arxiv: 2605.07137 · v1 · submitted 2026-05-08 · 💻 cs.LG · cs.AI

Recognition: no theorem link

Adaptive Negative Reinforcement for LLM Reasoning:Dynamically Balancing Correction and Diversity in RLVR

Ankit Yadav, Jaival Chauhan, Sudhakar Mishra, Yash Ingle

Authors on Pith no claims yet

Pith reviewed 2026-05-11 01:39 UTC · model grok-4.3

classification 💻 cs.LG cs.AI

keywords LLM reasoningnegative sample reinforcementadaptive RLconfidence weightingRLVRoverfitting defensetoken-level updatesmath reasoning

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The pith

Adaptive negative reinforcement with time-dependent scheduling and confidence-weighted penalties improves LLM reasoning by balancing early error correction and later exploration.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes two extensions to negative sample reinforcement for training LLMs on reasoning tasks. Adaptive Negative Sample Reinforcement uses time-dependent scheduling functions that apply strong corrections early in training and shift to subtler updates later. Confidence-Weighted Negative Reinforcement assigns larger penalties to wrong answers the model is highly confident about and lighter penalties to uncertain errors. These mechanisms are shown through formal analysis to control token-level probability updates in a way that redistributes prior-guided probabilities while defending against overfitting. A reader would care because fixed-penalty NSR methods limit performance gains compared to complex alternatives like PPO.

Core claim

By introducing time-dependent scheduling in A-NSR and confidence-weighted penalties in CW-NSR, the method governs token-level updates through prior-guided probability redistribution, providing a natural defense against overfitting while improving reasoning performance on datasets like MATH and AIME.

What carries the argument

Adaptive Negative Sample Reinforcement (A-NSR) with time-dependent scheduling functions that transition from heavy error correction to controlled updates, combined with Confidence-Weighted Negative Reinforcement (CW-NSR) that sets penalty strength according to normalized sequence likelihood of incorrect responses.

If this is right

Models apply heavier penalties to correct errors in early training phases and lighter updates later to maintain diversity.
Confident mistakes receive stronger penalties while uncertain errors are penalized less to encourage exploration.
Token-level updates follow prior-guided probability redistribution that defends against overfitting.
The approach matches or exceeds PPO and GRPO performance across the full Pass@k spectrum on reasoning benchmarks.
Evaluations on MATH, AIME 2025, and AMC23 show gains using the Qwen2.5-Math-1.5B model.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The scheduling and weighting rules could reduce reliance on more complex RL algorithms like PPO if they prove robust across model scales.
Similar adaptive mechanisms might apply to non-reasoning RL tasks where distinguishing confident errors from exploratory ones matters.
Testing the same schedules on larger models or non-math reasoning domains would reveal whether the benefits require dataset-specific retuning.

Load-bearing premise

Normalized sequence likelihood is a reliable proxy for the importance of different mistakes and the chosen time-dependent scheduling functions stabilize training without introducing new instabilities.

What would settle it

Training the same Qwen2.5-Math-1.5B model on the MATH dataset with fixed NSR versus the proposed A-NSR and CW-NSR and checking whether Pass@k scores fail to improve or training becomes unstable would falsify the central claim.

Figures

Figures reproduced from arXiv: 2605.07137 by Ankit Yadav, Jaival Chauhan, Sudhakar Mishra, Yash Ingle.

**Figure 1.** Figure 1: Pass@k curves for Qwen2.5-Math-1.5B across methods. Our methods (A-NSR, CWNSR) are shown in warm colors. A-NSR gives strong improvements at low k. Across two datasets (AIME25 and AMC23), A-NSR (blue curve) performs best in the low-k range (k ≤ 32) for AIME25 dataset. On AMC23 (figure 1c), it is consitently greater than W-REINFORCE AND reaches to 82.5% at Pass@256. These results show that adapting the rein… view at source ↗

