# PACR: Progressively Ascending Confidence Reward for LLM Reasoning

arXiv: https://arxiv.org/abs/2510.22255 · HTML: https://mlsanity.com/paper/2510.22255/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 17 of its 44 references that are in the map.
- First posted on arXiv 25 Oct 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 17 of 17)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [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)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [Free Process Rewards without Process Labels](https://mlsanity.com/paper/2412.01981/) (2024)
- [Stop Summation: Min-Form Credit Assignment Is All Process Reward Model Needs for Reasoning](https://mlsanity.com/paper/2504.15275/) (2025)
- [ProgRM: Build Better GUI Agents with Progress Rewards](https://mlsanity.com/paper/2505.18121/) (2025)
- [Beyond the First Error: Process Reward Models for Reflective Mathematical Reasoning](https://mlsanity.com/paper/2505.14391/) (2025)

## Built on by (most cited first, 9 of 9)

- [Decomposed On-Policy Distillation for Vision-Language Reasoning: Steering Gradients for Visual Grounding](https://mlsanity.com/paper/2606.00564/) (2026)
- [TACO: Tool-Augmented Credit Optimization for Agentic Tool Use](https://mlsanity.com/paper/2606.30251/) (2026)
- [Know What You Know: Metacognitive Entropy Calibration for Verifiable RL Reasoning](https://mlsanity.com/paper/2602.22751/) (2026)
- [PDCR: Perception-Decomposed Confidence Reward for Vision-Language Reasoning](https://mlsanity.com/paper/2605.13467/) (2026)
- [Why Self-Rewarding Works: Theoretical Guarantees for Iterative Alignment of Language Models](https://mlsanity.com/paper/2601.22513/) (2026)
- [Know Thy Reasoner: Not All Language Models Explore Alike](https://mlsanity.com/paper/2604.10827/) (2026)
- [Momentum for Reasoning: Dense Intrinsic Signals in Policy Optimization](https://mlsanity.com/paper/2606.08815/) (2026)
- [QVal: Cheaply Evaluating Dense Supervision Signals for Long-Horizon LLM Agents](https://mlsanity.com/paper/2606.32034/) (2026)
- [When Should a VLM Look? Paying Only for Visual Calls That Were Needed and Used](https://mlsanity.com/paper/2609.22910/) (2026)

## Abstract (arXiv)

Reinforcement Learning with Verifiable Rewards (RLVR) has significantly improved LLM reasoning, but its sparse, outcome-based reward provides no guidance for intermediate steps, slowing exploration. We propose Progressively Ascending Confidence Reward (PACR), a dense, model-intrinsic reward computed directly from the model's evolving belief in the correct answer. PACR encodes the inductive bias that, along a well-formed reasoning trajectory, the probability of the ground-truth answer should have a generally ascending trend. We provide empirical and theoretical analysis validating that such an inductive bias constrains the exploration search space to regions richer in logically sound reasoning. We demonstrate that PACR accelerates exploration, reaches reward saturation with fewer trajectories, and yields improvements on multiple benchmarks. Our results suggest that dense, model-intrinsic shaping signals can make RLVR training more effective and reliable.