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Temporal correlation detection using computational phase-change memory
Abu Sebastian, Tomas Tuma, Nikolaos Papandreou, Manuel Le Gallo, Lukas Kull, Thomas Parnell, Evangelos Eleftheriou
TL;DR
Conventional von Neumann systems separate processing and memory, motivating computational approaches that collocate computation and storage. This paper uses PCM crystallization dynamics to implement temporal-correlation detection in memory and demonstrates the approach experimentally at million-device scale, including weather data. The results support co-located computation and storage for dense, parallel computing systems.
Problem
Separated processing and memory require repeated data transfers, motivating computational memory that performs tasks within the storage unit.
Method
The paper exploits PCM crystallization dynamics to execute temporal-correlation detection largely within an array of memory devices.
Results
The approach was experimentally demonstrated at the scale of one million PCM devices and applied to real-world weather data.
Takeaways & Limitations
Computation and storage can coexist at the nanometer scale, supporting the prospect of massively parallel computational-memory systems.
Abstract
from arXiv · showhide
For decades, conventional computers based on the von Neumann architecture have performed computation by repeatedly transferring data between their processing and their memory units, which are physically separated. As computation becomes increasingly data-centric and as the scalability limits in terms of performance and power are being reached, alternative computing paradigms are searched for in which computation and storage are collocated. A fascinating new approach is that of computational memory where the physics of nanoscale memory devices are used to perform certain computational tasks within the memory unit in a non-von Neumann manner. Here we present a large-scale experimental demonstration using one million phase-change memory devices organized to perform a high-level computational primitive by exploiting the crystallization dynamics. Also presented is an application of such a computational memory to process real-world data-sets. The results show that this co-existence of computation and storage at the nanometer scale could be the enabler for new, ultra-dense, low power, and massively parallel computing systems.
Dynamics of phase-change memory devices
PCM crystallization dynamics convert electrical write pulses into progressive structural and conductance changes. The process is governed by interface temperature, thermal resistance, and temperature-dependent crystal growth.
- Device operation: A RESET pulse melts part of the phase-change material, which quenches into an amorphous, low-conductance region when stopped.The amorphous region blocks the bottom electrode.
- Crystallization dynamics: A SET pulse below the melting temperature partially crystallizes the amorphous region, progressively reducing its effective thickness.At nanometer scale, crystal growth dominates the crystallization mechanism.
- Crystallization dynamics: The amorphous-region thickness evolves with the interface temperature and the temperature-dependent crystal-growth velocity.The interface temperature depends on effective thermal resistance, input power, and ambient temperature.
- Crystallization dynamics: Crystal growth is negligible up to approx. 550 K and reaches its maximum at approx. 750 K.These estimates establish the strong temperature dependence of the crystallization rate.
- Device operation: Repeated SET pulses decrease the amorphous thickness and thereby progressively increase low-field conductance.The temperature distribution is shaped by the device’s effective thermal resistance.
Detecting statistical correlations using computational memory
The paper formulates unsupervised detection of mutually correlated binary event streams and implements it in PCM computational memory. Correlation is accumulated through pulse-controlled crystallization and read from device conductance.
- Problem formulation: The task is to identify an unknown subset of mutually correlated processes among N discrete-time binary stochastic streams.Correlated processes have correlation coefficient c > 0; the remainder are uncorrelated.
- Covariance-based detection: A conventional approach estimates an uncentered covariance matrix and sums each row or column to obtain process weights.The weights are used to distinguish correlated from uncorrelated groups by magnitude.
- Computational-memory implementation: Each process is assigned to one PCM device, and SET-pulse duration or amplitude is made proportional to the instantaneous sum of all processes.Processes with value 1 receive the pulse, potentially in parallel.
- Computational-memory implementation: Under constant pulse amplitude, the crystallization increment is proportional to the collective event count through the crystal-growth velocity.The simplified analysis assumes interface temperature is independent of amorphous thickness.
- Detection principle: After K time steps, correlated processes undergo a larger amorphous-thickness change than uncorrelated processes, separating their conductance values.Monitoring conductance or resistance therefore reveals the correlated group.
Experimental platform
The experimental platform combines a PCM array with integrated addressing and read/write circuitry, and characterizes how conductance accumulates under repeated SET pulses.
- Platform: The PCM array is organized as a matrix of word lines and bit lines with associated read/write circuitries.This organization provides the physical interface for addressing individual devices.
- Platform: The prototype platform is built around a PCM chip containing 3 million devices, with FPGA boards and a host computer coordinating experiments.The chip includes circuitry for device addressing and write/read operations.
- Characterization: 10,000 devices were RESET and then exposed to repeated 50 ns SET pulses while their conductance values were monitored.The resulting conductance-versus-pulse relationship is called an accumulation curve.
Experimental demonstration with a million correlated processes
The experiment maps one million binary processes onto PCM devices and uses conductance evolution to identify temporal correlations. Correlated processes separate from uncorrelated ones, including at correlation coefficient c = 0.01, but conductance dynamic range limits the detection window.
