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MM-OPD: Towards One More Bottleneck Between Perception and Reasoning
Jintao Tong, Yujing Lou, Zhanming Shen, Jiaqi Gu, Lubin Fan, Ruixuan Li, Yue Wu, Jieping Ye, Yixiong Zou
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Abstract
Abstract:Recent multimodal large language models (MLLMs) advance visual reasoning by strengthening both perception and reasoning, implicitly assuming a process that transitions seamlessly from perception to reasoning. However, we observe a counterintuitive phenomenon that challenges this assumption: holding the model, question, and decoding fixed, we replace images with their caption or code representations (symbolic views), which seems to be redundant given the clear image structures, but the performance surprisingly improves by 10.2% to 23.6% across model scales and datasets. We term this performance gap as the Symbolic Visual Gap and then take a closer look at it. Through experiments, we find that although the visual evidence can already appear in the reasoning trace for the image-input model, the symbolic-view-input model shows much higher attention to the correct evidence than the image-input model. This suggests that despite good capabilities from current works in perception and reasoning themselves, another bottleneck exists between perception and reasoning in selecting perceived visual information as appropriate evidence for subsequent reasoning. To handle this bottleneck, since the symbolic view steers attention toward correct evidence and is readily obtained at scale, it provides supervision for evidence selection without manually labeled evidence. Building on this, we introduce MM-OPD, a multimodal on-policy self-distillation framework for symbolic-to-visual correction that transfers guidance from symbolic-conditioned behavior to the image-conditioned policy through residual token-level targets, steering the model toward correct visual evidence. Experiments across benchmarks and model scales show that MM-OPD improves a broad range of multimodal abilities, with gains in visual perception, chart and document understanding, mathematical reasoning, and general VQA.
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- Source: https://arxiv.org/abs/2609.32690v1
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M-OPD : Towards One More Bottleneck Between Perception and Reasoning Jintao Tong1,2, Yujing Lou2,‡, Zhanming Shen2,3, Jiaqi Gu2, Lubin Fan2,† Ruixuan Li1,†, Yue Wu2, Jieping Ye2, Yixiong Zou1,† 1Huazhong University of Science and Technology 2Alibaba Token Hub, Alibaba Group 3Zhejiang University †Corresponding authors ‡Project leader Code M-OPD-4B M-OPD-9B M-OPD-32K Abstract Recent multimodal large language models (MLLMs) advance visual reasoning by strengthening both perception and reasoning, implicitly assuming a process that transitions seamlessly from perception to reasoning. However, we observe a counterintuitive phenomenon that challenges this assumption: holding the model, question, and decoding fixed, we replace images with their caption or code representations (symbolic views), which seems to be redundant given the clear image structures, but the performance surprisingly improves by 10.2%10.2\% to 23.6%23.6\% across model scales and datasets. We term this performance gap as the Symbolic Visual Gap and then take a closer look at it. Through experiments, we find that although the visual evidence can already appear in the reasoning trace for the image-input model, the symbolic-view-input model shows much higher attention to the correct evidence than the image-input model. This suggests that despite good capabilities from current works in perception and reasoning themselves, another bottleneck exists between perception and reasoning in selecting perceived visual information as appropriate evidence for subsequent reasoning. To handle this bottleneck, since the symbolic view steers attention toward correct evidence and is readily obtained at scale, it provides supervision for evidence selection without manually labeled evidence. Building on this, we introduce M-OPD, a multimodal on-policy self-distillation framework for symbolic-to-visual correction that transfers guidance from symbolic-conditioned behavior to the image-conditioned policy through residual token-level targets, steering the model toward correct