SKILL: Self-correcting Knowledge-guided Iterative Large Language Model Agent for Logic Optimization

# SKILL: Self-correcting Knowledge-guided Iterative Large Language Model Agent for Logic Optimization
Source: [https://arxiv.org/html/2608.14579](https://arxiv.org/html/2608.14579)
###### Abstract

Logic synthesis optimization poses significant challenges due to exponentially growing search spaces, sparse reward signals, and diverse logic structures\. Traditional expert\-designed flows lack adaptability, while reinforcement learning \(RL\) methods often suffer from low sample efficiency and limited interpretability\. We introduceSKILL, aSelf\-correcting Knowledge\-guided Iterative Large Language Model Agentthat unifies multi\-agent LLM reasoning and RL\-based environment interaction for automated synthesis optimization\. SKILL coordinates three specialized LLMs—GPT\-4o for strategic planning, Claude Sonnet 4 for detailed reasoning, and Gemini 2\.5 Pro for efficient analysis—with a PPO\-based RL agent that learns actionable policies through direct interaction with synthesis tools\. A novel self\-correcting module monitors environment feedback \(PDA metrics\), detects suboptimal behaviors, and invokes LLM\-guided recovery strategies\. Evaluations on IWLS, OpenCores, and EPFL benchmarks show SKILL achieves a 12\.4±\\pm2\.1% PDA improvement over expert flows and 86\.3% success rate on logic systems up to 500K gates\.

## 1Introduction

As digital system complexity grows, logic synthesis has become a critical optimization stage in modern design pipelines\. Traditional Electronic Design Automation \(EDA\) flows typically rely on expert\-authored scripts operating through tools like ABC[brayton2010abc](https://arxiv.org/html/2608.14579#bib.bib1)and Yosys[wolf2013yosys](https://arxiv.org/html/2608.14579#bib.bib2)\. While effective in constrained domains, these static methods struggle to generalize across diverse logic topologies and technology nodes[hosny2020drills](https://arxiv.org/html/2608.14579#bib.bib3);[rose2024robust](https://arxiv.org/html/2608.14579#bib.bib4)\. Moreover, the search space for optimization operations scales exponentially with system size, rendering exhaustive strategies impractical\.

Reinforcement learning \(RL\) offers a promising alternative by learning policies that adaptively guide optimization decisions[sutton2018reinforcement](https://arxiv.org/html/2608.14579#bib.bib15);[puterman2014markov](https://arxiv.org/html/2608.14579#bib.bib14)\. Frameworks such as DRiLLS[hosny2020drills](https://arxiv.org/html/2608.14579#bib.bib3)and EasySO[zhao2024easyso](https://arxiv.org/html/2608.14579#bib.bib5)formulate synthesis as a sequential decision\-making task, allowing agents to explore operation sequences that improve logic Power\-Delay\-Area \(PDA\) metrics\. However, RL agents must learn throughenvironment interaction—a closed loop where each action modifies the logic state, and subsequent PDA feedback determines the reward\. This interaction is complicated by sparse signals, delayed outcomes, and high\-dimensional spaces[shi2024lsoformer](https://arxiv.org/html/2608.14579#bib.bib7), representing a challenging combinatorial optimization problem[papadimitriou1998combinatorial](https://arxiv.org/html/2608.14579#bib.bib23);[garey1979computers](https://arxiv.org/html/2608.14579#bib.bib25)\.

Simultaneously, Large Language Models \(LLMs\) have shown strong capabilities in code understanding, structured reasoning, and long\-horizon planning[brown2020language](https://arxiv.org/html/2608.14579#bib.bib8);[openai2023gpt4](https://arxiv.org/html/2608.14579#bib.bib9);[vaswani2017attention](https://arxiv.org/html/2608.14579#bib.bib48)\. The emergence of powerful architectures like BERT[devlin2018bert](https://arxiv.org/html/2608.14579#bib.bib49), GPT series[radford2019language](https://arxiv.org/html/2608.14579#bib.bib50);[achiam2023gpt](https://arxiv.org/html/2608.14579#bib.bib51), LLaMA[touvron2023llama](https://arxiv.org/html/2608.14579#bib.bib52), and PaLM[chowdhery2022palm](https://arxiv.org/html/2608.14579#bib.bib53)has demonstrated remarkable emergent abilities[wei2022emergent](https://arxiv.org/html/2608.14579#bib.bib54)in complex reasoning tasks\. These models exhibit sophisticated in\-context learning capabilities[min2022rethinking](https://arxiv.org/html/2608.14579#bib.bib55);[dong2022survey](https://arxiv.org/html/2608.14579#bib.bib56), making them particularly suitable for optimization problems requiring adaptive strategy formulation\. Emerging research explores their application to logic design tasks, yet few integrate LLMs with low\-level toolchains for closed\-loop optimization\.

