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REVIEW 4 major objections 4 minor 60 references

This paper claims that a vision-language model can improve itself without ground-truth answers or external teachers by minimizing the divergence between its own predictions on corrupted and clean images.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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T0 review · deepseek-v4-flash

2026-08-03 01:45 UTC pith:YF74KT6Y

load-bearing objection A simple self-distillation recipe that seems to work—clean-image predictions as teacher for corrupted inputs—with real experimental support, but reproducibility gaps and the absence of any correctness signal keep it from being a clean accept. the 4 major comments →

arxiv 2607.23125 v2 pith:YF74KT6Y submitted 2026-07-25 cs.LG

Self-Boosting Vision-Language Models with Noisy Student On-Policy Self-Distillation

Shuai Wang , Daoan Zhang , Zhe Tang , Hao Cheng , Jiaheng Wei This is my paper
classification cs.LG
keywords vision-language modelsself-distillationnoisy studentself-improvementimage corruptionvisual reasoningpost-trainingon-policy learning
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper tries to establish that a vision-language model can improve its reasoning without any ground-truth answers, external teacher models, or verifiable rewards. The proposed method, NOPD, corrupts the input image (noise, downsampling, gamma changes), samples an answer from the model on the corrupted view, and trains the model to make that answer's token distribution match the distribution the same model produces on the clean image, with gradients blocked on the clean branch. Because the clean prediction is never checked against a correct answer, the method's success depends on the model's clean outputs being a trustworthy teacher. The authors report large gains: for example, training a 7-billion-parameter VLM on 2.1K geometry samples lifts its Geometry3K validation score by 20 points and MathVista by 7.4, with consistent gains across three models and twelve benchmarks. The paper notes the mechanism is specific to vision-language models because it requires corrupting images.

Core claim

The central claim is that the gap between a VLM's predictions on corrupted and clean inputs is a complete self-supervision signal. NOPD samples an on-policy answer from the model on a corrupted image, then minimizes the reverse KL divergence between the corrupted-input token distribution and the clean-input distribution, with stop-gradient on the clean branch. The resulting gradient is a contrastive policy gradient whose log-ratio term rewards tokens that differ between the two views. In the authors' experiments this single-model scheme matches or beats RLVR and teacher distillation on five visual-reasoning benchmarks and improves accuracy out of distribution.

What carries the argument

The load-bearing object is the asymmetric-input reverse-KL objective, Eq. (6): L = E_{q,x, y~πθ(·|q,T(x))} DKL(πθ(y|q,T(x)) ∥ πθ(y|q,x)), with a stop-gradient on the clean branch. The same network is both noisy student and clean teacher; the corruption operator T (Gaussian noise, downsampling, gamma) creates the asymmetry that makes the self-supervision non-trivial. The stop-gradient is essential: without it, the model could drive the loss to zero by producing identical outputs for any input, which the paper calls collapse.

Load-bearing premise

The load-bearing premise is that a model's own clean-image predictions are trustworthy enough to serve as a teacher: the clean branch is detached and never compared with a ground-truth answer, so if the model is confidently wrong on clean images, NOPD can amplify the error rather than fix it.

What would settle it

Train NOPD on a set where the base model's clean-image answers are known to be systematically wrong (e.g., a set with available labels where the model scores near chance), and check whether accuracy improves or degrades. Additionally, track the training loss against validation accuracy: if the consistency loss falls while accuracy falls, the model is being trained into stable, confident errors—falsifying the claim that clean predictions are a safe teacher.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Post-training a VLM can in principle be done with raw image-question pairs alone: no human labels, no external teacher, no verifiable rewards, and only one rollout per sample.
  • The method simultaneously shortens reasoning: on MathVista, output tokens dropped by roughly 58 percent while accuracy rose, suggesting the learning signal is compressing verbose reasoning rather than merely memorizing.
  • Gains transfer beyond the training distribution: training on a small geometry set improved scores on out-of-distribution benchmarks like MathVista and MMMU-Pro.
  • Scaling the training set (15.6K samples) continues to improve accuracy, so the reported gains are not an artifact of one small dataset.

Where Pith is reading between the lines

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

  • The consistency objective should be measurable as robustness: a model trained with NOPD should become less sensitive to the specific corruptions used (noise, resolution, gamma), and one could test this by evaluating on held-out corruption types; if robustness does not track accuracy, the mechanism is less about perception than about output regularization.
  • For a model whose clean outputs are already near-perfect, NOPD should produce little gain; the largest improvements should occur where the clean view is right and the corrupted view is wrong. One can test this by splitting training questions by base-model correctness and checking where the loss focuses.
  • The paper itself scopes the approach to VLMs, since the teacher-student asymmetry is created by corrupting images; extending the idea to text or audio would require finding a corruption that degrades the input without destroying the answer.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The manuscript proposes NOPD, a post-training method for vision-language models that uses no ground-truth answers, rewards, or external teachers. The training signal is a KL divergence between the model's distribution under a corrupted image T(x) (the 'student') and the same model's stop-gradient distribution under the clean image x (the 'teacher'), Eq. (6); responses are sampled on-policy from the corrupted branch. Experiments train on Geometry3K (2.1K pairs) and report gains on five reasoning benchmarks, with headline improvements of +20 on Geometry3K val and +7.4 on MathVista for Qwen2.5-VL-7B. Additional experiments on a larger mixed corpus report gains across 12 benchmarks for three VLM families, plus analyses of divergence choice, teacher update, generation length, corruption type, and an extension to captioning.

