TokMan:Tokenize Manhattan Mask Optimization for Inverse Lithography
Authors: Yiwen Wu
Yuyang Chen
Ye Xia
Yao Zhao
Jingya Wang
Xuming He
Hao GENG
Jingyi Yu
Venue: NeurIPS 2025 poster ()
Keywords: Structured Tokenization
Manhattan represenetation
Inverse Rendering
Primary area: machine_learning_for_sciences

Abstract: Manhattan representations, defined by axis-aligned, orthogonal structures, are widely used in vision, robotics, and semiconductor design for their geometric regularity and algorithmic simplicity. In integrated circuit (IC) design, Manhattan geometry is key for routing, design rule checking, and lithographic manufacturability. However, as feature sizes shrink, optical system distortions lead to inconsistency between intended layout and printed wafer. Although Inverse Lithography Technology(ILT) is proposed to compensates these effects, learning-based ILT methods, while achieving high simulation fidelity, often generate curvilinear masks on continuous pixel grids, violating Manhattan constraints. Therefore, we propose TokMan, the first framework to formulate mask optimization as a discrete, structure-aware sequence modeling task. Our method leverages a Diffusion Transformer to tokenize layouts into discrete geometric primitives with polygon-wise dependencies and denoise Manhattan-aligned point sequences corrupted by optical proximity effects, while ensuring binary, manufacturable masks. Trained with self-supervised lithographic feedback through differentiable simulation and refined with ILT post-processing, TokMan achieves state-of-the-art fidelity, runtime efficiency, and strict manufacturing compliance on a large-scale dataset of IC layouts.

TokMan:Tokenize: Manhattan Mask Optimization for Inverse Lithography
Yiwen Wu
Yuyang Chen
Ye Xia
Yao Zhao
Jingya Wang'
Xuming He*
Hao Geng
Jingyi Yut
SSanghaiTech University
Equal contribution
Corresponding author
Abstract
Manhattan representations, defined by axis-aligned, orthogonal structures, are widely used vision, robotics, and semiconductor design for their geometric regularity and algorithmic simplicity. In integrated circuit (IC) design, Manhattan geometry is key for routing, design rule checking, and lithographic manufac- turability. However, feature sizes shrink, optical system distortions lead inconsistency between intended layout and printed wafer. Although Inverse Lithog- raphy TeC)) is proposed compensates these effects, learning- based ILT methods, while achieving high simulation fidelity, often generate curvilinear masks continuous pixel grids, violating Manhattan constraints. Therefore, we propose TokMan, the first framework to formulate mask optimization as a discrete, structure-aware sequence modeling task. Our method leverages Diffusion Trans- former to tokenize layouts into discrete geometric primitives with polygon- wonewise dependencies and denoise Manhattan-aligma proximity effects, while ensuring binary, manufacturable masks. Trained with self- supervised lithographic feedback through differentiable simulation and refined with ILT post-po post-processing, TokMan achieves state-of of of-the-art fidelity, runtime efficiency, and strict manufacturing compliance large-scale dataset of IC layouts.
point sequences corrupted by optical
Introduction
Manhattan eppreentaions-chhaaccriieedd by axis-aligned, orthogonal structures -play a founda- tional role in computer vision and robotics by simplifying the geometric complexity of structured environments. These representations exploit the prevalence of right angles in man-made settings, enabling efficient solutions to fundamental tasks such as vanishing point detection ①. camera lo- calization 12). SLAM (simultaneous localization and mapping) (3], and 3D scene reconstruction [4]. By reducing spatial ambiguity and imposing global regularity, Manhattan models facilitate compact encodings and algorithmic tractability, particularly in indoor and urban domains. Beyond perception, this abstraction is also central to architecture and procedural generation, where structured geometry supports scalable and interpretable design.
This same geometrie prior is deeply embedded in the semiconductor industry, where inte- grated circuit (IC) layouts adhere to Manhattan constraints for both algorithmic and manufac- turing efficiency. Modern designs consist of features such as wires and vias in layout and mask, that are aligned to orthogonal grids, simplifying placement, routing, design rule check- iDgCD (5), and verification workflows. Critically, Manhattan mask are favored in pho- tolithography due to their compatibility with optical projection systems and EDA toolchains (6).
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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The axis- structure enhances manufactura- bility, particularly as process nodes scale into the nanometer regime.
Mask
Wafer
wio OPC
However, lithography technique nodes shrink, Manhattan layouts become more susceptible to pattern-dependnt deviations caused by optical phe-
nomena such as light diffraction and interference [7]. These distortions challenge the fidelity of pattern transfer. motivating the adoption of inverse lithogra- phy technology (ILT). ILT formulates the task as an inverse imaging problem: given desired target lay- out pattern, the objective is to compute a modified design, named mask that reproduces the intended pattern after optical projection. The whole process is called mask optimization. Recent advances in both classical mask optimization [8] and deep-learning approaches 10 have yielded powerful ILT solvers. These approaches relax the binary mask into continuous representation, allowing pixel-wise gradient descent optimization. Despite their outstanding performances, reconverting the continuous mask back to binary representation undo the benefits gained during the pixel-level optimization, As a result, the final binary mask often deviates from the intended objective and remains suboptimal. Moreover, masks reproduced by these methods frequently contain curvilinear irregular features that violate the Manhattan constraints essential for manufacturability and increase write-time complexity, thereby negatively impacting time-to-marker efficiency.
Design Target
w/ OPC
Figure I: Pattern distortion caused by optical system. It requires mask optimization to be correctly fabricated on the silicon wafer.
In this paper, we propose TokMan, the first framework to apply a sequence modeling technique approach popularized by large language models(LLMs) [I3] 15), to the task of lithography mask generation under strict geometry constraints 16. Rather than treat Manhattan compliance as a post- hoc constraint, TokMan integrates Manhattan representations inherently throughout the optimization process by formulating mask correction as a sequence tokenization problem over a discrete vocabulary of axis- aligned geometric primitives. This approach aligns with the broader "tokenize everything" trend in machine learning, where motion [17, geometry [18), and structure [9] are represented as symbolic sequences. Inspired by works such MeshGPT (20) for triangle meshes and EgoEgo (21 for human motion reconstruction, our method employs Diffusion Transformer architecture (2 to generate corrected masks in a tokenized Manhattan domain. In this formulation, token-based modeling is not merely convenient abstraction-it is a fundamentally aligned representation for Manhattan-constrainee layout synthesis. By discretizing geometry into axis-aligned tokens, the model operates natively within the design space dictated by manufacturing constraints, enabling not only structurally faithful mask generation but also scalable, context- aware reasoning across complex polygonal configurations. This intrinsic compatibility renders tokenization a conceptually elegant and practically powerful paradigm for Manhattan mask generation.
TokMan employs a conditional diffusion process that reinterprets the forward lithography as a struc- tured noise addition-where diffraction and interference degrade the mask into distorted aerial image-allowing ILT process to be cast as a denoising problem (33) The Diffusion Transformer simultaneously learns model this inverse process while capturing the spatial dependencies be- tween Manhattan primitives. Training is conducted in a self-supervised fashion, using a large-scale dataset derived from open-source IC libraries 244 that span wide range of real-world routing and standard cell patterns. For each layout, the model learns to predict token-level geometric cor- rections conditioned on the full context. Predicted token sequences are rendered into continuous mask representations via nvdiffrast (25). and their lithographic printability is evaluated through a differentiable imaging pipeline. The simulated aerial image compared against the target pattern to compute reconstruction loss, enabling end-to-end optimization without ground-truth mask an- notations. A lightweight ILT refnnmmnt is optionally applied after generation to enhance line-edge fidelity while maintaining strict Manhattan compliance. Empirically, our method achieves superior performance over existing baselines in terms of pattern fidelity, runtime efficiency, and manufacturing compliance, offering a scalable path toward practical, learning- based inverse lithography approach under strict manufacturing constraints.

