S-Crescendo: A Nested Transformer Weaving Framework for Scalable Nonlinear System in S-Domain Representation

Simulation of high-order nonlinear system requires extensive computational resources, especially in modern VLSI backend design where bifurcation-induced instability and chaos-like transient behaviors pose challenges. We present S-Crescendo - a nested transformer weaving framework that synergizes S-domain with neural operators for scalable time-domain prediction in high-order nonlinear networks, alleviating the computational bottlenecks of conventional solvers via Newton-Raphson method. By leveraging the partial-fraction decomposition of an n-th order transfer function into first-order modal terms with repeated poles and residues, our method bypasses the conventional Jacobian matrix-based iterations and efficiently reduces computational complexity from cubic $O(n^3)$ to linear $O(n)$.The proposed architecture seamlessly integrates an S-domain encoder with an attention-based correction operator to simultaneously isolate dominant response and adaptively capture higher-order non-linearities. Validated on order-1 to order-10 networks, our method achieves up to 0.99 test-set ($R^2$) accuracy against HSPICE golden waveforms and accelerates simulation by up to 18(X), providing a scalable, physics-aware framework for high-dimensional nonlinear modeling.

Attention Mechanisms Perspective: Exploring LLM Processing of Graph-Structured Data

Attention mechanisms are critical to the success of large language models (LLMs), driving significant advancements in multiple fields. However, for graph-structured data, which requires emphasis on topological connections, they fall short compared to message-passing mechanisms on fixed links, such as those employed by Graph Neural Networks (GNNs). This raises a question: ``Does attention fail for graphs in natural language settings?'' Motivated by these observations, we embarked on an empirical study from the perspective of attention mechanisms to explore how LLMs process graph-structured data. The goal is to gain deeper insights into the attention behavior of LLMs over graph structures. We uncovered unique phenomena regarding how LLMs apply attention to graph-structured data and analyzed these findings to improve the modeling of such data by LLMs. The primary findings of our research are: 1) While LLMs can recognize graph data and capture text-node interactions, they struggle to model inter-node relationships within graph structures due to inherent architectural constraints. 2) The attention distribution of LLMs across graph nodes does not align with ideal structural patterns, indicating a failure to adapt to graph topology nuances. 3) Neither fully connected attention nor fixed connectivity is optimal; each has specific limitations in its application scenarios. Instead, intermediate-state attention windows improve LLM training performance and seamlessly transition to fully connected windows during inference. Source code: \href{https://github.com/millioniron/LLM_exploration}{LLM4Exploration}

Fusing Global and Local: Transformer-CNN Synergy for Next-Gen Current Estimation

This paper presents a hybrid model combining Transformer and CNN for predicting the current waveform in signal lines. Unlike traditional approaches such as current source models, driver linear representations, waveform functional fitting, or equivalent load capacitance methods, our model does not rely on fixed simplified models of standard-cell drivers or RC loads. Instead, it replaces the complex Newton iteration process used in traditional SPICE simulations, leveraging the powerful sequence modeling capabilities of the Transformer framework to directly predict current responses without iterative solving steps. The hybrid architecture effectively integrates the global feature-capturing ability of Transformers with the local feature extraction advantages of CNNs, significantly improving the accuracy of current waveform predictions. Experimental results demonstrate that, compared to traditional SPICE simulations, the proposed algorithm achieves an error of only 0.0098. These results highlight the algorithm's superior capabilities in predicting signal line current waveforms, timing analysis, and power evaluation, making it suitable for a wide range of technology nodes, from 40nm to 3nm.

