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[00302] Manifold-Free Riemannian Optimization

  • Session Date & Time : 3C (Aug.23, 13:20-15:00)
  • Type : Contributed Talk
  • Abstract : Optimization problems constrained to a smooth manifold can be solved via the framework of Riemannian optimization. To that end, a geometrical description of the constraining manifold, e.g., tangent spaces, retractions, and cost function gradients, is required. In this talk, we present a novel approach that allows performing approximate Riemannian optimization based on a manifold learning technique, in cases where only a noiseless sample set of the cost function and the manifold’s intrinsic dimension are available.
  • Classification : 65K05, 53Z50, 65D15
  • Author(s) :
    • Boris Shustin (Tel-Aviv University)
    • Haim Avron (Tel-Aviv University)
    • Barak Sober (The Hebrew University of Jerusalem)


  • Session Date & Time : 3C (Aug.23, 13:20-15:00)
  • Type : Contributed Talk
  • Abstract : We develop a mesh-less, ray-based deep neural network method to solve the Helmholtz equation with high frequency. This method does not use an adaptive mesh refinement method, nor does it design a numerical scheme using some specially designed basis function to calculate the numerical solution, but it has the advantages of easy implementation and no mesh. We have carried out various numerical examples to prove the accuracy and efficiency of the proposed nnumerical method.
  • Classification : 65K05
  • Author(s) :
    • andy L yang (DutchFork High school)

[00842] Iterative projection methods for solving cone-constrained eigenvalue complementarity problems

  • Session Date & Time : 3C (Aug.23, 13:20-15:00)
  • Type : Contributed Talk
  • Abstract : Cone-constrained eigenvalue complementarity problems are associated with unstable modes and vibrations of dynamic systems in engineering. In this talk, iterative projection methods are proposed to quickly search the corresponding K-eigenvalues and K-eigenvectors. Particularly, it is also designed to find specific solutions of the considered problem. Convergence analysis is studied in detail and the sufficient conditions are given. Numerical results are shown to confirm the advantages of our algorithms.
  • Classification : 65K15, 15A42
  • Author(s) :
    • Nan Li (Nagoya University)
    • Tomohiro Sogabe (Nagoya University)
    • Jun-Feng Yin (Tongji University)
    • Tomoya Kemmochi (Nagoya University)
    • Shao-Liang Zhang (Nagoya University)

[00527] A fast Multiplicative Update algorithm for non-negative matrix factorization

  • Session Date & Time : 3C (Aug.23, 13:20-15:00)
  • Type : Contributed Talk
  • Abstract : This work proposes an efficient algorithm called fastMU (Multiplicative Updates) to deal with a Non-Negative Matrix Factorization problem, based on majorization minimization principle. We derive theoretical convergence results and show the effectiveness of our method through comparison with state-of-the-art methods on both synthetic and realistic data. Practical results show that fastMU is often several orders of magnitude faster than the regular MU proposed by Lee and Sung, and can even be competitive with state-of-the-art methods.
  • Classification : 65Kxx, 90Cxx
  • Author(s) :
    • Mai-Quyen PHAM (IMT Atlantique)
    • Jeremy Cohen (CREATIS, CNRS)
    • Thierry Chonavel (IMT Atlantique)

[00693] Enzyme: Fast and Effective Automatic Differentiation for Academia and Industry

  • Session Date & Time : 3C (Aug.23, 13:20-15:00)
  • Type : Industrial Contributed Talk
  • Abstract : Automatic differentiation (AD) is key to training neural networks, Bayesian inference, and scientific computing. Applying these techniques requires rewriting code in a machine learning framework or manually providing derivatives. We present Enzyme, an AD extension for the industry-standard LLVM/MLIR compiler. Enzyme differentiates programs in any LLVM-based language. Unlike traditional tools, Enzyme performs AD on optimized code, resulting in a 4.2x speedup on the CPU and orders of magnitude speedup on the GPU.
  • Classification : 65Kxx, 65Yxx, 68Vxx
  • Author(s) :
    • William Steven Moses (MIT)
    • Valentin Churavy (MIT)
    • Ludger Paehler (TUM)
    • Oleksandr Zinenko (Google)