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Segmentation
Self-Supervised Training for Manhattan Tokenizer
Post Processing
Mask Image M
Database
OPC Correction
Nydiffrast
81
NVIDIA
81
82
Ön
Coarse Mask
Denoising Diffusion
Litho Simulation
M
A
Layout
Post Refinement
S
W
FF
01
22
ÆN
3/2
Segmented Points
Manhattan Representation
Refined Mask
Target
Wafer Image W
Figure 2: Overview of TokMan. The input layout is first segmented into Manhattan representation via our litho-aware segmentation algorithm. A denoising diffusion model then trained tokenize and predict OPC corrections using segmented Manhattan points. These corrected points rendered to mask image M by Nvdiffrast and passed through a lithography simulator to produce a simulated wafer image W, where loss is used to supervise the generation of OPC correction. Finally, post process is applied to enhance fidelity of coarse mask after generation.
Related Work
Manhattan Representation. The Manhattan representation, Manhattan world assumption, posits that scenes are predominantly composed structures aligned along three orthogonal directions. This geometric prior has been extensively utilized in computer vision and machine learning to simplify complex spatial understanding tasks [26). Introduced by Coughlan and Yuille [27], this assumption enables robust camera calibration and 3D inference using edge orientations and vanishing points. Building upon this, Guo et al. (88 integrated planar constraints derived from the Manhattan assumption into neural implicit representations for 3ID scene reconstruction, achieving improved quality in low-texture indoor environments. Additionally, Wakai et al. (29) leveraged the Manhattan world prior for single-image camera calibration, utilizing heatmap regression estimate vanishing points and camera orientation, demonstrating robustness in challenging scenarios with fisheye distortions. These studies underscore the versatility and effectiveness of the Manhattan world assumption as a structural prior in various computer vision and machine learning applications.
Tokenization with Transformer. Tokenizztion, originally developed in natural language processing (NLP) to segment text into discrete, meaningful units, has become a new trend in modern machine learning. With the rise of transformer architectures like BERT (30] and GPT [31]. its importance has expanded across modalities, enabling unified and scalable representation of diverse data types 33 33
In 3D scene understanding, Chen al. 34 use the Segment Anything Model (SAM) tokenize 3D point clouds by aligning 2D masks, enhancing semantic segmentation through region-level learning. MeshGPT [20] formulates triangle mesh generation sequence modeling task, leveraging geometric tokens for compact and autoregressive 3D synthesis. PointMamba (35) introduces an efficient state space model that imposes token order via space-filling curves, enabling scalable point cloud analysis. In egocentric motion prediction, Chi et al. [1]] tokenize full-body trajectories through a conditional transformer based diffusion framework in the time domain. These developments highlight tokenization's 's pivotal role in enabling transformers to process complex, high-dimensional data structures, establishing as a universal mechanism for unifying representation and computation in contemporary machine learning.
Optical Proximity Correction. Optical Proximity Correction (OPC) plays a central role lithog- raphy, aiming to compensate for systematic pattern distortions caused by light diffraction, optical

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proximity effects, and process non-idealities. As feature sizes approach the resolution limits of lithographic systems, the printed patterns often deviate significantly from the intended layout, making OPC essential for ensuring pattern fidelity. Traditional rule-based and model-based OPC rely on calibrated optical models and heuristic correction strategies, where geometric features are modi- fied iteratively to align simulated contours with the target layout. These methods typically require expensive computational simulations and manual tuning. Recent academic work leverages deep neural networks and GPU acceleration to enhance both runtime and correction fidelity. For instance, long-standing level-set algorithms [36] have been migrated to GPUs. Generative models such as GANs [9] and task-specific neural networks [TO I1 12] applied for pixel-level mask synthesis and optimization. Nonetheless, many of these learning-basee methods lack explicit manufacturability
constraints, limiting their applicability in real-world industrial settings.
3 Preliminaries
Forward Simulation. Lithography is a core technology in semiconductor manufacturing, enabling the transfer of circuit patterns from photomasks onto silicon wafers using light exposure (37). The forward lithography process models how given mask pattern produces printed image on the wafer, governed primarily by optical diffraction and resist interactions [3] 39]. Mathematically, the aerial image I (z. y) formed on the wafer plane can be modeled as coherent or partially coherent imaging of the mask (x. y) through an optical system:
[(, 3) = |F (H( (I,
where FF denotes the Fourier transform, Hffz, fu) the optical transfer function (OTF) of the lithography system, and (x,, y) is the binary mask pattern. Post-processing steps, such as resist de- velopment and etching, are often approximated as thresholding or convolutional smoothing operations on (ar, y)-
Inverse I Lithography Technology (ILT). The inverse lithography process [40] aims to determine an optimal mask pattern M (x. y) that produces a target pattern T(x, y) on the wafer, effectively solving an inverse problem [41] (22.. This can be formulated minimizing the discrepancy between the simulated wafer image and the desired layout:
L(T(M), + R M(z.))
min
where L is a loss function measuring pattern fidelity (c.g.. Le loss. edge mismatch, or critical dimension error), and R is regularization term that encourages mask manufacturability and sparsity (e.g., enforcing Manhattan geometry or minimizing sub-resolution features). balances fidelity and regularity.
Recent ILT frameworks utilize differentiable lithography simulators to enable gradient- gradient-based opti- mization [4 44]. Notably, self-supervised learning approaches avoid requiring explicit ground-truth -ruth masks by computing the loss between simulated images and target layouts directly, allowing end-to- end optimization:
Lsel [(S(M) - 3
where S(M) denotes the simulated print image from mask M via forward lithography. Such frameworks facilitate mask learning driven by lithographic feedback, enhancing printability and robustness under process variations.
Methods
This section presents our proposed TokMan framework. We begin by describing the layout segmenta- tion strategy, which converts Manhattan circuit geometries into structured representations suitable for learning. We then detail the use of a Diffusion Transformer for generating OPC corrections in token space, followed by the self-supervised training procedure enabled by differentiable Man- hattan renderer and lithography forward simulation. Finally, we introduce a lightweight I..T-aased post-procces pest-processing step to ensure high-fidelity manufacturability deployment.