read the original abstract

Reinforcement learning with verifiable rewards (RLVR) has become a highly effective method for improving the reasoning abilities of Large Language Models (LLMs). Recent research shows that Negative Sample Reinforcement (NSR) -- which focuses on penalizing incorrect steps rather than simply rewarding correct ones -- can match or even exceed the performance of more complex frameworks like PPO and GRPO across the entire Pass@k spectrum. However, current NSR techniques usually apply a fixed penalty throughout the training process and treat every incorrect response with the same weight. To address these limitations, we propose two extensions to the NSR framework: Adaptive Negative Sample Reinforcement. Rather than using a fixed update rule, A-NSR uses time-dependent scheduling functions. In the initial training phases, the system focuses heavily on correcting errors to stabilize the model. As training continues, it shifts toward more subtle and controlled updates. We also introduce Confidence-Weighted Negative Reinforcement, which operates on the principle that different mistakes carry different levels of importance. CW-NSR assigns specific penalty weights based on the model's normalized sequence likelihood. If the model is highly confident in a wrong path, it receives a larger penalty and for uncertain errors -- where the model is effectively exploring -- are penalized less strictly. Our formal analysis shows how these mechanisms govern token-level updates, allowing the model to leverage prior-guided probability redistribution while providing a natural defense against overfitting. We evaluated these methods on difficult reasoning datasets, including MATH, AIME 2025, and AMC23, using the Qwen2.5-Math-1.5B architecture.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper adds two specific adaptive tweaks to negative sample reinforcement but the weighting assumption and missing details make the gains hard to judge from the abstract alone.

read the letter

The paper takes existing negative sample reinforcement for LLM reasoning and adds two concrete extensions. Adaptive NSR applies time-dependent scheduling that starts with heavy error correction and shifts to lighter updates later in training. Confidence-weighted NSR scales the penalty by the model's normalized sequence likelihood on wrong answers, hitting confident mistakes harder than uncertain ones. The authors claim this setup comes with a formal analysis of token-level updates and some built-in overfitting protection, and they test it on MATH, AIME 2025, and AMC23 using Qwen2.5-Math-1.5B. These are legitimate incremental moves beyond fixed-penalty NSR, and the scheduling and weighting ideas are specific enough to try out in practice. The evaluation benchmarks are standard for the area, which helps ground the claims. The work is aimed squarely at people already running RLVR loops on math reasoning tasks and looking for small stability tweaks rather than a new paradigm. A reader in that niche could pick up usable scheduling patterns or weighting logic if the full results hold. The soft spots are real but not fatal. Normalized sequence likelihood is a single scalar per response, so it is not obvious that it isolates the importance of particular mistakes instead of just rescaling the whole negative gradient. The scheduling functions are described only at a high level, with no indication whether their parameters are derived from first principles or fitted per dataset. The formal analysis is asserted but not shown in the abstract, which leaves the token-level redistribution claims unverified for now. Without the actual equations, ablation tables, and training curves it is difficult to tell whether the reported improvements come from the proposed mechanisms or from extra hyperparameter freedom. This paper deserves a serious referee. The ideas are clear, the problem is well-motivated, and the experimental setup is appropriate even if the evidence needs closer checking. I would send it to peer review rather than desk reject it.

Referee Report

2 major / 2 minor

Summary. The paper proposes two extensions to Negative Sample Reinforcement (NSR) within RLVR for LLMs: Adaptive NSR (A-NSR), which replaces fixed penalties with time-dependent scheduling functions that emphasize heavy correction early and subtler updates later, and Confidence-Weighted NSR (CW-NSR), which scales penalties for incorrect responses according to the model's normalized sequence likelihood. It asserts a formal analysis demonstrating that these mechanisms govern token-level updates to enable prior-guided probability redistribution and provide a defense against overfitting, with empirical support from evaluations on MATH, AIME 2025, and AMC23 using Qwen2.5-Math-1.5B.

Significance. If the formal analysis rigorously establishes the claimed token-level dynamics and the empirical results demonstrate stable gains across Pass@k without excessive hyperparameter sensitivity, the work would supply a simpler, more controllable alternative to PPO/GRPO for reasoning improvement, with explicit mechanisms for balancing correction and diversity.

major comments (2)

[Formal analysis / token-level updates] The formal analysis (asserted in the abstract and presumably detailed in the methods or theory section) claims that normalized sequence likelihood isolates the importance of different mistakes for token-level updates; however, as a global scalar it necessarily conflates path probability, length bias, and local errors, and the manuscript must provide an explicit derivation showing how this produces the claimed prior-guided redistribution rather than a uniform rescaling of the negative gradient.
[A-NSR description and analysis] A-NSR relies on time-dependent scheduling functions described only qualitatively (heavy correction early, subtle later); the analysis must specify the exact functional forms, derive the stability conditions they satisfy, and demonstrate that they avoid introducing oscillations or requiring per-dataset retuning, as these are load-bearing for the central claim of dynamic balancing without new instabilities.

minor comments (2)