visual evidence. Experiments across benchmarks and model scales show that M-OPD improves a broad range of multimodal abilities rather than a single targeted capability, with gains in visual perception, chart and document understanding, mathematical reasoning, and general VQA. 1 Introduction Recent advances in multimodal large language models (MLLMs) have shown promising capabilities in visual reasoning. Some efforts emphasize access to fine-grained visual information (Liu et al., 2025; Su et al., 2026), while others strengthen multi-step mathematical and logical reasoning through post-training (Shao et al., 2024; Hong et al., 2025), assuming an ideal visual reasoning process that seamlessly transitions from perception to reasoning. However, in this paper, we observe a counterintuitive phenomenon contradicting the seamless perception-reasoning transition. As in Figure 1, we use the generating code (or descriptive caption, which we term the symbolic view) to replace the question image as the model input, with the model, question, and the decoding fixed, and measure the reasoning performance. Since the input image is simple enough for perception, the image is ideally itself easier to understand than the generating code, making the replacement redundant. Surprisingly, such a seemingly redundant operation significantly improves performance by 10.2% to 23.6% across model scales and datasets (Figure 1, right). This phenomenon makes us question the widely assumed seamless transition from perception to reasoning in visual reasoning: do we need another symbolic-view step during visual reasoning? Visual inputSymbolic input30405060708090100Accuracy (%)Chartsymbolic view: codeMathsymbolic view: codeGeneral VQAsymbolic view: caption4B66.488.0+21.69B66.289.8+23.64B75.687.6+12.09B79.489.6+10.24B39.249.4+10.29B53.074.8+21.8 Figure 1: (Left) A case of replacing the question image with its symbolic view, under the same model, question, and decoding procedure. (Right) The Symbolic Visual Gap: symbolic views outperform visual inputs on every model and dataset pair from 4B to 9B. To answer this question, we refer to this discrepancy between image-conditioned reasoning and symbol-conditioned reasoning as the Symbolic Visual Gap and take a step closer to it. We first analyze the visual information expressed in the generated reasoning traces for image-input models. We find that the correct visual evidence can already appear in the trace, indicating that the model can already correctly perceive the visual information. However, we still find that the model tends to adopt distracting evidence (visual evidence leading to incorrect reasoning and answers) for its subsequent reasoning, showing a disadvantage in visual evidence selection. To verify it, we then quantitatively measure the answer-to-evidence attention between the image input and the symbolic-view input. We find that answer-to-evidence attention favors distracting evidence given the image input, and correct evidence given the symbolic-view input, verifying the difficulty in selecting correct evidence for the image-input model. In other words, despite good capabilities from current works in perception and reasoning themselves, another bottleneck exists between perception and reasoning in selecting perceived visual information as appropriate evidence for subsequent reasoning. To handle this bottleneck, based on the above analysis, as the symbolic view elicits the model to assign answer-to-evidence attention to correct visual evidence, this view naturally offers a direction for guiding the image-input model for evidence selection without manually labeling correct evidence. Moreover, since the symbolic view (generating code or descriptive caption) is easily obtained automatically, it is scalable for different data sizes. Therefore, we propose to take the symbolic view as auxiliary information and introduce M-OPD, a multimodal on-policy self-distillation framework for correcting visual-evidence selection. M-OPD takes the symbolic-view-input model as the teacher and uses the image-input model as the student, and then provides token-level supervision along trajectories generated by the student to guide the student to learn the evidence selection from the self-teacher. During inference, since the symbolic view is not available, only the image-input model, with the symbolic visual gap