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Revisiting Model Interpolation for Efficient Reasoning

Taiqiang Wu, Runming Yang, Tao Liu, Jiahao Wang, Ngai Wong

arXiv:2510.10977v2cs.AIcs.CL

TL;DR

Longer chain-of-thought can support complex reasoning but also brings over-thinking and latency trade-offs. This paper analyzes direct interpolation between Instruct and Thinking models, finding a three-stage trajectory. A strategically interpolated model surpasses sophisticated merging baselines across challenging benchmarks.

  • Problem

    Longer chain-of-thought brings over-thinking and high-latency trade-offs, leaving efficient reasoning without compromising performance a critical challenge.

    Source: §1 · p. 1

  • Method

    The paper systematically analyzes direct Instruct–Thinking model interpolation as coefficient λ sweeps from 0 to 1.

    Source: §1 · p. 1

  • Results

    Strategic interpolation surpasses sophisticated merging baselines across challenging benchmarks.

    Source: §1 · p. 2

  • Takeaways & Limitations

    The three-stage trajectory provides principled guidance for crafting models with targeted reasoning behaviors, including a desired token budget.

    Source: §1 · p. 2

    Empirical validation centers on Qwen3; whether the three-stage dynamic holds across other model families remains to be verified.

    Source: Limitation · p. 9

Abstract

from arXiv · show

Model merging, typically on Instruct and Thinking models, has shown remarkable performance for efficient reasoning. In this paper, we systematically revisit the simplest merging method that interpolates two weights directly. Particularly, we observe that model interpolation follows a three-stage evolutionary paradigm with distinct behaviors on the reasoning trajectory. These dynamics provide a principled guide for navigating the performance-cost trade-off. Empirical results demonstrate that a strategically interpolated model surprisingly surpasses sophisticated model merging baselines on both efficiency and effectiveness. We further validate our findings with extensive ablation studies on model layers, modules, and decoding strategies. Ultimately, this work demystifies model interpolation and offers a practical framework for crafting models with precisely targeted reasoning capabilities. Code is available at \href{https://github.com/wutaiqiang/MI}{Github}.

1 Introduction

Longer chain-of-thought can improve complex reasoning but brings over-thinking and latency trade-offs, making efficient reasoning without sacrificing performance a challenge. The paper examines Instruct–Thinking model interpolation, identifies a three-stage trajectory, and reports that strategic interpolation surpasses merging baselines across challenging benchmarks.

1 Introduction

  • Longer chain-of-thought supports complex tasks but carries over-thinking and high-latency trade-offs..Source: §1 · p. 1
  • Model merging combines specialized Thinking and Instruct weights to balance reasoning capability with token efficiency.The paper contrasts broader merging approaches with direct model interpolation.Source: §1 · p. 1
  • As λ increases, interpolation passes through three stages: rapid gains with little explicit reasoning, emergence of thinking, then longer outputs with diminishing marginal gains.In stage 2, Mean@k rises faster than Pass@k; stage 3 corresponds to overthinking.Source: §1 · pp. 1–2
  • Strategically interpolated models surpass mainstream merging baselines across math, instruction-following, and science benchmarks.Figure 2 reports that model interpolation outperforms the baselines on both efficiency and effectiveness.Source: §1 · p. 2, Figure 2 · p. 2
  • The authors report fine-grained ablations on layers, modules, and decoding strategies to probe interpolation’s behavior..Source: §1 · p. 2

2 Related Work

Prior efficient-reasoning work varies training, decoding, or prompts, while this paper focuses on training-free model interpolation. Model merging combines weights from specialized models, and interpolation extends an equal-weight averaging example by varying the coefficient.

2.1 Efficient Reasoning

  • Efficient-reasoning methods modify training objectives, decoding, or prompts; this work focuses on training-free model interpolation..Source: §2.1 · p. 2

2.2 Model Merging

  • Model merging combines same-structure models’ weights; Kimi k1.5’s long- and short-CoT average is described as interpolation at λ = 0.5.The paper extends this idea by analyzing different interpolation coefficients; Table 1 reports Qwen3 paired-model weight similarity.Source: §2.2 · pp. 2–3, Table 1 · p. 3

3 Preliminary

The section distinguishes quick-answer Instruct models from long-CoT Thinking models, then outlines model merging and its direct-interpolation variant. Model interpolation blends the two specialists without dependence on a base model.

