# System 1&2 Synergy via Dynamic Model Interpolation

arXiv: https://arxiv.org/abs/2601.21414 · HTML: https://mlsanity.com/paper/2601.21414/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 45 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Builds on (most cited first, 30 of 32)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen3-VL Technical Report](https://mlsanity.com/paper/2511.21631/) (2025)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [RouteLLM: Learning to Route LLMs with Preference Data](https://mlsanity.com/paper/2406.18665/) (2024)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)
- [Federated Learning with Matched Averaging](https://mlsanity.com/paper/2002.06440/) (2020)
- [What is being transferred in transfer learning?](https://mlsanity.com/paper/2008.11687/) (2020)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [AdaMerging: Adaptive Model Merging for Multi-Task Learning](https://mlsanity.com/paper/2310.02575/) (2023)
- [TokenSkip: Controllable Chain-of-Thought Compression in LLMs](https://mlsanity.com/paper/2502.12067/) (2025)
- [Token-Budget-Aware LLM Reasoning](https://mlsanity.com/paper/2412.18547/) (2024)
- [Training Language Models to Reason Efficiently](https://mlsanity.com/paper/2502.04463/) (2025)
- [Dynamic Early Exit in Reasoning Models](https://mlsanity.com/paper/2504.15895/) (2025)
- [ThinkPrune: Pruning Long Chain-of-Thought of LLMs via Reinforcement Learning](https://mlsanity.com/paper/2504.01296/) (2025)
- [S-GRPO: Early Exit via Reinforcement Learning in Reasoning Models](https://mlsanity.com/paper/2505.07686/) (2025)
- [Router-R1: Teaching LLMs Multi-Round Routing and Aggregation via Reinforcement Learning](https://mlsanity.com/paper/2506.09033/) (2025)
- [Unlocking Efficient Long-to-Short LLM Reasoning with Model Merging](https://mlsanity.com/paper/2503.20641/) (2025)
- [Scaling Laws for Optimal Data Mixtures](https://mlsanity.com/paper/2507.09404/) (2025)
- [Ada-R1: Hybrid-CoT via Bi-Level Adaptive Reasoning Optimization](https://mlsanity.com/paper/2504.21659/) (2025)
- [Thinking Fast and Right: Balancing Accuracy and Reasoning Length with Adaptive Rewards](https://mlsanity.com/paper/2505.18298/) (2025)
- [The Price of a Second Thought: On the Evaluation of Reasoning Efficiency in Large Language Models](https://mlsanity.com/paper/2505.22017/) (2025)
- [Activation-Guided Consensus Merging for Large Language Models](https://mlsanity.com/paper/2505.14009/) (2025)
- [Test-time Prompt Intervention](https://mlsanity.com/paper/2508.02511/) (2025)
- [Backward Compatibility During Data Updates by Weight Interpolation](https://mlsanity.com/paper/2301.10546/) (2023)
- [A Multi-Task Role-Playing Agent Capable of Imitating Character Linguistic Styles](https://mlsanity.com/paper/2411.02457/) (2024)
- [Multi-level Adaptive Contrastive Learning for Knowledge Internalization in Dialogue Generation](https://mlsanity.com/paper/2310.08943/) (2023)
- [VecInfer: Efficient LLM Inference with Low-Bit KV Cache via Outlier-Suppressed Vector Quantization](https://mlsanity.com/paper/2510.06175/) (2025)
- [Weights-Rotated Preference Optimization for Large Language Models](https://mlsanity.com/paper/2508.17637/) (2025)

## Built on by (most cited first, 3 of 3)

- [EasyVideoR1: Easier RL for Video Understanding](https://mlsanity.com/paper/2604.16893/) (2026)
- [Learning to Solve, Forgetting to Retain: Correct-Set Turnover in RLVR](https://mlsanity.com/paper/2606.03087/) (2026)
- [Online Self-Calibration Against Hallucination in Vision-Language Models](https://mlsanity.com/paper/2605.00323/) (2026)

## Abstract (arXiv)

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 textithow models think rather than textitwhat 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 DAMI (DynAmic Model Interpolation), 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.