largely reduced, will be used for visual reasoning. M-OPD improves a broad range of multimodal abilities rather than a single targeted capability. Experiments across diverse benchmarks show consistent gains in visual perception, chart and document understanding, mathematical reasoning, and general multimodal reasoning. Our contributions are as follows: ▶ We identify the Symbolic Visual Gap: with the model, question, and decoding fixed, replacing a visual input with its symbolic view improves accuracy by 10.210.2 to 23.623.6 percentage points across model scales and visual domains. ▶ We identify visual evidence selection as another critical bottleneck between perception and reasoning: correct visual information can appear in the generated trace without guiding the derivation, while image and symbolic conditioning exhibit opposite answer-to-evidence attention patterns. ▶ Based on this insight, we introduce M-OPD, a multimodal on-policy self-distillation framework, to transfer guidance from symbolic-conditioned behavior to the image-conditioned policy through residual token-level targets to help the model draw on correct visual evidence. ▶ Comprehensive experiments validate the effectiveness of M-OPD, demonstrating consistent improvements across model scales and diverse multimodal reasoning tasks. 2 Delve into the Symbolic Visual Gap The counterintuitive Symbolic Visual Gap inspires us to examine the assumed seamless transition from perception to reasoning more closely. In an ideal visual reasoning process, perceived information should become appropriate evidence for subsequent reasoning. We therefore examine (i) whether task-relevant visual information is correctly perceived and represented as language-accessible evidence, and (i) whether subsequent reasoning draws on the correct evidence. 2.1 From Visual Perception to Evidence Selection When input an image into the MLLM (i.e., the image-input model), in the model-generated reasoning, some tokens verbalize information obtained from the input image that may be used to answer the question. We refer to these as visual evidence tokens. For a given question, correct evidence tokens express visual information that supports a correct answer, whereas distracting evidence tokens express competing information that can mislead subsequent reasoning or answer generation. To distinguish visual perception from evidence use, we examine whether correct visual information already appears in the generated trace. Its explicit presence indicates that this information is available in a language-accessible form. We then inspect which evidence is used in subsequent reasoning and compare answer-to-evidence attention for correct and distracting evidence, thereby characterizing how strongly answer generation is associated with each type of candidate evidence. Figure 2 illustrates that correctly perceived visual information may not be selected as appropriate evidence for subsequent reasoning. The relevant values and their ordering are explicitly stated in the trace, yet the model still selects distracting evidence as a premise. The subsequent comparison is valid given that premise. Distracting evidence also receives more attention, including the evidence used in the derivation. Thus, having relevant visual information available in the trace does not ensure that it is used appropriately to answer the question. Additional cases are provided in Appendix A. Figure 2: A case study. Task-relevant visual information is correctly perceived and verbalized, yet distracting evidence receives more attention and is selected as the premise for subsequent reasoning. Finding 1 Correctly perceiving and verbalizing task-relevant visual information does not ensure correct evidence use. The model may select distracting evidence for subsequent reasoning. 