3.1 Instruct and Thinking Models

  • Long-CoT Thinking models target complex tasks with explicit reasoning but greater latency, while short-CoT Instruct models prioritize direct answers and efficiency.The paper describes both a hybrid model supporting both modes and separately posttrained specialist models.Source: §3.1 · p. 3
  • Qwen3-4B-series paired models are highly similar in weights, and Qwen3-4B is more similar to Qwen3-4B-Thinking-2507 than to Qwen3-4B-Base.The authors interpret this as suggesting a potential inheritance relationship.Source: §3.1 · p. 3

3.2 Model Merging Methods

  • Model merging applies parameter-wise operations to shared-architecture models, commonly combining task vectors with a base model; α scales all task vectors.The paper presents parameter averaging as an intuitive baseline.Source: §3.2 · p. 3
  • TIES-Merging sparsifies task vectors by retaining high-magnitude parameters, then resolves the sparse vectors by sign voting before merging.It is presented as a response to neural networks’ overparameterized nature.Source: §3.2 · p. 3
  • Model interpolation blends Thinking and Instruct weights directly and is base-model agnostic, making it a special case of Task Arithmetic.The Task Arithmetic formulation equivalently combines their task vectors with scaling factors λ and (1 − λ).Source: §3.2 · pp. 3–4

4 Revisiting Model Interpolation

Experiments on Qwen3 models trace interpolation’s performance and reasoning behavior across three stages, then compare it with model-merging baselines. A selected interpolation achieves strong benchmark performance, efficiency, and control over reasoning prevalence.

4.1 Experimental Setup

  • Experiments merge official Qwen3-4B and Qwen3-30B-A3B Instruct-2507 and Thinking-2507 variants, evaluating instruction following, scientific reasoning, and mathematical reasoning.The evaluation uses IFEval, GPQA-Diamond, and AIME’25, with official baseline sampling configurations and Thinking-model decoding settings for merged models.Source: §4.1 · p. 4

4.2 Three-Stage Paradigm

  • The three-stage dynamics recur across Qwen3-4B and Qwen3-30B-A3B, but Qwen3-30B-A3B’s Stage #2 occurs later, at λ ∈ [0.5, 0.8].The authors also report consistent conclusions across stages for Llama-3.1-8B.Source: §4.2 · pp. 4–5, Figure 3 · p. 5
  • For Qwen3-4B, Stage #1 (λ ∈ [0, 0.4)) lengthens outputs without explicit thinking; IFEval Token #N rises from 1174 to 6492, while IFEval performance drops.Think #R remains near zero, and Mean@k and Vote@k rise more gently on AIME’25 and GPQA-Diamond.Source: §4.2 · p. 4
  • For Qwen3-4B, Stage #2 (λ ∈ [0.4, 0.6]) brings rapid emergence of explicit long-CoT reasoning; AIME’25 Mean@64 rises from 55.8 to 71.0, while Pass@64 is unchanged.Source: §4.2 · pp. 4–5
  • In Stage #3 (λ ∈ (0.6, 1.0]), token counts keep increasing as performance gains diminish; Pass@k may plateau or decline, although MI can outperform pure Thinking at λ = 0.8.The authors describe this as diminishing returns and evidence of overthinking.Source: §4.2 · p. 5

4.3 Compared with More Baselines

  • 80.5 Mean@64 on AIME’25 for MI-0.8 is 10.9 above best baseline TA-Base; on IFEval, MI-0.8 uses 1556 tokens versus TA-Base’s 2810.The comparison covers Qwen3-4B-Instruct-2507 and Qwen3-4B-Thinking-2507; the authors report MI’s superiority across performance, efficiency, and controllability.Source: Table 2 · p. 6, §4.3 · p. 6
  • The baseline comparison includes Task Arithmetic, TIES-Merging, DARE, and SLERP, using either the pretrained model or hybrid reasoning model as the task-vector base.For TA and TIES, using the hybrid Qwen3-4B base performs worse than using Qwen3-4B-Base.Source: §4.3 · p. 6
  • Think #R rises smoothly from 0% to 99.9% as λ moves from 0.2 to 0.8, providing control over reasoning prevalence.The authors characterize this as a reliable and interpretable way to craft models with a desired reasoning verbosity.Source: §4.3 · p. 6

5 Extensive Analysis

The analyses find that interpolation results are robust to decoding changes, depend on where and which Transformer modules are interpolated, and vary by backbone. A case study reports a trade-off between accuracy and token efficiency for a strategically interpolated model.