We proposeSKILL, a multi\-agent architecture combining LLM reasoning with RL\-based environment interaction for logic synthesis\. LLMs offer high\-level strategy, root cause analysis, and correction planning, while a PPO agent[schulman2017proximal](https://arxiv.org/html/2608.14579#bib.bib16)performs fine\-grained tool invocation based on reward\-driven learning[sutton2018reinforcement](https://arxiv.org/html/2608.14579#bib.bib15)\. A novel self\-correcting mechanism monitors optimization trajectories and re\-engages LLMs upon detecting performance regressions, addressing the fundamental challenges of combinatorial optimization[korte2012combinatorial](https://arxiv.org/html/2608.14579#bib.bib24);[nemhauser1988integer](https://arxiv.org/html/2608.14579#bib.bib22)\.

Our key contributions are:

1. 1\.Multi\-agent LLM\-RL Architecture: We combine three specialized LLMs with a PPO agent to bridge abstract reasoning and low\-level synthesis action spaces\.
2. 2\.Self\-Correcting Optimization Loop: We propose a mechanism that uses environmental PDA feedback to detect suboptimal decisions, invoke failure diagnosis, and trigger LLM\-based corrective plans\.
3. 3\.Hierarchical Action Decomposition: A two\-level abstraction bridges LLM guidance and executable tool actions, improving learning efficiency\.
4. 4\.Scalable Benchmarking: We validate SKILL across IWLS, OpenCores, and EPFL logic systems up to 500K gates, achieving consistent improvements over both expert and RL\-only baselines\.

## 2Related Work

### 2\.1Reinforcement Learning in Logic Synthesis

RL has gained traction in EDA for optimizing placement[mirhoseini2021graph](https://arxiv.org/html/2608.14579#bib.bib10), routing, and logic synthesis flows\. DRiLLS[hosny2020drills](https://arxiv.org/html/2608.14579#bib.bib3)demonstrated that logic synthesis can be cast as a Markov Decision Process \(MDP\)[puterman2014markov](https://arxiv.org/html/2608.14579#bib.bib14), with each action modifying the logic and yielding a reward based on quality\-of\-result \(QoR\) metrics\. While effective, it faced challenges with convergence and generalization\.

Subsequent works like EasySO[zhao2024easyso](https://arxiv.org/html/2608.14579#bib.bib5)introduced hybrid PPO\-based models[schulman2017proximal](https://arxiv.org/html/2608.14579#bib.bib16)for higher sample efficiency and better reward propagation\. BOiLS[grosnit2022boils](https://arxiv.org/html/2608.14579#bib.bib6)applied Bayesian optimization[shahriari2015taking](https://arxiv.org/html/2608.14579#bib.bib45);[brochu2010tutorial](https://arxiv.org/html/2608.14579#bib.bib47)to navigate tool operation sequences\. Nonetheless, these methods remain constrained by sparse PDA feedback and lack interpretability—factors that SKILL addresses via LLM\-guided exploration and a self\-correcting feedback loop grounded in environment interaction\.

### 2\.2LLMs in Logic Design

The application of LLMs to logic tasks has accelerated rapidly\. Recent work has demonstrated applications in logic comprehension, improving code quality and verification coverage\. RTLCoder demonstrated 87% correctness in RTL generation from language prompts, outperforming earlier models\.

For analog design, various approaches have used LLMs for topology synthesis and parameter estimation, achieving higher success rates under practical constraints\. Surveys highlight LLMs’ potential to automate and accelerate EDA stages via natural language interfaces\. However, most efforts remain limited to one\-shot generation or static analysis, rather than continuous toolchain feedback loops\.

### 2\.3Multi\-Agent Collaboration and LLM Architectures

Recent progress in multi\-agent LLM systems demonstrates the value of dividing complex reasoning across specialized agents\. AutoGen[wu2023autogen](https://arxiv.org/html/2608.14579#bib.bib11)and MetaGPT[hong2023metagpt](https://arxiv.org/html/2608.14579#bib.bib12)showed that role\-based collaboration among LLM agents improves success rates on software tasks\.

SKILL adopts this principle by assigning distinct roles—strategy planning \(GPT\-4o\), detailed analysis \(Claude\), and structural refinement \(Gemini\)—with centralized coordination through an RL agent\. The agents operate within a closed environment\-interaction loop, where PDA outcomes inform future decisions and trigger adaptive correction\.

