# Weight Ensembling Improves Reasoning in Language Models

arXiv: https://arxiv.org/abs/2504.10478 · HTML: https://mlsanity.com/paper/2504.10478/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 28 of its 35 references that are in the map.
- First posted on arXiv 14 Apr 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 28 of 28)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Robust fine-tuning of zero-shot models](https://mlsanity.com/paper/2109.01903/) (2021)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [Demystifying Long Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2502.03373/) (2025)
- [Diverse Beam Search: Decoding Diverse Solutions from Neural Sequence Models](https://mlsanity.com/paper/1610.02424/) (2016)
- [Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models](https://mlsanity.com/paper/2408.00724/) (2024)
- [Rewarding Progress: Scaling Automated Process Verifiers for LLM Reasoning](https://mlsanity.com/paper/2410.08146/) (2024)
- [Making Large Language Models Better Reasoners with Step-Aware Verifier](https://mlsanity.com/paper/2206.02336/) (2022)
- [Is Self-Repair a Silver Bullet for Code Generation?](https://mlsanity.com/paper/2306.09896/) (2023)
- [AlphaMath Almost Zero: Process Supervision without Process](https://mlsanity.com/paper/2405.03553/) (2024)
- [Turning Up the Heat: Min-p Sampling for Creative and Coherent LLM Outputs](https://mlsanity.com/paper/2407.01082/) (2024)
- [Jasper and Stella: distillation of SOTA embedding models](https://mlsanity.com/paper/2412.19048/) (2024)
- [Self-Improvement in Language Models: The Sharpening Mechanism](https://mlsanity.com/paper/2412.01951/) (2024)
- [Inference-Aware Fine-Tuning for Best-of-N Sampling in Large Language Models](https://mlsanity.com/paper/2412.15287/) (2024)
- [BOND: Aligning LLMs with Best-of-N Distillation](https://mlsanity.com/paper/2407.14622/) (2024)
- [Forcing Diffuse Distributions out of Language Models](https://mlsanity.com/paper/2404.10859/) (2024)
- [Generating High-Quality and Informative Conversation Responses with Sequence-to-Sequence Models](https://mlsanity.com/paper/1701.03185/) (2017)
- [Submodularity In Machine Learning and Artificial Intelligence](https://mlsanity.com/paper/2202.00132/) (2022)
- [Rethinking Fine-Tuning when Scaling Test-Time Compute: Limiting Confidence Improves Mathematical Reasoning](https://mlsanity.com/paper/2502.07154/) (2025)
- [Mind the Gap: Examining the Self-Improvement Capabilities of Large Language Models](https://mlsanity.com/paper/2412.02674/) (2024)

