# DynScaling: Efficient Verifier-free Inference Scaling via Dynamic and Integrated Sampling

arXiv: https://arxiv.org/abs/2506.16043 · HTML: https://mlsanity.com/paper/2506.16043/

## Key facts

- Cited by 7 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 25 of its 32 references that are in the map.
- First posted on arXiv 19 Jun 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, 25 of 25)

- [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)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Alphazero-like Tree-Search can Guide Large Language Model Decoding and Training](https://mlsanity.com/paper/2309.17179/) (2023)
- [Making Large Language Models Better Reasoners with Step-Aware Verifier](https://mlsanity.com/paper/2206.02336/) (2022)
- [Scalable Best-of-N Selection for Large Language Models via Self-Certainty](https://mlsanity.com/paper/2502.18581/) (2025)
- [Beyond Chinchilla-Optimal: Accounting for Inference in Language Model Scaling Laws](https://mlsanity.com/paper/2401.00448/) (2023)
- [From Decoding to Meta-Generation: Inference-time Algorithms for Large Language Models](https://mlsanity.com/paper/2406.16838/) (2024)
- [Can 1B LLM Surpass 405B LLM? Rethinking Compute-Optimal Test-Time Scaling](https://mlsanity.com/paper/2502.06703/) (2025)
- [Theoretical guarantees on the best-of-n alignment policy](https://mlsanity.com/paper/2401.01879/) (2024)
- [Let's Sample Step by Step: Adaptive-Consistency for Efficient Reasoning and Coding with LLMs](https://mlsanity.com/paper/2305.11860/) (2023)
- [Learning How Hard to Think: Input-Adaptive Allocation of LM Computation](https://mlsanity.com/paper/2410.04707/) (2024)
- [Adaptive Inference-Time Compute: LLMs Can Predict if They Can Do Better, Even Mid-Generation](https://mlsanity.com/paper/2410.02725/) (2024)
- [SETS: Leveraging Self-Verification and Self-Correction for Improved Test-Time Scaling](https://mlsanity.com/paper/2501.19306/) (2025)
- [Think Smarter not Harder: Adaptive Reasoning with Inference Aware Optimization](https://mlsanity.com/paper/2501.17974/) (2025)
- [Rethinking Inference-Time Scaling: Efficiency Limits and Linguistic Signals](https://mlsanity.com/paper/2504.14047/) (2025)
- [Scaling LLM Inference with Optimized Sample Compute Allocation](https://mlsanity.com/paper/2410.22480/) (2024)
- [MetaScale: Test-Time Scaling with Evolving Meta-Thoughts](https://mlsanity.com/paper/2503.13447/) (2025)
- [When Hindsight is Not 20/20: Testing Limits on Reflective Thinking in Large Language Models](https://mlsanity.com/paper/2404.09129/) (2024)
- [DISC: Dynamic Decomposition Improves LLM Inference Scaling](https://mlsanity.com/paper/2502.16706/) (2025)

## Built on by (most cited first, 7 of 7)

- [Recursive Self-Aggregation Unlocks Deep Thinking in Large Language Models](https://mlsanity.com/paper/2509.26626/) (2025)
- [Best-of-∞ -- Asymptotic Performance of Test-Time LLM Ensembling](https://mlsanity.com/paper/2509.21091/) (2025)
- [Efficient Paths and Dense Rewards: Probabilistic Flow Reasoning for Large Language Models](https://mlsanity.com/paper/2601.09260/) (2026)
- [CITE: Anytime-Valid Statistical Inference in LLM Self-Consistency](https://mlsanity.com/paper/2605.05873/) (2026)
- [Improving reasoning at inference time via uncertainty minimisation](https://mlsanity.com/paper/2603.07159/) (2026)
- [PrimeScientist: Strategic Allocation of Research Effort in Autonomous Research](https://mlsanity.com/paper/2609.17846/) (2026)
- [Test-Time Scaling via Budgeted Multi-Attribute Verification](https://mlsanity.com/paper/2609.34322/) (2026)

## Abstract (arXiv)

Inference-time scaling has proven effective in boosting large language model (LLM) performance through increased test-time computation. Yet, its practical application is often hindered by reliance on external verifiers or a lack of optimization for realistic computational constraints. We propose DynScaling, which addresses these limitations through two primary innovations: an integrated parallel-sequential sampling strategy and a bandit-based dynamic budget allocation framework. The integrated sampling strategy unifies parallel and sequential sampling by constructing synthetic sequential reasoning chains from initially independent parallel responses, promoting diverse and coherent reasoning trajectories. The dynamic budget allocation framework formulates the allocation of computational resources as a multi-armed bandit problem, adaptively distributing the inference budget across queries based on the uncertainty of previously sampled responses, thereby maximizing computational efficiency. By combining these components, DynScaling effectively improves LLM performance under practical resource constraints without the need for external verifiers. Experimental results demonstrate that DynScaling consistently surpasses existing verifier-free inference scaling baselines in both task performance and computational cost.