Significance. The contribution is potentially significant: if the reported effects are real, NOPD would be a rare example of a VLM post-training method that improves on external benchmarks without any external supervision, which could lower the cost of adapting VLMs. The paper is also unusually broad empirically: three model families, twelve benchmarks, several ablations, and a comparison against RLVR/OPD/OPSD. The self-referential training signal is a genuine correctness risk, and the current manuscript does not contain the diagnostics needed to rule out self-consistency collapse. I therefore view the contribution as interesting but not yet established.

major comments (4)
  1. [§4.1, §4.2 (Tables 1–3)] Hyperparameters and design choices are selected on the same benchmarks that later serve as the headline results. Table 2 reports accuracy on MathVista to choose the loss type, full-vocab vs sampled-token computation, teacher update rule, and generation length; Table 3 chooses the corruption schedule on the Geometry3K test set. Table 1 then presents MathVista and Geometry3K as held-out evidence, including the headline +7.4 and +20 gains. This is model selection on the test set. Please either use a separate validation split for ablations or report the full set of ablated configurations on all benchmark suites so the reader can see that the design choices do not flip the conclusions.
  2. [§3 Eq. (6) and Appendix C] Eq. (6) writes L = E_{y~πθ(·|q,T(x))} DKL(πθ(y|q,T(x)) || πθ(y|q,x)), but the KL divergence is a deterministic function of θ, so the outer expectation over y is not meaningful as written. The Appendix C derivation only goes through for a per-token KL with a fixed prefix, and even then Eq. (8) drops the dependence of the prefix distribution on θ. Please define the exact token-level objective used in the implementation, state clearly whether Eq. (8) is an approximation, and provide a derivation that matches the stated objective.
  3. [§3 (Eq. 6) and §4.2 (Table 2c, Fig. 4)] The stop-gradient clean prediction is the only training signal, so the fixed points of Eq. (6) include any θ for which the clean and corrupted distributions coincide, regardless of whether that shared distribution is correct. The paper does not report the clean teacher's accuracy or calibration over training, nor the training loss trajectory; Figure 4 shows only benchmark accuracy curves. Because the teacher is fully synchronous (Table 2c), the target can drift during training. Please add a diagnostic tracking (i) the consistency loss, (ii) clean-teacher accuracy on a held-out set, and (iii) output diversity during training for at least the Geometry3K and MMK12 setups. If the clean accuracy does not improve or degrades, the claimed self-boosting effect would need to be reframed as a regularizer rather than evidence of teacher-driven improvement.
  4. [Tables 1, 4; §4.1–4.3] No multiple seeds or error bars are reported anywhere. Several Table 4 entries are small negative/positive deltas (e.g., GLM-4.6V-Flash MMBench-EN -0.2, ChartQA-Pro -0.2; Qwen3-VL-8B BLINK -0.6), and Qwen3.5-2B results use avg@16 random sampling. Without variance estimates, 'consistent gains' cannot be distinguished from noise. Please provide at least three seeds or confidence intervals for the main comparisons, or a bootstrapped significance analysis.
minor comments (4)
  1. [Table 7] The column header 'Off-polocy KD' is a typo; it should read 'Off-policy KD'.
  2. [Related Work / Title] The name 'Noisy Student' coincides with a well-known semi-supervised learning method (Xie et al., 2020). The related-work section should cite and explicitly differentiate NOPD from that line of work.
  3. [Table 1] The header 'testmini' for MathVision should be expanded or defined in the table caption.
  4. [§4.3 / Appendix B.1] The evaluation uses GPT-OSS-120B as an answer judge for some tasks. Since the paper's selling point is 'no external models,' it would help to state clearly that this judge is used only at evaluation time, not during training.

