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Abstract Can one recover a matrix efficiently from only matrix‐vector products? If so, how many are needed? This article describes algorithms to recover matrices with known structures, such as tridiagonal, Toeplitz, Toeplitz‐like, and hierarchical low‐rank, from matrix‐vector products. In particular, we derive a randomized algorithm for recovering an unknown hierarchical low‐rank matrix from only matrix‐vector products with high probability, where is the rank of the off‐diagonal blocks, and is a small oversampling parameter. We do this by carefully constructing randomized input vectors for our matrix‐vector products that exploit the hierarchical structure of the matrix. While existing algorithms for hierarchical matrix recovery use a recursive “peeling” procedure based on elimination, our approach uses a recursive projection procedure.
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A High-Speed Photonic Tensor Accelerator
We propose a coherent multi-dimensional (wavelength, spatial mode, polarization, etc.) photonic tensor accelerator capable of matrix-vector, matrix-matrix, and batch matrix multiplications in a single clock cycle. A proof-of-concept 2x2 matrix-matrix multiplication at 25GBd with 4.67 bit precision was experimentally demonstrated.
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- Award ID(s):
- 1932858
- PAR ID:
- 10451777
- Date Published:
- Journal Name:
- IEEE Photonics Conference
- Page Range / eLocation ID:
- 1 to 2
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/IPC53466.2022.9975540