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Polygun
Polygon 2
Polygon k
Noise Level
31
Up
pa Bog
MLP
6
5%
Embedding
Linear
Transtormer
Add
Polygon-wise
Linear
Positional Embedding
Corner Rounding
Spatial Alignment
Long-Range
Point-wise
Partition
Positional Embedding
N
(a)
(b)
Figure 3: (a) Segmentation Algorithm Visualization. (b) Model Architecture of denoising network in single step of the reverse diffusion process.
4.1 Segmetation Algorithm
Augmentation for Spatial Perception. Segmentation serves the foundational step our method, transforming raw geometric input into structured form amenable to learning. Starting from sparse polygonal contours in the Manhattan layout, we subdivide each polygon edge into densely sampled, axis-aligned line segments. This densification is essential not only for capturing the full resolution of layout boundaries also for constructing a high-resolution optimization space tailored for Manhattan representation. These segments produce sequence of discrete points {(r,, y:) Ja)). precisely aligned to horizontal or vertical directions, which serve as the input to our model. By converting sparse geometric data into dense and grid-aligned format, impose geometric regularity and uniform sampling across the layout. This regularized structure allows the Diffusion Transformer to operate over consistent and interpretable representation, enabling it to model correction patterns with both local precision and global coherence. By ensuring consistency and interpretability in the input representation, this step enables the network to reason fine-graine layout details while maintaining strict alignment with Manhattan geometry.
Lithography-awann Points Segmentation. Beyond structural regularization, our segmentation algorithm is designed capture key lithographic phenomena and integrate manufacturability con- straints, particularly corner rounding and feature coherence under optical proximity effects. First, detected corners,
to mitigate corner rounding, we enforce high-resolution segment splits ensuring that the discretization granularity at curvature-critical regions is maximized. This uniform corner-based refinement enables accurate modeling of sharp edges where lithographic deformation most pronounced. Second, to enhance connectivity and contextual consistency among parallel edges, we implement spatial alignment casting: for any given edge, we detect all parallel edges within a con- figurable aathorraphy-influeee
zone and identify their nearby corner vertices. These corner positions are then transposed across space and aligned onto the current edge as candidate segmentation anchors. This facilitates implicit edge-to-edge communication, reinforcing Manhattan structure consistency through spatial correlation. Finally, to maintain manufacturability. the remaining longer segments are adaptively partitioned using evenly distributed anchor points that satisfy minimum printable feature length requirements. Each resulting sub-segment conforms to rules, ensuring that the final augmented representation remains both accurate and fabrication-friendly,
faf.-manfaatttaabiiityy (DFM)
4.2 Manhattan Layout Tokenization
Diffusion Transformer for Manhattan Representation. Given a decomposed layout consisting of seahattan--liggned polygons, first extract set of uniformly sampled edge points {(x,, w)) W where each point lies on either a horizontal or vertical polygon edge. These coordinates form a fixed, structured matrix X Nx2 which serves the conditioning input for the model.
The objective OPC in Manhattan representation to predict set of per-point corrections {6, N. where each 8, R denotes the scalar offset applied along single axis (horizontal correction
5

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for vertical edges and vice versa). These corrections are learned via a conditional diffusion framework,
where the correction field A the target variable being progressively noised and denoised.
To simulate the correction refinement process, we apply a forward diffusion process over the correction vector A, generating noisy version A, at timestep
q( ( Ao) = (id: vor (1 -;)));
where Do is the clean ground-truth correction from self-supervised learning, (B+) is fixed noise schedule, and O₁ IT Bg). This process introduces Gaussian noise to simulate uncertainty and process-inducer variation in mask design.
The Diffusion Transformer (DiT) is trained to reverse this process by predicting the added noise from the noisy correction A,, conditioned on the fixed layout geometry X and the timestep t:
Lieacis = Es [|ee t,,,,,,))11
(5)
where c NO,,I), and A, = Vā + āte āec.
To enhance the model's spatial understanding, we incorporate two forms of positional encoding alongside X: (1) Point-level encoding, using sinusoidal embeddings of (Ia, yt); and (2) Polygon-level encoding, assigning shared embedding to all points belonging to the same polygon, promoting shape-level consistency.
By constraining each A; to a single axis (depending on the orientation of its associated edge), the model learns to predict minimal, axis-aligned displacements that compatible with standard manufacturing rules. The final output has shape (N, 1), with each scalar correction applied to the corresponding layout point.
Through this formulation, our method integrates two complementary modeling paradigms. The diffusion component explicitly simulates the inverse lithography process, treating optical proximity effects as a structured forward diffusion that corrupts an ideal mask, and framing mask generation as a reverse denoising process that refines corrections to recover the intended pattern. In parallel, the Transformer serves as a powerful sequence model that captures lithography-aware correction patterns by attending to both local geometry and global layout context. By tokenizing the Manhattan layout into a discrete sequence of axis-aligned primitives, it operates directly within the geometric and manufacturing constraints of the design space, enabling it to reason over structural regularities and long-range interactions in compact token domain. Together, the diffusion mechanism ensures a physically grounded formulation of OPC, while the Transformer enables the learning of complex, context-dependent correction behaviors. The architecture captures both local geometry and long- range context, and the reverse diffusion process refines corrections in geometry-consisten and manufacturable way.
Self-supervieed Learning by nydiffrast Renderer. In alignment with the OPC objec- tive-where the corrected mask should produce a wafer image that closely matches the target layout-we supervise the DiT using differentiable lithographic simulation pipeline.
After the DiT predicts scalar offsets for the input point set, the adjusted points define new Manhattan-aligned segments, which are rasterized into a binary mask image M E {0, 1) " using nvdiffrast. 255,, a GPU-accelerated di differentiable renderer. This mask then passed through a differentiable lithography simulator, which models projection optics and resist behavior to generate an aerial image A TR. xWW
The reference layout is similarly rasterized into a binary target image T E {0, 1] Hx The aerial image is compared against the target layout using pixel-wise Mean Squared Error (MSB) loss:
H
W (Ag - T.
LMSE
HW
This loss signal is backpropagated through both the lithography simulation and the mask rasterization steps, enabling end-to-end training. The model thus learns to adjust the layout geometry not by direct supervision from ground truth OPC masks, but by minimizing the deviation between simulated and desired lithographic outcomes. The entire pipeline-geommerry geometry encoding, mask generation, rendering, and acrial image prediction- is differentiable, supporting fully self-supervised learning.