## 3SKILL Framework

### 3\.1Problem Formulation and Theoretical Foundation

We formulate logic optimization as an augmented Partially Observable Markov Decision Process \(POMDP\)[puterman2014markov](https://arxiv.org/html/2608.14579#bib.bib14)incorporating multi\-agent LLM guidance and self\-correcting mechanisms\. The conventional RL formulation for logic optimization consists of the tupleℳ=⟨𝒮,𝒜,𝒯,ℛ,𝒪,Ω⟩\\mathcal\{M\}=\\langle\\mathcal\{S\},\\mathcal\{A\},\\mathcal\{T\},\\mathcal\{R\},\\mathcal\{O\},\\Omega\\rangle, where:

- •𝒮\\mathcal\{S\}: State space representing logic configurations, encompassing structural features, timing characteristics, power profiles, and technology parameters
- •𝒜\\mathcal\{A\}: Action space of available optimization transformations including logic optimization operations and technology mapping decisions
- •𝒯:𝒮×𝒜→Δ​\(𝒮\)\\mathcal\{T\}:\\mathcal\{S\}\\times\\mathcal\{A\}\\rightarrow\\Delta\(\\mathcal\{S\}\): Transition function representing deterministic transformations based on EDA tool execution results
- •ℛ:𝒮×𝒜→ℝ\\mathcal\{R\}:\\mathcal\{S\}\\times\\mathcal\{A\}\\rightarrow\\mathbb\{R\}: Reward function based on Power\-Delay\-Area product optimization and constraint satisfaction metrics

We extend this formulation to create the SKILL\-POMDP:ℳS​K​I​L​L=⟨𝒮,𝒜,𝒯,ℛ,𝒪,Ω,𝒢,𝒞,ℰ⟩\\mathcal\{M\}\_\{SKILL\}=\\langle\\mathcal\{S\},\\mathcal\{A\},\\mathcal\{T\},\\mathcal\{R\},\\mathcal\{O\},\\Omega,\\mathcal\{G\},\\mathcal\{C\},\\mathcal\{E\}\\rangle, introducing:

- •𝒢\\mathcal\{G\}: LLM guidance space containing strategic insights and optimization recommendations from the multi\-agent ensemble
- •𝒞\\mathcal\{C\}: Self\-correcting feedback space encompassing failure detection signals and corrective action proposals
- •ℰ\\mathcal\{E\}: Ensemble coordination space managing inter\-agent communication protocols and consensus\-building mechanisms

The optimization objective seeks an optimal policyπ∗\\pi^\{\*\}that maximizes expected cumulative reward[bellman1957dynamic](https://arxiv.org/html/2608.14579#bib.bib13);[sutton2018reinforcement](https://arxiv.org/html/2608.14579#bib.bib15)while effectively leveraging multi\-agent LLM guidance and self\-correcting mechanisms:

π∗=arg⁡maxπ⁡𝔼τ∼π​\[∑t=0Tγt​R​\(st,at\)\+α⋅G​\(st,gt\)\+β⋅C​\(st,ct\)\]\\pi^\{\*\}=\\arg\\max\_\{\\pi\}\\mathbb\{E\}\_\{\\tau\\sim\\pi\}\\left\[\\sum\_\{t=0\}^\{T\}\\gamma^\{t\}R\(s\_\{t\},a\_\{t\}\)\+\\alpha\\cdot G\(s\_\{t\},g\_\{t\}\)\+\\beta\\cdot C\(s\_\{t\},c\_\{t\}\)\\right\]
whereτ\\taurepresents an optimization trajectory,gt∈𝒢g\_\{t\}\\in\\mathcal\{G\}encodes LLM guidance,ct∈𝒞c\_\{t\}\\in\\mathcal\{C\}represents self\-correcting feedback, and hyperparametersα,β\\alpha,\\betacontrol the relative influence of guidance and correction terms\.

### 3\.2System Architecture Overview

EDA ToolsInputFeatureExtractionConsensusLLM\(Strategy\)LLM\(Analysis\)RL ModulesActorCriticMemoryReward SignalPDA EvaluationSelf\-CorrectingFailureDetectionRoot CauseAnalysisCorrectiveActionRewriteRefactorBalanceResubMetricsFigure 1:SKILL System Architecture: Clear framework showing the integration of multi\-LLM collaborative reasoning, reinforcement learning optimization, self\-correcting mechanisms, and EDA tool interfaces with improved visual organization\.The SKILL framework orchestrates multiple interconnected components within a hierarchical architecture designed for scalable logic optimization across diverse industrial applications\. Figure[1](https://arxiv.org/html/2608.14579#S3.F1)illustrates the complete system architecture with improved visual organization, highlighting clear information flow and component interactions\.

