arXiv subjects

Cunxi Yu

Publications and source records attributed to Cunxi Yu.

At least 37 records · Page 2Linked to original sources

arXiv2025

e-boost: Boosted E-Graph Extraction with Adaptive Heuristics and Exact Solving

E-graphs have attracted growing interest in many fields, particularly in logic synthesis and formal verification. E-graph extraction is a challenging NP-hard combinatorial optimization problem. It requires identifying optimal terms from exponentially many equivalent expressions, serving as the primary performance bottleneck in e-graph based optimization tasks. However, traditional extraction methods face a critical trade-off: heuristic approaches offer speed but sacrifice optimality, while exact methods provide optimal solutions but face prohibitive computational costs on practical problems. We present e-boost, a novel framework that bridges this gap through three key innovations: (1) parallelized heuristic extraction that leverages weak data dependence to compute DAG costs concurrently, enabling efficient multi-threaded performance without sacrificing extraction quality; (2) adaptive search space pruning that employs a parameterized threshold mechanism to retain only promising candidates, dramatically reducing the solution space while preserving near-optimal solutions; and (3) initialized exact solving that formulates the reduced problem as an Integer Linear Program with warm-start capabilities, guiding solvers toward high-quality solutions faster. Across the diverse benchmarks in formal verification and logic synthesis fields, e-boost demonstrates 558x runtime speedup over traditional exact approaches (ILP) and 19.04% performance improvement over the state-of-the-art extraction framework (SmoothE). In realistic logic synthesis tasks, e-boost produces 7.6% and 8.1% area improvements compared to conventional synthesis tools with two different technology mapping libraries. e-boost is available at https://github.com/Yu-Maryland/e-boost.

cs.AI↗

arXiv2025

Revisit Choice Network for Synthesis and Technology Mapping

Choice network construction is a critical technique for alleviating structural bias issues in Boolean optimization, equivalence checking, and technology mapping. Previous works on lossless synthesis utilize independent optimization to generate multiple snapshots, and use simulation and SAT solvers to identify functionally equivalent nodes. These nodes are then merged into a subject graph with choice nodes. However, such methods often neglect the quality of these choices, raising the question of whether they truly contribute to effective technology mapping. This paper introduces Cristal, a novel methodology and framework for constructing Boolean choice networks. Specifically, Cristal introduces a new flow of choice network-based synthesis and mapping, including representative logic cone search, structural mutation for generating diverse choice structures via equality saturation, and priority-ranking choice selection along with choice network construction and validation. Through these techniques, Cristal constructs fewer but higher-quality choices. Our experimental results demonstrate that Cristal outperforms the state-of-the-art Boolean choice network construction implemented in ABC in the post-mapping stage, achieving average reductions of 3.85%/8.35% (area/delay) in delay-oriented mode, 0.11%/2.74% in area-oriented mode, and a 63.77% runtime reduction on large-scale cases across a diverse set of combinational circuits from the IWLS 2005, ISCAS'89, and EPFL benchmark suites.

cs.AR↗

arXiv2025

Mapping Fusion: Improving FPGA Technology Mapping with ASIC Mapper

LUT (Look-Up Table) mapping is a critical step in FPGA logic synthesis, where a logic network is transformed into a form that can be directly implemented using the FPGA's LUTs. An FPGA LUT is a flexible digital memory structure that can implement any logic function of a limited number of inputs, typically 4 to 6 inputs, depending on the FPGA architecture. The goal of LUT mapping is to map the Boolean network into LUTs, where each LUT can implement any function with a fixed number of inputs. In parallel to FPGA technology mapping, ASIC technology mapping maps the Boolean network to user-defined standard cells, which has traditionally been developed separately from LUT mapping algorithms. However, in this work, our motivating examples demonstrate that ASIC technology mappers can potentially improve the performance of LUT mappers, such that standard cell mapping and LUT mapping work in an incremental manner. Therefore, we propose the FuseMap framework, which explores this opportunity to improve LUT mapping in the FPGA design flow by utilizing reinforcement learning to make design-specific choices during cell selection. The effectiveness of FuseMap is evaluated on a wide range of benchmarks, different technology libraries, and technology mappers. The experimental results demonstrate that FuseMap achieves higher mapping accuracy while reducing delay and area across diverse circuit designs collected from ISCAS 85/89, ITC/ISCAS 99, VTR 8.0, and EPFL benchmarks.

