May 2019 - talks - lists.cs.princeton.edu

Mina Tahmasbi Arashloo will present her FPO "Stateful Programming of High-Speed Network Hardware" on Thursday, 5/16/2019 at 1:30pm, in CS 401
by Nicki Mahler 07 May '19

07 May '19

Mina Tahmasbi Arashloo will present her FPO "Stateful Programming of High-Speed Network Hardware" on Thursday, 5/16/2019 at 1:30pm, in CS 401. The members of her committee are Jennifer Rexford (adviser); Readers: David Walker and Arvind Krishnamurthy (University of Washington); Nonreaders: Nick Feamster and Michael Freedman. A copy of her thesis, is available upon request. Everyone is invited to attend her talk. The talk title and abstract follow below: Modern networks need to operate at speeds as high as 100Gbps while running sophisticated algorithms and protocols to provide strict performance, security and reliability guarantees. Moreover, they need to flexibly adapt to the rapidly evolving requirements of online services. Thus, emerging network hardware devices, i.e. switches inside the network and Network Interface Cards (NICs) at the end hosts, are high-speed and programmable, with on-chip memory accessible on a per-packet basis to support stateful packet processing. However, the programming interfaces of these devices are quite low-level, tied to each device's architecture, and only suitable for programming a single device. Thus, programming collections of stateful network devices to realize a local or network-wide functionality efficiently and correctly is extremely difficult and error-prone. This dissertation focuses on the design and implementation of high-level programming abstractions for stateful programming of high-speed network hardware, both at the end hosts and inside the network. At the end host, we focus on the transport layer, the most complicated, constantly-evolving, and stateful component of the network stack. Transport-layer algorithms maintain state across packets to decide what data segments to transmit and when, and are notoriously difficult to implement on programmable NICs at high-speed. We propose Tonic, a hardware architecture for transport algorithms that can support 100Gbps for 128-byte packets while being programmable with a simple API. In designing Tonic, we exploit common patterns across transport algorithms to create efficient fixed-function reusable hardware modules, thus significantly reducing the functionality programmers must specify. To facilitate network-wide stateful programming, we propose SNAP, a programming language that abstracts the entire network as "one big stateful switch". Using SNAP, operators can program using persistent arrays on one big switch without deciding how to distribute and access them in the network's switches. The SNAP compiler discovers read/write dependencies between arrays, translates one-big-switch programs into an efficient internal representation based on binary decision diagrams, and uses it to jointly optimize array placement and routing across the network. All in all, Tonic's modular interface and SNAP's one-big-stateful-switch abstraction relieve programmers from the low-level details of stateful programming of high-speed network hardware throughout the entire network.

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Lance Goodridge will present his MSE Talk "Systems to Scale CS Education" on Friday, May 10th, 2019 at 1pm in CS 401
by Nicki Mahler 07 May '19

07 May '19

Lance Goodridge will present his MSE Talk "Systems to Scale CS Education" on Friday, May 10th, 2019 at 1pm in CS 401. The members of his committee are as follows: Jeremie Lumbroso (adviser) and Szymon Rusinkiewicz. Everyone is invited to attend his talk. His abstract follows below. The enrollment numbers for Computer Science courses have been increasing for the last decade, and many institutions have realized that they don't have the faculty / teaching staff to adequately support the growing demand. Recently, a certain solution has become popular: hire talented undergraduates to supplement the course staff and perform tasks requiring a lot of manpower, such as grading or providing assistance on homework assignments. However, this comes with its own set of problems, which universities are only now beginning to realize. Principally, managing a fleet of undergraduate assistants requires significant administrative overhead to hire and organize these workers, and care must be taken to ensure the quality of undergraduate peer interactions is acceptable and consistent. Institutions that do not adequately handle these two pain points will struggle to reap the benefits of incorporating peer teaching, as the course staff will instead waste their effort on managing the assistants rather than the students directly. The systems we have built, TigerUHR, LabQueue, and PersonalityDB, address these issues, and help CS departments scale appropriately with their growing enrollment numbers.