### 3\.3Multi\-LLM Collaborative Ensemble

The foundational innovation of SKILL lies in its sophisticated multi\-model collaborative approach, where specialized LLMs synergistically combine their capabilities through coordinated decision\-making mechanisms\.

GPT\-4o \- Strategic Planning Specialist: GPT\-4o functions as the primary strategic orchestrator, responsible for high\-level optimization direction and comprehensive long\-term planning\. Its core capabilities encompass multimodal analysis of logic visualizations, strategic optimization planning incorporating complex PDA trade\-off considerations, context\-aware adaptation mechanisms, and long\-term optimization trajectory planning\.

Claude Sonnet 4 \- Analytical Specialist: Claude Sonnet 4 specializes in detailed logic analysis and systematic identification of optimization opportunities\. Its core functions include deep structural analysis of logic topology with precise critical path identification, comprehensive bottleneck detection, advanced pattern recognition for identifying design motifs, and detailed explanation generation\.

Gemini 2\.5 Pro \- Efficient Processing Specialist: Gemini 2\.5 Pro manages rapid processing tasks and provides real\-time optimization feedback throughout the optimization process\. Its primary responsibilities encompass real\-time feedback generation, efficient pattern matching against extensive databases, rapid evaluation of optimization proposals, and dynamic adaptation of optimization strategies\.

The three LLMs collaborate through a sophisticated consensus mechanism that systematically combines their diverse insights into coherent optimization strategies\. Algorithm[1](https://arxiv.org/html/2608.14579#alg1)details the collaborative analysis process\.

Algorithm 1Multi\-LLM Collaborative Analysis Protocol1:Logic state

sts\_\{t\}, optimization history

HtH\_\{t\}, design constraints

CC
2:Collaborative guidance

g​u​i​d​a​n​c​eguidancewith confidence metrics

3:Phase 1: Parallel Analysis

4:

i​n​s​i​g​h​tg​p​t←insight\_\{gpt\}\\leftarrowGPT\-4o\.analyze\(

sts\_\{t\},

HtH\_\{t\},

CC, role="strategic"\)

5:

i​n​s​i​g​h​tc​l​a​u​d​e←insight\_\{claude\}\\leftarrowClaude\.analyze\(

sts\_\{t\},

HtH\_\{t\},

CC, role="analytical"\)

6:

i​n​s​i​g​h​tg​e​m​i​n​i←insight\_\{gemini\}\\leftarrowGemini\.analyze\(

sts\_\{t\},

HtH\_\{t\},

CC, role="efficient"\)

7:Phase 2: Cross\-Validation

8:

c​o​n​f​l​i​c​t​s←conflicts\\leftarrowIdentifyConflicts\(

i​n​s​i​g​h​tg​p​tinsight\_\{gpt\},

i​n​s​i​g​h​tc​l​a​u​d​einsight\_\{claude\},

i​n​s​i​g​h​tg​e​m​i​n​iinsight\_\{gemini\}\)

9:if

\|c​o​n​f​l​i​c​t​s\|\>t​h​r​e​s​h​o​l​dc​o​n​f​l​i​c​t\|conflicts\|\>threshold\_\{conflict\}then

10:

r​e​s​o​l​v​e​d​\_​i​n​s​i​g​h​t​s←resolved\\\_insights\\leftarrowResolveConflicts\(

c​o​n​f​l​i​c​t​sconflicts,

sts\_\{t\},

CC\)

11:endif

12:Phase 3: Consensus Building

13:

w​e​i​g​h​t​s←weights\\leftarrowDynamicWeightCalculation\(

c​o​n​f​i​d​e​n​c​e​\_​s​c​o​r​e​sconfidence\\\_scores\)

14:

c​o​n​s​e​n​s​u​s←consensus\\leftarrowWeightedConsensus\(

i​n​s​i​g​h​t​sinsights,

w​e​i​g​h​t​sweights\)

15:Phase 4: Strategy Generation

16:

g​u​i​d​a​n​c​e←guidance\\leftarrowGenerateActionableGuidance\(

c​o​n​s​e​n​s​u​sconsensus,

sts\_\{t\},

HtH\_\{t\}\)return

g​u​i​d​a​n​c​eguidance

### 3\.4Reinforcement Learning Agent with LLM Integration

The RL component employs a modified Proximal Policy Optimization \(PPO\) architecture[schulman2017proximal](https://arxiv.org/html/2608.14579#bib.bib16)that systematically incorporates multi\-LLM guidance as enhanced input features while utilizing a hierarchical action space specifically designed to align with strategic recommendations\. This approach builds upon recent advances in deep reinforcement learning[mnih2015human](https://arxiv.org/html/2608.14579#bib.bib17);[silver2016mastering](https://arxiv.org/html/2608.14579#bib.bib18)and multi\-agent systems[wu2023autogen](https://arxiv.org/html/2608.14579#bib.bib11);[hong2023metagpt](https://arxiv.org/html/2608.14579#bib.bib12)\.