cs.AR↗

arXiv2025

Differentiable Quadratic Optimization For The Maximum Independent Set Problem

Combinatorial Optimization (CO) addresses many important problems, including the challenging Maximum Independent Set (MIS) problem. Alongside exact and heuristic solvers, differentiable approaches have emerged, often using continuous relaxations of ReLU-based or quadratic objectives. Noting that an MIS in a graph is a Maximum Clique (MC) in its complement, we propose a new quadratic formulation for MIS by incorporating an MC term, improving convergence and exploration. We show that every maximal independent set corresponds to a local minimizer, derive conditions with respect to the MIS size, and characterize stationary points. To tackle the non-convexity of the objective, we propose optimizing several initializations in parallel using momentum-based gradient descent, complemented by an efficient MIS checking criterion derived from our theory. We dub our method as parallelized Clique-Informed Quadratic Optimization for MIS (pCQO-MIS). Our experimental results demonstrate the effectiveness of the proposed method compared to exact, heuristic, sampling, and data-centric approaches. Notably, our method avoids the out-of-distribution tuning and reliance on (un)labeled data required by data-centric methods, while achieving superior MIS sizes and competitive runtime relative to their inference time. Additionally, a key advantage of pCQO-MIS is that, unlike exact and heuristic solvers, the runtime scales only with the number of nodes in the graph, not the number of edges. Our code is available at the GitHub repository: https://github.com/ledenmat/pCQO-mis-benchmark/tree/refactor.

cs.DM↗

arXiv2025

HEC: Equivalence Verification Checking for Code Transformation via Equality Saturation

In modern computing systems, compilation employs numerous optimization techniques to enhance code performance. Source-to-source code transformations, which include control flow and datapath transformations, have been widely used in High-Level Synthesis (HLS) and compiler optimization. While researchers actively investigate methods to improve performance with source-to-source code transformations, they often overlook the significance of verifying their correctness. Current tools cannot provide a holistic verification of these transformations. This paper introduces HEC, a framework for equivalence checking that leverages the e-graph data structure to comprehensively verify functional equivalence between programs. HEC utilizes the MLIR as its frontend and integrates MLIR into the e-graph framework. Through the combination of dynamic and static e-graph rewriting, HEC facilitates the validation of comprehensive code transformations. We demonstrate effectiveness of HEC on PolyBenchC benchmarks, successfully verifying loop unrolling, tiling, and fusion transformations. HEC processes over 100,000 lines of MLIR code in 40 minutes with predictable runtime scaling. Importantly, HEC identified two critical compilation errors in mlir-opt: loop boundary check errors causing unintended executions during unrolling, and memory read-after-write violations in loop fusion that alter program semantics. These findings demonstrate HEC practical value in detecting real-world compiler bugs and highlight the importance of formal verification in optimization pipelines.