Circularity Check

0 steps flagged

No significant circularity: the self-referential teacher is an explicit design choice, and all claimed gains are externally benchmarked.

full rationale

The paper's central claim is empirical: minimizing Eq. (6) improves held-out benchmark accuracy. No derived quantity used in the argument is defined in terms of the claimed outcome. The teacher in Eq. (6) is the same model's clean-input distribution with stop-gradient; this is an explicitly acknowledged design choice, not a hidden identification between a fitted parameter and a prediction. The paper states in Sec. 2 that 'when the teacher is derived from the same model as the student (e.g., sharing parameters) rather than an external model, we refer to this setting as on-policy self-distillation,' and in Sec. 3 that 'we use the outputs of the same model πθ under clean inputs (q, x) as the “teacher” output.' The gradient derivation in Eq. (8) / Appendix Eq. (11) is a parameter-free algebraic identity from the stated reverse-KL objective, so it does not smuggle in the result. Benchmark gains are measured against external test sets (Geometry3K val, MathVista, MMMU, etc.) that are not used to fit any parameter, so the improvement is externally falsifiable. The only substantive limitation is a correctness risk: because the target is the student's own clean distribution, the objective's fixed points include confidently wrong self-consistent pairs, and the paper does not track the teacher's accuracy over training. That is an unverified assumption about teacher quality, not a circular derivation; per the reviewing rules it does not raise the circularity score. No load-bearing self-citation or imported uniqueness theorem appears; references [56,20] are contextual. Therefore the derivation chain is self-contained and non-circular.

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 0 invented entities

The method's core premise is that a model's own clean-input predictions provide a useful learning target. This premise is not externally grounded; the paper relies on benchmark experiments to validate it. The image corruption choices and decoding hyperparameters are selected from ablations and prior work, not derived.

free parameters (3)
  • Image corruption schedule (noise sigma levels, gamma range, downsampling factors) = sigma in {0.08, 0.12, 0.18, 0.26, 0.38}; gamma ~ U[0.5, 2]; downsampling x2/x4
    Chosen from prior work and combined after ablation (Table 3); NOPD's effective signal depends on these choices. Not tuned, but selected as the best-performing combination.
  • Maximum generation length = 2048
    Selected after ablation comparing 1024/2048/4096 (Table 2d); longer generation yields only marginal gains.
  • Divergence objective = Reverse KL
    Selected after comparing forward KL, JSD, reverse KL (Table 2a); affects training objective and results.
axioms (4)
  • domain assumption The model's own clean-input predictions are a reliable teacher: minimizing KL between corrupted-input and clean-input distributions improves task accuracy.
    Invoked in Sec 3, Eq (6); no ground-truth anchor, so the method can in principle reinforce confident errors. This is the load-bearing premise of 'self-boosting'.
  • domain assumption Image corruption (noise, downsampling, gamma) produces a useful 'difficult environment' that transfers to reasoning ability, not just robustness to the same corruptions.
    Motivates the method in Sec 3 and is tested via OOD benchmarks, but not proven.
  • domain assumption Distributions of training datasets (Geometry3K, MMK12, etc.) are representative and do not overlap evaluation benchmarks in a way that inflates gains.
    The paper removes similar images/questions (Sec 4.3), but no automated contamination check is reported.
  • standard math Standard probability/optimization facts (KL divergence, policy-gradient identity, stop-gradient prevents collapse).
    Used in Sec 3 and Appendix C derivation.

pith-pipeline@v1.3.0-alltime-deepseek · 18174 in / 11554 out tokens · 116741 ms · 2026-08-03T01:45:47.572900+00:00 · methodology

0 comments
read the original abstract

Post-training enables vision-language models (VLMs) to understand human instructions and perform various downstream tasks. Current post-training methods usually rely on human-annotated data, distillation from external models, reinforcement learning with human feedback, or verifiable answers. This limits their ability to improve without external supervision. To tackle this, we propose NOPD (Noisy Student On-Policy Self-Distillation), a simple yet effective self-distillation approach that improves VLMs without any external models or ground-truth answers. Our key insight is that prediction discrepancies between clean and corrupted inputs naturally induce a self-supervision signal. In NOPD, the model learns from corrupted inputs while using its own predictions under clean inputs as token-level supervision. We show the effectiveness of NOPD on five visual reasoning tasks; it can match and even outperform reinforcement learning approaches or distillation from external models. Notably, when trained with 2.1K samples from Geometry3K, NOPD improves Qwen2.5-VL-7B by 20 points on its validation set. It also shows generalization on out-of-distribution test sets and achieves 7.4 point gains on MathVista. Furthermore, we demonstrate that NOPD is a general approach to enhance VLMs, achieving improvements across three models on 12 benchmarks.

Figures

Figures reproduced from arXiv: 2607.23125 by Daoan Zhang, Hao Cheng, Jiaheng Wei, Shuai Wang, Zhe Tang.