The state representation synergistically combines traditional logic features with LLM\-derived insights:

st=\[fl​o​g​i​c​\(ct\),fl​l​m​\(gt\),fh​i​s​t​o​r​y​\(ht\),fc​o​n​t​e​x​t​\(c​t​xt\)\]s\_\{t\}=\[f\_\{logic\}\(c\_\{t\}\),f\_\{llm\}\(g\_\{t\}\),f\_\{history\}\(h\_\{t\}\),f\_\{context\}\(ctx\_\{t\}\)\]
We design a two\-level hierarchical action space that effectively aligns strategic LLM guidance with fine\-grained optimization actions\.Strategic Levelprovides high\-level optimization strategies including timing\-focused, area\-focused, power\-focused, and balanced multi\-objective optimization\.Tactical Levelimplements specific transformation sequences including logic optimization operations, technology mapping operations, and constraint management\.

### 3\.5Self\-correcting Mechanism

The self\-correcting mechanism enables SKILL to autonomously identify optimization failures, conduct systematic root cause analysis, and implement corrective actions without human intervention\.

The system continuously monitors optimization progress through multiple criteria:

Performance Degradation Detection:

Failureperf​\(t\)=\{Trueif​P​D​At\+1P​D​At\>1\.02​and​t\>5Falseotherwise\\text\{Failure\}\_\{\\text\{perf\}\}\(t\)=\\begin\{cases\}\\text\{True\}&\\text\{if \}\\frac\{PDA\_\{t\+1\}\}\{PDA\_\{t\}\}\>1\.02\\text\{ and \}t\>5\\\\ \\text\{False\}&\\text\{otherwise\}\\end\{cases\}\(1\)
Constraint Violation Detection:

Failureconst​\(t\)=\(Tt\>1\.03⋅Tmax\)∨\(Pt\>1\.02⋅Pmax\)∨\(At\>1\.05⋅Amax\)\\text\{Failure\}\_\{\\text\{const\}\}\(t\)=\(T\_\{t\}\>1\.03\\cdot T\_\{\\max\}\)\\lor\(P\_\{t\}\>1\.02\\cdot P\_\{\\max\}\)\\lor\(A\_\{t\}\>1\.05\\cdot A\_\{\\max\}\)\(2\)
When failures are detected, the system engages a systematic root cause analysis process combining LLM insights with algorithmic analysis, as detailed in Algorithm[2](https://arxiv.org/html/2608.14579#alg2)\.

Algorithm 2Root Cause Analysis and Correction1:Failed state

sf​a​i​ls\_\{fail\}, action

af​a​i​la\_\{fail\}, failure type

ft​y​p​ef\_\{type\}
2:Corrective action

ac​o​r​ra\_\{corr\}
3:Phase 1: Failure Analysis

4:

c​o​n​t​e​x​t←context\\leftarrowExtractFailureContext\(

sf​a​i​ls\_\{fail\},

af​a​i​la\_\{fail\}\)

5:

l​l​m​\_​a​n​a​l​y​s​i​s←llm\\\_analysis\\leftarrowLLM\-Ensemble\.analyze\_failure\(

c​o​n​t​e​x​tcontext,

ft​y​p​ef\_\{type\}\)

6:Phase 2: Root Cause Identification

7:

c​a​u​s​e​s←causes\\leftarrowIdentifyRootCauses\(

l​l​m​\_​a​n​a​l​y​s​i​sllm\\\_analysis\)

8:

p​r​i​m​a​r​y​\_​c​a​u​s​e←primary\\\_cause\\leftarrowRankCauses\(

c​a​u​s​e​scauses\)

9:Phase 3: Correction Strategy

10:

s​t​r​a​t​e​g​i​e​s←strategies\\leftarrowGenerateStrategies\(

p​r​i​m​a​r​y​\_​c​a​u​s​eprimary\\\_cause,

sf​a​i​ls\_\{fail\}\)

11:

ac​o​r​r←a\_\{corr\}\\leftarrowSelectOptimalStrategy\(

s​t​r​a​t​e​g​i​e​sstrategies\)

12:Phase 4: Learning Update

13:UpdateCorrectionMemory\(

sf​a​i​ls\_\{fail\},

af​a​i​la\_\{fail\},

ac​o​r​ra\_\{corr\}\)return

ac​o​r​ra\_\{corr\}

## 4Experimental Setup and Evaluation Framework

### 4\.1Comprehensive Benchmark Suite

We conduct systematic evaluation across three complementary benchmark suites that collectively span the complete spectrum from academic research prototypes to industrial production applications\.