cs.AR↗

arXiv2025

BoolE: Exact Symbolic Reasoning via Boolean Equality Saturation

Boolean symbolic reasoning for gate-level netlists is a critical step in verification, logic and datapath synthesis, and hardware security. Specifically, reasoning datapath and adder tree in bit-blasted Boolean networks is particularly crucial for verification and synthesis, and challenging. Conventional approaches either fail to accurately (exactly) identify the function blocks of the designs in gate-level netlist with structural hashing and symbolic propagation, or their reasoning performance is highly sensitive to structure modifications caused by technology mapping or logic optimization. This paper introduces BoolE, an exact symbolic reasoning framework for Boolean netlists using equality saturation. BoolE optimizes scalability and performance by integrating domain-specific Boolean ruleset for term rewriting. We incorporate a novel extraction algorithm into BoolE to enhance its structural insight and computational efficiency, which adeptly identifies and captures multi-input, multi-output high-level structures (e.g., full adder) in the reconstructed e-graph. Our experiments show that BoolE surpasses state-of-the-art symbolic reasoning baselines, including the conventional functional approach (ABC) and machine learning-based method (Gamora). Specifically, we evaluated its performance on various multiplier architecture with different configurations. Our results show that BoolE identifies $3.53\times$ and $3.01\times$ more exact full adders than ABC in carry-save array and Booth-encoded multipliers, respectively. Additionally, we integrated BoolE into multiplier formal verification tasks, where it significantly accelerates the performance of traditional formal verification tools using computer algebra, demonstrated over four orders of magnitude runtime improvements.

cs.AR↗

arXiv2025

E-morphic: Scalable Equality Saturation for Structural Exploration in Logic Synthesis

In technology mapping, the quality of the final implementation heavily relies on the circuit structure after technology-independent optimization. Recent studies have introduced equality saturation as a novel optimization approach. However, its efficiency remains a hurdle against its wide adoption in logic synthesis. This paper proposes a highly scalable and efficient framework named E-morphic. It is the first work that employs equality saturation for resynthesis after conventional technology-independent logic optimizations, enabling structure exploration before technology mapping. Powered by several key enhancements to the equality saturation framework, such as direct e-graph-circuit conversion, solution-space pruning, and simulated annealing for e-graph extraction, this approach not only improves the scalability and extraction efficiency of e-graph rewriting but also addresses the structural bias issue present in conventional logic synthesis flows through parallel structural exploration and resynthesis. Experiments show that, compared to the state-of-the-art delay optimization flow in ABC, E-morphic on average achieves 12.54% area saving and 7.29% delay reduction on the large-scale circuits in the EPFL benchmark.

cs.AR↗

arXiv2024

Optical Neural Engine for Solving Scientific Partial Differential Equations

Solving partial differential equations (PDEs) is the cornerstone of scientific research and development. Data-driven machine learning (ML) approaches are emerging to accelerate time-consuming and computation-intensive numerical simulations of PDEs. Although optical systems offer high-throughput and energy-efficient ML hardware, there is no demonstration of utilizing them for solving PDEs. Here, we present an optical neural engine (ONE) architecture combining diffractive optical neural networks for Fourier space processing and optical crossbar structures for real space processing to solve time-dependent and time-independent PDEs in diverse disciplines, including Darcy flow equation, the magnetostatic Poisson equation in demagnetization, the Navier-Stokes equation in incompressible fluid, Maxwell's equations in nanophotonic metasurfaces, and coupled PDEs in a multiphysics system. We numerically and experimentally demonstrate the capability of the ONE architecture, which not only leverages the advantages of high-performance dual-space processing for outperforming traditional PDE solvers and being comparable with state-of-the-art ML models but also can be implemented using optical computing hardware with unique features of low-energy and highly parallel constant-time processing irrespective of model scales and real-time reconfigurability for tackling multiple tasks with the same architecture. The demonstrated architecture offers a versatile and powerful platform for large-scale scientific and engineering computations.

physics.optics↗

arXiv2024

Digitized Phase Change Material Heterostack for Diffractive Optical Neural Network

All-optical and fully reconfigurable diffractive optical neural network (DONN) architectures are promising for high-throughput and energy-efficient machine learning (ML) hardware accelerators for broad applications. However, current device and system implementations have limited performance. This work demonstrates a novel diffractive device architecture, which is named digitized heterostack and consists of multiple layers of nonvolatile phase change materials (PCMs) with different thicknesses. This architecture can both leverage the advantages of PCM optical properties and mitigate challenges associated with implementing multilevel operations in a single PCM layer. Proof-of-concept experiments demonstrate the electrical tuning of one PCM layer in a spatial light modulation device, and thermal analysis guides the design of DONN devices and systems to avoid thermal crosstalk if individual heterostacks are assembled into an array. Further, heterostacks containing three PCM layers are designed to have a large phase modulation range and uniform coverage and the ML performance of DONN systems with designed heterostacks is evaluated. The developed device architecture provides new opportunities for desirable energy-efficient, fast-reconfigured, and compact DONN systems in the future.