- Experimental demonstration: One million processes were mapped to the pixels of a 1000 × 1000 black-and-white image, whose pixels represented instantaneous binary process values.The experiment used the image of Albert Einstein and his signature as the process-mapping visualization.
- Correlation detection: Correlated processes drove their assigned devices toward high conductance, separating correlated from uncorrelated process distributions.The reported inaccuracies were attributed to device variability and conductance fluctuations, while the authors described the detection accuracy as significantly high.
- Limitation: The conductance dynamic range saturates after a certain number of pulses, requiring correlations to be detected within a limited time window before RESET.Shorter SET pulses or multiple devices per process could enlarge the dynamic range, but the tested chip was limited to 50 ns minimum pulse width.
- Correlation detection: c = 0.01 was sufficient for detecting correlated groups, although precise evaluation of the correlation coefficient remained difficult.The authors also state that multiple correlated groups with different coefficients could potentially be detected.
Experiment with the weather data
Rainfall records from 270 US weather stations were converted into binary processes and analyzed in computational memory. A 2 µS conductance threshold produced substantial agreement with k-means clustering.
- Data preparation: Rainfall data from 270 weather stations across the USA were converted into binary stochastic processes at one-hour time steps over six months.The process value was 1 when rainfall occurred in the preceding one-hour window and 0 otherwise.
- Correlation structure: The uncentered covariance matrix revealed several correlated groups, including one predominant group with strong geographical correlation.The conductance map likewise showed higher values for devices corresponding to the predominant group.
- Classification: 245 of 270 weather stations matched the classifications produced by computational memory and k-means clustering.The two approaches disagreed on 12 stations classified as uncorrelated by computational memory and 13 classified as correlated.
- Classification: A 2 µS conductance threshold classified the weather stations into correlated and uncorrelated groups.This threshold enabled direct comparison with the established k-means clustering method.
II. DISCUSSION
The paper demonstrates computational memory using PCM dynamics to execute high-level tasks within the memory array, including correlation detection and machine-learning processing at million-device scale.
- II. DISCUSSION: The work experimentally demonstrates computational memory performing high-level computational tasks by exploiting the dynamics of resistive memory devices.The demonstration uses an array containing one million PCM devices.
- II. DISCUSSION: A computational memory module could accelerate correlation detection by a factor of 200 compared with state-of-the-art computing hardware.The estimate assumes sufficient write modules to program devices in parallel.
- II. DISCUSSION: Compared with CMOS-only implementations, computational phase-change memory has a much smaller areal footprint at the 90 nm technology node, with comparable dynamic power.The paper expects these gains to increase with smaller devices and shorter write pulses.
- II. DISCUSSION: PCM crystallization dynamics can support additional primitives, including number factoring and matrix-vector multiplication.Matrix elements and vector elements are encoded in crystallizing-pulse durations and amplitudes, with conductance monitoring estimating the product.
- II. DISCUSSION: PCM structural relaxation can encode temporal information from write pulses for detecting process rates as well as temporal correlations.The paper also suggests coupling device dynamics and extending the approach to photonic PCM.
- II. DISCUSSION: The work presents a significant experimental demonstration in which PCM dynamics execute a high-level machine-learning algorithm almost entirely in the memory array.It demonstrates computation and storage co-existing at the nanometer scale, with potential for massively parallel systems.
Phase-change memory chip
The chip integrates PCM devices into 90 nm CMOS technology using doped Ge2Sb2Te2 phase-change material and nanometric electrode structures.
- Phase-change memory chip: The PCM devices were integrated into a chip fabricated in 90 nm CMOS technology using doped Ge2Sb2Te2 phase-change material.The bottom electrode has an approximately 20 nm radius and 65 nm length; the phase-change material is approximately 100 nm thick.
Generation of one million correlated processes and experimental details
The experiment generated one million binary processes with controlled temporal correlations, mapping them onto a 1000 × 1000 black-and-white image.
- Generation of one million correlated processes and experimental details: The processes were generated from a discrete binary reference process whose probability of state 1 is p and state 0 is 1 −p.The reference process is used to generate N binary processes through stochastic functions.
- Generation of one million correlated processes and experimental details: The stochastic construction preserves each generated process's mean p and variance p(1 −p), while pairwise correlation equals c.The conditional probabilities are specified by Equations 10–12.
- Generation of one million correlated processes and experimental details: With p = 0.01, the experiment generated one million binary processes, including 95,525 correlated processes and 904,475 mutually uncorrelated processes.Each process was mapped to one pixel of a 1000 × 1000 black-and-white Albert Einstein image.
Generation of weather data-based processes and experimental details
The weather-data experiment used hourly climatological records from approximately 1600 U.S. stations over six months to generate one binary stochastic process per station.
- Generation of weather data-based processes and experimental details: The weather data came from NOAA quality-controlled local climatological records covering approximately 1600 U.S. weather stations.Measurements span January 2015 to June 2015, totaling 181 days and 4344 hours.
- Generation of weather data-based processes and experimental details: One binary stochastic process was generated for each weather station from whether it rained during a given period.