AttentionCap: Transformer Based Capacitance Matrix Learning Toward Full-Chip Extraction

We present Flash-CNNCap, a CNN-based capacitance extractor that reformulates full-matrix capacitance prediction as image-to-image regression over spatial contribution maps. Prior scalar CNN-based extractors require $O(n^2)$ forward passes to recover all pairwise capacitances in a window with $n$ conductors. Flash-CNNCap replaces the scalar target with dense contribution maps: a total-capacitance model and a master-conditioned coupling model each predict a spatial map that is reduced to conductor-level values through mask aggregation, cutting full-matrix reconstruction to $O(n)$ passes. The resulting totals and symmetrized pairwise couplings define the corresponding Maxwell-style capacitance matrix under the standard off-diagonal sign convention. The maps are learned from conductor-level labels without per-pixel supervision. An ablation study over 13 model configurations selects a U-Net that matches ResNet baselines on total capacitance (1.5-3.1% MARE) and achieves the strongest coupling accuracy (3.0-4.6% MARE) across all evaluated CapBench subsets, with a $17.5\times$ full-matrix speedup on windows containing 134 conductors on average. A deployed pipeline reads Design Exchange Format (DEF) geometry and writes Standard Parasitic Exchange Format (SPEF) output, processing 1,024 windows in 51.23 seconds with a $4.4\times$ speedup over OpenRCX on the same benchmark. Code and trained models are available at https://github.com/THU-numbda/flash-cnncap.

Neural scaling laws for transformer language models predict smooth improvements in pretraining loss with increasing parameters, but downstream capabilities such as in-context learning are known to emerge abruptly past a certain model scale. In this paper, we show that emergent capabilities arise stochastically throughout training, with larger models acquiring them earlier on average. We demonstrate that the emergence of capabilities such as pattern completion and indirect object identification corresponds to the abrupt learning of task-relevant attention patterns. To isolate this phenomenon, we train transformer models on synthetic linear map and cellular automata datasets, and we show that the difficulty of learning attention patterns depends on context length and pattern sparsity. Moreover, scaling the number of attention heads improves learning efficiency on our synthetic tasks, while increasing the head dimension yields diminishing returns past a minimum capacity. We additionally investigate architectures with alternative attention mechanisms, showing that MLP-Mixer outperforms a transformer on linear map tasks with complex attention patterns. Our findings provide a mechanistic insight into emergence, showing that downstream capabilities arise abruptly due to the intrinsic difficulty of learning sparse attention patterns in transformer models.

Electronic design automation (EDA) addresses placement, routing, timing analysis, and power-integrity verification for integrated circuits. Learning methods -- attention (Transformer) and reinforcement learning (RL) -- have recently emerged on EDA tasks, yet face two common bottlenecks: vanilla attention's quadratic complexity limits scaling, and data-scarce models overfit statistical noise and amplify weak long-range correlations against the underlying physics. We observe that EDA tasks share a physical prior -- pairwise electrical and routing interactions decay exponentially along Manhattan distance -- and integrate it as a unified inductive bias into both architecture and training. We propose PhysEDA, comprising two components Physics-Structured Linear Attention (PSLA) folds the separable Manhattan decay into the linear-attention kernel as a multiplicative bias, reducing complexity from quadratic to linear; Potential-Based Reward Shaping (PBRS) constructs a physical potential from the same kernel, providing dense reward signal under sparse RL while preserving the optimal policy via the policy-invariance theorem. Across three EDA scenarios -- decoupling-capacitor placement, macro placement, and IR-drop prediction -- PhysEDA improves zero-shot cross-scale transfer by 56.8% and achieves 14x inference speedup with 98.5% memory savings on 100x100 grids; PBRS adds another 10.8% in sparse-reward DPP.