Figure 1
Figure 1. Figure 1: Comparison of different post-training approaches for VLMs. Top: demonstration of different approaches. q denotes text query and x denotes image. We omit the subscripts of loss functions except GRPO for simplicity. We highlight all sampling operations with red, e.g., y ∼ πθ(·|q, x). πθ denotes the policy model in (a) and (b), and the student model for distillation in (c), (d), and (e). π ∗ denotes the teach… view at source ↗
Figure 2
Figure 2. Figure 2: Examples of different distorted images. The types of image distortions (from left to right): [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The number of output tokens and accuracy on three benchmarks. [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Accuracy on three benchmarks during training with two different training sets. We train Qwen3.5-2B with MMK12 and Geometry3K, respectively. Corruption type of images. We conduct experiments with different image corruption types to verify their importance. As shown in [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Win-rate comparison on CapArena with Gemini-3-Flash and GPT-5. [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗

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Works this paper leans on

60 extracted references · 17 linked inside Pith

  1. [1]

    On-policy distillation of language models: Learning from self-generated mistakes

    Rishabh Agarwal, Nino Vieillard, Yongchao Zhou, Piotr Stanczyk, Sabela Ramos Garea, Matthieu Geist, and Olivier Bachem. On-policy distillation of language models: Learning from self-generated mistakes. InICLR, 2024

    2024

  2. [2]

    Qwen3-vl technical report.arXiv preprint arXiv:2511.21631, 2025

    Shuai Bai, Yuxuan Cai, Ruizhe Chen, Keqin Chen, Xionghui Chen, Zesen Cheng, Lianghao Deng, Wei Ding, Chang Gao, Chunjiang Ge, et al. Qwen3-vl technical report.arXiv preprint arXiv:2511.21631, 2025

    Pith/arXiv arXiv 2025

  3. [3]

    Qwen2.5-vl technical report

    Shuai Bai, Keqin Chen, Xuejing Liu, Jialin Wang, Wenbin Ge, Sibo Song, Kai Dang, Peng Wang, Shijie Wang, Jun Tang, Humen Zhong, Yuanzhi Zhu, Mingkun Yang, Zhaohai Li, Jianqiang Wan, Pengfei Wang, Wei Ding, Zheren Fu, Yiheng Xu, Jiabo Ye, Xi Zhang, Tianbao Xie, Zesen Cheng, Hang Zhang, Zhibo Yang, Haiyang Xu, and Junyang Lin. Qwen2.5-vl technical report. a...

    Pith/arXiv arXiv 2025

  4. [4]

    An augmented benchmark dataset for geometric question answering through dual parallel text encoding

    Jie Cao and Jing Xiao. An augmented benchmark dataset for geometric question answering through dual parallel text encoding. InProceedings of the 29th international conference on computational linguistics, pages 1511–1520, 2022

    2022

  5. [5]

    Are we on the right way for evaluating large vision-language models? InNeurIPS, 2024

    Lin Chen, Jinsong Li, Xiaoyi Dong, Pan Zhang, Yuhang Zang, Zehui Chen, Haodong Duan, Jiaqi Wang, Yu Qiao, Dahua Lin, and Feng Zhao. Are we on the right way for evaluating large vision-language models? InNeurIPS, 2024

    2024

  6. [6]

    Caparena: Benchmarking and analyzing detailed image captioning in the llm era

    Kanzhi Cheng, Wenpo Song, Jiaxin Fan, Zheng Ma, Qiushi Sun, Fangzhi Xu, Chenyang Yan, Nuo Chen, Jianbing Zhang, and Jiajun Chen. Caparena: Benchmarking and analyzing detailed image captioning in the llm era. InACL, 2025

    2025

  7. [7]

    Enhancing large vision language models with self-training on image comprehension

    Yihe Deng, Pan Lu, Fan Yin, Ziniu Hu, Sheng Shen, Quanquan Gu, James Zou, Kai-Wei Chang, and Wei Wang. Enhancing large vision language models with self-training on image comprehension. InNeurIPS, 2024

    2024

  8. [8]

    Self-boosting large language models with synthetic preference data

    Qingxiu Dong, Li Dong, Xingxing Zhang, Zhifang Sui, and Furu Wei. Self-boosting large language models with synthetic preference data. InICLR, 2025

    2025

  9. [9]

    Gemini 3 pro: the frontier of vision ai

    Rohan Doshi. Gemini 3 pro: the frontier of vision ai. https://blog.google/ innovation-and-ai/technology/developers-tools/gemini-3-pro-vision/ , De- cember 2025. Google Blog

    2025

  10. [10]

    Blink: Multimodal large language models can see but not perceive

    Xingyu Fu, Yushi Hu, Bangzheng Li, Yu Feng, Haoyu Wang, Xudong Lin, Dan Roth, Noah A Smith, Wei-Chiu Ma, and Ranjay Krishna. Blink: Multimodal large language models can see but not perceive. InECCV, 2024

    2024

  11. [11]

    G-llava: Solving geometric problem with multi-modal large language model.arXiv preprint arXiv:2312.11370, 2023

    Jiahui Gao, Renjie Pi, Jipeng Zhang, Jiacheng Ye, Wanjun Zhong, Yufei Wang, Lanqing Hong, Jianhua Han, Hang Xu, Zhenguo Li, et al. G-llava: Solving geometric problem with multi-modal large language model.arXiv preprint arXiv:2312.11370, 2023

    Pith/arXiv arXiv 2023

  12. [12]

    Making the v in vqa matter: Elevating the role of image understanding in visual question answering

    Yash Goyal, Tejas Khot, Douglas Summers-Stay, Dhruv Batra, and Devi Parikh. Making the v in vqa matter: Elevating the role of image understanding in visual question answering. In CVPR, 2017

