System 1&2 Synergy via Dynamic Model Interpolation

TL;DR

This work tackles the challenge of unifying fast, intuition-driven System 1 and slow, deliberative System 2 reasoning in large language models by shifting from output control to capability control through dynamic parameter interpolation. It introduces DAMI, a framework that yields a query-specific Reasoning Intensity $\lambda(q)$ to modulate cognitive depth without retraining, via training-based (DAMI-Pref) and training-free (DAMI-Conf) estimation. The authors demonstrate that linear interpolation between Instruct and Thinking checkpoints yields a monotonic, continuous trade-off between accuracy and efficiency, underpinned by Linear Mode Connectivity and representation continuity, and provide theoretical justifications in appendices. Empirically, DAMI improves reasoning accuracy while reducing token usage across five mathematical benchmarks and generalizes to multimodal tasks, offering a practical approach to adaptive reasoning suitable for diverse domains.

Abstract

Training a unified language model that adapts between intuitive System 1 and deliberative System 2 remains challenging due to interference between their cognitive modes. Recent studies have thus pursued making System 2 models more efficient. However, these approaches focused on output control, limiting what models produce. We argue that this paradigm is misaligned: output length is merely a symptom of the model's cognitive configuration, not the root cause. In this work, we shift the focus to capability control, which modulates \textit{how models think} rather than \textit{what they produce}. To realize this, we leverage existing Instruct and Thinking checkpoints through dynamic parameter interpolation, without additional training. Our pilot study establishes that linear interpolation yields a convex, monotonic Pareto frontier, underpinned by representation continuity and structural connectivity. Building on this, we propose \textbf{DAMI} (\textbf{D}yn\textbf{A}mic \textbf{M}odel \textbf{I}nterpolation), a framework that estimates a query-specific Reasoning Intensity $λ(q)$ to configure cognitive depth. For training-based estimation, we develop a preference learning method encoding accuracy and efficiency criteria. For zero-shot deployment, we introduce a confidence-based method leveraging inter-model cognitive discrepancy. Experiments on five mathematical reasoning benchmarks demonstrate that DAMI achieves higher accuracy than the Thinking model while remaining efficient, effectively combining the efficiency of System 1 with the reasoning depth of System 2.

Figures (11)

• Figure 1: Capability control outperforms output control across different efficiency levels on both tasks. Linear interpolation between Instruct and Thinking yields a monotonic Pareto frontier.
• Figure 2: The monotonicity and continuity of reasoning intensity.
• Figure 3: An overview of our DAMI method. DAMI estimates query difficulty through either preference learning (training-based) or confidence signals (training-free), then dynamically adjusts the Reasoning Intensity $\lambda(q)$ to configure cognitive depth accordingly.
• Figure 4: Accuracy-efficiency scatter plot aggregated over five benchmarks. DAMI methods (starred) achieve the best accuracy-efficiency trade-offs on both Qwen3-4B and Qwen2.5-7B.
• Figure 5: Ablation study results on the Qwen3-4B model pair.

Theorems & Definitions (24)

• Definition 1: Loss Barrier
• Definition 2: Linear Mode Connectivity
• Theorem 1: Same-Basin Property of Fine-tuned Models, neyshabur2020what
• Corollary 1: LMC for Co-originated Models
• proof
• Proposition 1: Interpolation Validity for Instruct-Thinking Pairs
• proof
• Remark 1
• Remark 2
• Theorem 2: Monotonicity of Expected Accuracy