## Built on by (most cited first, 30 of 38)

- [The Surprising Effectiveness of Negative Reinforcement in LLM Reasoning](https://mlsanity.com/paper/2506.01347/) (2025)
- [Outcome-based Exploration for LLM Reasoning](https://mlsanity.com/paper/2509.06941/) (2025)
- [Rewarding the Unlikely: Lifting GRPO Beyond Distribution Sharpening](https://mlsanity.com/paper/2506.02355/) (2025)
- [RL Squeezes, SFT Expands: A Comparative Study of Reasoning LLMs](https://mlsanity.com/paper/2509.21128/) (2025)
- [KL-Regularized Reinforcement Learning is Designed to Mode Collapse](https://mlsanity.com/paper/2510.20817/) (2025)
- [Roll the dice & look before you leap: Going beyond the creative limits of next-token prediction](https://mlsanity.com/paper/2504.15266/) (2025)
- [Differential Smoothing Mitigates Sharpening and Improves LLM Reasoning](https://mlsanity.com/paper/2511.19942/) (2025)
- [Representation-Based Exploration for Language Models: From Test-Time to Post-Training](https://mlsanity.com/paper/2510.11686/) (2025)
- [The Debate on RLVR Reasoning Capability Boundary: Shrinkage, Expansion, or Both? A Two-Stage Dynamic View](https://mlsanity.com/paper/2510.04028/) (2025)
- [Replaying pre-training data improves fine-tuning](https://mlsanity.com/paper/2603.04964/) (2026)
- [Unveiling Over-Memorization in Finetuning LLMs for Reasoning Tasks](https://mlsanity.com/paper/2508.04117/) (2025)
- [F-GRPO: Don't Let Your Policy Learn the Obvious and Forget the Rare](https://mlsanity.com/paper/2602.06717/) (2026)
- [Reasoning Path Divergence: A New Metric and Curation Strategy to Unlock LLM Diverse Thinking](https://mlsanity.com/paper/2510.26122/) (2025)
- [Understanding and Steering the Cognitive Behaviors of Reasoning Models at Test-Time](https://mlsanity.com/paper/2512.24574/) (2025)
- [Revisiting Test-Time Scaling: A Survey and a Diversity-Aware Method for Efficient Reasoning](https://mlsanity.com/paper/2506.04611/) (2025)
- [Diversity-Enhanced Reasoning for Subjective Questions](https://mlsanity.com/paper/2507.20187/) (2025)
- [Distilled Pretraining: A modern lens of Data, In-Context Learning and Test-Time Scaling](https://mlsanity.com/paper/2509.01649/) (2025)
- [LaDi-RL: Latent Diffusion Reasoning Prevents Entropy Collapse in Reinforcement Learning](https://mlsanity.com/paper/2602.01705/) (2026)
- [Steer2Adapt: Dynamically Composing Steering Vectors Elicits Efficient Adaptation of LLMs](https://mlsanity.com/paper/2602.07276/) (2026)
- [How Does RL Post-training Induce Skill Composition? A Case Study on Countdown](https://mlsanity.com/paper/2512.01775/) (2025)
- [Do Instruction-Tuned Models Always Perform Better Than Base Models? Evidence from Math and Domain-Shifted Benchmarks](https://mlsanity.com/paper/2601.13244/) (2026)
- [Teacher-Free Self-Training Amplifies but Does Not Compound: A Pass@K Crossover on a Free-Verifier Domain](https://mlsanity.com/paper/2606.07856/) (2026)
- [When Inverse Data Outperforms: Exploring the Pitfalls of Mixed Data in Multi-Stage Fine-Tuning](https://mlsanity.com/paper/2509.13079/) (2025)
- [Exploring Diverse Generation Paths via Inference-time Stiefel Activation Steering](https://mlsanity.com/paper/2601.22010/) (2026)
- [On Advantage Estimates for Max@K Policy Gradients](https://mlsanity.com/paper/2606.06080/) (2026)
- [OrderGrad: Optimizing Beyond the Mean with Order-Statistic Policy Gradient Estimation](https://mlsanity.com/paper/2606.06096/) (2026)
- [Beyond the Best Guess: Improving LLM Solution Coverage with Evolution Strategies](https://mlsanity.com/paper/2608.12679/) (2026)
- [Rate or Fate? RLV^varepsilonR: Reinforcement Learning with Verifiable Noisy Rewards](https://mlsanity.com/paper/2601.04411/) (2026)
- [Computational Arbitrage in AI Model Markets](https://mlsanity.com/paper/2603.22404/) (2026)
- [Fork-Think with Confidence](https://mlsanity.com/paper/2606.31484/) (2026)

## Abstract (arXiv)

We investigate a failure mode that arises during the training of reasoning models, where the diversity of generations begins to collapse, leading to suboptimal test-time scaling. Notably, the Pass@1 rate reliably improves during supervised finetuning (SFT), but Pass@k rapidly deteriorates. Surprisingly, a simple intervention of interpolating the weights of the latest SFT checkpoint with an early checkpoint, otherwise known as WiSE-FT, almost completely recovers Pass@k while also improving Pass@1. The WiSE-FT variant achieves better test-time scaling (Best@k, majority vote) and achieves superior results with less data when tuned further by reinforcement learning. Finally, we find that WiSE-FT provides complementary performance gains that cannot be achieved only through diversity-inducing decoding strategies, like temperature scaling. We formalize a bias-variance tradeoff of Pass@k with respect to the expectation and variance of Pass@1 over the test distribution. We find that WiSE-FT can reduce bias and variance simultaneously, while temperature scaling inherently trades off between bias and variance.