Initialization is critical in analytical placement to prevent optimizers from being trapped in suboptimal local minima. We introduce BADGE, a Boundary-Aware Dirichlet Graph Embedding that leverages fixed macros as boundary conditions. By minimizing a weighted quadratic energy under Dirichlet constraints, BADGE generates a globally coherent initial placement. We further design boundary-attraction weighting and boundary-biased filler initialization to preserve embedding quality. Experiments on MMS benchmarks demonstrate that BADGE consistently reduces half-perimeter wirelength (HPWL) and global placement iterations compared to random and GiFt initializations. These results highlight the efficiency of boundary-aware initialization for scalable placers.

Recent advances in neural network architectures, such as the Transformer, have enabled a shift from task-specific models to unified foundation models, significantly enhancing generalization and scalability. In contrast, analog circuit design has traditionally relied on bespoke optimization models tailored to individual circuits. To address this gap, we propose M3, a novel unified reinforcement learning (RL) that concurrently optimizes multiple circuits with different topologies to meet target specifications, without requiring task-specific adjustments. The M3 framework employs the Mamba architecture, a recently emerging model regarded as a potential alternative to the Transformer. It combines model-based RL with a dynamic scheduling mechanism that adapts RL parameters to balance exploration (seeking novel designs) and exploitation (refining existing ones). Experimental results demonstrate that M3 successfully trains RL agents capable of simultaneously optimizing multiple circuits, having different topologies, to achieve target performance levels while prior RL-based methods are unable to do. This approach highlights the potential of developing a unified model for optimizing circuits across varying topologies and target specifications1.

As signal frequency increases, signal integrity, a measure of how well a signal is transferred from one component to another, becomes critical in modern electronic products. Thorough signal integrity analysis is essential in design process and S-parameters are often used to model electromagnetic characteristics of a channel such as PCB traces. However, numerous iterations are inevitable due to design changes in components of a product such as different placement on PCBs. Traditional approaches to S-parameter extraction rely on computationally expensive electromagnetic simulations, becoming a bottleneck in the design process. To tackle this issue, we present PCBFormer, a novel deep learning framework that predicts S-parameters of PCBs with high accuracy and efficiency. Our framework effectively captures multiple traces’ electromagnetic interactions across multiple layers in 3D PCB structure, taking each layer’s properties into account. For realistic PCB examples with 10 traces and 25 layers, PCBFormer achieves 0.86 R2 score across 210 S-parameters and DC to 1GHz frequency range.

Graph Transformers (GTs) have emerged as a powerful alternative to message-passing neural networks, yet their performance heavily depends on effectively embedding structural inductive biases. In this work, we introduce novel structural encodings (SEs) grounded in a rigorous analysis of random walks (RWs), leveraging Green and Martin kernels that we have carefully redefined for AI applications while preserving their mathematical essence.These kernels capture the long-term behavior of RWs on graphs and allow for enhanced representation of complex topologies, including non-aperiodic and directed acyclic substructures.Empirical evaluations across eight benchmark datasets demonstrate strong performance across diverse tasks, notably in molecular and circuit domains.We attribute this performance boost to the improved ability of our kernel-based SEs to encode intricate structural information, thereby strengthening the global attention and inductive bias within GTs.This work highlights the effectiveness of theoretically grounded kernel methods in advancing Transformer-based models for graph learning.