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In-memory Accelerators with Memristors

NVM. MEM. PU. In-memory Accelerators with Memristors. Yuval Cassuto Koby Crammer Avinoam Kolodny Technion – EE ICRI-CI Retreat May 8, 2013. 3-way Collaboration. K. Crammer. ML App. Y. Cassuto. Representations. A. Kolodny. Devices. The Data Deluge. Computing. Mobile,

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In-memory Accelerators with Memristors

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  1. NVM MEM PU In-memory Accelerators with Memristors Yuval Cassuto Koby Crammer AvinoamKolodny Technion – EE ICRI-CI Retreat May 8, 2013

  2. 3-way Collaboration K. Crammer ML App. Y. Cassuto Representations A. Kolodny Devices

  3. The Data Deluge Computing Mobile, Cloud

  4. Non-Volatile Memories 101 density + logic! Memristors NANDFlash Mass Storage PROM EPROM E2PROM functionality

  5. Non-Volatile Memories 101 density + logic! Memristors NANDFlash Main Memory PROM EPROM E2PROM functionality

  6. Memristor Crossbar Arrays

  7. Memristor Readout Vg cij cij=0 high resistance  low current sensed cij=1 low resistance  high current sensed Vo RL

  8. Sneak Paths Vg 1 1 0 1 cij=0 high resistance  low current sensed cij=1 low resistance  high current sensed 1 1 Vo RL Desired Path Sneak Path

  9. Two Solutions 0 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 Poor capacity High read power

  10. Our Mixed Solution b YC, E. Yaakobi, S. Kvatinsky, ISIT 2013

  11. Results Summary 1) Fixed partition 2) Sliding window • Higher capacity • e.g. 0.465 vs. 0.423 for b=7 • Column-by-column encoding, optimal YC, E. Yaakobi, S. Kvatinsky, ISIT 2013

  12. In-memory Acceleration • Motivation: transfer bottlenecks • Method: compute in memory, transfer results • What to compute?

  13. Similarity Inner Products Trial 110011000101 Hyp. 1 000011011011 010111010101 Hyp. 2 110011000101 110011000101 000011000001 010011000101 ∑ ∑ =3 =5 Less similar More similar

  14. Inner Products in ML • K-Nearest Neighbors • Distance (Euclidean or Hamming) • Kernel Methods • Low-dim nonlinear → high-dim linear • -2 high dimension image for K • Graph based ML

  15. Memristor Inner Products (ideal) Trial 110011000101 Hyp. 1 000011011011 R GT=3/2R 2R 2R 2R R=∞ Output = 3· Const Inner product

  16. Ideal Inner Products Hamming distance in 3 measurements: 1 3 2

  17. Real Inner Products Error terms

  18. Evaluation • Can compute Hamming distance as if ideal • 3 measurements • plus arithmetic • Cannot compute inner product precisely in 1 measurement

  19. Continued Research Transform input vectors to maximize precision • ML Theory: provable optimality (information-theoretic learning) • ML Practice: optimize transformations within real ML algorithms

  20. Multi-level Inner Products R3 R2 R1 R3+R1 2R3 R1+R2 R=∞ + +

  21. Thank You!

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