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EE Seminar - Friday, May 10, 2019, 11:00 am, E-Quad B205 - Ted K. Woodward, Ph.D. Facebook, Inc.
by Emily Lawrence 07 May '19

07 May '19

Updated date, time and location Department of Electrical Engineering Seminar Speaker: Ted K. Woodward, Ph.D., Facebook, Inc. Title: Facebook Connectivity: challenges and progress in bringing more people to a faster Internet Date: Friday, May 10, 2019 Time: 11:00 am Room: E-Quad, Room B205 Host: Prof. Kaushik Sengupta Abstract: The Facebook connectivity organization works to stimulate global broadband connectivity. I will summarize some of the many challenges associated with the task and describe some of the work the group is doing to make progress toward the goal. For more information visit: http://connectivity.fb.com/ Bio: Ted K. Woodward, Ph.D. manages the Connectivity Labs group at Facebook, a program-centric organization focused on early stage activity in support of the larger Facebook Connectivity organization. Before joining the Connectivity team at Facebook, from 2015 to 2018 Dr. Woodward was a Program Manager in the Strategic Technologies Office of the Defense Advanced Research Projects Agency (DARPA), where he led programs in Communications, Networking, and RF systems. Before that, he spent more than 25 years in diverse communication and networking research, development, and product companies including Telcordia Technologies and follow-on entities, Bell Laboratories Research, Ciena Corporation, and Internet Photonics, Inc., which he co-founded.

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Mohamed El-Dirany will present his MSE thesis talk "Plagiarism in Privacy Policies" on Wednesday, May 8, 2019 at 4pm in CS 402
by Nicki Mahler 07 May '19

07 May '19

Mohamed El-Dirany will present his MSE thesis talk "Plagiarism in Privacy Policies" on Wednesday, May 8, 2019 at 4pm in CS 402. The members of his committee are Barbara Engelhardt and Arvind Narayanan. Everyone is invited to attend his talk. His abstract follows below. New laws and regulations are increasingly focusing on privacy policies. The General Data Protection Regulation (GDPR) in Europe, and the California Online Privacy Protection Act (CalOPPA) both require commercial websites to have privacy policies. Ideally, these privacy policies would be accurately describe to users what happens with their data, and what data exactly is covered. However, many websites do not comply with these regulations. With the release of privacy policy generators, it has become easy to create generic privacy policies, but this fails to fully capture the ways in which a company uses a consumer's data. In this work, we analyze a set of 10,000 policies after the introduction of the GDPR, and find that there are widespread similarities between policies and large amounts of plagiarism. This indicates that there is most likely a good deal of non-compliance with these laws, and that privacy policies may not be completely informing consumers of how their data is being used.

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Sven Dorkenwald will present his General Exam "A spatial graph database for proofreading and analyzing dynamic segmentations in connectomics" on May 16, 2019 at 10am in in PNI 130.
by Nicki Mahler 07 May '19

07 May '19

Sven Dorkenwald will present his General Exam "A spatial graph database for proofreading and analyzing dynamic segmentations in connectomics" on May 16, 2019 at 10am in in PNI 130. The members of his committee are as follows: Sebastian Seung (adviser), Michael Freedman, and Kai Li. Everyone is invited to attend his talk, and those faculty wishing to remain for the oral exam following are welcome to do so. His abstract and reading list follow below. Title: A spatial graph database for proofreading and analyzing dynamic segmentations in connectomics Connectomics is concerned with high resolution imaging of brain tissue and analysis of the neurons, their connectivity and ultrastructure within these datasets. Ongoing improvements in volume electron microscopy and automatic segmentation have created large, fully reconstructed datasets with cubic-millimeter sized datasets (PBs of data) in reach. However, current automated segmentations still contain errors prohibiting immediate analysis and requiring proofreading, both automated and manual. Proofreading such segmentations can be viewed as a graph problem with nodes representing supervoxels (SVs), accumulations of voxels, and neurons being connected components in this graph. Proofreading edits add and remove edges and trigger recomputations of connected components (CCs). Interactive proofreading requires fast CC computations and two-way lookups (CC id <-> SV id), as well as versioning, multiuser support, and spatially restricted queries. We present a database management system, the PyChunkedGraph, which enables interactive proofreading of graphs from large datasets (more than tens of billions of nodes and hundreds of billions of edges). We achieve this by decoupling the local nature of proofreading changes from the spatially distributed nature of neurons by implementing an octree on top of the SV graph storing the CC information. Hence, changes to the graph only need to propagate through the height of the tree lending it great scalability. We implemented the PyChunkedGraph with Google’s BigTable making use of its timestamp feature for versioning and read-modify-write guarantees for locking. We present performance on large automatically segmented datasets. Reading list Papers: DVID: Distributed Versioned Image-Oriented Dataservice Katz WT, Plaza SM; Frontiers in Neural Circuits, 2019 NeuTu: Software for Collaborative, Large-Scale, Segmentation-Based Connectome Reconstruction Zhao T, Olbris DJ, Yu Y, Plaza SM; Frontiers in Neural Circuits, 2018 NeuroBlocks – Visual Tracking of Segmentation and Proofreading for Large Connectomics Projects Al-Awami AK et al.; IEEE Transactions on visualization and computer graphics, 2016 Design and Evaluation of Interactive Proofreading Tools for Connectomics Haehn D et al.; IEEE Transactions on visualization and computer graphics, 2014 Dense connectomic reconstruction in layer 4 of the somatosensory cortex Motta A, Berning M, Boergens KM, Staffler B, et al.; bioarxiv, 2018 Bigtable: A Distributed Storage System for Structured Data Chang F, et al., 2006 Large-scale Incremental Processing Using Distributed Transactions and Notifications Peng D and Dabek F; OSDI'10 Proceedings of the 9th USENIX conference on Operating systems design and implementation, 2010 Pregel: A System for Large-Scale Graph Processing Malewicz et al., SIGMOD '10 Proceedings of the 2010 ACM SIGMOD International Conference on Management of data, 2010 Functional selectivity and specific connectivity of inhibitory neurons in primary visual cortex Znamenskiy P, Kim MH, Muir DR et al.; bioarxiv, 2018 Single-neuron perturbations reveal feature-specific competition in V1 Chettih SN and Harvey CD; nature, 2019 Functional specificity of local synaptic connections in neocortical networks Ko H, Hofer SB et al.; nature, 2011 Book: Principles of Neurobiology, Luo et al.

