Coupled networks for physics-based machine learning
A system for physics-based learning and computation including two networks, each having a plurality of identical edges and feedback circuitry to compare the voltage drop at a given edge of the first network with the voltage drop at the corresponding edge of the second network. In both networks, at least one corresponding node is designated for input and at least one corresponding node is designated for output. In the first network, the at least one output node remains free and produces output voltage in response to the input voltage(s). In the second network, the at least one output node is clamped at voltage(s) closer to the desired value for the specified input voltage(s). Feedback circuitry compares voltages across corresponding edges and adjusts their effective resistances in order to learn.
1 . A coupled learning system, comprising:
at least one feedback circuit associated with (i) a first edge in a first network and (ii) a second edge in a second network, wherein the second edge corresponds to the first edge, and wherein a feedback circuit is configured to:
determine an electrical state of the first edge in the first network;
determine an electrical state of the second edge in the second network, wherein the second network receives a clamped input; and
iteratively adjust, based on the electrical state of the first edge and the electrical state of the second edge, an electrical characteristic of the first edge and the second edge, so as to cause an output associated with the first edge to approach the clamped input.
2 . The coupled learning system of claim 1 , wherein the electrical state of the first edge is associated with at least one of: a first voltage input, a first current input, and a first physical input, and wherein the electrical state of the second edge is associated with least one of: a second voltage input, a second current input, and a second physical input.
3 . The coupled learning system of claim 1 , wherein the first network comprises a first plurality of nodes, and wherein the second network comprises a second plurality of nodes corresponding to the first plurality of nodes.
4 . The coupled learning system of claim 1 , wherein the first network and the second network are structurally identical.
5 . The coupled learning system of claim 1 , wherein the clamped input comprises a voltage determined from training data associated with a task.
6 . The coupled learning system of claim 1 , wherein iteratively adjusting the electrical characteristic solves at least one of a classification task, an allosteric task, a regression task, and a sequential task.
7 . The coupled learning system of claim 1 , wherein the at least one feedback circuit comprises a capacitor.
8 . The coupled learning system of claim 1 , wherein the electrical characteristic is an effective resistance.
9 . The coupled learning system of claim 1 , wherein an effective resistance, ΔR i , of one or more edges iteratively adjusts according to:
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wherein ΔV i F corresponds to the electrical state of the first network and ΔV i C corresponds to the electrical state of the second network.
10 . The coupled learning system of claim 1 , wherein Δ{right arrow over (V)} C O corresponds to the clamped input, and wherein {right arrow over (V)} C O is changed according to:
{right arrow over (V)} C O =η{right arrow over (V)} D +(1−η) {right arrow over (V)} F O
wherein {right arrow over (V)} D is a desired output, {right arrow over (V)} F O is the first input, and 0<η≤1.
11 . The coupled learning system of claim 1 , wherein the first network and the second network have a same number of edges.
12 . The coupled learning system of claim 11 , wherein the first network and the second network both have 16 edges.
13 . The couple learning system of claim 1 , wherein the first network and the second network are linear networks.
14 . The couple learning system of claim 1 , wherein the first network and the second network are non-linear networks.
15 . A coupled learning method, comprising:
determining an electrical state of a first edge in a first network;
determining an electrical state of a second edge in a second network, wherein the second edge corresponds to the first edge, and wherein the second network receives a clamped input; and
iteratively adjusting, based on the electrical state of the first edge and the electrical state of the second edge, an electrical characteristic of the first edge and the second edge, so as to cause an output associated with the first edge to approach the clamped input.
16 . The coupled learning method of claim 15 , wherein the electrical state of the first edge is associated with at least one of: a first voltage input, a first current input, and a first physical input, and wherein the second electrical state is associated with least one of: a second voltage input, a second current input, and a second physical input.
17 . The coupled learning method of claim 15 , wherein the first network comprises a first plurality of nodes, and wherein the second network comprises a second plurality of nodes corresponding to the first plurality of nodes.
18 . The coupled learning method of claim 15 , wherein the clamped input comprises at least one voltage determined from training data associated with a task.
19 . A non-transitory computer readable storage medium comprising instructions stored thereon, which when executed by a processor cause a computing device to:
determine a first difference between a first edge of a first network and a second edge of a second network, wherein the second edge corresponds to the first edge; and
iteratively adjust, based on the first difference, an electrical characteristic of at least one of the first edge of the first network and the second edge of the second network so as to cause a first output of the first network to approach a clamped input provided at the second edge.