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Bench
Metries
GAN-OPC 9
Neural-ILT
10
DevelSet S
Multi-ILT f
IL-IIT
12
Ours
EPE
8.86
6.51
5.20
3.18
2.70
2.16
ICCADI3-S
shotss
861.5
1463.1
955.4
6734.8
4948.4 4
287.6
TAT
15.69
14.37
1.53
1.23
2.87
0.89
EPE
4.73
4.29
3.64
2.22
1.80
1.38
ICCADI3-L
#shots
1823.3
2616.4
2195.8
6786.9
7916.4
642.3
TAT
16.89
11.20
1.54
1.33
2.92
1,57
Table I: Comparison of SOTA methods on ICCADI3 benchmarks
4.3 Post-Processing for Manufacturability
Although TokMan produces geometrically valid and lithographically informed mask predictions, model training statistical in nature and optimized across large-scale datasets. In practice, layout- specific variations may require additional fine-tuning to ensure manufacturability under strict process windows.
To address this, we apply lightweight ILT refinement step after inference. This post-processing module performs localized corrections to the DiT output, further minimizing aerial image error while preserving Manhattan structure. Since the model's prediction already adheres closely the correct pattern, ILT operates in narrow solution space, improving convergence speed and climinating the risk generating non- non-Mankin Manhattan features. This hybrid approach-combinng combining learning-base based generalization with deterministic refinement- grade requirements for fidelity, printability, and integration into EDA workflows.
that each generated mask meets industrial-
5 Experiments
5.1
Experimental Settings
Training Settings. TokMan model uses Transformer blocks with embedding dimension 512 and 16 heads of self-attention, followed by linear projection layer for ope correction output. We implement our work wth PyTorch-Geometric 32x NVIDIA H20 Graphics Cards, requiring approximately 80 GB of memory for batch size of 40 and test on 1x A100 Graphics Card. For lithography simulator settings, the photoresist intensity threshold for lithography settings is set at 0.225, and sigmoid steepness is 50. The lithography wavelength is 193 nm with a defocus range of +30 nm and dose range of +3%. The resolution of the mask and corresponding wafer image are all 1nm/pixel.
Geometric toolkit and train our model on the platform that possesses
Dataset. To train our model effectively on Manhattan-aligned layout patterns, we construct large-scale dataset derived from the publicly available benchmark [24]. Specifically, we extract polygonal shapes from the original layouts and systematically regenerate
samples by rearranging these polygons based on realistic placement characteristics observed in actual design environments. This data generation strategy ensures that the resulting samples remain consistent with typical layout design constraints while significantly enriching the diversity of polygon combinations. In total, we generate 89,697 layout samples as training data. We evaluate our method the ICCAD2013 benchmark [45] which includes simple and complex cases: ICCAD13-S and ICCAD13-L.
Evaluation Metrics. To comprehensively assess the performance of our OPC approach, we adopt three key metries: Edge Placement Error (EPE), mask shots, and Turn-Around Time (TAT).
Edge Placement Error (EPE) 46 used evaluate the lithographic fidelity of the optimized mask. It measures the difference between the wafer image simulated from the corrected mask and the intended target layout. While prior works typically use an Eg distance metric that compares the wafer and target images pixel-wise, this approach is overly influenced by background regions and fails to EPE
emphasize pattern fidelity around critical edges. contrast, we adopt the industry-standant metric, as shown in Figure where merit points are placed along the edges of the target layout to measure their distance to the corresponding contour in the wafer image. Both inner errors and outer errors are taken into consideration.

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DevelSet
IL-ILT
Ours
S3 Mask
S3 Target
S3 Resist
S6
Mask
-
S6 Target
S6 Resist
Figure Results Visualization.
Network Architecture Parameters
Post Processing Iternations
10
MPE
Wafer Image
Mask Image
1024
16
50 Here
1001 Hoys
2001 Hers
ieers
350
500
Inner Emor
Edge Merit Points
shots
Outer Emor
450
EPE
Mask Shots
340
400
335
Figure 5: Metrics used for Comparison.
350
330
250
512
16 33
50 Here
no
doc layer num
Figure 6: Ablation Study.
Formally, given sampled points {ps N distances d; to the wafer image contour, define the mean EPE as:
on the target layout boundary, and their respective
N
EPE
dc
Unlike Zheng et al. (24, who report only the number violations exceeding a given threshold, mean- mean-based formulation provides continuous and more sensitive indicator that better reflects lithographic performance improvements.
Mask shots 47 measure the manufacturability of the generated mask. In practice, the mask layout is decomposed into a series of rectangular fragments, or "shots", which are individually written by an Electron Beam Lithography (EBL) system, as shown in Figure Fewer mask shots imply a shorter writing time and higher production efficiency. Therefore, we count the number shots required to fabricate each layout and use this value to evaluate the mask efficiency of both our method and competing baselines.
Turn-Around
Time (TAT) quantifies the computational efficiency of each method. For optimization- based approaches, we record total runtime under fixed number iterations. For model-based baselines, we measure the forward inference time. For our method, report the sum of inference time and post-processe processccssn duration (e.g., ILT refinement). TAT measurements exclude file I/O, such reading input saving results, ensure fair benchmarking.

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5.2 Comparison with SOTA Methods
We compare our method against several recent state-of-the-ai approaches, including GAN-OPC, Neural-ILT, Devel-Set, Multi-ILT, and IL-ILT. All methods are evaluated using the same metrics introduced earlier.
In terms of EPE, as shown in Table which directly reflects the accuracy of the resist pattern after photolithographic simulation, method achieves over 20% improvement over the SOTA, IL-ILT. This improvement is not only numerical but also visually significant. As shown in our visualization Figure[4 our method yields printed wires with fine alignment and topological consistency to the intended circuit, especially in fine and densely packed regions.
We also observe substantial gains in mask shot count, illustrated in Table I key indicator of how easily a mask can be manufactured. Thanks to the Manhattanized mask design produced by our framework, we achieve approximately 4x reduction in mask shot count compared to other methods, indicating that our approach far more production- frienndl.
In terms of TAT, our method maintains a speed comparable to the fastest existing techniques. Despite introducing ILT refinement, our optimizations ensure the overall pipeline remains efficient and practical for deployment.
5.3 Ablation Study
We conduct ablation experiments on the augmented dataset with 100,000 training iterations. All other configurations follow Section [S] We evaluate both lithographic fidelity (EPE) and manufacturability (#shots), as summarized Figure
Architecture Parameters. We investigate the effect of key architectural hyperparameters, including feature dimension, number of attention heads, and number of Transformer layers. As shown on the left side of Figure(o increasing the feature dimension from 256 to 512 yields a clear improvement in EPE, while further enlargement provides diminishing returns. Adjusting the number of heads or layers exhibits no consistent benefit and occasionally degrades performance, likely due to overfitting to local geometric patterns. The #shots metric remains relatively stable across configurations, indicating that network capacity primarily influences lithographic accuracy rather than manufacturability.
ILT Refinement. We further examine the effect of post-processing iterations on mask quality. As shown on the right of Figure [6] additional ILT iterations substantially reduce EPE but lead to steady increase in #shots and computational cost. Performance gains saturate beyond 100 iterations, where further refinement slightly improves fidelity but at the expense of higher mask complexity. This suggests that moderate ILT refinement (around 100 iterations) offers the best trade-off between accuracy and efficiency.
6 Discussion
Limitations. While our approach offers notable improvements in lithographic fidelity and mask manufacturabilityy several limitations remain. First, although operating in the Manhattan space significantly reduces optimization redundancy and simplifies pattern representation, it currently lacks scalability in certain aspects-most notably, the inability to freely incorporate Manhattan sub-resolution assist features (SRAFs) within the framework. Second, all evaluations in this work are conducted on sliced layout datasets, which isolate regions for targeted optimization. As result, the method has not yet been tested on full-chip, unsliced layouts. where scalability and context- aware performance are critical. Finally, while our results show strong promise on synthetic and research-oriented data, further validation on real industrial production datasets is essential to assess generalizability and practical deployment viability.
This paper presents TokMan, tokenized Manhattan representation framework for optical proximity correction under strict geometric constraints. By aligning the OPC task with a sequence modeling paradigm, TokMan leverages a conditional Diffusion Transformer to operate directly on axis-aligned layout tokens, capturing both local and global spatial dependencies while inherently respecting Manhattan compliance. The model interprets lithographic distortion
Conclusions.