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Sixue Liu will present his General Exam "Faster and Simpler Concurrent Algorithms for Graph Problems" on May 13, 2019 at 2pm in CS 105.
by Nicki Mahler 07 May '19

07 May '19

Sixue Liu will present his General Exam "Faster and Simpler Concurrent Algorithms for Graph Problems" on May 13, 2019 at 2pm in CS 105. The members of his committee are Robert Tarjan (adviser), Bernard Chazelle, Matt Weinberg. Everyone is invited to attend his talk, and those faculty wishing to remain for the oral exam following are welcome to do so. His abstract and reading list follow below. Abstract : Many classical graph problems have efficient sequential algorithms, with some of them even running in linear time in the input size, which is best possible. But linear time is not fast enough for massive datasets, for which we turn to concurrency. We study concurrent algorithms for two classic problems: the connected components of an undirected graph, and the strongly connected components of a directed graph. The first problem has been extensively studied in the concurrent setting, especially on the classical Parallel Random Access Machines (PRAM). However, many fast PRAM algorithms are hard to implement due to the complications in the algorithms. Our first result is several new elegant PRAM algorithms for the connected components problem, which achieve the same time complexity comparing to the existing best ones but are significantly simpler. Our algorithms are deterministic, use linear number of processors, and run in $O(\log n)$ time. This is joint work with Robert Tarjan. Our second result is a simple PRAM algorithm for connected components and spanning forest that runs faster than any existing ones when the input graph has small diameter, which is usually the case in real-world applications. The algorithm is randomized, uses linear number of processors, and runs in $O(\log d \log\log n)$ time with high probability where $d$ is the diameter of the input graph. This is joint work with Robert Tarjan and Peilin Zhong. We also examine the strongly connected components problem, for which a truly sublinear time and nearly linear work concurrent algorithm is only known recently. We show that the current time bound $\tilde{O}(n^{2/3})$ for this algorithm is tight by constructing a hard example. It is possible to design new algorithms to improve this upper bound. This is joint work with Sepehr Assadi and Robert Tarjan. Reading list : [1] T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein. Introduction to Algorithms, 3rd Edition. MIT Press, 2009. [2] B. Awerbuch and Y. Shiloach. New connectivity and MSF algorithms for shuffle-exchange network and PRAM. IEEE Trans. Computers, 36(10):1258–1263, 1987. [3] R. M. Karp and V. Ramachandran. Parallel algorithms for shared-memory machines. In Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity (A), pages 869–942. 1990. [4] J. H. Reif. Optimal parallel algorithms for graph connectivity. Technical report, HARVARD UNIV CAMBRIDGE MA AIKEN COMPUTATION LAB, 1984. [5] Y. Shiloach and U. Vishkin. An O(log n) parallel connectivity algorithm. J. Algorithms, 3(1):57–67, 1982. [6] R. E. Tarjan and J. van Leeuwen. Worst-case analysis of set union algorithms. J. ACM, 31(2):245–281, 1984. [7] A. Andoni, Z. Song, C. Stein, Z. Wang, and P. Zhong. Parallel graph connectivity in log diameter rounds. In 59th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2018, Paris, France, October 7-9, 2018, pages 674–685, 2018. [8] K. W. Chong and T. W. Lam. Finding connected components in O(log n log log n) time on the EREW PRAM. J. Algorithms, 18(3):378–402, 1995. [9] J. T. Fineman. Nearly work-efficient parallel algorithm for digraph reachability. In Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2018, Los Angeles, CA, USA, June 25-29, 2018, pages 457–470, 2018. [10] D. B. Johnson and P. T. Metaxas. Connected components in O (logˆ3/2 n) parallel time for the CREW PRAM. J. Comput. Syst. Sci., 54(2):227–242, 1997. [11] S. Halperin and U. Zwick. An optimal randomised logarithmic time connectivity algorithm for the EREW PRAM. J. Comput. Syst. Sci., 53(3):395–416, 1996.

