# Intrinsic Selection and Particle Resampling for Inference-Time Scaling Beyond Domain Verifiability

arXiv: https://arxiv.org/abs/2606.08850 · HTML: https://mlsanity.com/paper/2606.08850/

## Key facts

- Cited by 1 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 41 of its 61 references that are in the map.
- First posted on arXiv 7 Jun 2026.

## 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, 30 of 41)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Contrastive Decoding: Open-ended Text Generation as Optimization](https://mlsanity.com/paper/2210.15097/) (2022)
- [Kimi K2: Open Agentic Intelligence](https://mlsanity.com/paper/2507.20534/) (2025)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [HealthBench: Evaluating Large Language Models Towards Improved Human Health](https://mlsanity.com/paper/2505.08775/) (2025)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [Agentic Context Engineering: Evolving Contexts for Self-Improving Language Models](https://mlsanity.com/paper/2510.04618/) (2025)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs](https://mlsanity.com/paper/2506.14245/) (2025)
- [Deep Think with Confidence](https://mlsanity.com/paper/2508.15260/) (2025)
- [Universal Self-Consistency for Large Language Model Generation](https://mlsanity.com/paper/2311.17311/) (2023)
- [Scalable Best-of-N Selection for Large Language Models via Self-Certainty](https://mlsanity.com/paper/2502.18581/) (2025)
- [Stay on topic with Classifier-Free Guidance](https://mlsanity.com/paper/2306.17806/) (2023)
- [Probabilistic Inference in Language Models via Twisted Sequential Monte Carlo](https://mlsanity.com/paper/2404.17546/) (2024)
- [Sequential Monte Carlo Steering of Large Language Models using Probabilistic Programs](https://mlsanity.com/paper/2306.03081/) (2023)
- [Contrastive Decoding Improves Reasoning in Large Language Models](https://mlsanity.com/paper/2309.09117/) (2023)

## Built on by (most cited first, 1 of 1)

- [Chopthin-Consensus Power Sampling: A Diversity-Preserving Approach to LLM Decoding](https://mlsanity.com/paper/2609.12243/) (2026)

## Abstract (arXiv)

Inference-Time Scaling (ITS) has largely succeeded in verifiable domains like math and coding, where cheap verification enables scalable output selection. However, extending ITS to tasks prone to systematic failure - driven by faulty initial assumptions or unmet multidimensional constraints - typically relies on costly external solvers or brittle, model-based verifiers. Our key insight is that the intrinsic statistics of parallel sample sets, specifically length-adjusted tail entropy, provide a robust discriminative signal for solution quality without access to ground truth. Crucially, these statistics serve as a difficulty gate for adaptive compute allocation, dynamically routing problems across scaling regimes. First, Intrinsic Selection (iS) ranks candidates post-hoc, matching consensus-based algorithms across three domains and improving engineering design selection by 20% over pass@1 baselines. Second, Intrinsic Particle Filtering (iPF) generalizes this to step-level resampling, guiding generation toward high-confidence reasoning trajectories to improve pass@1 by 6.1 points on average on hard math problems. Finally, Particle Distillation (dPF) injects privileged guidance via early logit blending and KL-guided resampling, steering generation past systematic reasoning errors to satisfy expert rubrics, yielding up to 26.5% gains on complex clinical responses. Our pipeline applies seamlessly across broad-purpose, domain-specialized, and multimodal architectures, successfully extending ITS to open-ended domains without requiring trained reward models or exact ground-truth verification.