physics.optics↗

arXiv2024

MapTune: Advancing ASIC Technology Mapping via Reinforcement Learning Guided Library Tuning

Technology mapping involves mapping logical circuits to a library of cells. Traditionally, the full technology library is used, leading to a large search space and potential overhead. Motivated by randomly sampled technology mapping case studies, we propose MapTune framework that addresses this challenge by utilizing reinforcement learning to make design-specific choices during cell selection. By learning from the environment, MapTune refines the cell selection process, resulting in a reduced search space and potentially improved mapping quality. The effectiveness of MapTune is evaluated on a wide range of benchmarks, different technology libraries and technology mappers. The experimental results demonstrate that MapTune achieves higher mapping accuracy and reducing delay/area across diverse circuit designs, technology libraries and mappers. The paper also discusses the Pareto-Optimal exploration and confirms the perpetual delay-area trade-off. Conducted on benchmark suites ISCAS 85/89, ITC/ISCAS 99, VTR8.0 and EPFL benchmarks, the post-technology mapping and post-sizing quality-of-results (QoR) have been significantly improved, with average Area-Delay Product (ADP) improvement of 22.54\% among all different exploration settings in MapTune. The improvements are consistently remained for four different technologies (7nm, 45nm, 130nm, and 180 nm) and two different mappers.

cs.AR↗

arXiv2024

DAG-aware Synthesis Orchestration

The key methodologies of modern logic synthesis techniques are conducted on multi-level technology-independent representations such as And-Inverter-Graphs (AIGs) of the digital logic via directed-acyclic-graph (DAGs) traversal based structural rewriting, resubstitution, and refactoring. Existing state-of-the-art DAG-aware logic synthesis algorithms are all designed to perform stand-alone optimizations during a single DAG traversal. However, we empirically identify and demonstrate that these algorithms are limited in quality-of-results and runtime complexity due to this design concept. This work proposes Synthesis Orchestration, which orchestrates stand-alone operations within the single traversal of AIG. Thus, orchestration method explores more optimization opportunities and results in better performance. Our experimental results are comprehensively conducted on all 104 designs collected from ISCAS'85/89/99, VTR, and EPFL benchmark suites, with consistent logic minimization improvements over rewriting, resubstitution, refactoring, leading to an average of 4% more node reduction with improved runtime efficiency for the single optimization. Moreover, we evaluate orchestration as a plug-in algorithm in resyn and resyn3 flows in ABC, which demonstrates consistent logic minimization improvements (3.8% and 10.9% more node reduction on average). The runtime analysis demonstrates the orchestration outperforms stand-alone algorithms in both AIG minimization and runtime efficiency. Finally, we integrate the orchestration into OpenROAD for end-to-end performance evaluation. Our results demonstrate the advantages of the orchestration optimization technique, even after technology mapping and post-routing in the design flow have been conducted.

cs.AR↗

arXiv2024

Differentiable Combinatorial Scheduling at Scale

This paper addresses the complex issue of resource-constrained scheduling, an NP-hard problem that spans critical areas including chip design and high-performance computing. Traditional scheduling methods often stumble over scalability and applicability challenges. We propose a novel approach using a differentiable combinatorial scheduling framework, utilizing Gumbel-Softmax differentiable sampling technique. This new technical allows for a fully differentiable formulation of linear programming (LP) based scheduling, extending its application to a broader range of LP formulations. To encode inequality constraints for scheduling tasks, we introduce \textit{constrained Gumbel Trick}, which adeptly encodes arbitrary inequality constraints. Consequently, our method facilitates an efficient and scalable scheduling via gradient descent without the need for training data. Comparative evaluations on both synthetic and real-world benchmarks highlight our capability to significantly improve the optimization efficiency of scheduling, surpassing state-of-the-art solutions offered by commercial and open-source solvers such as CPLEX, Gurobi, and CP-SAT in the majority of the designs.

