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

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

3. The Data Deluge Mobile, Cloud Computing

4. Non-Volatile Memories 101 functionality density PROMEPROM E 2 PROM Memristors Mass Storage NAND Flash + logic!

5. Non-Volatile Memories 101 functionality density PROMEPROM E 2 PROM NAND Flash Main Memory Memristors + logic!

6. Memristor Crossbar Arrays

7. VgVg RLRL VoVo c ij c ij =0  high resistance  low current sensed c ij =1  low resistance  high current sensed Memristor Readout

8. VgVg RLRL VoVo 0 1 1 1 Desired Path Sneak Path 1 1 c ij =0  high resistance  low current sensed c ij =1  low resistance  high current sensed Sneak Paths

9. Two Solutions 111 111 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 Poor capacity High read power

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

11. Results Summary YC, E. Yaakobi, S. Kvatinsky, ISIT 2013 1) Fixed partition2) Sliding window Higher capacity e.g. 0.465 vs. 0.423 for b=7 Column-by-column encoding, optimal

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

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

14. Inner Products in ML

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

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

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 R= ∞ R1R1 R1+R2R1+R2 R2R2 R3R3 R3+R1R3+R1 2R 3

21. Thank You!