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structured noise process and learns to reverse it through self-supervised denoising, eliminating the need for ground-truth masks. Experimental results demonstrate that TokMan not only achieves high pattern fidelity and manufacturability but also offers improved runtime efficiency compared to traditional and learning-based ILT methods. This work highlights the effectiveness of combining discrete geometric priors with modern generative modeling, advancing scalable and production-ready solutions for layout correction in semiconductor manufacturing.
Future Work. While TokMan is designed for Manhattan-constraine mask correction, the broader idea of tokenizing structured geometry may inspire new paradigm for inverse problems across computational imaging. In many crystallography and 3D reconstruction-obess structure-regular domains. By introducing discrete, symbolic representation aligned with domain- specific priors, token-based modeling can disentangle complex imaging processes and enable robust, interpretable, and scalable reconstruction pipelines. This perspective opens up promising directions for structured inverse rendering, symbolic image reconstruction, and hybrid physical- learning systems.
from remote sensing and medical imaging to signals are projections or distortions of latent,
10

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Acknowledgement
This work is supported in part by the National Natural Science Foundation of China under Grants W2431046 and 62350610269. It is also sponsored by Natural Science Foundation of Shanghai (Project No.25JD1403000 and by MoE Key Lab of Intelligent Perception and Human-Machine Collaboration (ShanghaiTech University), the Shanghai Frontiers Science Center of Human-centered Artificial Intelligence, and the HPC Platform of ShanghaiTech University.
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A Additional Results of TokMan
To further demonstrate the robustness and generalizability of our TokMan framework, we provide detailed comparisons across 20 benchmark layouts from the ICCAD2013 datasets. As shown in Table our method consistently outperforms previous state-of-the tae--o--thhhaaee art OPC approaches including GAN-OPC()). Jeural-ILT(IO) Bevel-Set[8) Multi-ILT and IL-ILT[[2 across all three key evaluation metries: Edge Placement Error (EPE), mask shot count, and Turn-Around Time (TAT).
Compared to the SOTA, IL-ILT, our method achieves an average of over 20% improvement in EPE, and 4-7x reduction in mask shots, underscoring its manufacturability advantage. Importantly, this performance is achieved with minimal runtime overhead, and even with ILT refinement included, our TAT remains competitive with the fastest basclines.
In addition to numerical metrics, Figure 8 and presents qualitative comparisons on several repre- sentative layouts, which is more critical than others. The masks generated by TokMan are not only visually cleaner and Manhattan-aligner but also produce resist patterns that closely match the desired targets, validating the effectiveness of our discrete token correction process. Notably, TokMan avoids the wavy, curvilinear artifacts observed in other methods, preserving edge integrity and topological consistency, while effectively preventing feature bridging and line-end breakage, which helps ensure the functional reliability of the underlying circuit.
These comprchensive results reinforce TokMan's strength in balancing fidelity, manufacturabiliiyy and efficiency, offering a production-ready solution for OPC under strict design rules.
Bench
GAN-OPC|)
Neurab-ILar(10)
DevelSet S
Multi [I]
I1-1
Ours #-chots
LFC
#-chots
TAT
EPE
gichote
TXT
EPC
4-ohots
TAT
EPC
#-shots
TAT
EFC
aichote
EXT
EPC
TXT
1.70
10:30
4.00
53
1476
29.56
15:07
9.75
69805
1.30
7.56
54
8:23
408
11008
4.30
10.35
5.88
2.55
7025
1.34
2.03
2.8%
0.31
112
0.69
85
4.31
4.64
4.09
2.36
6743
2.87
1.40
3.31
2.43
7170
1.60
2.90
2.07
14.95
2.75
5836
3.59
3.17
3.41
1.97
1.30
7,00
3.50
S10
2.68
1.25
1.90
0.65
1.38
1971
2,40
5.02
3.54
2.52
L3
10.59
13:35
7.59
5.36
L4
1.32
1.5
3356
2:56
18
3.20
1.42
3.44
2.27
110
2.77
10.45
2,30
2.32
1.00
0742
1.28
Table 2: Comparison of six OPC methods across 20 benchmark layouts with evaluation metrics: EPE, mask shots, and TAT.
0.12
0.10
Loss
0.08
0.06
0.04
0.02
20,000
40,000
60,000
Steps
Figure 7: Training loss.
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B Results Visualization
GAN-OPO
Neural-ILT
DevelSet
Multi-ILT
IL-ILT
Ours
S1 Mask
S1 Target
S1 Resist
$2 Mask
$2
Target
$2
3:5
3:5
Resist
S3 Mask
S3 Target
S3 Resist
+
Mask
+
S5
Target
S5
fft
Ft
FF
Resist
#
FF
f
F FE
S6
Mask
S6 Target
f
K
f
#
Resist
S9
Mask
Target
S9 Resist
Figure 8: Visualization Comparison with SOTA on selected critical layouts of ICCAD13-S.
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GAN-OPC
Neural-ILT
DevelSet
Multi-ILT
IL-ILT
Ours
Ll Mask
L1
Target
LI Resist
L.2 Mask
1.2 Target
1.2 Resist
Mask
L3 Target
1.3 Resist
Mask
1.5 Target
20
LS Resist
F L6 Target
Mask
K
Ki
L6 Resist
Mask
L9 Target
L9 Resist
Figure 9: Visualization Comparison with SOTA selected critical layouts of ICCAD13-L.
23