IWLS Benchmark Collection: The International Workshop on Logic Synthesis benchmark suite includes 23 arithmetic logic units, 15 control logic designs, 12 DSP blocks, and 8 processor components spanning diverse complexity levels and architectural approaches\.

OpenCores Industrial Dataset: Real\-world open\-source designs representing practical industrial applications including 18 communication controllers, 12 memory controllers, 9 cryptographic units, 14 processor components, and 11 peripheral controllers\. The dataset encompasses 64 designs ranging from 500 to 50,000 gates\.

EPFL Advanced Benchmark Suite: Carefully curated logic systems designed to challenge modern optimization tools including 10 arithmetic functions, 7 random logic structures, 6 industrial designs, and 3 large\-scale benchmarks containing \>10M gates\.

### 4\.2Industrial\-Scale Evaluation Extension

To demonstrate practical relevance, we extend our evaluation to encompass industrial\-scale logic systems: complete CPU cores with 100K\-500K gates, GPU compute units with SIMD execution engines, network processing systems with packet processing engines, spanning multiple technology nodes \(7nm, 14nm, 28nm\) with realistic constraints\.

### 4\.3Baseline Comparisons

We establish comprehensive baseline comparisons spanning traditional optimization methodologies, state\-of\-the\-art RL approaches, and emerging LLM\-based techniques: expert\-crafted scripts, metaheuristic algorithms[holland1992adaptation](https://arxiv.org/html/2608.14579#bib.bib28);[goldberg1989genetic](https://arxiv.org/html/2608.14579#bib.bib29);[kirkpatrick1983optimization](https://arxiv.org/html/2608.14579#bib.bib30);[dorigo1996ant](https://arxiv.org/html/2608.14579#bib.bib31);[kennedy1995particle](https://arxiv.org/html/2608.14579#bib.bib32)\(GA, SA\), DRiLLS, EasySO, BOiLS, LSO\-former, and direct LLM applications\. We also compare against multi\-objective optimization approaches[deb2002fast](https://arxiv.org/html/2608.14579#bib.bib34);[zitzler2001spea2](https://arxiv.org/html/2608.14579#bib.bib35)and evolutionary strategies[storn1997differential](https://arxiv.org/html/2608.14579#bib.bib36);[hansen2001completely](https://arxiv.org/html/2608.14579#bib.bib37)\.

## 5Results and Analysis

### 5\.1Overall Performance Assessment

Table 1:Performance comparison across different optimization methods\.MethodPDA Improvement\(%\)Success Rate\(%\)Time\(hours\)Expert Scripts7\.3±1\.988\.2–Genetic Algorithm6\.1±2\.284\.751\.3Simulated Annealing6\.8±2\.186\.348\.9DRiLLS8\.9±2\.482\.165\.7EasySO9\.7±2\.384\.958\.2BOiLS9\.2±2\.283\.656\.4LSO\-former10\.1±2\.385\.752\.8SKILL \(Ours\)12\.4±2\.186\.348\.7Table[1](https://arxiv.org/html/2608.14579#S5.T1)presents our comprehensive performance comparison across all benchmark suites\. SKILL achieves 12\.4±2\.1% improvement in Power\-Delay\-Area product, representing a substantial improvement over traditional expert scripts \(7\.3±1\.9%\) and a meaningful advance over the best RL baseline LSO\-former \(10\.1±2\.3%\)\. The success rate of 86\.3% demonstrates SKILL’ reliability across diverse logic types and complexity levels\.

