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1. Accelerated primal-dual methods for convex-strongly-concave saddle point problems

   Khalafi, Mohammad ; Boob, Digvijay ( July 2023 , Proceedings of Machine Learning Research)

   We investigate a primal-dual (PD) method for the saddle point problem (SPP) that uses a linear approximation of the primal function instead of the standard proximal step, resulting in a linearized PD (LPD) method. For convex-strongly concave SPP, we observe that the LPD method has a suboptimal dependence on the Lipschitz constant of the primal function. To fix this issue, we combine features of Accelerated Gradient Descent with the LPD method resulting in a single-loop Accelerated Linearized Primal-Dual (ALPD) method. ALPD method achieves the optimal gradient complexity when the SPP has a semi-linear coupling function. We also present an inexact ALPD method for SPPs with a general nonlinear coupling function that maintains the optimal gradient evaluations of the primal parts and significantly improves the gradient evaluations of the coupling term compared to the ALPD method. We verify our findings with numerical experiments. 

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2. Automated Generation of Stand-Alone Source Codes for Software Libraries

   Machi, L. ; Carscadden, H.L. ; Kuhlman, C.J. ; Machi, D. ; Ravi, S.S. ( January 2021 , ISCA 30th International Conference)

   Harris, F. ; Wu, R. ; Redei, A. (Ed.)

   Networks are pervasive in society: infrastructures (e.g., telephone), commercial sectors (e.g., banking), and biological and genomic systems can be represented as networks. Con- sequently, there are software libraries that analyze networks. Containers (e.g., Docker, Singularity), which hold both runnable codes and their execution environments, are in- creasingly utilized by analysts to run codes in a platform-independent fashion. Portability is further enhanced by not only providing software library methods, but also the driver code (i.e., main() method) for each library method. In this way, a user only has to know the invocation for the main() method that is in the container. In this work, we describe an automated approach for generating a main() method for each software library method. A single intermediate representation (IR) format is used for all library methods, and one IR instance is populated for one library method by parsing its comments and method signature. An IR for the main() method is generated from that for the library method. A source code generator uses the main() method IR and a set of small, hand-generated source code templates|with variables in the templates that are automatically customized for a particular library method|to produce the source code main() method. We apply our approach to two widely used software libraries, SNAP and NetworkX, as examplars, which combined have over 400 library methods. 

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3. Automated Generation of Stand-Alone Source Codes for Software Libraries

   Machi, Lucas ; Carscadden, Henry L ; Kuhlman, Chris J ; Machi, Dustin ; Ravi, S S. ( October 2021 , Software Engineering and Data Engineering)

   Networks are pervasive in society: infrastructures (e.g., telephone), commercial sectors (e.g., banking), and biological and genomic systems can be represented as networks. Consequently, there are software libraries that analyze networks. Containers (e.g., Docker, Singularity), which hold both runnable codes and their execution environments, are increasingly utilized by analysts to run codes in a platform-independent fashion. Portability is further enhanced by not only providing software library methods, but also the driver code (i.e., main() method) for each library method. In this way, a user only has to know the invocation for the main() method that is in the container. In this work, we describe an automated approach for generating a main() method for each software library method. A single intermediate representation (IR) format is used for all library methods, and one IR instance is populated for one library method by parsing its comments and method signature. An IR for the main() method is generated from that for the library method. A source code generator uses the main() method IR and a set of small, hand-generated source code templates|with variables in the templates that are automatically customized for a particular library method|to produce the source code main() method. We apply our approach to two widely used software libraries, SNAP and NetworkX, as exemplars, which combined have over 400 library methods. 

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4. Verification of Recurrent Neural Networks with Star Reachability

   https://doi.org/10.1145/3575870.3587128  

   Tran, Hoang Dung ; Choi, Sung Woo ; Yang, Xiaodong ; Yamaguchi, Tomoya ; Hoxha, Bardh ; Prokhorov, Danil ( May 2023 , The 26th ACM International Conference on Hybrid Systems: Computation and Control)

   The paper extends the recent star reachability method to verify the robustness of recurrent neural networks (RNNs) for use in safety-critical applications. RNNs are a popular machine learning method for various applications, but they are vulnerable to adversarial attacks, where slightly perturbing the input sequence can lead to an unexpected result. Recent notable techniques for verifying RNNs include unrolling, and invariant inference approaches. The first method has scaling issues since unrolling an RNN creates a large feedforward neural network. The second method, using invariant sets, has better scalability but can produce unknown results due to the accumulation of overapproximation errors over time. This paper introduces a complementary verification method for RNNs that is both sound and complete. A relaxation parameter can be used to convert the method into a fast overapproximation method that still provides soundness guarantees. The method is designed to be used with NNV, a tool for verifying deep neural networks and learning-enabled cyber-physical systems. Compared to state-of-the-art methods, the extended exact reachability method is 10 × faster, and the overapproximation method is 100 × to 5000 × faster. 

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5. An isogeometric collocation method for efficient random field discretization

   https://doi.org/10.1002/nme.5959  

   Jahanbin, Ramin ; Rahman, Sharif ( October 2018 , International Journal for Numerical Methods in Engineering)

   This paper presents an isogeometric collocation method for a computationally expedient random field discretization by means of the Karhunen‐Loève expansion. The method involves a collocation projection onto a finite‐dimensional subspace of continuous functions over a bounded domain, basis splines (B‐splines) and nonuniform rational B‐splines (NURBS) spanning the subspace, and standard methods of eigensolutions. Similar to the existing Galerkin isogeometric method, the isogeometric collocation method preserves an exact geometrical representation of many commonly used physical or computational domains and exploits the regularity of isogeometric basis functions delivering globally smooth eigensolutions. However, in the collocation method, the construction of the system matrices for ad‐dimensional eigenvalue problem asks for at mostd‐dimensional domain integrations, as compared with 2d‐dimensional integrations required in the Galerkin method. Therefore, the introduction of the collocation method for random field discretization offers a huge computational advantage over the existing Galerkin method. Three numerical examples, including a three‐dimensional random field discretization problem, illustrate the accuracy and convergence properties of the collocation method for obtaining eigensolutions.

    

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