Exact Stochastic Computing Multiplication in Memristive Memory
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Solution Overview
Problem
Conventional in-memory multiplication methods using memristive technology face challenges due to process variations and noise, making them unreliable and inefficient compared to CMOS technology, while stochastic computing methods are inefficient due to high overhead in converting data between binary and stochastic representations.
Innovation Solution
The development of an exact stochastic computing-based in-memory multiplier using memristive crossbar memory arrays and Memristor-Aided Logic (MAGIC) that generates deterministic bit-streams for accurate multiplication, reducing latency and energy consumption by performing bitwise operations in parallel and utilizing NOR operations within memory.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional in-memory multiplication methods using memristive technology are used, then multiplication can be performed within memory, but the process variations and noise make the results unreliable and inefficient
Solution Approach 1:
The patent replaces the physical memristive multiplication mechanism with a stochastic computing approach. Instead of relying on precise memristor resistance values for multiplication, the system uses probabilistic bitstream operations where the probability of a '1' bit represents the input value. This substitution of deterministic physical multiplication with probabilistic stochastic operations makes the computation immune to process variations and noise in the memristive technology.
Solution Approach 2:
The patent transforms the representation of data from fixed-point binary to stochastic bitstreams. By changing the parameter representation from deterministic binary values to probabilistic bitstream densities (where the ratio of 1s to total bits represents the value), the system can perform multiplication through simple logical operations that are inherently more robust against hardware variations and noise.
2Reliability
If stochastic computing methods are used for in-memory multiplication, then fault tolerance improves, but the overhead of converting data between binary and stochastic representations reduces efficiency
Solution Approach 1:
The patent merges the data representation format with the computation location by performing stochastic operations directly within the memory array. Instead of converting binary data to stochastic format in separate logic circuits and then performing multiplication, the system integrates the stochastic computation engine within the memory fabric itself, allowing binary data to be converted and multiplied in-place without external conversion overhead.
Solution Approach 2:
The patent introduces an in-memory stochastic computation engine that acts as an intermediary between binary data storage and stochastic operations. This intermediary component resides within the memory array and can directly process binary data using stochastic logic (such as MAGIC circuits), eliminating the need for external binary-to-stochastic conversion circuits and reducing the time loss associated with data format transitions.
3Speed
If fixed-point binary multiplication methods are used in memory, then computation speed improves, but the vulnerability to fault and noise reduces reliability
Solution Approach 1:
The patent introduces dynamic stochastic bitstream operations instead of static fixed-point binary computation. By using time-varying bitstream sequences where the statistical properties (density of 1s) represent values, the system achieves both fast parallel computation and inherent noise immunity. The dynamic nature of stochastic bitstreams allows the system to tolerate transient faults and noise that would corrupt fixed-point binary operations.
Data Source
AI summary
The multiplication method disclosed herein benefits from the complementary advantages of both Stochastic Computing (SC) and memristive In-Memory Computation (IMC) to enable energy-efficient and low-latency multiplication of data. In summary, the following method are disclosed. (a) Performing deterministic and accurate bit-stream-based multiplication in memory. To this end, the invention disclosed herein uses memristive crossbar memory arrays and Memory-Aided Logic (MAGIC). (b) Using an efficient in-memory method for generating deterministic bit-streams from binary data, which takes advantage of inherent properties of memristive memories. (c) Improving the speed and reducing the memory usage as compared to the State-of-the-Art (SoA) limited-precision in-memory binary multipliers. (d) Reducing latency and energy consumption compared to the SoA accurate off-memory SC multiplication techniques.