cs.LG↗

arXiv2024

Less is More: Hop-Wise Graph Attention for Scalable and Generalizable Learning on Circuits

While graph neural networks (GNNs) have gained popularity for learning circuit representations in various electronic design automation (EDA) tasks, they face challenges in scalability when applied to large graphs and exhibit limited generalizability to new designs. These limitations make them less practical for addressing large-scale, complex circuit problems. In this work we propose HOGA, a novel attention-based model for learning circuit representations in a scalable and generalizable manner. HOGA first computes hop-wise features per node prior to model training. Subsequently, the hop-wise features are solely used to produce node representations through a gated self-attention module, which adaptively learns important features among different hops without involving the graph topology. As a result, HOGA is adaptive to various structures across different circuits and can be efficiently trained in a distributed manner. To demonstrate the efficacy of HOGA, we consider two representative EDA tasks: quality of results (QoR) prediction and functional reasoning. Our experimental results indicate that (1) HOGA reduces estimation error over conventional GNNs by 46.76% for predicting QoR after logic synthesis; (2) HOGA improves 10.0% reasoning accuracy over GNNs for identifying functional blocks on unseen gate-level netlists after complex technology mapping; (3) The training time for HOGA almost linearly decreases with an increase in computing resources.

cs.LG↗

arXiv2024

E-Syn: E-Graph Rewriting with Technology-Aware Cost Functions for Logic Synthesis

Logic synthesis plays a crucial role in the digital design flow. It has a decisive influence on the final Quality of Results (QoR) of the circuit implementations. However, existing multi-level logic optimization algorithms often employ greedy approaches with a series of local optimization steps. Each step breaks the circuit into small pieces (e.g., k-feasible cuts) and applies incremental changes to individual pieces separately. These local optimization steps could limit the exploration space and may miss opportunities for significant improvements. To address the limitation, this paper proposes using e-graph in logic synthesis. The new workflow, named Esyn, makes use of the well-established e-graph infrastructure to efficiently perform logic rewriting. It explores a diverse set of equivalent Boolean representations while allowing technology-aware cost functions to better support delay-oriented and area-oriented logic synthesis. Experiments over a wide range of benchmark designs show our proposed logic optimization approach reaches a wider design space compared to the commonly used AIG-based logic synthesis flow. It achieves on average 15.29% delay saving in delay-oriented synthesis and 6.42% area saving for area-oriented synthesis.

cs.AR↗

arXiv2024

BoolGebra: Attributed Graph-learning for Boolean Algebraic Manipulation

Boolean algebraic manipulation is at the core of logic synthesis in Electronic Design Automation (EDA) design flow. Existing methods struggle to fully exploit optimization opportunities, and often suffer from an explosive search space and limited scalability efficiency. This work presents BoolGebra, a novel attributed graph-learning approach for Boolean algebraic manipulation that aims to improve fundamental logic synthesis. BoolGebra incorporates Graph Neural Networks (GNNs) and takes initial feature embeddings from both structural and functional information as inputs. A fully connected neural network is employed as the predictor for direct optimization result predictions, significantly reducing the search space and efficiently locating the optimization space. The experiments involve training the BoolGebra model w.r.t design-specific and cross-design inferences using the trained model, where BoolGebra demonstrates generalizability for cross-design inference and its potential to scale from small, simple training datasets to large, complex inference datasets. Finally, BoolGebra is integrated with existing synthesis tool ABC to perform end-to-end logic minimization evaluation w.r.t SOTA baselines.