2.2 Answer-to-Evidence Attention under Image and Symbolic Conditions We next quantitatively examine whether the attention preference observed in the case study extends beyond this example and how it differs between image and symbolic conditioning. Specifically, we sample 200200 examples from each of three task families (general VQA, chart reasoning, and mathematical reasoning), yielding 600600 examples in total. Using Qwen3.5-4B, we measure at each full-attention layer the head-averaged attention from the answer token to correct and distracting evidence tokens under image and symbolic conditioning, and report both layer-wise and overall results. Figure 3: Answer-to-evidence attention under image and symbolic conditioning. (a,b) Layer-wise results at the observed full-attention layers. (c) Overall mean attention to correct and distracting evidence, together with their ratio. (d) The signed score F=log2(C/X)F= _2(C/X); positive and negative values indicate stronger association with correct and distracting evidence, respectively. i) The two conditions exhibit opposite evidence orderings across depth. As in Figure 3(a,b), distracting evidence receives more attention than correct evidence at every observed layer under image conditioning. Symbolic conditioning consistently exhibits the opposite ordering. This reversal persists across all observed layers and is therefore not driven by an isolated layer. i) The overall means and evidence ratios preserve the same trend. The overall statistics in Figure 3(c) agree with the layer-wise results. Let C and X denote the mean attention to correct and distracting evidence, respectively. We define their correct-to-distracting ratio as R=CX,R= CX, (1) where R>1.0R>1.0 and R<1.0R<1.0 indicate stronger association with correct and distracting evidence, respectively. The ratio is above 1.01.0 under symbolic conditioning and below 1.01.0 under image conditioning. i) A signed score summarizes the reversal. For a signed summary of the same relative attention, we define F=log2R=log2(C/X).F= _2R= _2(C/X). (2) Positive values indicate a stronger association with correct evidence, whereas negative values indicate a stronger association with distracting evidence. As shown in Figure 3(d), F is positive at every observed layer under symbolic conditioning and negative at every observed layer under image conditioning. The overall scores retain the same signs. Together with the case study, the consistent attention preference for distracting evidence under image conditioning points to a difficulty in using perceived information as evidence for reasoning. Finding 2 Visual evidence selection is one more bottleneck between perception and reasoning. Beyond perception and reasoning, effective multimodal capability also depends on whether perceived information is selected as appropriate evidence for subsequent reasoning. 2.3 Summary and Discussion The above analyses challenge the assumed seamless transition from perception to reasoning. Relevant visual information can already appear in the generated trace, yet the model may still select distracting evidence for subsequent reasoning. In other words, perceiving the required information does not ensure that it becomes appropriate evidence for answering the question. To address this bottleneck, the comparison with symbolic views offers a natural direction. With the model and question fixed, symbolic conditioning elicits stronger performance and an attention preference for correct evidence. This contrast suggests that the behavior elicited by symbolic views can guide evidence selection under image conditioning. Moreover, symbolic views, instantiated as generating code or descriptive captions, can be obtained automatically at scale, providing a scalable source of guidance without manually labeling correct evidence. Insight Symbolic Visual Gap reveals a missing link between perception and reasoning: visual information may be perceived without being correctly selected. Symbolic views elicit better evidence selection that can guide image-conditioned reasoning without manual evidence labeling. 3 Method Figure 4: Overview of M-OPD, a multimodal OPSD framework for symbolic-to-visual correction. Symbolic views provide privileged supervision, while residual targets discount token preferences induced by these views alone and guide image-conditioned reasoning toward correct visual evidence. The above analysis reveals visual evidence selection as one more bottleneck between perception and reasoning. It also shows that symbolic views steer answer-to-evidence attention toward correct visual evidence. Since these views can be obtained automatically at scale, this finding motivates us to introduce M-OPD, a multimodal on-policy self-distillation framework for symbolic-to-visual correction. A frozen self-teacher uses additional symbolic information to supervise the student along student-generated trajectories. Residual