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A fast algorithm to simulate nonlinear resistive networks
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Frames steady-state of ideal nonlinear resistive networks (resistors, diodes, ideal sources) as a convex QP and solves it with exact (block) coordinate descent, enabling EP training of DRNs on MNIST far larger and faster than SPICE.
Problem
Simulating nonlinear resistive networks (with diodes) used as analog learning machines is very slow with SPICE and prior methods are limited to linear networks.
Approach
Under ideal circuit elements, the steady state is the minimizer of a convex quadratic energy (power dissipation) over a feasible set defined by diode and voltage-source linear constraints; exact coordinate descent gives closed-form node updates (average of neighbors, then clipping), and the bipartite layered DRN allows exact block coordinate descent with parallel GPU updates.
Key results
- DRN-XL with 51.7M weights reaches 1.33% MNIST test error, 327x more weights than the SPICE-based DRN-XS (0.16M, 3.43% error).
- Training time for DRN-XL is 10h27min for 100 epochs versus one week for 10 epochs with SPICE, giving about 50,000x larger network-size-to-epoch-duration ratio.
- DRN simulations converge in few iterations (e.g., 6 for 3-hidden-layer DRN vs 100 for a 3-hidden-layer deep Hopfield network).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use DRN-XL with exact block coordinate descent instead of the SPICE XS setup | MNIST training with resistive networks · MNIST test | test error (%): 3.43% vs 1.33% | Helped |
| use the proposed simulation method instead of SPICE-based simulation | DRN steady-state simulation · MNIST training | simulation speed: 160 times faster | Helped |
| scale from DRN-XS to DRN-XL | DRN trained with EP · MNIST | network size: 327 times | Helped |
| use DRN-XL rather than DRN-XS | DRN trained with EP · MNIST | training wall-clock time: 10 hours 27 min vs 1 week | Helped |
| use a 3-hidden-layer DRN rather than a 3-hidden-layer DHN | steady-state simulation · 3-hidden-layer network | iterations to convergence: 6 iterations vs 100 iterations | Helped |
Surprising findings
- Exact block coordinate descent on DRNs needs far fewer iterations to converge than deep Hopfield networks, though both reach comparable performance.
- Backpropagation through the solver trajectory performs comparably to equilibrium propagation on these networks.
Limitations
- Relies on ideal circuit element assumptions (ideal diodes, no forward drop or leakage), which deviate from real devices.
- Results are simulation only; no hardware validation is provided.
- Method for DRNs relies on bipartite layered structure; general topologies are less straightforward to parallelize.
Experimental setup
Datasets: MNIST
Benchmarks: MNIST
Metrics: test error rate (%) wall-clock time network size (number of weights) epochs
Baselines: SPICE-based simulation (DRN-XS) backpropagation through the coordinate descent trajectory
Builds on: equilibrium propagation deep resistive network principle of minimum dissipated power deep Hopfield network
Closest papers by meaning
- Towards training digitally-tied analog blocks via hybrid gradient computation (NeurIPS 2024 · similarity 0.87)
- Analog In-memory Training on General Non-ideal Resistive Elements: The Impact of Response Functions (NeurIPS 2025 · similarity 0.85)
- LaMAGIC: Language-Model-based Topology Generation for Analog Integrated Circuits (ICML 2024 · similarity 0.84)
- Analog Foundation Models (NeurIPS 2025 · similarity 0.84)
- Rethinking Neural Nonlinearity as Gating (NeurIPS 2026 · similarity 0.84)
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