Problem
Research questions and friction points this paper is trying to address.
nonlinear deep resistive networks
circuit simulation
coordinate-descent solvers
realistic nonlinearities
energy-based computation
Fast simulation of nonlinear deep resistive networks for energy-based computation
🤖 AI Summary
该研究通过扩展坐标下降法模拟实际单调非线性元件，如肖克利二极管等，解决了深电阻网络中非线性电路平衡计算成本高的问题。
📝 Abstract
Deep resistive networks are electronic energy-based systems in which computation is performed by the steady-state voltages of nonlinear circuits. Nonlinear devices enable expressive input-output transformations, but make the circuit equilibria costly to compute during simulation and training. Recent coordinate-descent solvers have achieved large speedups over SPICE-class circuit simulators, but only for nonlinearities modeled as ideal-diode models. This mathematical simplification is not sufficient for practical analog circuits. Here we extend coordinate-descent simulation to realistic monotone nonlinearities, including Shockley diodes, antiparallel diode pairs, and piecewise-linear current-voltage characteristics. With neighboring voltages fixed, each node update remains a scalar Kirchhoff-law solve. Single-exponential characteristics admit closed-form Lambert-(W) updates, while more general monotone characteristics can be handled with scalar root-finding methods. Across networks with one to three hidden layers and hidden widths from 64 to 1024, the solver reproduces matched SPICE steady-state voltages with relative $L_1$ errors below $1.1\times10^{-4}$ for 90% of validation samples, while achieving speedups up to $(1.7\times10^3)$. We further train a $1568\times100\times20$ double-Shockley network on MNIST, reaching about 3.0% test error and reducing the per-epoch training time by roughly $4.4\times10^2$. Together, these results establish a practical route to the circuit-level design and training of large-scale analog energy-based systems incorporating realistic nonlinear devices.
Innovation
Methods, ideas, or system contributions that make the work stand out.
coordinate-descent solver
monotone nonlinearities
Lambert-W updates
scalar root-finding methods
energy-based systems
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