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ILILT: Implicit Learning of Inverse Lithography Technologies
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Proposes ILILT, a weight-tied implicit-layer model that unrolls a learned mask-update step conditioned on a differentiable lithography simulator, producing optimized masks without an ILT solver in the loop.
Problem
Inverse lithography technology (mask optimization) is non-convex and numerical ILT solvers depend on good initialization and many costly simulator calls; prior ML methods only produce initial masks or design-to-mask mappings without lithography grounding.
Approach
Formulate ILT as a fixed-point (implicit) layer and train a weight-tied sequence model that, at each unrolled step, takes the current mask, its simulated wafer image, and the target design, with depth-weighted BPTT loss on intermediate masks; this imitates the ILT optimization trajectory without gradient computation at inference.
Key results
- ILILT-P2PHD-8-45M reaches 0.08 average EPE violations, versus 0.21 for GPU-ILT, the numerical solver used to generate training data, with PVB 4695 vs 4656.
- ILILT-CFNO-8 with about 130K parameters reaches 0.25 EPE, comparable to GPU-ILT, at a model size reported as 400x smaller.
- The paper reports roughly 10x speedup over the numerical ILT solver; L2O baselines with 8 unrolled steps degrade EPE (1.59 and 0.87).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ILILT with a Pix2PixHD backbone and 8 unrolling steps instead of the GPU-ILT solver | LithoBench mask optimization · LithoBench | EPE violations: 0.21 -> 0.08 | Helped |
| Use ILILT with a Pix2PixHD backbone and 8 unrolling steps instead of the standalone Pix2PixHD backbone | Pix2PixHD · LithoBench | EPE violations: 0.12 -> 0.08 | Helped |
| Use ILILT with a CFNO backbone and 8 unrolling steps instead of standalone CFNO | CFNO · LithoBench | EPE violations: 0.51 -> 0.25 | Helped |
| Increase ILILT-CFNO unrolling depth from 2 to 8 steps (ablation) | ILILT-CFNO · LithoBench | EPE violations: 0.39 -> 0.25 | Helped |
| Increase ILILT-Pix2PixHD unrolling depth from 2 to 8 steps (ablation) | ILILT-P2PHD · LithoBench | EPE violations: 0.13 -> 0.08 | Helped |
| Increase ILILT unrolling depth from 2 to 8 steps (ablation) | ILILT · LithoBench | PVB area: 4704 -> 4674; 5056 -> 4695 | No clear effect |
| Replace weight-tied ILILT with an 8-step L2O-CFNO using independent layer weights | CFNO backbone · LithoBench | EPE violations: 0.25 -> 1.59 | Hurt |
| Replace weight-tied ILILT with an 8-step L2O-Pix2PixHD using independent layer weights | Pix2PixHD backbone · LithoBench | EPE violations: 0.08 -> 0.87 | Hurt |
| Add weight-tied sequence training to the standalone backbone | CFNO and Pix2PixHD · LithoBench | EPE violations: 50% and 33% reduced EPE violation | Helped |
| Extend unrolling depth beyond 8 steps (ablation) | ILILT · LithoBench | EPE violations | No clear effect |
Surprising findings
- Weight-tied ILILT outperforms the numerical GPU-ILT solver that generated its training labels on EPE violations.
- Standard learning-to-optimize unrolling with independent per-step weights degrades substantially compared with the standalone backbones.
Limitations
- Evaluated only on LithoBench designs; authors note production-level designs are needed to verify manufacturing-standard QoR.
- Performance gains saturate at T=8 and longer unrolling increases compute and training cost linearly.
- PVB area is not improved over baselines because the objective does not explicitly target process variation.
Experimental setup
Datasets: LithoBench
Benchmarks: LithoBench
Metrics: EPE violations PVB area throughput (s/tile)
Baselines: GPU-ILT GAN-OPC Neural-ILT Pix2PixHD CFNO L2O-CFNO-8-Step L2O-P2PHD-8-Step
Builds on: deep equilibrium models GAN-OPC Fourier neural operator learning-to-optimize algorithm unrolling
Closest papers by meaning
- LithoBench: Benchmarking AI Computational Lithography for Semiconductor Manufacturing (NeurIPS 2023 · similarity 0.91)
- Co-PiLOT: Constrained Physics-Informed Latent Optimization for Target-Driven Inverse Design (NeurIPS 2026 · similarity 0.81)
- Learning Surrogates for Offline Black-Box Optimization via Gradient Matching (ICML 2024 · similarity 0.80)
- GradQ-ViT: Robust and Efficient Gradient Quantization for Vision Transformers (AAAI 2025 · similarity 0.80)
- DeepLayout: Learning Neural Representations of Circuit Placement Layout (ICML 2025 · similarity 0.80)
- Accelerating Augmentation Invariance Pretraining (NeurIPS 2024 · similarity 0.79)
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