    2017

  13. [13]

    MiniLLM: Knowledge distillation of large language models

    Yuxian Gu, Li Dong, Furu Wei, and Minlie Huang. MiniLLM: Knowledge distillation of large language models. InICLR, 2024

    2024

  14. [14]

    Reinforced self-training (rest) for language modeling.arXiv preprint arXiv:2308.08998, 2023

    Caglar Gulcehre, Tom Le Paine, Srivatsan Srinivasan, Ksenia Konyushkova, Lotte Weerts, Abhishek Sharma, Aditya Siddhant, Alex Ahern, Miaosen Wang, Chenjie Gu, et al. Reinforced self-training (rest) for language modeling.arXiv preprint arXiv:2308.08998, 2023

    Pith/arXiv arXiv 2023

  15. [15]

    Deepseek-r1 incentivizes reasoning in llms through reinforcement learning.Nature, 645(8081):633–638, 2025

    Daya Guo, Dejian Yang, Haowei Zhang, Junxiao Song, Peiyi Wang, Qihao Zhu, Runxin Xu, Ruoyu Zhang, Shirong Ma, Xiao Bi, et al. Deepseek-r1 incentivizes reasoning in llms through reinforcement learning.Nature, 645(8081):633–638, 2025

    2025

  16. [16]

    Self-distillation zero: Self-revision turns binary rewards into dense supervision.arXiv preprint arXiv:2604.12002, 2026

    Yinghui He, Simran Kaur, Adithya Bhaskar, Yongjin Yang, Jiarui Liu, Narutatsu Ri, Liam Fowl, Abhishek Panigrahi, Danqi Chen, and Sanjeev Arora. Self-distillation zero: Self-revision turns binary rewards into dense supervision.arXiv preprint arXiv:2604.12002, 2026. 10

    Pith/arXiv arXiv 2026

  17. [17]

    Benchmarking neural network robustness to common corruptions and perturbations

    Dan Hendrycks and Thomas Dietterich. Benchmarking neural network robustness to common corruptions and perturbations. InICLR, 2019

    2019

  18. [18]

    Distilling the knowledge in a neural network

    Geoffrey Hinton, Oriol Vinyals, and Jeff Dean. Distilling the knowledge in a neural network. arXiv preprint arXiv:1503.02531, 2015

    Pith/arXiv arXiv 2015

  19. [19]

    Glm-4.5 v and glm-4.1 v-thinking: Towards versatile multimodal reasoning with scalable reinforcement learning.arXiv preprint arXiv:2507.01006, 2025

    Wenyi Hong, Wenmeng Yu, Xiaotao Gu, Guo Wang, Guobing Gan, Haomiao Tang, Jiale Cheng, Ji Qi, Junhui Ji, Lihang Pan, et al. Glm-4.5 v and glm-4.1 v-thinking: Towards versatile multimodal reasoning with scalable reinforcement learning.arXiv preprint arXiv:2507.01006, 2025

    Pith/arXiv arXiv 2025

  20. [20]

    Reinforcement learning via self-distillation.arXiv preprint arXiv:2601.20802, 2026

    Jonas Hübotter, Frederike Lübeck, Lejs Behric, Anton Baumann, Marco Bagatella, Daniel Marta, Ido Hakimi, Idan Shenfeld, Thomas Kleine Buening, Carlos Guestrin, et al. Reinforcement learning via self-distillation.arXiv preprint arXiv:2601.20802, 2026

    Pith/arXiv arXiv 2026

  21. [21]

    Hudson and Christopher D

    Drew A. Hudson and Christopher D. Manning. Gqa: A new dataset for real-world visual reasoning and compositional question answering. InCVPR, 2019

    2019

  22. [22]

    Geomverse: A systematic evaluation of large models for geometric reasoning.arXiv preprint arXiv:2312.12241, 2023

    Mehran Kazemi, Hamidreza Alvari, Ankit Anand, Jialin Wu, Xi Chen, and Radu Soricut. Geomverse: A systematic evaluation of large models for geometric reasoning.arXiv preprint arXiv:2312.12241, 2023

    Pith/arXiv arXiv 2023

  23. [23]

    Sequence-level knowledge distillation

    Yoon Kim and Alexander M Rush. Sequence-level knowledge distillation. InEMNLP, 2016

    2016

  24. [24]

    Multimodal arxiv: A dataset for improving scientific comprehension of large vision-language models

    Lei Li, Yuqi Wang, Runxin Xu, Peiyi Wang, Xiachong Feng, Lingpeng Kong, and Qi Liu. Multimodal arxiv: A dataset for improving scientific comprehension of large vision-language models. InACL, 2024

    2024

  25. [25]

    Visual instruction tuning

    Haotian Liu, Chunyuan Li, Qingyang Wu, and Yong Jae Lee. Visual instruction tuning. In NeurIPS, 2023

