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Demonstration of Decentralized, Physics-Driven Learning
Sam Dillavou, Menachem Stern, Andrea J. Liu, Douglas J. Durian
TL;DR
Physical contrastive learning has been difficult to realize because systems must compare responses to two sets of boundary conditions. This paper implements that comparison with twin variable-resistor networks, demonstrating multiple tasks and estimating that a 100-fold larger network could outperform a simulation implementation.
Problem
Physical contrastive learning requires comparing system responses under two distinct boundary conditions, a challenge for laboratory realization.
Source: APPROACH · p. 3Method
The system uses twin identical resistor networks and local edge updates to compare free and clamped states without a central processor or external memory.
Source: APPROACH · p. 2, DISCUSSION · p. 6Results
The 16-edge circuit learned allostery, regression, and classification; the authors estimate that a 100-fold larger network could outperform a simulation implementation without a speed change.
Source: DISCUSSION · pp. 6–7Takeaways & Limitations
Because all edges adjust in parallel, adding edges does not increase computation time per training step in the described system.
Source: DISCUSSION · p. 7The current prototype has 16 edges, and its voltage application and measurement hardware limits training to 3–5 Hz.
Source: DISCUSSION · p. 7
Abstract
from arXiv · showhide
In typical artificial neural networks, neurons adjust according to global calculations of a central processor, but in the brain neurons and synapses self-adjust based on local information. Contrastive learning algorithms have recently been proposed to train physical systems, such as fluidic, mechanical, or electrical networks, to perform machine learning tasks from local evolution rules. However, to date such systems have only been implemented in silico due to the engineering challenge of creating elements that autonomously evolve based on their own response to two sets of global boundary conditions. Here we introduce and implement a physics-driven contrastive learning scheme for a network of variable resistors, using circuitry to locally compare the response of two identical networks subjected to the two different sets of boundary conditions. Using this innovation, our system effectively trains itself, optimizing its resistance values without use of a central processor or external information storage. Once the system is trained for a specified allostery, regression, or classification task, the task is subsequently performed rapidly and automatically by the physical imperative to minimize power dissipation in response to the given voltage inputs. We demonstrate that, unlike typical computers, such learning systems are robust to extreme damage (and thus manufacturing defects) due to their decentralized learning. Our twin-network approach is therefore readily scalable to extremely large or nonlinear networks where its distributed nature will be an enormous advantage; a laboratory network of only 500 edges will already outpace its in silico counterpart.
1 Edge
The paired-resistor learning machine uses physical energy minimization and local edge updates to train from free and clamped network states. Its 16-edge prototype demonstrates allostery, regression, classification, task switching, and recovery after damage.
APPROACH
- Twin identical resistor networks let edges compare local voltage drops between free and clamped states, approximating global gradient descent without a central processor or external memory.The clamped network receives target output voltages; each edge updates its own resistance.Source: APPROACH · pp. 2–3
- In the voltage-divider demonstration, the free output followed changing target voltages, while comparator noise below 0.01 V produced an error floor and allowed resistance values to drift among valid solutions.The target changed every 100 training steps.Source: Figure 2 · p. 3, APPROACH · p. 4
RESULTS
- Allostery mean-squared error fell by over four orders of magnitude, regression test mean-squared error by over two orders, and iris test accuracy exceeded 95% versus 98% for logistic regression.These results use different tasks and metrics; the regression result is for the test set.Source: RESULTS · pp. 4–5
- The 16-edge network learned seven successive classification, allostery, and regression tasks without resetting edges, and repeatedly learned an allostery task using different resistance configurations.The authors report that capacity and retention of previous tasks remain future questions.Source: RESULTS · p. 5, Figure 4 · p. 6
- After nearly one-third of its structure was destroyed, the network recovered the two-output allostery task by finding a new solution, although the removed edges were selected for causing error spikes.Some pruned edges caused only modest error changes, and retraining was often unnecessary in this linear system.Source: RESULTS · pp. 5–6, Figure 5 · p. 7
DISCUSSION
- The learning rule stays the same across tasks, while each task can use a different cost function; the system has enough adjustable resistances to satisfy the demonstrated constraints.The paper distinguishes learning degrees of freedom (edge resistances) from physical degrees of freedom (node voltages).Source: DISCUSSION · p. 6
- The prototype has only 16 edges and hardware-limited training steps of 3–5 Hz; nonlinear circuit elements are needed for operations such as XOR.The network itself is described as capable of operating multiple orders of magnitude faster than the voltage application and measurement hardware.Source: DISCUSSION · p. 7
- The authors estimate that readily available fabrication could scale edge count and training frequency by at least six orders of magnitude, with a footprint five orders smaller than the prototype.They also estimate that a 100-fold increase in network size, without a speed change, would outperform the cited simulation implementation.Source: DISCUSSION · p. 7
Appendix A: Task Details
Appendix A specifies the node voltages used for the tasks and explains how regression and classification targets are set. The figure maps task voltages onto network nodes, distinguishing inputs from outputs.