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Orestis Plevrakis will present his General Exam "A Theoretical Analysis of Contrastive Unsupervised Representation Learning" on May 13, 2019 at 2pm in CS 401
by Nicki Mahler 07 May '19

07 May '19

Orestis Plevrakis will present his General Exam "A Theoretical Analysis of Contrastive Unsupervised Representation Learning" on May 13, 2019 at 2pm in CS 401. The members of his committee are Sanjeev Arora (adviser), Elad Hazan, and Rob Schapire. Everyone is invited to attend his talk, and those faculty wishing to remain for the oral exam following are welcome to do so. His abstract and reading list follow below. Abstract: Recent empirical works have successfully used unlabeled data to learn feature representations that are broadly useful in downstream classification tasks. Several of these methods are reminiscent of the well-known word2vec embedding algorithm: leveraging availability of pairs of semantically “similar” data points and “negative samples,” the learner forces the inner product of representations of similar pairs with each other to be higher on average than with negative samples. We use the term contrastive learning for such algorithms and we present a theoretical framework for analyzing them by introducing latent classes and hypothesizing that semantically similar points are sampled from the same latent class. This framework allows us to show provable guarantees on the performance of the learned representations on the average classification task that is comprised of a subset of the same set of latent classes. Our generalization bound also shows that learned representations can reduce the (labeled) sample complexity on downstream tasks. We conduct controlled experiments in both the text and image domains to support the theory. References: 1. Shalev-Shwartz, Shai, and Shai Ben-David. Understanding machine learning: From theory to algorithms. Cambridge university press, 2014. 2. Logeswaran, L. and Lee, H. An efficient framework for learning sentence representations. In Proceedings of the International Conference on Learning Representations , 2018. 3. Sanjeev Arora, Yuanzhi Li, Yingyu Liang, Tengyu Ma, and Andrej Risteski. 2015. Rand-walk: A latent variable model approach to word embeddings. arXiv preprint arXiv:1502.03520 (2015). 4. Mikolov, T., Sutskever, I., Chen, K., Corrado, G. S., and Dean, J. Distributed representations of words and phrases and their compositionality. In Neural Information Processing Systems , 2013. 5. Blum, A. and Mitchell, T. Combining labeled and unlabeled data with co-training. In Proceedings of the Eleventh Annual Conference on Computational Learning Theory , COLT’ 98, 1998. 6. Kumar, A., Niculescu-Mizil, A., Kavukcoglu, K., and Daume ́, H. A binary classification framework for two-stage multiple kernel learning. In Proceedings of the 29th International Conference on Machine Learning , ICML’12, 2012. 7. Srebro, N. How Good is a Kernel When Used as a Similarity Measure. In COLT , 2007. 8. Brian Kulis. Metric learning: A survey. Foundations and Trends in Machine Learning , 5(4):287–364, 2012. 9. Gutmann, M. and Hyvarinen, A. Noise-contrastive estimation: A new estimation principle for unnormalized statistical models. In Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics , pp. 297–304, 2010. 10. Ma, Z. and Collins, M. (2018). Noise contrastive estimation and negative sampling for conditional models: Consistency and statistical efficiency. arXiv preprint arXiv:1809.01812 .