token-level targets reduce the influence of token preferences induced by the symbolic view alone and refine image-conditioned predictions. The overview framework is shown in Figure 4, with training pseudocode in Algorithm 1 3.1 Symbolic-to-Visual Correction Given the curated dataset =(Ii,Qi,Pi)i=1ND=\(I_i,Q_i,P_i)\_i=1^N, where PiP_i is privileged symbolic information, we initialize a trainable student πθ _θ and a frozen self-teacher πϕ _φ from the same pretrained MLLM checkpoint. For each (I,Q,P)∼(I,Q,P) , the image-conditioned student generates an on-policy response: y=(y1,…,y|y|)∼πθ(⋅∣I,Q),ht=y<t,y=(y_1,…,y_|y|) _θ(· I,Q), h_t=y_<t, (3) where hth_t is the student-generated prefix at position t. Let V denote the model vocabulary and v∈v a candidate next token. We evaluate four distributions on the same prefix: St(v) S_t(v) =πθ(v∣I,Q,ht), = _θ(v I,Q,h_t), Tt(v) T_t(v) =πϕ(v∣I,Q,P,ht), = _φ(v I,Q,P,h_t), (4) Bt(v) B_t(v) =πϕ(v∣I,Q,ht), = _φ(v I,Q,h_t), Rt(v) R_t(v) =πϕ(v∣P,ht). = _φ(v P,h_t). Here, StS_t is the current student prediction. The other three distributions are obtained from the single frozen self-teacher under different conditioning views: TtT_t combines the image, question, and privileged symbolic information; BtB_t is the clean image-conditioned prediction; and RtR_t estimates the preference induced by P without direct access to the image or question. Their differences reflect the conditioning view rather than different generated trajectories. Residual target construction Directly distilling TtT_t would conflate the task-conditioned benefit of P with token preferences that P can induce on its own. M-OPD therefore uses RtR_t as a privilege-only reference and contrasts it with TtT_t. For the same token, the log-ratio logTt(v)−logRt(v) T_t(v)- R_t(v) discounts the preference explained by P alone, leaving a correction associated with interpreting P in the full image–question context. For tractable token-level distillation, the privileged teacher defines a shared candidate set t=TopK(Tt)K_t=Top_K(T_t) containing its K most probable tokens; probabilities outside this set are later aggregated into a tail bucket. We remove the vocabulary-wide offset from the log-ratio: d~t(v)=logTt(v)−logRt(v)−u∈[logTt(u)−logRt(u)]. d_t(v)= T_t(v)- R_t(v)-E_u [ T_t(u)- R_t(u) ]. (5) The expectation is uniform over V. Subtracting it removes a token-independent shift, which carries no information about the relative preference among candidate tokens. Thus, d~t(v) d_t(v) measures how the full task context changes the relative preference for v beyond what is induced by P alone. Rather than replacing the image-conditioned prediction with the privileged teacher, we use this residual to correct the clean anchor BtB_t: q^t=softmaxt(logBt+γtanh(d~tγ)). q_t=softmax_K_t ( B_t+γ ( d_tγ ) ). (6) Adding the residual in log-probability space reweights the token preferences of BtB_t, so privileged information acts as a correction to the prediction made from the actual inference input. The saturation function remains approximately linear for moderate residuals while suppressing extreme log-ratios, with γ>0γ>0 controlling its scale. Finally, let MB,t=∑v∈tBt(v)M_B,t= _v _tB_t(v) be the probability mass that the clean anchor assigns to the selected support. We preserve this mass and distribute it according to q^t q_t: qt⋆(v)=MB,tq^t(v),v∈t.q_t (v)=M_B,t q_t(v), v _t. (7) Writing tailtail for all tokens outside tK_t, we retain the remaining anchor mass: qt⋆(tail)=1−MB,t=Bt(tail).q_t (tail)=1-M_B,t=B_t(tail). (8) Hence, the residual changes only the relative probabilities within the teacher-selected support; the total Top-K and tail masses remain grounded in the clean image-conditioned prediction. 3.2 Training Objective The target qt⋆q_t is defined on the shared support t∪tailK_t∪\tail\. To evaluate the student on the same coordinates, we retain its probabilities on tK_t and aggregate all remaining probability mass into a single tail bucket: S~t(v)=St(v)(v∈t),S~t(tail)=1−∑u∈tSt(u). S_t(v)=S_t(v) (v _t), S_t(tail)=1- _u _tS_t(u). (9) Both S~t S_t and qt⋆q_t are therefore normalized distributions on the same support. Let Mt=12(S~t+qt⋆)M_t= 12( S_t+q_t ) denote their equal-weight mixture. At each response position, we minimize the symmetric Jensen–Shannon divergence DJS(S~t∥qt⋆)=12DKL(S~t∥Mt)+12DKL(qt⋆∥Mt).D_JS ( S_t\, \|\,q_t )= 12D_KL ( S_t\, \|\,M_t )+ 12D_KL (q_t \, \|\,M_t ). (10) The overall training objective averages this dense token-level signal over both the curated data and on-policy rollouts: ℒM-OPD(θ)=(I,Q,P)∼y∼πθ(⋅∣I,Q)[1|y|∑t=1|y|DJS(S~t∥qt⋆)].L_M -OPD(θ)=E_ subarrayc(I,Q,P) \\ y _θ(· I,Q) subarray [ 1|y| _t=1^|y|D_JS ( S_t\, \|\,q_t ) ]. (11) The teacher-side distributions TtT_t, BtB_t, and RtR_t are detached, and qt⋆q_t is treated as a fixed target; gradients flow only through the image-conditioned student. Since each prefix is generated by the student itself, the objective supplies token-level supervision on the state distribution encountered at inference time. Algorithm 1 M-OPD Training 1: Student πθ _θ, frozen self-teacher πϕ _φ, training sample (I,Q,P)(I,Q,P), rollout number n, residual saturation scale γ 2: Sample n independent on-policy responses =y(j)j=1nY=\y^(j)\_j=1^n from πθ(⋅∣I,Q) _θ(· I,Q) ⊳ Eq. 3 3: for each y∈y and position t with prefix ht=y<th_t=y_<t do 4: Evaluate StS_t, TtT_t, BtB_t, and RtR_t on hth_t ⊳ Eq. 4 5: Select t←TopK(Tt)K_t _K(T_t) 6: Extract the centered privileged residual d~t d_t ⊳ Eq. 5 7: Construct the residual-corrected distribution q^t q_t ⊳ Eq. 6 8: Preserve the anchor’s head and tail masses to obtain qt⋆q_t ⊳ Eqs. 7 and 8 9: Compress StS_t onto t∪tailK_t∪\tail\ as S~t S_t ⊳ Eq. 9 10: end for 11: Update θ by minimizing ℒM-OPD(θ)L_M -OPD(θ) ⊳ Eq. 11 Training and inference Training draws n independent on-policy student rollouts per prompt and performs three gradient-free teacher evaluations of each trajectory under the joint privileged, clean visual, and privilege-only views. At inference, the symbolic information and all teacher-side evaluations are removed; the trained student decodes normally from (I,Q)(I,Q) without additional inputs or computation. 3.3 Training Dataset Curation To turn the Symbolic Visual Gap into a training signal, we construct =(Ii,Qi,Pi)i=1ND=\(I_i,Q_i,P_i)\_i=1^N, where PiP_i is privileged symbolic information, instantiated as a caption for a natural image or executable code for a structured visual. We use the following three-stage curation pipeline. Cross-View Validation. We sample paired examples from V-Interaction (Qiao et al., 2025b), Mulberry (Yao et al., 2026), and ChartX (Xia et al., 2025), covering general VQA, mathematical reasoning, and chart understanding. The corresponding captions and code are taken directly from the source datasets. For natural images, we discard caption–image pairs whose contents are semantically inconsistent. For structured visuals, we execute the code and discard any sample whose code fails to execute, including those with syntax errors or missing dependencies. Symbolic-View Normalization. The dataset-provided captions and code follow heterogeneous formats. We use Qwen3.5-397B to reorganize and normalize these existing symbolic views while preserving their original visual content; no new caption or code content is generated. Existing captions are reorganized into a consistent descriptive format, with boilerplate and image-irrelevant content removed. For code, we remove environment-specific elements, including hard-coded file paths and output operations such as savefig, while retaining the statements that construct the visual. This step reduces formatting variation and removes environment-dependent code across data sources. Symbolic-View Utility Filtering. A valid image–symbolic pair does not necessarily improve the model’s ability to answer its question. We estimate Pass@8Pass@8 with the original visual input (I,Q)(I,Q) and with the additional symbolic view (I,P,Q)(I,P,Q). We retain only examples satisfying Pass@8(I,Q)≤Pass@8(I,P,Q)Pass@8(I,Q) @8(I,P,Q), excluding cases in which access to P lowers Pass@8Pass@8. The resulting dataset contains 32K examples spanning general VQA, mathematical diagrams, and charts. 