    2023

  26. [26]

    Noisyrollout: Reinforcing visual reasoning with data augmentation

    Xiangyan Liu, Jinjie Ni, Zijian Wu, Chao Du, Longxu Dou, Haonan Wang, Tianyu Pang, and Michael Qizhe Shieh. Noisyrollout: Reinforcing visual reasoning with data augmentation. In NeurIPS, 2025

    2025

  27. [27]

    Mmbench: Is your multi-modal model an all-around player? InECCV, 2024

    Yuan Liu, Haodong Duan, Yuanhan Zhang, Bo Li, Songyang Zhang, Wangbo Zhao, Yike Yuan, Jiaqi Wang, Conghui He, Ziwei Liu, et al. Mmbench: Is your multi-modal model an all-around player? InECCV, 2024

    2024

  28. [28]

    Mathvista: Evaluating mathematical reasoning of foundation models in visual contexts

    Pan Lu, Hritik Bansal, Tony Xia, Jiacheng Liu, Chunyuan Li, Hannaneh Hajishirzi, Hao Cheng, Kai-Wei Chang, Michel Galley, and Jianfeng Gao. Mathvista: Evaluating mathematical reasoning of foundation models in visual contexts. InICLR, 2024

    2024

  29. [29]

    Inter-gps: Interpretable geometry problem solving with formal language and symbolic reasoning

    Pan Lu, Ran Gong, Shibiao Jiang, Liang Qiu, Siyuan Huang, Xiaodan Liang, and Song-Chun Zhu. Inter-gps: Interpretable geometry problem solving with formal language and symbolic reasoning. InACL, 2021

    2021

  30. [30]

    Chartqa: A benchmark for question answering about charts with visual and logical reasoning

    Ahmed Masry, Xuan Long Do, Jia Qing Tan, Shafiq Joty, and Enamul Hoque. Chartqa: A benchmark for question answering about charts with visual and logical reasoning. InACL, 2022

    2022

  31. [31]

    Chartqapro: A more diverse and challenging benchmark for chart question answering

    Ahmed Masry, Mohammed Saidul Islam, Mahir Ahmed, Aayush Bajaj, Firoz Kabir, Aaryaman Kartha, Md Tahmid Rahman Laskar, Mizanur Rahman, Shadikur Rahman, Mehrad Shahmo- hammadi, et al. Chartqapro: A more diverse and challenging benchmark for chart question answering. InACL, 2025

    2025

  32. [32]

    Mm-eureka: Exploring the frontiers of multimodal reasoning with rule-based reinforcement learning.arXiv preprint arXiv:2503.07365, 2025

    Fanqing Meng, Lingxiao Du, Zongkai Liu, Zhixiang Zhou, Quanfeng Lu, Daocheng Fu, Tiancheng Han, Botian Shi, Wenhai Wang, Junjun He, et al. Mm-eureka: Exploring the frontiers of multimodal reasoning with rule-based reinforcement learning.arXiv preprint arXiv:2503.07365, 2025

    Pith/arXiv arXiv 2025

  33. [33]

    2 olmo 2 furious.arXiv preprint arXiv:2501.00656, 2024

    Team OLMo, Pete Walsh, Luca Soldaini, Dirk Groeneveld, Kyle Lo, Shane Arora, Akshita Bhagia, Yuling Gu, Shengyi Huang, Matt Jordan, et al. 2 olmo 2 furious.arXiv preprint arXiv:2501.00656, 2024. 11

    Pith/arXiv arXiv 2024

  34. [34]

    Training language models to follow instructions with human feedback

    Long Ouyang, Jeffrey Wu, Xu Jiang, Diogo Almeida, Carroll Wainwright, Pamela Mishkin, Chong Zhang, Sandhini Agarwal, Katarina Slama, Alex Gray, John Schulman, Jacob Hilton, Fraser Kelton, Luke Miller, Maddie Simens, Amanda Askell, Peter Welinder, Paul Christiano, Jan Leike, and Ryan Lowe. Training language models to follow instructions with human feedback...

    2022

  35. [35]

    Learning transferable visual models from natural language supervision

    Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, et al. Learning transferable visual models from natural language supervision. InICML, 2021

    2021

  36. [36]

    Direct preference optimization: Your language model is secretly a reward model

    Rafael Rafailov, Archit Sharma, Eric Mitchell, Christopher D Manning, Stefano Ermon, and Chelsea Finn. Direct preference optimization: Your language model is secretly a reward model. InNeurIPS, 2023

    2023

  37. [37]

    Deepseekmath: Pushing the limits of mathematical reasoning in open language models.arXiv preprint arXiv:2402.03300, 2024

    Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Xiao Bi, Haowei Zhang, Mingchuan Zhang, YK Li, Yang Wu, et al. Deepseekmath: Pushing the limits of mathematical reasoning in open language models.arXiv preprint arXiv:2402.03300, 2024

    Pith/arXiv arXiv 2024

  38. [38]