[Experiments] The evaluation section should include ablations isolating the contribution of the scheduling parameters and confidence weighting scale, as these are listed as free parameters and could otherwise explain performance differences.
[Results] Add explicit comparison tables reporting Pass@k metrics against PPO, GRPO, and standard NSR baselines, with statistical significance or variance across runs.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments on our manuscript. We address the major comments point by point below and will make the necessary revisions to strengthen the formal analysis and provide explicit details on the proposed methods.

read point-by-point responses

Referee: [Formal analysis / token-level updates] The formal analysis (asserted in the abstract and presumably detailed in the methods or theory section) claims that normalized sequence likelihood isolates the importance of different mistakes for token-level updates; however, as a global scalar it necessarily conflates path probability, length bias, and local errors, and the manuscript must provide an explicit derivation showing how this produces the claimed prior-guided redistribution rather than a uniform rescaling of the negative gradient.

Authors: We agree that an explicit derivation is necessary to fully substantiate the claims regarding token-level dynamics. The manuscript asserts that the formal analysis demonstrates these properties, but we acknowledge the need for greater clarity. In the revised version, we will include a detailed derivation in the theory section that shows how the normalized sequence likelihood, when used as a weighting factor in the loss, leads to prior-guided probability redistribution at the token level. This will explicitly address the distinction from uniform rescaling by breaking down the gradient computation and showing the role of sequence-specific probabilities. revision: yes
Referee: [A-NSR description and analysis] A-NSR relies on time-dependent scheduling functions described only qualitatively (heavy correction early, subtle later); the analysis must specify the exact functional forms, derive the stability conditions they satisfy, and demonstrate that they avoid introducing oscillations or requiring per-dataset retuning, as these are load-bearing for the central claim of dynamic balancing without new instabilities.

Authors: We concur that the current description of A-NSR is primarily qualitative and requires more rigorous specification. The revised manuscript will explicitly define the functional forms of the time-dependent scheduling functions. Additionally, we will derive the stability conditions and provide analysis demonstrating the absence of oscillations and the lack of need for per-dataset retuning. This will be incorporated into the methods section to support the claims of dynamic balancing. revision: yes

Circularity Check

0 steps flagged

No circularity: mechanisms proposed as extensions without reduction to inputs by construction

full rationale

The paper introduces A-NSR via time-dependent scheduling functions and CW-NSR via normalized sequence likelihood weighting, then asserts that a formal analysis demonstrates governance of token-level updates and defense against overfitting. No equations, derivations, or self-citations are exhibited that reduce the claimed predictions or analyses to fitted parameters, self-definitions, or prior author results by construction. The scheduling functions and likelihood proxy are presented as design choices whose parameters and effects are described qualitatively rather than shown to be tautological with the performance claims. The derivation chain therefore remains self-contained as a proposal of new RLVR extensions evaluated on standard benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claims rest on two unstated assumptions about how model likelihood maps to mistake importance and how time-dependent functions should be chosen; no free parameters are explicitly listed but the scheduling and weighting rules imply tunable components.

free parameters (2)

time-dependent scheduling function parameters
The abstract states that A-NSR uses time-dependent scheduling functions whose exact form and any scaling constants are not specified.
confidence weighting scale
CW-NSR assigns penalty weights based on normalized sequence likelihood, but the mapping from likelihood to penalty multiplier is not given.

axioms (1)

domain assumption Normalized sequence likelihood serves as a valid measure of model confidence that should determine penalty magnitude.
Invoked to justify larger penalties for high-confidence errors.

pith-pipeline@v0.9.0 · 5593 in / 1393 out tokens · 40937 ms · 2026-05-11T01:39:56.979890+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

34 extracted references · 34 canonical work pages · 19 internal anchors

[1]

Curriculum learning

Yoshua Bengio, J \'e r \^o me Louradour, Ronan Collobert, and Jason Weston. Curriculum learning. In ICML, pages 41--48, 2009

work page 2009
[2]

Large Language Monkeys: Scaling Inference Compute with Repeated Sampling

Bradley Brown, Jordan Juravsky, Ryan Ehrlich, Ronald Clark, Quoc V Le, Christopher R \'e , and Azalia Mirhoseini. Large language monkeys: Scaling inference compute with repeated sampling. arXiv preprint arXiv:2407.21787, 2024

work page internal anchor Pith review arXiv 2024
[3]

Evaluating Large Language Models Trained on Code

Mark Chen, Jerry Tworek, Heewoo Jun, Qiming Yuan, Henrique Pond \'e de Oliveira Pinto, Jared Kaplan, et al. Evaluating large language models trained on code. arXiv preprint arXiv:2107.03374, 2021

work page internal anchor Pith review Pith/arXiv arXiv 2021
[4]