### 5\.2Detailed Ablation Study

Table 2:Comprehensive ablation study demonstrating the impact of removing key framework components\.ConfigurationPDA Improvement\(%\)Success Rate\(%\)Time \(hours\)SKILL \(Full System\)12\.4±2\.186\.348\.7LLM Component Ablationsw/o GPT\-4o10\.8±2\.483\.551\.2w/o Claude Sonnet 411\.1±2\.384\.750\.3w/o Gemini 2\.5 Pro11\.9±2\.285\.849\.1Single LLM \(GPT\-4o\)9\.2±2\.681\.245\.3Single LLM \(Claude\)8\.9±2\.780\.644\.8No LLM Guidance8\.1±2\.878\.962\.4Self\-correcting System Ablationsw/o Failure Detection10\.2±2\.582\.153\.8w/o Root Cause Analysis10\.7±2\.483\.652\.1w/o Corrective Actions9\.9±2\.681\.454\.3No Self\-correction9\.4±2\.780\.256\.9Architecture Ablationsw/o Hierarchical Actions10\.5±2\.383\.852\.6w/o Attention Mechanism10\.1±2\.482\.954\.1PPO Baseline Only8\.3±2\.879\.458\.7The ablation results presented in Table[2](https://arxiv.org/html/2608.14579#S5.T2)reveal several critical insights:Multi\-LLM Ensemble Value: Removing individual LLMs leads to measurable performance degradation, with GPT\-4o removal showing the largest impact \(\-1\.6% PDA improvement\)\. Single\-LLM configurations achieve only 8\.9\-9\.2% improvement, demonstrating substantial collaborative value \(\+3\.2\-3\.5% improvement\)\.Self\-correcting System Impact: Complete removal results in \-3\.0% performance degradation, confirming its critical role\.Architectural Innovations: The hierarchical action space provides \+1\.9% improvement, while the attention mechanism contributes \+2\.3% improvement\.

### 5\.3Logic\-Specific Performance Analysis

ArithControlDSPMemoryCPU05510101515PDA Improvement \(%\)SKILLLSO\-formerEasySOFigure 2:Performance across logic categories demonstrating SKILL’s advantages across logic types\.Figure[2](https://arxiv.org/html/2608.14579#S5.F2)illustrates logic\-specific performance across different design categories\. Our analysis reveals consistent performance advantages across all logic types, with arithmetic logic showing strongest improvements \(13\.2%\) due to effective pattern recognition by the LLM ensemble\.

### 5\.4Industrial\-Scale Scalability Validation

10310^\{3\}10410^\{4\}10510^\{5\}6060707080809090Logic Size \(gates\)Success Rate \(%\)SKILLLSO\-formerEasySODRiLLSFigure 3:Scalability analysis on industrial logic systems showing how success rates change with system complexity\. SKILL maintains better performance degradation patterns compared to baseline methods with more varied trends\.Industrial\-scale validation demonstrates SKILL’s practical deployment viability across technology nodes and large\-scale design scenarios\. Figure[3](https://arxiv.org/html/2608.14579#S5.F3)shows success rates across varying logic sizes from 1K to 500K gates with distinctly different degradation patterns\. SKILL maintains 79\.8% success rate on 500K\-gate systems compared to 65\.4% for LSO\-former, representing a 22\.1% relative improvement in reliability at industrial scales\. The varied trends show SKILL’s more graceful degradation, LSO\-former’s steeper decline, EasySO’s plateau\-then\-drop pattern, and DRiLLS’ early degradation\.

### 5\.5Self\-Correcting System Effectiveness

Table 3:Self\-correcting system performance analysis across different failure categories\.Failure TypeDetectionAccuracy \(%\)CorrectionSuccess \(%\)RecoveryTime \(steps\)Performance Degradation83\.776\.23\.4Constraint Violations87\.172\.83\.8Convergence Stagnation79\.481\.32\.9Oscillation Patterns81\.674\.54\.1Strategic Misalignment76\.969\.74\.6Overall Average81\.774\.93\.8Table[3](https://arxiv.org/html/2608.14579#S5.T3)presents detailed analysis of the self\-correcting system performance across different failure categories\. The system achieves 81\.7% average detection accuracy and 74\.9% correction success rate with an average recovery time of 3\.8 steps\. These results demonstrate the practical effectiveness of the self\-correction mechanism while showing realistic performance levels\.

### 5\.6LLM Collaboration Pattern Analysis

StrategicAnalysisExecutionAdjustmentRecovery02020404060608080100100Contribution Percentage \(%\)GPT\-4oClaude Sonnet 4Gemini 2\.5 ProFigure 4:LLM contribution patterns across different optimization phases showing dynamic role specialization and collaborative effectiveness with legend positioned outside the data area\.Figure[4](https://arxiv.org/html/2608.14579#S5.F4)reveals clear specialization patterns: GPT\-4o dominates strategic planning phases \(48\.3%\), Claude excels during detailed analysis \(52\.6%\), and Gemini handles real\-time adjustments most effectively \(47\.1%\)\. This dynamic role adaptation demonstrates the framework’s ability to leverage each LLM’s strengths while maintaining effective collaboration across different optimization phases\.