    Chartmuseum: Testing visual reasoning capabilities of large vision-language models.arXiv preprint arXiv:2505.13444, 2025

    Liyan Tang, Grace Kim, Xinyu Zhao, Thom Lake, Wenxuan Ding, Fangcong Yin, Prasann Singhal, Manya Wadhwa, Zeyu Leo Liu, Zayne Sprague, et al. Chartmuseum: Testing visual reasoning capabilities of large vision-language models.arXiv preprint arXiv:2505.13444, 2025

    arXiv 2025

  39. [39]

    Kimi Team, Tongtong Bai, Yifan Bai, Yiping Bao, SH Cai, Yuan Cao, Y Charles, HS Che, Cheng Chen, Guanduo Chen, et al. Kimi k2. 5: Visual agentic intelligence.arXiv preprint arXiv:2602.02276, 2026

    Pith/arXiv arXiv 2026

  40. [40]

    Cambrian-1: A fully open, vision-centric exploration of multimodal LLMs

    Shengbang Tong, Ellis L Brown II, Penghao Wu, Sanghyun Woo, ADITHY A JAIRAM IYER, Sai Charitha Akula, Shusheng Yang, Jihan Yang, Manoj Middepogu, Ziteng Wang, Xichen Pan, Rob Fergus, Yann LeCun, and Saining Xie. Cambrian-1: A fully open, vision-centric exploration of multimodal LLMs. InNeurPS, 2024

    2024

  41. [41]

    Learning using privileged information: Similarity control and knowledge transfer.Journal of Machine Learning Research, 16(61):2023–2049, 2015

    Vladimir Vapnik and Rauf Izmailov. Learning using privileged information: Similarity control and knowledge transfer.Journal of Machine Learning Research, 16(61):2023–2049, 2015

    2023

  42. [42]

    Measuring multimodal mathematical reasoning with MATH-vision dataset

    Ke Wang, Junting Pan, Weikang Shi, Zimu Lu, Houxing Ren, Aojun Zhou, Mingjie Zhan, and Hongsheng Li. Measuring multimodal mathematical reasoning with MATH-vision dataset. In NeurIPS, 2024

    2024

  43. [43]

    Charxiv: Charting gaps in realistic chart understanding in multimodal LLMs

    Zirui Wang, Mengzhou Xia, Luxi He, Howard Chen, Yitao Liu, Richard Zhu, Kaiqu Liang, Xindi Wu, Haotian Liu, Sadhika Malladi, Alexis Chevalier, Sanjeev Arora, and Danqi Chen. Charxiv: Charting gaps in realistic chart understanding in multimodal LLMs. InNeurIPS, 2024

    2024

  44. [44]

    Dai, and Quoc V Le

    Jason Wei, Maarten Bosma, Vincent Zhao, Kelvin Guu, Adams Wei Yu, Brian Lester, Nan Du, Andrew M. Dai, and Quoc V Le. Finetuned language models are zero-shot learners. InICLR, 2022

    2022

  45. [45]

    Chi, Quoc V Le, and Denny Zhou

    Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, brian ichter, Fei Xia, Ed H. Chi, Quoc V Le, and Denny Zhou. Chain of thought prompting elicits reasoning in large language models. InNeurIPS, 2022

    2022

  46. [46]

    Captionqa: Is your caption as useful as the image itself?arXiv preprint arXiv:2511.21025, 2025

    Shijia Yang, Yunong Liu, Bohan Zhai, Ximeng Sun, Zicheng Liu, Emad Barsoum, Manling Li, and Chenfeng Xu. Captionqa: Is your caption as useful as the image itself?arXiv preprint arXiv:2511.21025, 2025

    Pith/arXiv arXiv 2025

  47. [47]

    Scaling text-rich image understanding via code-guided synthetic multimodal data generation

    Yue Yang, Ajay Patel, Matt Deitke, Tanmay Gupta, Luca Weihs, Andrew Head, Mark Yatskar, Chris Callison-Burch, Ranjay Krishna, Aniruddha Kembhavi, and Christopher Clark. Scaling text-rich image understanding via code-guided synthetic multimodal data generation. InACL, 2025

    2025

  48. [48]

    DAPO: An open-source LLM reinforcement learning system at scale

    Qiying Yu, Zheng Zhang, Ruofei Zhu, Yufeng Yuan, Xiaochen Zuo, YuYue, Weinan Dai, Tiantian Fan, Gaohong Liu, Juncai Liu, LingJun Liu, Xin Liu, Haibin Lin, Zhiqi Lin, Bole Ma, Guangming Sheng, Yuxuan Tong, Chi Zhang, Mofan Zhang, Ru Zhang, Wang Zhang, Hang Zhu, Jinhua Zhu, Jiaze Chen, Jiangjie Chen, Chengyi Wang, Hongli Yu, Yuxuan Song, 12 Xiangpeng Wei, H...

