LevelSet-ILT Architecture Audit

Status: continuous-mask gradient-descent ILT, faithful to the level-set / SimpleILT-style formulation surveyed in Yang2023_LithoBench §3.3. Last audited: 2026-05-23 against the formulation in Yang2023_LithoBench (NeurIPS 2023, openreview.net/forum?id=jWHU4b7Yk6) and the lineage papers cited in the model docstring. Re-audited 2026-05-23 (later) to reflect the threading.Lock cache-guard backport from OpenILTModel.

OpenLithoHub ships a LevelSetILTModel adapter (src/openlithohub/models/levelset_ilt.py) used as the canonical ILT-via-gradient-descent baseline. This page records what we implement, what the surveyed formulation specifies, and where they diverge.

Audit method

Compared models/levelset_ilt.py against:

• Yang2023_LithoBench §3.3 — survey of the SimpleILT-style L2 + total-variation formulation. The model docstring cites this as the open-access substitute for the paywalled Granik / Pang lineage.
• Pang, Liu & Abrams, Inverse lithography technology principles in practice (Proc. SPIE 5992, 2005) — original level-set / continuous-mask formulation.
• Poonawala & Milanfar, Mask design for optical microlithography — an inverse imaging problem (IEEE TIP 16(3), 2007) — gradient-based inversion of the imaging operator.

Confidence:

• A — verified against the source in this repo.
• B — verified against the LithoBench survey description; constants here (lr=0.1, sigma_px=2.0, tv_weight=0.01) are this project's defaults, not literal paper values — the model docstring already states this explicitly.
• C — derived from a paper note rather than an audited primary source.

What the surveyed formulation specifies

Item	Survey / paper specification	Confidence
Loss	‖Z − Z_T‖² + λ · TV(mask) — L2 fidelity + total-variation regularisation.	B (LithoBench §3.3)
Mask representation	Continuous, sigmoid-bounded [0, 1]. Update via gradient descent on a logit.	B
Optimizer	Gradient descent — surveyed as "SGD/Adam"; the survey does not pin a choice.	B
Forward model	Convolution against an optical PSF (Gaussian) or a Hopkins/SOCS partial-coherent kernel.	B
Resist	Sigmoid-thresholded aerial intensity.	B
Process window	Multi-corner sweeps (dose × defocus) feed into a weighted-mean fidelity loss.	C (Pang2005 / Granik)

What OpenLithoHub implements

src/openlithohub/models/levelset_ilt.py :: LevelSetILTModel:

Item	OpenLithoHub	Matches survey?	Confidence
Loss (default)	mse_loss(resist_nom, target) + tv_weight · TV(mask) per predict() ll. ~270–272. tv_weight=0.01 default.	Yes in shape. Constants are our defaults.	A
Loss (PW mode)	process_window=True swaps the nominal-only fidelity term for workflow.process_window.pw_fidelity_loss over DEFAULT_PW_CORNERS. Currently only on the gaussian forward model — Hopkins multi-corner sweeps deferred (an explicit ValueError enforces this).	Yes in shape — multi-corner mean. Hopkins coverage is a known gap.	A
Mask init	mask_logit = 4 · target − 2 per ll. ~213. After sigmoid, ≈ 0.12 at target=0 and ≈ 0.88 at target=1 — non-saturated.	Different from OpenILTModel's 2 · target − 1 PixelInit but the survey does not pin an init. Our choice gives a slightly stronger initial signal.	A
Optimizer	torch.optim.Adam(lr=0.1).	Different from OpenILTModel's SGD-with-momentum — Adam is the project's choice for this baseline. Survey-compatible.	A
Forward model	gaussian (default) — simulate_aerial_image(sigma_px=2.0). hopkins — simulate_aerial_image_hopkins(...) reusing _utils/hopkins.py. SOCS kernels are cached per (grid_size, device).	Yes — both modes match the survey's optical-core options.	A
Resist	differentiable_threshold(aerial, threshold=0.5, steepness=50.0).	Yes. Constants are our defaults.	A
Hopkins kernel cache	Cached per (grid_size, device), invalidated when hopkins_params changes. Lock-guarded via threading.Lock — concurrent predict() callers cannot race on the check-then-rebuild. Pattern backported from OpenILTModel 2026-05-23.	Project-level — survey is silent.	A
Compile path	compile_forward=True triggers torch.compile(hopkins_fn, mode="reduce-overhead") cached per (shape, device, dtype, forward_model). Falls back to eager on torch < 2.0 / no-Triton platforms.	Project-level optimisation beyond the survey scope.	A
Checkpoint / resume	checkpoint_dir + save_freq + resume_from: writes mask_logit + Adam state every save_freq iterations; resume from any such file restarts the iteration counter and runs the remainder.	Project-level — survey is silent.	A
Halo / receptive field	RECEPTIVE_FIELD_PX = 64, matching OpenILTModel.	Project-level — survey does not tile.	A