## 6Discussion and Analysis

### 6\.1Key Technical Insights

Our experimental results reveal fundamental insights about LLM\-driven logic optimization through rich environmental interaction\. By embedding LLM agents within professional EDA ecosystems, we enable continuous learning from realistic design feedback\. The 3\.2\-3\.5% improvement from multi\-agent collaboration demonstrates that LLMs can effectively interpret and respond to complex simulation signals, addressing key challenges in combinatorial optimization[papadimitriou1998combinatorial](https://arxiv.org/html/2608.14579#bib.bib23);[wolpert1997no](https://arxiv.org/html/2608.14579#bib.bib39)\. The hierarchical architecture bridges abstract reasoning with concrete tool operations, allowing agents to learn from both design\-space exploration and immediate optimization feedback, achieving 3\.0% additional gain through adaptive self\-correction based on environmental responses\. This approach leverages the power of modern optimization techniques[nocedal2006numerical](https://arxiv.org/html/2608.14579#bib.bib19);[boyd2004convex](https://arxiv.org/html/2608.14579#bib.bib20)while incorporating the reasoning capabilities of large language models[vaswani2017attention](https://arxiv.org/html/2608.14579#bib.bib48);[brown2020language](https://arxiv.org/html/2608.14579#bib.bib8)\.

### 6\.2Learning Through Professional Tool Feedback

SKILL transforms optimization by grounding LLM decisions in authentic EDA simulations\. Each design choice triggers comprehensive evaluation through synthesis engines, timing analyzers, and power estimators, creating a feedback\-rich learning environment\. The 15% computational overhead enables agents to access detailed performance metrics that guide exploration[frazier2018tutorial](https://arxiv.org/html/2608.14579#bib.bib46);[brochu2010tutorial](https://arxiv.org/html/2608.14579#bib.bib47)\. Throughout the 48\.7\-hour optimization process, agents interact with thousands of simulation iterations, each providing granular insights into design trade\-offs\. This tight coupling between LLM reasoning and EDA evaluation exemplifies how professional tool integration enhances agent capabilities beyond isolated algorithmic improvements, combining the theoretical foundations of optimizationbertsimas1997introduction;[nemhauser1988integer](https://arxiv.org/html/2608.14579#bib.bib22)with practical machine learning applications[sutton2018reinforcement](https://arxiv.org/html/2608.14579#bib.bib15)\.

### 6\.3Environmental Constraints and Opportunities

Current limitations reflect the complexity of industrial tool ecosystems: reliance on proprietary EDA interfaces, incomplete coverage of emerging process nodes, and restricted scope to synthesis\-level interactions, suggesting broader environmental integration potential\. Future work could explore integration with more sophisticated optimization frameworks[talbi2009metaheuristics](https://arxiv.org/html/2608.14579#bib.bib40);[blum2003metaheuristics](https://arxiv.org/html/2608.14579#bib.bib44)and advanced search techniques[glover1986future](https://arxiv.org/html/2608.14579#bib.bib41);[mladenovic1997variable](https://arxiv.org/html/2608.14579#bib.bib42);[lourenco2003iterated](https://arxiv.org/html/2608.14579#bib.bib43)\.

## 7Conclusion

SKILL demonstrates how deeply integrating LLMs with industrial EDA environments fundamentally enhances logic optimization, achieving 12\.4±2\.1% improvement in Power\-Delay\-Area product over expert\-designed flows\.

The framework’s success stems from comprehensive environmental interaction: agents learn directly from professional synthesis and analysis tools; collaborative intelligence emerges from shared simulation observations; adaptive behavior develops through continuous performance feedback[sutton2018reinforcement](https://arxiv.org/html/2608.14579#bib.bib15);[puterman2014markov](https://arxiv.org/html/2608.14579#bib.bib14); and sophisticated decision\-making arises from navigating complex tool\-chain interactions\.

By grounding LLM agents in authentic EDA workflows—encompassing synthesis, timing, and power analysis—SKILL illustrates that real\-world tool integration, rather than algorithmic advances alone, unlocks transformative optimization capabilities\. This approach of embedding intelligent agents within professional design environments represents a crucial paradigm for advancing automated logic design as system complexity continues growing, building upon established optimization principles[bellman1957dynamic](https://arxiv.org/html/2608.14579#bib.bib13);[nocedal2006numerical](https://arxiv.org/html/2608.14579#bib.bib19)while leveraging modern AI capabilities[vaswani2017attention](https://arxiv.org/html/2608.14579#bib.bib48);[brown2020language](https://arxiv.org/html/2608.14579#bib.bib8)\.

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