Training Verifiers to Solve Math Word Problems

Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Mark Chen, Heewoo Jun, Lukasz Kaiser, et al. Training verifiers to solve math word problems. arXiv preprint arXiv:2110.14168, 2021

work page internal anchor Pith review Pith/arXiv arXiv 2021
[5]

The Llama 3 Herd of Models

Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, et al. The Llama 3 herd of models. arXiv preprint arXiv:2407.21783, 2024

work page internal anchor Pith review Pith/arXiv arXiv 2024
[6]

DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning

Daya Guo, Dejian Yang, Haowei Zhang, Junxiao Song, et al. DeepSeek-R1 : Incentivizing reasoning capability in LLMs via reinforcement learning. arXiv preprint arXiv:2501.12948, 2025

work page internal anchor Pith review Pith/arXiv arXiv 2025
[7]

Measuring mathematical problem solving with the MATH dataset

Dan Hendrycks, Collin Burns, Saurav Kadavath, Akul Arora, Steven Basart, Eric Tang, Dawn Song, and Jacob Steinhardt. Measuring mathematical problem solving with the MATH dataset. In NeurIPS Datasets and Benchmarks, 2021

work page 2021
[8]

SWE -bench: Can language models resolve real-world GitHub issues? In ICLR, 2024

Carlos E Jimenez, John Yang, Alexander Wettig, Shunyu Yao, Kexin Pei, Ofir Press, and Karthik R Narasimhan. SWE -bench: Can language models resolve real-world GitHub issues? In ICLR, 2024

work page 2024
[9]

Language Models (Mostly) Know What They Know

Saurav Kadavath, Tom Conerly, Amanda Askell, et al. Language models (mostly) know what they know. arXiv preprint arXiv:2207.05221, 2022

work page internal anchor Pith review Pith/arXiv arXiv 2022
[10]

Kimi k1.5: Scaling Reinforcement Learning with LLMs

Kimi Team, Angang Du, Bofei Gao, et al. Kimi K1.5 : Scaling reinforcement learning with LLMs . arXiv preprint arXiv:2501.12599, 2025

work page internal anchor Pith review Pith/arXiv arXiv 2025
[11]

Self-paced learning for latent variable models

M Pawan Kumar, Benjamin Packer, and Daphne Koller. Self-paced learning for latent variable models. In NeurIPS, pages 1189--1197, 2010

work page 2010
[12]

Tulu 3: Pushing Frontiers in Open Language Model Post-Training

Nathan Lambert, Jacob Morrison, Valentina Pyatkin, et al. T\"ULU 3: Pushing frontiers in open language model post-training. arXiv preprint arXiv:2411.15124, 2024

work page internal anchor Pith review arXiv 2024
[13]

Don't say that! Making inconsistent dialogue unlikely with unlikelihood training

Margaret Li, Stephen Roller, Ilia Kulikov, Sean Welleck, Y-Lan Boureau, Kyunghyun Cho, and Jason Weston. Don't say that! Making inconsistent dialogue unlikely with unlikelihood training. In ACL, pages 4715--4728, 2020

work page 2020
[14]

Let's verify step by step

Hunter Lightman, Vineet Kosaraju, Yuri Burda, et al. Let's verify step by step. In ICLR, 2024

work page 2024
[15]

Focal loss for dense object detection

Tsung-Yi Lin, Priya Goyal, Ross Girshick, Kaiming He, and Piotr Doll \'a r. Focal loss for dense object detection. In ICCV, pages 2980--2988, 2017

work page 2017
[16]

Understanding R1-Zero-Like Training: A Critical Perspective

Zichen Liu, Changyu Chen, Wenjun Li, et al. Understanding R1 -zero-like training: A critical perspective. arXiv preprint arXiv:2503.20783, 2025

work page internal anchor Pith review arXiv 2025
[17]

s1: Simple test-time scaling

Niklas Muennighoff, Zitong Yang, Weijia Shi, et al. s1: Simple test-time scaling. arXiv preprint arXiv:2501.19393, 2025

work page Pith review arXiv 2025
[18]

GPQA : A graduate-level google-proof Q&A benchmark

David Rein, Betty Li Hou, Asa Cooper Stickland, et al. GPQA : A graduate-level google-proof Q&A benchmark. In First Conference on Language Modeling, 2024

work page 2024
[19]