Appendix A: Task Details
- Classification targets are each flower’s species-average network response, recalculated every 30 training steps and eventually settling to consistent values.Because the network is linear, the response to the average input equals the average response over that species’ training examples.Source: Appendix A · p. 8
- Regression inputs and test inputs are sampled uniformly from 1 to 5 V, with desired outputs given by task-specific functions of those inputs..Source: Appendix A · p. 8
- For allosteric tasks, the specified input and desired output voltages are single values; Fig. 6 maps task voltages by node, marking inputs red and outputs with purple outlines.Node numbers correspond to the network structure shown in the figure inset.Source: Figure 6 · p. 8, Appendix A · p. 8
Appendix B: Scaling the Electronics
The prototype was not optimized for speed or scale, and the appendix estimates possible CMOS improvements using component-density and speed figures.
Appendix B: Scaling the Electronics
- The prototype occupies several square feet and runs at about 3–5 Hz, limited by data-acquisition and voltage-setting hardware.The authors estimate a CMOS implementation with 10 million edges could occupy less than 10 mm2, using their stated transistor-density and per-edge estimates.Source: Appendix B · p. 8
- The estimated 10 million-edge CMOS system would represent a 10^6 increase in edge count, a 10^5 decrease in footprint, and a 10^8 increase in speed over the prototype.These are estimates based on stated CMOS fabrication and analog-network component figures.Source: Appendix B · p. 8
Appendix C: Circuitry
Appendix C describes how discrete resistor updates approximate the coupled learning rule and how circuitry compares free and clamped network states. The implementation uses matched twin networks and sequenced digital logic to update each edge.
Appendix C: Circuitry
- Each digipot has 128 evenly spaced resistance values, so edge resistances change in discrete steps of ±δR, with δR ≈ 781 Ω.The step size is based on 100 kΩ/128.Source: Appendix C · p. 8
- The simplified update uses a Boolean comparison of voltage drops instead of calculating an energy-dissipation difference, but still requires both free and clamped states.The implementation assumes the two drops have the same sign, which the authors report is nearly always true, especially for η ≪ 1.Source: Appendix C · pp. 8–9
- Noise spreads the resistance-change transition around the ideal voltage-difference threshold, and comparator bias shifts the plotted curves to the right.The figure plots average resistance change against comparator voltage and the difference between comparator voltages.Source: Figure 7 · p. 9
- Two identical networks run the free and clamped states, with corresponding edges sharing the same resistance.Comparators and an XOR gate determine the resistance-change direction from the two voltage drops.Source: Appendix C · p. 9, Figure 7 · p. 9
- Each edge uses comparators, an XOR gate, and a D flip-flop to store the update direction before it reaches the digipot’s up/down input.A sequenced global clock samples the XOR output before triggering the resistance change, avoiding direct use of a potentially fluctuating signal.Source: Appendix C · pp. 9–10, Figure 7 · p. 9