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Jiaxin Guan will present his General Exam "Simple Schemes in the Bounded Storage Model" on May 13, 2019 at 2pm in CS 402.
by Nicki Mahler 07 May '19

07 May '19

Jiaxin Guan will present his General Exam "Simple Schemes in the Bounded Storage Model" on May 13, 2019 at 2pm in CS 402. The members of his committee are Mark Zhandry (adviser), Arvind Narayanan, and Ran Raz. Everyone is invited to attend his talk, and those faculty wishing to remain for the oral exam following are welcome to do so. His abstract and reading list follow below. Abstract: The bounded storage model promises unconditional security proofs against computationally unbounded adversaries, so long as the adversary’s space is bounded. In this work, we develop simple new constructions of two-party key agreement, bit commitment, and oblivious transfer in this model. In addition to simplicity, our constructions have several advantages over prior work, including an improved number of rounds and enhanced correctness. Our schemes are based on Raz’s lower bound for learning parities. Reading List: Textbook: Katz, Jonathan, and Yehuda Lindell. Introduction to modern cryptography. CRC press, 2014. Papers (in alphabetic order): Badrinarayanan, Saikrishna, et al. "Post-zeroizing obfuscation: New mathematical tools, and the case of evasive circuits." Annual International Conference on the Theory and Applications of Cryptographic Techniques. Springer, Berlin, Heidelberg, 2016. Barak, Boaz, et al. "On the (im) possibility of obfuscating programs." Annual International Cryptology Conference. Springer, Berlin, Heidelberg, 2001. De Santis, Alfredo, Giuseppe Persiano, and Moti Yung. "One-message statistical Zero-Knowledge Proofs and space-bounded verifier." International Colloquium on Automata, Languages, and Programming. Springer, Berlin, Heidelberg, 1992. Ding, Yan Zong, et al. "Constant-round oblivious transfer in the bounded storage model." Theory of Cryptography Conference. Springer, Berlin, Heidelberg, 2004. Ding, Yan Zong. "Oblivious transfer in the bounded storage model." Annual International Cryptology Conference. Springer, Berlin, Heidelberg, 2001. Goldreich, Oded, and Leonid A. Levin. "A hard-core predicate for all one-way functions." Proceedings of the twenty-first annual ACM symposium on Theory of computing. ACM, 1989. Goldwasser, Shafi, Silvio Micali, and Charles Rackoff. "The knowledge complexity of interactive proof systems." SIAM Journal on computing 18.1 (1989): 186-208. Kilian, Joe. "Founding crytpography on oblivious transfer." Proceedings of the twentieth annual ACM symposium on Theory of computing. ACM, 1988. Maurer, Ueli M. "Conditionally-perfect secrecy and a provably-secure randomized cipher." Journal of Cryptology 5.1 (1992): 53-66. Raz, Ran. "Fast learning requires good memory: A time-space lower bound for parity learning." Journal of the ACM (JACM) 66.1 (2018): 3.

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Princeton Research Day, Thursday, May 9!
by Emily Lawrence 06 May '19

06 May '19

Princeton Research Day 2019 <http://www.cs.princeton.edu/events/25857> Time: 10 a.m. to 5 p.m. Date: Thursday, May 9, 2019 Location: Frist Campus Center Hashtag: #PRD19 Schedule of CS participants: http://www.cs.princeton.edu/events/25857 Facebook Event: https://www.facebook.com/events/245031396189128/ Come celebrate the research and creative endeavors of Princeton University students and early career researchers at the fourth annual Princeton Research Day on Thursday, May 9. Princeton Research Day highlights all types of discovery at the University, from laboratory research to the creation and interpretation of artistic work. Enjoy the more than 200 talks, posters, performances, art exhibitions, demonstrations and digital presentations on topics in the natural sciences, social sciences, engineering, humanities and the arts. Princeton Research Day is free and open to the public. No registration is required. Drop in for a few presentations, or stay the whole time. Each presentation is designed to be accessible to all. You'll have a great time and - we hope - learn a thing or two. Definitely stay for the highlight talks on the Mainstage beginning at 3 p.m. Check out the schedule and plan your day with the Guidebook app <https://guidebook.com/g/prd2019/> . Princeton Research Day is a collaborative initiative between the offices of the Dean of the College, the Dean of the Faculty, the Dean of the Graduate School and the Dean for Research, with support from the Office of the Provost.

