Chain of Simulation: A Dual-Mode Reasoning Framework for Large Language Models with Dynamic Problem Routing

TL;DR

Chain of Simulation (CoS) introduces a dynamic, dual-mode reasoning framework that routes problems to one of three specialized modes—computational flow for arithmetic, symbolic state tracking via JSON for spatial tasks, and a hybrid multi-hop mode—thereby leveraging latent capabilities within pre-trained models without additional training. The approach combines problem analysis, mode selection, and mode-specific execution with an answer extraction step, achieving 71.5% on GSM8K, 90.0% on StrategyQA, and 19.0% on bAbI while reducing computation by about 54% relative to Self-Consistency. Empirical results demonstrate that correct mode routing is essential, with computational mode reaching 81.2% accuracy when correctly applied to mathematical problems and failing completely when misapplied to symbolic tasks, indicating non-transferable reasoning subsystems. CoS outperforms strong baselines across benchmarks and offers practical trade-offs between accuracy and efficiency, particularly benefiting smaller models and enabling more resource-constrained deployments. The findings imply that prompt design can unlock latent, specialized reasoning pathways in LLMs, suggesting a broader paradigm where problem analysis and adaptive mode selection drive robust, efficient artificial reasoning.

Abstract

We present Chain of Simulation (CoS), a novel dual-mode reasoning framework that dynamically routes problems to specialized reasoning strategies in Large Language Models (LLMs). Unlike existing uniform prompting approaches, CoS employs three distinct reasoning modes: (1) computational flow with self-consistency for mathematical problems, (2) symbolic state tracking with JSON representations for spatial reasoning, and (3) hybrid fact-extraction for multi-hop inference. Through comprehensive evaluation on GSM8K, StrategyQA, and bAbI benchmarks using four state-of-the-art models (Gemma-3 27B, LLaMA-3.1 8B, Mistral 7B, and Qwen-2.5 14B), we demonstrate that CoS achieves 71.5% accuracy on GSM8K (1.0% absolute improvement), 90.0% on StrategyQA (2.5% improvement), and 19.0% on bAbI (65.2% relative improvement) compared to the strongest baselines. The analysis reveals that problem-specific mode selection is crucial, with computational mode achieving 81.2% accuracy when correctly applied to mathematical problems, while misrouting leads to 0% accuracy. We provide detailed algorithms for mode selection, state tracking, and answer extraction, establishing CoS as an effective approach for improving LLM reasoning without additional training. The framework provides superior trade-offs between accuracy and efficiency compared to Self-Consistency, achieving comparable performance at 54% lower computational cost.

Figures (4)

• Figure 1: Chain of Simulation (CoS) system pipeline. The Problem Analyzer extracts mathematical, spatial, multi-hop, and tracking indicators from the input problem. The Mode Selector performs dynamic routing to Computational Flow, Symbolic State Tracking, or Hybrid reasoning modes. Each mode produces a candidate answer, which is then normalized by the Answer Extractor to produce the final output.
• Figure 2: Performance comparison across benchmarks showing CoS (Dual-Mode) consistently outperforming baselines. Error bars represent 95% confidence intervals computed using bootstrap sampling with B=1000 iterations.
• Figure 3: Performance heatmap showing CoS consistently achieving high accuracy (darker colors) across model sizes. The heatmap reveals that CoS provides the most consistent performance across different model scales.
• Figure 4: Computational cost comparison showing accuracy vs. inference time trade-off. CoS provides a near-optimal balance between accuracy and computational efficiency.