Dr.E Bridges Graphs with Large Language Models through Words

Significant efforts have been directed toward integrating powerful Large Language Models (LLMs) with diverse modalities, particularly focusing on the fusion of vision, language, and audio data. However, the graph-structured data, inherently rich in structural and domain-specific knowledge, have not yet been gracefully adapted to LLMs. Existing methods either describe the graph with raw text, suffering the loss of graph structural information, or feed Graph Neural Network (GNN) embeddings directly into LLM at the cost of losing semantic representation. To bridge this gap, we introduce an innovative, end-to-end modality-aligning framework, equipped with a pretrained Dual-Residual Vector Quantized-Variational AutoEncoder (Dr.E). This framework is specifically designed to facilitate token-level alignment with LLMs, enabling an effective translation of the intrinsic `language' of graphs into comprehensible natural language. Our experimental evaluations on standard GNN node classification tasks demonstrate competitive performance against other state-of-the-art approaches. Additionally, our framework ensures interpretability, efficiency, and robustness, with its effectiveness further validated under both fine-tuning and few-shot settings. This study marks the first successful endeavor to achieve token-level alignment between GNNs and LLMs.

LangTopo: Aligning Language Descriptions of Graphs with Tokenized Topological Modeling

Recently, large language models (LLMs) have been widely researched in the field of graph machine learning due to their outstanding abilities in language comprehension and learning. However, the significant gap between natural language tasks and topological structure modeling poses a nonnegligible challenge. Specifically, since natural language descriptions are not sufficient for LLMs to understand and process graph-structured data, fine-tuned LLMs perform even worse than some traditional GNN models on graph tasks, lacking inherent modeling capabilities for graph structures. Existing research overly emphasizes LLMs' understanding of semantic information captured by external models, while inadequately exploring graph topological structure modeling, thereby overlooking the genuine capabilities that LLMs lack. Consequently, in this paper, we introduce a new framework, LangTopo, which aligns graph structure modeling with natural language understanding at the token level. LangTopo quantifies the graph structure modeling capabilities of GNNs and LLMs by constructing a codebook for the graph modality and performs consistency maximization. This process aligns the text description of LLM with the topological modeling of GNN, allowing LLM to learn the ability of GNN to capture graph structures, enabling LLM to handle graph-structured data independently. We demonstrate the effectiveness of our proposed method on multiple datasets.

Enhancing Collaborative Semantics of Language Model-Driven Recommendations via Graph-Aware Learning

Large Language Models (LLMs) are increasingly prominent in the recommendation systems domain. Existing studies usually utilize in-context learning or supervised fine-tuning on task-specific data to align LLMs into recommendations. However, the substantial bias in semantic spaces between language processing tasks and recommendation tasks poses a nonnegligible challenge. Specifically, without the adequate capturing ability of collaborative information, existing modeling paradigms struggle to capture behavior patterns within community groups, leading to LLMs' ineffectiveness in discerning implicit interaction semantic in recommendation scenarios. To address this, we consider enhancing the learning capability of language model-driven recommendation models for structured data, specifically by utilizing interaction graphs rich in collaborative semantics. We propose a Graph-Aware Learning for Language Model-Driven Recommendations (GAL-Rec). GAL-Rec enhances the understanding of user-item collaborative semantics by imitating the intent of Graph Neural Networks (GNNs) to aggregate multi-hop information, thereby fully exploiting the substantial learning capacity of LLMs to independently address the complex graphs in the recommendation system. Sufficient experimental results on three real-world datasets demonstrate that GAL-Rec significantly enhances the comprehension of collaborative semantics, and improves recommendation performance.

A Dynamic Capacitance Matching (DCM)-based Current Response Algorithm for Signal Line RC Network

This paper proposes a dynamic capacitance matching (DCM)-based RC current response algorithm for calculating the current waveform of a signal line without performing SPICE simulation. Specifically, unlike previous method such as CCS model, driver linear representation, waveform functional fitting or equivalent load capacitance, our algorithm does not rely on fixed reduced model of both standard cell driver and RC load. Instead, our algorithm approaches the current waveform dynamically by computing current responses of the target driver for various load scenarios. Besides, we creatively use symbolic expression to combine the y-parameter of RC network with the pre-characterized driver library in order to perform capacitance matching by considering over/under-shoot effect. Our algorithm is experimentally verified on 40nm CMOS technology and has been partially adopted by latest commercial tool for other nodes. Experimental results show that our algorithm has excellent resolution and promising efficiency compared with traditional methods and SPICE golden result, especially for application in computing delay, power and signal line electromigration.