Proximal Policy Optimization Algorithms

John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. Proximal policy optimization algorithms. arXiv preprint arXiv:1707.06347, 2017

work page internal anchor Pith review Pith/arXiv arXiv 2017
[20]

DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models

Zhihong Shao, Peiyi Wang, Qihao Zhu, et al. DeepSeekMath : Pushing the limits of mathematical reasoning in open language models. arXiv preprint arXiv:2402.03300, 2024

work page internal anchor Pith review Pith/arXiv arXiv 2024
[21]

HybridFlow: A Flexible and Efficient RLHF Framework

Guangming Sheng, Chi Zhang, Zilingfeng Ye, et al. HybridFlow : A flexible and efficient RLHF framework. arXiv preprint arXiv:2409.19256, 2024

work page internal anchor Pith review arXiv 2024
[22]

Training region-based object detectors with online hard example mining

Abhinav Shrivastava, Abhinav Gupta, and Ross Girshick. Training region-based object detectors with online hard example mining. In CVPR, pages 761--769, 2016

work page 2016
[23]

Defining and characterizing reward gaming

Joar Skalse, Nikolaus Howe, Dmitrii Krasheninnikov, and David Krueger. Defining and characterizing reward gaming. In NeurIPS, volume 35, pages 9460--9471, 2022

work page 2022
[24]

Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters

Charlie Snell, Jaehoon Lee, Kelvin Xu, and Aviral Kumar. Scaling LLM test-time compute optimally can be more effective than scaling model parameters. arXiv preprint arXiv:2408.03314, 2024

work page internal anchor Pith review Pith/arXiv arXiv 2024
[25]

Math-Shepherd : Verify and reinforce LLMs step-by-step without human annotations

Peiyi Wang, Lei Li, Zhihong Shao, et al. Math-Shepherd : Verify and reinforce LLMs step-by-step without human annotations. In ACL, pages 9426--9439, 2024

work page 2024
[26]

Neural text generation with unlikelihood training

Sean Welleck, Ilia Kulikov, Stephen Roller, Emily Dinan, Kyunghyun Cho, and Jason Weston. Neural text generation with unlikelihood training. In ICLR, 2020

work page 2020
[27]

Simple statistical gradient-following algorithms for connectionist reinforcement learning

Ronald J Williams. Simple statistical gradient-following algorithms for connectionist reinforcement learning. Machine Learning, 8:229--256, 1992

work page 1992
[28]

Qwen3 Technical Report

An Yang, Anfeng Li, Baosong Yang, et al. Qwen3 technical report. arXiv preprint arXiv:2505.09388, 2025

work page internal anchor Pith review Pith/arXiv arXiv 2025
[29]

Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement

An Yang, Beichen Zhang, Binyuan Hui, et al. Qwen2.5-Math technical report: Toward mathematical expert model via self-improvement. arXiv preprint arXiv:2409.12122, 2024

work page internal anchor Pith review arXiv 2024
[30]

DAPO: An Open-Source LLM Reinforcement Learning System at Scale

Qiying Yu, Zheng Zhang, Ruofei Zhu, et al. DAPO : An open-source LLM reinforcement learning system at scale. arXiv preprint arXiv:2503.14476, 2025

work page internal anchor Pith review Pith/arXiv arXiv 2025
[31]

VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks

Yufeng Yuan, Qiying Yu, Xiaochen Zuo, et al. VAPO : Efficient and reliable reinforcement learning for advanced reasoning tasks. arXiv preprint arXiv:2504.05118, 2025

work page internal anchor Pith review arXiv 2025
[32]

Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?

Yang Yue, Zhiqi Chen, Rui Lu, et al. Does reinforcement learning really incentivize reasoning capacity in LLMs beyond the base model? arXiv preprint arXiv:2504.13837, 2025

work page internal anchor Pith review Pith/arXiv arXiv 2025
[33]

SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild

Weihao Zeng, Yuzhen Huang, Qian Liu, et al. SimpleRL-Zoo : Investigating and taming zero reinforcement learning for open base models in the wild. arXiv preprint arXiv:2503.18892, 2025

work page internal anchor Pith review arXiv 2025
[34]

The surprising effectiveness of negative reinforcement in LLM reasoning

Xinyu Zhu, Mengzhou Xia, Zhepei Wei, Wei-Lin Chen, Danqi Chen, and Yu Meng. The surprising effectiveness of negative reinforcement in LLM reasoning. In NeurIPS, 2025

work page 2025