cs.AR↗

arXiv2023

Verilog-to-PyG -- A Framework for Graph Learning and Augmentation on RTL Designs

The complexity of modern hardware designs necessitates advanced methodologies for optimizing and analyzing modern digital systems. In recent times, machine learning (ML) methodologies have emerged as potent instruments for assessing design quality-of-results at the Register-Transfer Level (RTL) or Boolean level, aiming to expedite design exploration of advanced RTL configurations. In this presentation, we introduce an innovative open-source framework that translates RTL designs into graph representation foundations, which can be seamlessly integrated with the PyTorch Geometric graph learning platform. Furthermore, the Verilog-to-PyG (V2PYG) framework is compatible with the open-source Electronic Design Automation (EDA) toolchain OpenROAD, facilitating the collection of labeled datasets in an utterly open-source manner. Additionally, we will present novel RTL data augmentation methods (incorporated in our framework) that enable functional equivalent design augmentation for the construction of an extensive graph-based RTL design database. Lastly, we will showcase several using cases of V2PYG with detailed scripting examples. V2PYG can be found at \url{https://yu-maryland.github.io/Verilog-to-PyG/}.

cs.LG↗

arXiv2023

LightRidge: An End-to-end Agile Design Framework for Diffractive Optical Neural Networks

To lower the barrier to diffractive optical neural networks (DONNs) design, exploration, and deployment, we propose LightRidge, the first end-to-end optical ML compilation framework, which consists of (1) precise and differentiable optical physics kernels that enable complete explorations of DONNs architectures, (2) optical physics computation kernel acceleration that significantly reduces the runtime cost in training, emulation, and deployment of DONNs, and (3) versatile and flexible optical system modeling and user-friendly domain-specific-language (DSL). As a result, LightRidge framework enables efficient end-to-end design and deployment of DONNs, and significantly reduces the efforts for programming, hardware-software codesign, and chip integration. Our results are experimentally conducted with physical optical systems, where we demonstrate: (1) the optical physics kernels precisely correlated to low-level physics and systems, (2) significant speedups in runtime with physics-aware emulation workloads compared to the state-of-the-art commercial system, (3) effective architectural design space exploration verified by the hardware prototype and on-chip integration case study, and (4) novel DONN design principles including successful demonstrations of advanced image classification and image segmentation task using DONNs architecture and topology.

cs.AR↗

arXiv2023

AIM: Accelerating Arbitrary-precision Integer Multiplication on Heterogeneous Reconfigurable Computing Platform Versal ACAP

Arbitrary-precision integer multiplication is the core kernel of many applications in simulation, cryptography, etc. Existing acceleration of arbitrary-precision integer multiplication includes CPUs, GPUs, FPGAs, and ASICs. Among these accelerators, FPGAs are promised to provide both good energy efficiency and flexibility. Surprisingly, in our implementations, FPGA has the lowest energy efficiency, i.e., 0.29x of the CPU and 0.17x of the GPU with the same generation fabrication. Therefore, key questions arise: Where do the energy efficiency gains of CPUs and GPUs come from? Can reconfigurable computing do better? If can, how to achieve that? We identify that the biggest energy efficiency gains of the CPUs and GPUs come from the dedicated vector units. FPGA uses DSPs and lookup tables to compose the needed computation, which incurs overhead when compared to using vector units directly. New reconfigurable computing, e.g., 'FPGA+vector units' is a novel and feasible solution to improve energy efficiency. In this paper, we propose to map arbitrary-precision integer multiplication onto such a heterogeneous platform, i.e., AMD/Xilinx Versal ACAP architecture. Designing on Versal ACAP incurs several challenges and we propose AIM: Arbitrary-precision Integer Multiplication on Versal ACAP to automate and optimize the design. AIM framework includes design space exploration and AIM automatic code generation to facilitate the system design and verification. We deploy the AIM framework on three different applications, including large integer multiplication (LIM), RSA, and Mandelbrot, on the AMD/Xilinx Versal ACAP VCK190 evaluation board. Our experimental results show that AIM achieves up to 12.6x, and 2.1x energy efficiency gains over the Intel Xeon Ice Lake 6346 CPU, and NVidia A5000 GPU respectively, which brings reconfigurable computing the most energy-efficient platform among CPUs and GPUs.

cs.AR↗