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Reviews:
[{"review_id": "r9J4ViG7mw", "reviewer": "Reviewer_RP47", "summary": "The work proposes a DiT-based method for the ILT method, which achieves SOTA performance.", "questions": "How does the work customize for patterns other than piecewise constant?\n\nIs this work derived from some ideas on inverse problems in imaging? Cite relevant works, if any.", "limitations": "The work could have been written better. To motivate readers.", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "1. This framework provides an effective approach to optimizing masks for the Imaging Lithography Technology (ILT) problem, showcasing its versatility in addressing complex design challenges.\n\n2. It achieves state-of-the-art (SOTA) performance, setting a new benchmark in the field and demonstrating significant improvements over previous methodologies.\n\n3. This technique is valuable for engineers and designers in the semiconductor industry, as it streamlines the process of designing masks, ultimately improving manufacturing efficiency and yield.\n\n4. The research appears to benefit significantly from the implementation of a novel tokeniser module, which enhances the overall performance and flexibility of the optimization process.", "was_revised": true, "final_justification": "The rebuttal is strong and I am inclined to accept.", "rebuttal": "We sincerely thank the reviewer for the valuable comments. Below, we address each of the raised questions and concerns.\n\nQ1: How does the work customize for patterns other than piecewise constant?\n\nThank you for raising this important question. In Section 4.1 of our paper, we detail our lithography-aware segmentation algorithm, which currently focuses on Manhattan geometries—i.e., piecewise constant patterns composed of axis-aligned polygon edges. The segmentation process involves three key stages: (1) dense sampling at corners to mitigate rounding artifacts, (2) spatial alignment casting to enhance consistency across neighboring features, and (3) minimum-feature-length–based partitioning to enforce DFM constraints.\n\nWhile this paper targets Manhattan mask optimization, we believe the segmentation algorithm is highly extensible to non-axis-aligned and even curvilinear masks. For example, diagonal edges can still be segmented uniformly along their linear span. In the case of curved features—such as Bézier or circular arcs—the segmentation can be performed based on curvature, control points, or arc length to ensure optical fidelity.\n\nExploring such generalizations to non-piecewise-constant layouts represents an exciting direction for future work, particularly in adapting tokenized representations to richer geometric primitives while preserving compatibility with differentiable lithography pipelines.\n\n\nQ2: Is this work derived from some ideas on inverse problems in imaging? Cite relevant works, if any.\n\nOur work is conceptually grounded in the framework of inverse problems in imaging. Inverse lithography itself is a classical inverse imaging task, where the goal is to infer a mask pattern that, under a forward optical projection model, reproduces a desired resist pattern on the wafer. Beyond the classical formulation, our main novelty lies in recasting inverse lithography as a sequence modeling problem, inspired by the \"tokenize everything\" paradigm recently adopted in vision and geometry tasks. Works such as MeshGPT [Shue et al., 2023] and EgoEgo [Chi et al., 2023] demonstrate that structured geometric data can be effectively represented and optimized through discrete token sequences. We extend this idea to lithographic mask optimization under Manhattan constraints, enabling our model to operate directly in a manufacturable token space rather than pixel grids. To our knowledge, this is the first work to apply tokenized diffusion transformers to inverse lithography.\n\n\nQ3: Limitations — The paper could be written better to motivate readers.\n\nWe appreciate this suggestion and acknowledge that the manuscript could benefit from clearer motivation and exposition. In future revisions, we will improve the introduction to better highlight the industrial need for scalable, manufacturable OPC solutions and clarify why tokenization is well-suited for lithography. Structured layouts such as Manhattan masks naturally align with discrete token sequences, making our formulation both geometrically meaningful and fabrication-aware. We will make this connection more explicit and warmly welcome any specific suggestions the reviewer may have. Our broader goal is to bring cutting-edge AI techniques—particularly tokenized generative modeling—into semiconductor lithography, and we hope this work helps bridge these two technically rich and impactful domains."}, {"review_id": "JHKMxvFW0e", "reviewer": "Reviewer_54em", "summary": "This paper introduces TokMan, a framework for Inverse Lithography Technology (ILT). The key problem the authors address is that existing deep learning-based ILT methods often produce masks with curvilinear features, which are difficult and expensive to manufacture and violate the industry-standard \"Manhattan\" (axis-aligned, orthogonal) geometry constraints.\nThe main contribution is to reframe the mask optimization problem as a sequence modeling task. TokMan first segments the target IC layout into a sequence of Manhattan-aligned points. It then uses a Diffusion Transformer (DiT) model to learn how to predict precise, axis-aligned positional corrections for these points. The model is trained in a self-supervised manner, using a differentiable renderer and a lithography simulator to provide feedback, thus eliminating the need for ground-truth corrected masks. The authors demonstrate that their method achieves state-of-the-art results on standard benchmarks.", "questions": "1. Would it be possible to include visualization results for the ablation study of each module to better understand their individual contributions?\n\n2. Could the authors consider clarifying where the improvements occur in the visual comparisons to make the gains more interpretable? For example, highlighting the regions with more noticeable improvements in the figure using zoomed-in views.", "limitations": "Yes", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1. The core idea of \"tokenizing\" a Manhattan layout is novel and significant. It cleverly translates a geometric correction problem into a sequence-to-sequence task.\n2. The methodology is well-designed and technically sound. \n3. The paper presents an evaluation against multiple recent state-of-the-art methods on standard benchmarks. \n\nWeaknesses:\n\n1. There are no visualization results for the ablation study of each module.\n2. The current visualizations for comparison do not clearly highlight where the improvements occur, which may make it harder to interpret the gains.\n3. The visualization results comparing different methods are not included in the main text to show the improvements.", "was_revised": true, "final_justification": "I carefully reviewed the rebuttal. While I understand that numerical improvements (e.g., in EPE) might be difficult to observe visually, the lack of compelling qualitative evidence still makes it challenging to fully assess the contribution of individual modules. Even subtle differences, if critical to manufacturability, should ideally be more clearly communicated, perhaps with domain-specific visualization strategies. A more rigorous ablation could help build confidence. Therefore, I maintain the score at this time.", "rebuttal": "We sincerely thank the reviewer for the constructive comments and suggestions. Below, we address the raised concerns.\n\nQ1: Would it be possible to include visualization results for the ablation study of each module to better understand their individual contributions? Could the authors clarify where the improvements occur in visual comparisons, for example using zoomed-in regions?\n\nThank you for the valuable suggestion. We initially chose not to include extensive visualizations for ablation studies because, in Manhattan mask layouts, even significant numerical improvements (e.g., in EPE) may correspond to visually subtle changes. Unlike natural images, lithographic masks are discrete and highly structured, making qualitative differences harder to perceive. This also highlights an important insight: CV-based models, when properly adapted, can be effectively transferred to non-visual, high-precision domains such as computational lithography.\n\nThat said, we agree that focused zoomed-in visualizations can improve interpretability. In the revised version, we will include annotated printed wafer images highlighting localized improvements—for instance, better reconstruction of M-shaped patterns or reduced line-edge deformation in dense regions, which can be seen in Supplementary Figures 2 and 3. These changes, although subtle, are critical for manufacturability and print fidelity."}, {"review_id": "h1wkvR9uOr", "reviewer": "Reviewer_DJnG", "summary": "This paper proposes TokMan, a novel framework for inverse lithography that reframes mask optimization as a sequence modeling task. The method utilizes a Diffusion Transformer to generate masks that inherently comply with Manhattan geometry constraints. Trained in a self-supervised fashion using a differentiable simulator, TokMan demonstrates state-of-the-art performance on standard industry benchmarks in both pattern fidelity and manufacturability.", "questions": "1. Could you please elaborate on the details of post-processing?