5.1 Decoding Strategy

  • On IFEval, MI-0.4 Mean@8 varies by only 1.6 points, from 69.7 to 71.3, across the tested temperature and Top-p grid.The paper reports that the Thinking model’s decoding setting is a good choice despite the possibility of searching for slightly better results.Source: §5.1 · pp. 6–7, Figure 4 · p. 7

5.2 Ablation on Layers

  • Interpolating only the last two-thirds of layers achieves Think #R of 100% and relatively strong performance approaching full interpolation, whereas any third alone fails to induce thinking behavior.The study uses a 36-layer Qwen3-4B model and varies the positions of 12- and 24-layer subsets.Source: §5.2 · p. 7, Table 3 · p. 7

5.3 Ablation on Transformer Modules

  • Skipping FFN sub-layers reduces Think Ratio from 99.95% to 0.68%; skipping MHA leaves Think Ratio at 99.90% but lowers Mean@64 from 80.47 to 71.46.The authors characterize FFNs as drivers of long-CoT patterns and MHA as important for reasoning quality and correctness.Source: §5.3 · pp. 7–8, Figure 5 · p. 8

5.4 Interpolation with More Backbones

  • On AIME’25, the Qwen3-4B-Base backbone’s Mean@64 drops from 80.5 to 67.7 despite Pass@64 of 93.3, while IFEval decreases from 87.0 to 85.0.The Qwen3-4B backbone often performs on par or slightly better than the original Instruct model on general-purpose benchmarks; the Base backbone fails on AIME’25.Source: Table 4 · p. 8, §5.4 · p. 8

5.5 Case Study

  • A case study reports that a strategically interpolated model achieves a good trade-off between accuracy and token efficiency.The detailed examples and analysis are in Appendix D.Source: §5.5 · p. 8

6 Conclusion

The conclusion presents model interpolation as a simple approach to merging Instruct and Thinking models for efficient reasoning. It highlights a three-stage paradigm as guidance for navigating performance and cost, alongside reported benchmark advantages and ablation insights.

6 Conclusion

  • The paper reports that a strategically interpolated model can consistently surpass more sophisticated merging baselines.The conclusion frames this result as based on the three-stage paradigm.Source: §6 · p. 8
  • The discovered three-stage evolutionary paradigm provides a principled guide for navigating the performance-cost trade-off.The authors describe this as demystifying the interpolation process.Source: §6 · p. 8
  • Ablations on model layers and modules provide mechanistic insights into interpolation.The conclusion presents these analyses alongside the benchmark comparison and three-stage finding.Source: §6 · p. 8

Limitation

The paper identifies two boundaries of its findings: empirical validation centered on Qwen3 models and interpolation limited to two specialists. It points to testing other model families and interpolating three or more specialists as future work.

Limitation

  • The authors say the three-stage findings are consistent across Qwen3 models of various sizes, while acknowledging these scope limits.The stated limitations concern model-family coverage and the number of interpolated specialists.Source: Limitation · p. 9
  • Empirical validation is centered on Qwen3 models, so the three-stage dynamic remains to be verified across diverse families such as Llama or Mistral.The authors state that such verification would strengthen the findings.Source: Limitation · p. 9
  • The work is confined to interpolating two models: the Instruct and Thinking specialists.Simultaneous interpolation of three or more specialist models is proposed as a future direction.Source: Limitation · p. 9

A Details of Benchmarks

The benchmark appendix describes three evaluations spanning mathematics, instruction following, and scientific reasoning. Each passage specifies the task and reported evaluation setting.

