering invariant rationales for graph neural networks. In 10th International Conference on Learning Representations. OpenReview.net.Google Scholar
[76] Xu Le, Cheng Lei, Wong Ngai, and Wu Yik-Chung. 2021. Overfitting avoidance in tensor train factorization and completion: Prior analysis and inference. In IEEE International Conference on Data Mining. IEEE, 1439–1444.Google ScholarCross Ref
[77] Yamaguchi Fabian, Golde Nico, Arp Daniel, and Rieck Konrad. 2014. Modeling and discovering vulnerabilities with code property graphs. In IEEE Symposium on Security and Privacy. 590–604.Google Scholar
[78] Yun Seongjun, Jeong Minbyul, Kim Raehyunal. et2019. Graph transformer networks. In Annual Conference on Neural Information Processing Systems. 11960–11970.Google Scholar
[79] Zhang Wei, Lin Zhouchen, and Tang Xiaoou. 2009. Tensor linear Laplacian discrimination (TLLD) for feature extraction. Pattern Recognit. 42, 9 (2009), 1941–1948.Google ScholarDigital Library
[80] Zhang Yu, Tiño Peter, Leonardis Ales, and Tang Ke. 2021. A survey on neural network interpretability. IEEE Trans. Emerg. Top. Comput. Intell. 5, 5 (2021), 726–742.Google ScholarCross Ref
[81] Zhou Yaqin, Liu Shangqing, Siow Jing Kaial. et2019. Devign: Effective vulnerability identification by learning comprehensive program semantics via graph neural networks. In Annual Conference on Neural Information Processing Systems. 10197–10207.Google Scholar

Index Terms

Toward Interpretable Graph Tensor Convolution Neural Network for Code Semantics Embedding
1. Security and privacy
  1. Software and application security
    1. Software security engineering
2. Software and its engineering

Recommendations

Code comment generation based on graph neural network enhanced transformer model for code understanding in open-source software ecosystems
Abstract
In open-source software ecosystems, the scale of source code is getting larger and larger, and developers often use various methods (good code comments or method names, etc.) to make the code easier to read and understand. However, high-quality ...
Read More
Multi-location cryptographic code repair with neural-network-based methodologies
ESEC/FSE 2021: Proceedings of the 29th ACM Joint Meeting on European Software Engineering Conference and Symposium on the Foundations of Software Engineering

Java Cryptographic API libraries are error-prone and result in vulnerabilities. The fixes of them often require security expertise and extra consideration for cryptographic consistency at multiple code locations. My Ph.D. research aims to help ...
Read More
Detecting Condition-Related Bugs with Control Flow Graph Neural Network
ISSTA 2023: Proceedings of the 32nd ACM SIGSOFT International Symposium on Software Testing and Analysis

Automated bug detection is essential for high-quality software development and has attracted much attention over the years. Among the various bugs, previous studies show that the condition expressions are quite error-prone and the condition-related ...
Read More

Comments

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

Published in
ACM Transactions on Software Engineering and Methodology Volume 32, Issue 5
September 2023
905 pages
ISSN:1049-331X
EISSN:1557-7392
DOI:10.1145/3610417
Editor:
Mauro Pezzè
USI Università della Svizzera italiana and SIT Schaffhausen Institute of Technology, Switzerland
Issue’s Table of Contents
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].
Sponsors
In-Cooperation
Publisher
Association for Computing Machinery
New York, NY, United States
Publication History
- Published: 21 July 2023
- Online AM: 20 February 2023
- Accepted: 4 January 2023
- Revised: 17 November 2022
- Received: 18 July 2022
Published in tosem Volume 32, Issue 5

Permissions
Request permissions about this article.
Request Permissions

Check for updates
Author Tags
Tensor computation
code embedding
graph neural network
Qualifiers
- research-article
Conference
Funding Sources
Other Metrics
View Article Metrics

Article Metrics
- 0
  Total Citations
  View Citations
- 630
  Total Downloads
- Downloads (Last 12 months)483
- Downloads (Last 6 weeks)41
Other Metrics
View Author Metrics
Cited By
This publication has not been cited yet

PDF Format

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Full Text

View this article in Full Text.

View Full Text

Toward Interpretable Graph Tensor Convolution Neural Network for Code Semantics Embedding

ACM Transactions on Software Engineering and Methodology

Abstract

REFERENCES

Cited By

Index Terms

Recommendations

Code comment generation based on graph neural network enhanced transformer model for code understanding in open-source software ecosystems

Multi-location cryptographic code repair with neural-network-based methodologies

Detecting Condition-Related Bugs with Control Flow Graph Neural Network