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Zhiyuan Li will present his General Exam "A trajectory analysis for gradient descent on over-paramterized neural nets" on May 16, 2019 at 2pm in CS 301.
by Nicki Mahler 03 May '19

03 May '19

Zhiyuan Li will present his General Exam " A trajectory analysis for gradient descent on over-paramterized neural nets " on May 16, 2019 at 2pm in CS 301. The members of his committee are as follows: Sanjeev Arora (adviser), Elad Hazan, and Ryan Adams Everyone is invited to attend his talk, and those faculty wishing to remain for the oral exam following are welcome to do so. His abstract and reading list follow below. Abstract: Rademacher complexity measures the ability of a funciton class to fit random labels, and thus upper bounds the gap between training loss and testing loss. Traditional wisdom thinks that optimization over a function class with high rademacher complexity, such as a over-parametrized neurel net, will induce overfitting, and thus harm the generalization. However, recent works showed empirically that over-parametrization will not degenerate the test accuracy, and that the trajectory of the parameters by (stochastic) gradient descent seem to have much better properties than the whole parameter space, which motivates people to study the trajectory determined by the algorithm. In this talk, we will use trajectory analysis to show gradient descent over an over-parametrized two-layer net with relu activation has some kernel-like limiting behaviour. Informally, when the net is sufficiently wide, gd always converge to 0 training loss while the l2 distance moved by parameters from initialization remains bounded by some RKHS norm of the training labels, indepedent of width, and the trained network make the almost same predictions on unseen data to the kernel regression solution with the so-called Neural Tangent Kernel(NTK). We also prove a generalization bound for this over-parametrized 2 layer neural nets with relu activation which only relies on the l2 distance moved by the parameter. Thus we conclude that the generalization gap is bounded by the data-dependent RKHS norm, and this explains why adding noise to labels will suffer larger generalization gap while using the same network architecture. Our recent work also shows that this kernel-type limiting behavior holds for multilayer overparametrized neural net. This talk is based on a joint work with Sanjeev Arora(Princeton University & IAS), Simon S. Du(CMU), Wei Hu(Princeton University) and Ruosong Wang(CMU), “Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks”, and another joint work with Sanjeev Arora(Princeton University & IAS), Simon S. Du(CMU), Wei Hu(Princeton University), Ruslan Salakhutdinov(CMU) and Ruosong Wang(CMU), “On Exact Computation with an Infinitely Wide Neural Net”. References: 1. Shalev-Shwartz, Shai, and Shai Ben-David. Understanding machine learning: From theory to algorithms. Cambridge university press, 2014. 2. Jacot, Arthur, Franck Gabriel, and Clément Hongler. Neural tangent kernel: Convergence and generalization in neural networks. In Advances in neural information processing systems. 2018. 3. Youngmin Cho and Lawrence K Saul. Kernel methods for deep learning. In Advances in neural information processing systems, pages 342–350, 2009. 4. Simon S. Du, Xiyu Zhai, Barnabas Poczos, and Aarti Singh. Gradient descent provably optimizes over-parameterized neural networks. In International Conference on Learning Representations, 2019. 5. Christopher KI Williams. Computing with infinite networks. In Advances in neural information processing systems, pages 295–301, 1997. 6. Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals. Understanding deep learning requires rethinking generalization. In Proceedings of the International Conference on Learning Representations (ICLR), 2017, 2017. 7. Peter L. Bartlett and Shahar Mendelson. Rademacher and gaussian complexities: Risk bounds and structural results. JMLR, 3:463–482, Nov 2002. 8. Neyshabur, Behnam, Srinadh Bhojanapalli, and Nathan Srebro. "A pac-bayesian approach to spectrally-normalized margin bounds for neural networks." arXiv preprint arXiv:1707.09564 (2017). 9. Karen Simonyan and Andrew Zisserman. Very Deep Convolutional Networks for Large-Scale Image Recognition. arXiv Prepr. arXiv1409.1556, Sep 2014. 10. Zeyuan Allen-Zhu, Yuanzhi Li, and Zhao Song. A convergence theory for deep learning via over- parameterization. arXiv preprint arXiv:1811.03962, 2018b. 11. Alexander G de G Matthews, Mark Rowland, Jiri Hron, Richard E Turner, and Zoubin Ghahramani. Gaussian process behaviour in wide deep neural networks. arXiv preprint arXiv:1804.11271, 2018.

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