A Details of Benchmarks

  • AIME’25 evaluates challenging mathematics problem-solving and reports accuracy in a 0-shot setting.The problems come from the 2025 American Invitational Mathematics Examination.Source: A Details of Benchmarks · p. 11
  • IFEval evaluates instruction following across 25 types of verifiable instructions and reports prompt_level_strict accuracy in a 0-shot setting.The benchmark contains around 500 prompts, each with one or more verifiable instructions.Source: A Details of Benchmarks · p. 11
  • GPQA-Diamond evaluates scientific reasoning on 198 selected expert-written biology, physics, and chemistry questions, reporting accuracy in a 0-shot setting.The questions require step-by-step reasoning to arrive at the correct answer.Source: A Details of Benchmarks · p. 11

B Results on Qwen3-30B-A3B

On Qwen3-30B-A3B, model interpolation retains a three-stage trajectory, with Stage #2 occurring at λ ∈[0.5, 0.8]. MI-0.8 through MI-0.95 outperform the listed merging baselines across three benchmarks, with strong efficiency and controllable reasoning progression.

B Results on Qwen3-30B-A3B

  • For Qwen3-30B-A3B, Stage #2 occurs later, at λ ∈[0.5, 0.8], than for Qwen3-4B.The paper says the overall conclusions are consistent with Qwen3-4B, while stage ranges differ.Source: B Results on Qwen3-30B-A3B · p. 11
  • MI-0.8 through MI-0.95 outperform TA, TA-Base, TIES, and TIES-Base across all three benchmarks; MI-0.9 reaches 100.0 Pass@64 on AIME’25.The paper describes this as state-of-the-art performance; Table 5 compares the methods across three benchmarks.Source: B Results on Qwen3-30B-A3B · p. 11
  • On IFEval, MI-0.8 achieves Mean@8 of 87.01 with 1257 tokens, while TIES uses 1806 tokens for a lower score.Think #R progresses smoothly as λ increases, unlike the reported erratic behavior of TA and TIES.Source: B Results on Qwen3-30B-A3B · p. 11
  • Peak performance across benchmarks is found at λ ∈[0.8, 0.95] for the 30B-A3B model, versus around λ = 0.8 for the 4B model.The authors suggest larger models may require more influence from the Thinking model to unlock reasoning potential.Source: B Results on Qwen3-30B-A3B · p. 11
  • The authors conclude that model interpolation scales effectively and can create high-performance, efficient reasoning models at various scales.They characterize the method as a superior merging strategy for smaller models as well as effective at larger scale.Source: B Results on Qwen3-30B-A3B · p. 11

C Results on Llama-3.1-8B

Experiments interpolating Llama-3.1-8B-Instruct with DeepSeek-R1-Distill-Llama-8B reaffirm the three-stage paradigm. The reasoning-pattern transition and Mean@k gains occur in Stage #2, while optimal λ ranges and stability zones vary by architecture.

C Results on Llama-3.1-8B

  • The Llama-3.1-8B experiments reaffirm the three-stage evolutionary paradigm for model interpolation.The interpolation pairs Llama-3.1-8B-Instruct with DeepSeek-R1-Distill-Llama-8B as the Thinking specialist.Source: C Results on Llama-3.1-8B · p. 11
  • The Think #R reasoning-pattern transition and Mean@k performance improvements both appear in Stage #2, at λ ∈[0.4, 0.8].Source: C Results on Llama-3.1-8B · p. 11
  • The results support MI's effectiveness while indicating that optimal λ ranges and stability zones may vary across model architectures.Source: C Results on Llama-3.1-8B · p. 11

D Case Study

The case-study examples associate larger λ with more explicit thinking and better performance. Figures 6 and 7 describe a three-stage trajectory while noting that λ divisions differ.

D Case Study

  • The case-study discussion reports more explicit thinking with </think> and better performance at relatively larger λ.It points to examples from IFEval and GPQA-Diamond.Source: D Case Study · p. 11
  • Figures 6 and 7 depict a three-stage interpolation trajectory, with different λ division ranges across the model pairs.Figure 6 covers Qwen3-30B-A3B-Instruct-2507 and Thinking-2507; Figure 7 covers Llama-3.1-8B-Instruct and DeepSeek-R1-Distill-Llama-8B.Source: Figure 6 · p. 12, Figure 7 · p. 12
  • For the IFEval example, MI-0.8 includes </think>, whereas MI-0.4 does not.The caption identifies this as one case from the benchmark.Source: Table 6 · p. 14
  • For the GPQA-Diamond example, MI-0.2 fails while all other shown models solve the case; its opening style resembles the Instruct model.Source: Table 7 · p. 15
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