    2025

  49. [49]

    Self-rewarding language models

    Weizhe Yuan, Richard Yuanzhe Pang, Kyunghyun Cho, Xian Li, Sainbayar Sukhbaatar, Jing Xu, and Jason E Weston. Self-rewarding language models. InICML, 2024

    2024

  50. [50]

    Mmmu: A massive multi-discipline multimodal understanding and reasoning benchmark for expert agi

    Xiang Yue, Yuansheng Ni, Kai Zhang, Tianyu Zheng, Ruoqi Liu, Ge Zhang, Samuel Stevens, Dongfu Jiang, Weiming Ren, Yuxuan Sun, Cong Wei, Botao Yu, Ruibin Yuan, Renliang Sun, Ming Yin, Boyuan Zheng, Zhenzhu Yang, Yibo Liu, Wenhao Huang, Huan Sun, Yu Su, and Wenhu Chen. Mmmu: A massive multi-discipline multimodal understanding and reasoning benchmark for exp...

    2024

  51. [51]

    Mmmu-pro: A more robust multi-discipline multimodal understanding benchmark

    Xiang Yue, Tianyu Zheng, Yuansheng Ni, Yubo Wang, Kai Zhang, Shengbang Tong, Yuxuan Sun, Botao Yu, Ge Zhang, Huan Sun, Yu Su, Wenhu Chen, and Graham Neubig. Mmmu-pro: A more robust multi-discipline multimodal understanding benchmark. InACL, 2025

    2025

  52. [52]

    STar: Bootstrapping reasoning with reasoning

    Eric Zelikman, Yuhuai Wu, Jesse Mu, and Noah Goodman. STar: Bootstrapping reasoning with reasoning. InNeurIPS, 2022

    2022

  53. [53]

    ReST-MCTS*: LLM self-training via process reward guided tree search

    Dan Zhang, Sining Zhoubian, Ziniu Hu, Yisong Yue, Yuxiao Dong, and Jie Tang. ReST-MCTS*: LLM self-training via process reward guided tree search. InNeurIPS, 2024

    2024

  54. [54]

    Lmms-eval: Reality check on the evaluation of large multimodal models

    Kaichen Zhang, Bo Li, Peiyuan Zhang, Fanyi Pu, Joshua Adrian Cahyono, Kairui Hu, Shuai Liu, Yuanhan Zhang, Jingkang Yang, Chunyuan Li, et al. Lmms-eval: Reality check on the evaluation of large multimodal models. InNAACL, 2025

    2025

  55. [55]

    Kdflow: A user-friendly and efficient knowledge distillation framework for large language models.arXiv preprint arXiv:2603.01875, 2026

    Songming Zhang, Xue Zhang, Tong Zhang, Bojie Hu, Yufeng Chen, and Jinan Xu. Kdflow: A user-friendly and efficient knowledge distillation framework for large language models.arXiv preprint arXiv:2603.01875, 2026

    Pith/arXiv arXiv 2026

  56. [56]

    Self-distilled reasoner: On-policy self-distillation for large language models.arXiv preprint arXiv:2601.18734, 2026

    Siyan Zhao, Zhihui Xie, Mengchen Liu, Jing Huang, Guan Pang, Feiyu Chen, and Aditya Grover. Self-distilled reasoner: On-policy self-distillation for large language models.arXiv preprint arXiv:2601.18734, 2026

    Pith/arXiv arXiv 2026

  57. [57]

    Group sequence policy optimization.arXiv preprint arXiv:2507.18071, 2025

    Chujie Zheng, Shixuan Liu, Mingze Li, Xiong-Hui Chen, Bowen Yu, Chang Gao, Kai Dang, Yuqiong Liu, Rui Men, An Yang, et al. Group sequence policy optimization.arXiv preprint arXiv:2507.18071, 2025. 13 A Limitations and Social Impact A.1 Limitations. We propose NOPD, an effective self-boosting approach that improves VLMs without external information. The on...

    Pith/arXiv arXiv 2025

  58. [58]

    - Therefore, AP:P D= 2 : 1 and CP:P E= 2 : 1

    **Identify the properties of the medians and centroid:** - The medians of a triangle intersect at the centroid P , which divides each median into a ratio of 2:1. - Therefore, AP:P D= 2 : 1 and CP:P E= 2 : 1 . 2. **Determine the lengths of the segments:** - Given P E= 1.5 and P D= 2, we can find P Dand P Ein terms of the total length of the median. - Since...

  59. [59]

    **Set up the equation using the total length of the chordP Q:** - Since P Q=P T+T Q: P Q= 3x−4 2 + 3x−4 2 = 3x−4

  60. [60]

    **Solve for x:** - We know P Q= 3x−4 and from the diagram, P Q= 16 (since T and U are midpoints and the total length is twice the segment from the center to the midpoint of the chord). - Set up the equation: 3x−4 = 16 - Solve forx: 3x= 20 x= 20 3 Therefore, the value ofxis 20 3 .✘ NOPD To solve for x in the given problem, we need to use the properties of ...