\n2. Why does high heads num or dec layer num, as shown in figure 6, result in worse effect?", "limitations": "yes", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1.The paper is well-written, and the proposed methodology is clearly explained.\n2.The formulation of inverse lithography as a token-based sequence modeling problem is novel and original.\n3.Extensive experiments show the outstanding effects of proposed framework over previous learning-bases works.\n\n\nWeaknesses:\n1. As shown in Figure 6, the framework's final performance is heavily dependent on an ILT post-processing step, which weakens the contribution of the core learning model. However, the details of the post-processing step are not explained.\n2. The paper claims to be state-of-the-art but only compares to learning models that don't all focus on optimizing manufacturability. Comparing to more relevant works, such as \"Fracturing-aware Curvilinear ILT via Circular E-beam Mask Writer\", would be more convincing.\n3. The ablation study only targets EPE, not mentioning #shots or TAT. The reason for the effect of hyper-parameters on EPE is not fully explained.", "was_revised": true, "final_justification": "Thank you for your rebuttal. I will maintain my score. My main concern is the significant reliance on the post-processing step. When a traditional method accounts for nearly half of the EPE improvement, it overshadows the contribution of the core learning model, which is a critical issue for a paper at a top learning conference. Furthermore, the evaluation feels incomplete without crucial robustness metrics like the Process Variation Band (PVB). The ablation study is similarly limited by focusing only on EPE, which doesn't provide a full picture of the trade-offs involved. Therefore, while I acknowledge the originality of the approach, these combined issues prevent me from recommending a higher score.", "rebuttal": "We thank the reviewer for their thoughtful feedback and helpful questions. We address the concerns as follows.\n\nQ1: Could you please elaborate on the details of post-processing?\n\nWe apologize for not providing sufficient details in the original manuscript. As briefly mentioned in Section 4.3, we apply a lightweight ILT refinement as a post-processing step. Specifically, as illustrated on the right side of Figure 2, we treat the predicted displacements from the DiT model as optimization variables. These displacements are first rasterized into a mask image via a differentiable renderer and then passed through our lithography simulator. The simulated wafer image is compared against the target layout using a differentiable loss, and the resulting gradient is backpropagated to refine the displacements.\n\nImportantly, Manhattan mask optimization is an NP-hard, highly underdetermined problem with a vast solution space. Our approach alleviates this by using a learning-based model to generate high-quality initializations that significantly reduce the computational burden during refinement, while remaining fully compatible with traditional optimization-based industrial flows for seamless downstream integration. The entire pipeline is independently designed to align closely with existing industry practices, making it easy to adopt in real-world settings. While the learning-based model remains the core of our method—responsible for producing manufacturable and high-fidelity initial solutions—the hybrid formulation accelerates convergence and has been particularly well-received in early-stage industrial validation. This fast-generation-plus-refinement strategy has been preliminarily validated on industrial datasets and is actively being tested in production environments.\n\nQ2: Why does increasing the number of decoder layers or attention heads (as in Figure 6) result in degraded performance?\n\nThis is a great question. In our ablation study, we observed that while small values of feature dimension, number of attention heads, or decoder layers can lead to underfitting (i.e., insufficient model capacity), simply increasing these parameters does not always yield better results.\n\nWhen the number of attention heads or decoder layers becomes too large, the model becomes over-parameterized relative to the dataset size and task complexity. This can lead to optimization instability and difficulty in generalization, especially given the statistical nature of the training data and the limited number of correction tokens per sample. In particular, for OPC corrections, the model must resolve fine-grained, spatially localized variations—which excessive global attention capacity can dilute.\n\nThis effect is most noticeable with large feature dimensions, where the model may struggle to converge within the given training schedule and may overfit to high-frequency noise. Therefore, careful architectural balancing is critical for achieving both accuracy and generalization. We will clarify this analysis in the ablation section.\n\nQ3: Regarding the comparison with \"Fracturing-aware Curvilinear ILT via Circular E-beam Mask Writer\"\n\nWe appreciate the reviewer’s suggestion to consider broader comparisons. However, we believe that a direct comparison with “Fracturing-aware Curvilinear ILT via Circular E-beam Mask Writer” may not be entirely appropriate due to fundamental differences in target mask formats and downstream manufacturing flows.\n\t\nSpecifically, the referenced work focuses on curvilinear masks designed for circular e-beam writers, whereas TokMan is tailored for Manhattan masks, which remain the dominant format in optical lithography pipelines due to their compatibility with existing EDA tools and manufacturing standards. Comparing across such fundamentally different mask paradigms may not yield meaningful insights, as they operate under different assumptions and optimization goals.\n\nMoreover, from a process integration perspective, the manufacturing flow differs: curvilinear masks typically undergo fracturing before EPC (Electron Proximity Correction), while Manhattan masks require EPC before fracturing. Our work is designed to align with the latter flow, aiming to significantly improve both fidelity and efficiency within the existing Manhattan mask infrastructure widely adopted in industry.\n\nWe acknowledge the value of curvilinear ILT approaches in their respective subdomain, but we believe it is more appropriate to view them as addressing a different formulation of the ILT problem, rather than as the SOTA baseline for our target setting. We will consider including a brief discussion of curvilinear ILT approaches in the final version to clarify this distinction and position our work more clearly."}, {"review_id": "YV3MtgYBqK", "reviewer": "Reviewer_Kk3P", "summary": "This paper presents TokMan, a novel approach for optical proximity correction (OPC) in semiconductor lithography that formulates mask optimization as a discrete sequence modeling problem. The key insight is to maintain Manhattan geometric constraints throughout the optimization process rather than treating them as post-hoc constraints.\n\nThe experimental evaluation on ICCAD2013 benchmarks shows significant improvements: >20% better edge placement error compared to state-of-the-art IL-ILT", "questions": "- What is a clearer explanation of \"lithography-aware points segmentation\"?\n- What are the specific criteria for \"spatial alignment casting\" and corner detection?\n- How sensitive is overall performance to segmentation parameters?", "limitations": "Yes.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "## Strengths\n\n**Technical Quality:**\n- The core technical approach is sound - using diffusion transformers for sequence modeling of Manhattan geometries is well-motivated and properly executed. The mathematical formulation clearly connects forward lithography simulation to structured noise addition, making the denoising perspective natural.\n- Experimental validation is comprehensive with proper baselines (GAN-OPC, Neural-ILT, etc.) and industry-standard metrics (EPE, mask shots, TAT). The >20% EPE improvement and 4x mask shot reduction are substantial and well-documented.\n- Authors are honest about limitations, explicitly discussing scalability issues with SRAFs, evaluation only on sliced layouts, and need for industrial dataset validation.\n\n**Clarity and Organization:**\n- Paper is generally well-written with clear motivation and problem setup. The connection between Manhattan constraints and tokenization is well-articulated.\n- Method section logically progresses from segmentation → tokenization → training → post-processing.\n\n**Significance and Impact:**\n- First work to apply sequence modeling to lithography mask optimization - could inspire broader adoption of tokenization approaches in computational imaging.\n- Results demonstrate practical viability for semiconductor manufacturing, not just academic benchmarks.\n\n**Originality:**\n- Novel combination of diffusion models, transformers, and Manhattan geometric constraints. While individual components exist, their integration for this specific problem is original.