Findings

1. Implementation tracks the surveyed formulation faithfully. L2 + TV with sigmoid-bounded mask logit, gradient descent, optical-core convolution, sigmoid-thresholded resist — all present.

2. Two divergences from OpenILTModel are deliberate and worth knowing: (a) Init is 4·target−2 here vs. 2·target−1 in OpenILTModel. Stronger initial signal. (b) Optimizer is Adam (lr=0.1) here vs. SGD+momentum in OpenILTModel. Adam converges faster on the L2+TV loss surface; SGD-with-momentum is the SimpleILT-paper-faithful choice for the L2+PVBand objective. Both are survey-consistent — the survey does not pin the optimizer.

3. Process-window mode does not cover the Hopkins forward. predict(process_window=True, forward_model="hopkins") raises ValueError. This is a documented gap, not a bug — multi-corner Hopkins sweeps would multiply SOCS kernel rebuilds (defocus changes invalidate kernels per HopkinsSimulator._hparams_match). Closing it requires either per-corner kernel caches (mirroring what compute_pvband(simulator=…) now does) or a PW-corner sweep that holds defocus constant.

4. Hopkins kernel cache is lock-guarded (as of 2026-05-23). Concurrent predict() callers serialize on self._cache_lock (a threading.Lock) for the check-then-rebuild path, mirroring the pattern in OpenILTModel. The compile-cache (self._compiled_hopkins_cache) is still unguarded — concurrent callers with different (shape, device, dtype, forward_model) keys are fine, but two callers with the same key racing on the first compile will both run torch.compile. That's a minor perf hit, not a correctness bug, so it is left for now. Multithread safety for the rest of predict() (e.g., the optimizer step) is still not guaranteed — keep one model instance per request unless you've audited the full path.

5. save_freq=N semantics double-checked. it+1 is the count of completed steps; resume restarts at it+1 and runs iterations - (it+1) more steps — total work equals an uninterrupted run. The inline comment at ll. ~283–286 is correct.

Implications for users

• Default vs. SimpleILT-paper-faithful choice: if you want the SimpleILT formulation byte-for-byte, use OpenILTModel. LevelSetILTModel is the "level-set / continuous-mask gradient descent" baseline, more general than SimpleILT.
• Process-window mode + Hopkins: unsupported as of 2026-05-23. Use either process_window=True, forward_model="gaussian" or process_window=False, forward_model="hopkins".
• Multithread safety: the Hopkins kernel cache is now lock-guarded, but the rest of predict() (optimizer state, in-place tensor updates) has not been audited for concurrent use. Use a per-process model instance behind any concurrent inference path.
• Citation hygiene: when reporting numbers, cite Yang2023_LithoBench for the survey lineage. The Pang2005 / Poonawala2007 papers are the deeper lineage references — cite them only if you also vouch for the level-set numerical equivalence (this implementation is closer to "continuous-mask gradient descent" than to Pang's Hamilton-Jacobi level-set evolution).

Re-audit triggers

Re-run this audit when any of the following change:

• Mask init scheme (mask_logit = ...) changes.
• Optimizer or learning-rate default changes.
• process_window gains Hopkins forward support.
• The _compiled_hopkins_cache gains lock guards, or the rest of predict() is audited for full multithread safety.
• The Pang2005 / Poonawala2007 paper PDFs land in docs/papers/ — items marked C can be promoted to A.