\n- The \"tokenize everything\" perspective applied to semiconductor manufacturing is fresh and well-motivated.\n\n## Weaknesses\n\n**Technical Limitations:**\n- The segmentation algorithm description lacks sufficient detail for reproduction. The \"lithography-aware points segmentation\" process needs clearer algorithmic specification and parameter settings.\n- Limited theoretical analysis of why tokenization should work better than continuous optimization. The paper relies heavily on empirical validation without deeper theoretical insights.\n\n**Experimental Concerns:**\n- Evaluation limited to ICCAD2013 benchmarks which may not represent modern lithography challenges. More diverse and recent benchmarks would strengthen claims.\n- Training dataset is synthetically generated by \"rearranging polygons\" - unclear how well this represents real design patterns and whether the model would generalize to actual industrial layouts.\n- Some results may not align with those in the original referenced papers, such as the number of shots.\n\n\n**Minor issues**\n- Should the text in Figure 1 read \"w/ OPC\" instead of \"w/ OPT\"?\n\nThe paper would benefit from deeper theoretical analysis of why tokenization helps, more comprehensive evaluation on diverse datasets, and clearer algorithmic specifications for key components like the segmentation algorithm.", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank the reviewer for the detailed and thoughtful feedback. Below, we provide clarification and responses to the raised questions and concerns.\n\nQ1&2: What is a clearer explanation of “lithography-aware points segmentation” and the specific criteria for \"spatial alignment casting\" and corner detection?\n\nThank you for highlighting the need for further clarification. The lithography-aware points segmentation module is the foundation of our sequence formulation. The key motivation stems from the fact that, under a fixed forward lithography model, the printability of a given layout pattern is influenced not only by its own shape but also by the spatial arrangement of nearby patterns.\n\nOur segmentation algorithm converts polygonal edges into a dense sequence of axis-aligned points by incorporating both intrinsic and contextual lithographic considerations:\n\nCorner-based refinement: Corners are known to suffer from corner rounding due to diffraction. To mitigate this, we apply fine-grained segmentation near detected corners, increasing sampling resolution in these regions to allow for more precise correction.\n\nSpatial alignment casting: For a given edge, we detect other parallel edges in its lithographic interaction zone (a configurable spatial window). The corner vertices of these nearby features are then projected onto the edge being segmented. These projections act as segmentation anchors, embedding cross-feature contextual awareness into the point sequence.\n\nLong-segment partitioning: For extended edges that exceed a lithography-aware printable length threshold, we insert uniformly spaced anchor points, ensuring compliance with minimum printable feature rules.\n\nThis process yields a point sequence that not only represents the geometric structure of a polygon, but also encodes interactions and proximity effects from surrounding patterns, making it lithography-aware by construction.\n\n\nQ3: How sensitive is overall performance to segmentation parameters?\n\nThe segmentation parameters—such as corner refinement granularity, alignment radius, and minimum printable length—are selected to reflect realistic manufacturing constraints based on industrial guidelines.\n\nWhile the model is relatively robust to minor variations in these settings, overly coarse segmentation (e.g., skipping fine corner refinement or disabling spatial alignment casting) can degrade model performance, particularly in terms of Edge Placement Error (EPE), due to insufficient resolution in geometrically or optically sensitive regions.\n\nConversely, excessive segmentation granularity may lead to longer sequences and increased computational burden, without proportional gain in accuracy. In our experiments, we tuned these parameters empirically to balance manufacturability, simulation accuracy, and training stability. We will add a supplementary ablation of segmentation granularity in the revised version.\n\nQ4: Lack sufficient detail for reproduction for segmentation algorithm; Lack of theoretical analysis\n\nOur segmentation pipeline is described in detail in Section 4.1, where we explicitly introduce three key components: (1) corner rounding mitigation through dense segment splits at polygon corners, (2) spatial alignment casting that ensures connectivity across neighboring edges by projecting parallel corner anchors, and (3) minimum printable segment enforcement that guarantees DFM compliance. These rules are visually illustrated in Figure 3a and are grounded in real lithographic considerations. We also provide extensive descriptions in the Introduction (lines 13–16, 68–72) to motivate this segmentation from both geometric and manufacturing perspectives.\n\nOur work is primarily empirical, but we do motivate the effectiveness of tokenization in Sections 1 and 4.2. The key insight is that Manhattan layouts exhibit strong geometric structure and low entropy, making them highly compatible with sequence modeling. By operating on axis-aligned point tokens rather than pixel grids, our model inherits inductive biases that align with manufacturable mask design. This results in better generalization, stability, and manufacturability, as shown empirically.\n\nQ5: Evaluation is limited to ICCAD2013; synthetic training data; potential mismatch in referenced baseline results\n\nThese are important concerns, and we appreciate the chance to clarify.\n\nICCAD2013 Benchmarks: We chose ICCAD2013 because it remains the most widely used open-source benchmark in OPC literature, allowing direct comparison to prior works such as Neural-ILT and Multi-ILT. We fully agree that more diverse and modern datasets would strengthen the evaluation, and we are currently working with industry partners to validate TokMan on more advanced technique nodes.\n\nSynthetic Dataset Generation: While our training dataset is generated by rearranging real polygons from open benchmarks, we preserve authentic design characteristics such as density, edge alignment, and spacing constraints. Empirically, our model generalizes well to unseen real layouts within the ICCAD2013 test set. These properties are governed by standard design rules, ensuring that the synthesized layouts remain representative and manufacturable.\n\nPotential Mismatch in Baseline Results: All baseline results are obtained using either publicly available open-source implementations or reproduction code that has been acknowledged by the respective authors. Some numerical differences from the originally reported results arise due to differences in evaluation methodology. For instance, in certain official implementations, the mask shot count is computed on a downsampled version of the mask (e.g., from 2048×2048 to 512×512), which we believe does not reflect actual manufacturability and leads to underestimation. We recomputed mask shots at native resolution for fairness. Similarly, our EPE calculation differs slightly from some prior works; we follow a more precise, industry-standard method based on merit points and contour distances, as described in detail in Section 5.1. We believe these choices ensure a more accurate and consistent comparison across all methods.\n\n\nQ6: Minor issue in Figure 1 (\"w/ OPT\")\n\nThank you for spotting this. It should indeed read \"w/ OPC.\" We will correct this in the final version."}]

Author rebuttal:

Meta-review: This is an interesting paper that studies a novel application of Inverse Lithography Technology (ILT). The authors address a limitation of existing ILT methods that produce masks with curvilinear features, which are difficult and expensive to manufacture and violate the industry-standard "Manhattan" constraints. The main contribution of the paper is to reframe the mask optimization problem as a sequence modeling task. The pipeline combines a IC layout segmentation module that outputs a sequence of Manhattan-aligned points, a DIT module that predicts precise, axis-aligned positional corrections for these points. The model is trained in a self-supervised manner, using a differentiable renderer and a lithography simulator to provide feedback. The authors demonstrate that their method achieves state-of-the-art results on standard benchmarks.. 

The ratings are mixed. The major concerns are in the experimental evaluations. In particular, one reviewer commented that post-processing contributes more than 50% of performance gains. However, the AC believes this is an issue that is shared by many existing methods (including VGGT). Another concern was on the results. It is recommended that in the final version the authors clearly highlight and discuss the specific aspects in both comparative and ablation study visualizations where their method demonstrates advantages in the revised manuscript. 

The paper was accepted because it introduces a new application of ML that brings fresh air to the NeurIPS community and the technical contributions are above the bar for NeurIPS.
Decision: Accept (poster)