4 Experiments 4.1 Experimental Setup Models and training data. We apply M-OPD to Qwen3.5-4B and Qwen3.5-9B (Qwen Team, 2026), both trained on MMOPD-32K, which pairs each image-question example with a symbolic view: a descriptive caption for a natural image or executable code for a mathematical diagram or chart. The symbolic view is used only during training and in the controlled gap analysis; all standard benchmark evaluations use only the original image and question. The construction and filtering of the training set are described in Section 3.3. Implementation details. Unless stated otherwise, M-OPD uses a frozen self-teacher initialized from the student checkpoint and the Jensen-Shannon divergence (JSD) as the distillation objective. Token-level distillation is computed over the top-K support with K=100K=100, and the residual saturation scale is set to γ=10γ=10. Each prompt produces n=2n=2 on-policy rollouts with a maximum response length of 81928192 tokens. We train for one epoch with a global batch size of 256256 and a learning rate of 1e−61e-6 on 8×8× 141141 GB H20 GPUs. Controlled baselines reuse the same backbone, training data, and prompts; we match the number of updates and the generated-token budget where applicable while keeping method-specific optimization settings. At inference, M-OPD requires neither the symbolic view nor the self-teacher. Benchmarks and metrics. We evaluate four groups of capabilities. General VQA includes MMStar (Chen et al., 2024), RealWorldQA (XAI, 2024), MMBench v1.1 (Liu et al., 2024a), and SimpleVQA (Cheng et al., 2025). Multimodal reasoning includes MathVista-mini (Lu et al., 2024), MathVerse-mini (Zhang et al., 2024), DynaMath (Zou et al., 2025), We-Math (Qiao et al., 2025a), LogicVista (Xiao et al., 2024), MMMU (Yue et al., 2024), and MMMU-Pro (Yue et al., 2025). Fine-grained perception includes V* Bench (Wu and Xie, 2024) and the 4K and 8K splits of HR-Bench (Wang et al., 2025). Document and chart understanding includes ChartQA (Masry et al., 2022), the descriptive (DQ) and reasoning (RQ) tracks of CharXiv (Wang et al., 2024), DocVQA (Mathew et al., 2021), OCRBench (Liu et al., 2024b), and the English-task average of OCRBench v2 (Fu et al., 2026). Compared methods. All controlled methods start from the corresponding Qwen3.5 checkpoint and share the same training dataset MMOPD-32K. Base denotes the unchanged model. SFT performs teacher-forced fine-tuning on reference responses (Ouyang et al., 2022). GRPO (Shao et al., 2024), GSPO (Zheng et al., 2025), and DAPO (Yu et al., 2026a) are RLVR baselines trained with the same judge Qwen3-32B. Vanilla OPSD (Zhao et al., 2026) transplants on-policy self-distillation to the multimodal setting in its original form: the frozen self-teacher is conditioned on the reference answer as privileged information, and the student model distills the resulting teacher distribution over its own rollouts. It therefore shares the on-policy sampling procedure, the frozen self-teacher, and the top-K support with M-OPD, and differs both in what privileges the teacher and in how the distillation target is formed. The three families are separated by the supervision they consume: SFT and RLVR take the reference answer as a training target or a verifier label, vanilla OPSD conditions its teacher on the reference answer, and M-OPD uses only the symbolic view P and never accesses the reference answer. Evaluation protocol. For a fair comparison, all checkpoints are evaluated with VLMEvalKit (Duan et al., 2024) using the same prompts, image preprocessing, answer extraction, and benchmark-specific metrics. For benchmarks requiring an LLM judge, we use Qwen3-32B with identical judging prompts across all methods. This unified protocol controls evaluation-related variation across methods. 4.2 Main Results We first compare M-OPD with controlled post-training baselines across all benchmarks. Table 1: Main results across diverse multimodal benchmarks. We compare different post-training methods on the Qwen3.5-4B and Qwen3.5-9B backbones. Benchmarks are grouped into general VQA, reasoning, perception, and document understanding. Results are obtained with VLMEvalKit using each benchmark’s evaluation metric. The best result in is shown in bold and the second best is underlined. Category Benchmark Qwen3.5-4B Qwen3.5-9B Baseline SFT GRPO GSPO DAPO OPSD M-OPD Baseline SFT GRPO GSPO DAPO OPSD M-OPD General VQA MMStar 72.9 70.1 73.8 72.1 68.7 72.8 74.6 74.9 70.5 73.4 74.5 73.0 75.4 75.9 RealWorldQA 75.7 75.4 77.8 76.5 74.2 76.1 77.4 78.0 78.3 76.1 76.2 76.1 77.9 77.5 MMBench v1.1 85.7 83.5 86.5 86.3 84.8 85.2 86.6 87.2 84.4 86.1 85.7 86.0 87.2 87.7 SimpleVQA 50.7 49.9 51.2 47.5 52.2 48.4 51.7 51.6 49.2 52.4 53.3 52.9 53.2 53.2 Reasoning Tasks MathVistamini 81.4 75.9 81.8 80.5 75.7 81.8 82.2 82.9 77.9 83.2 82.9 83.4 83.0 84.1 MathVersemini 53.9 50.2 53.3 53.9 54.3 53.4 54.5 54.1 52.0 47.9 49.9 54.9 52.9 57.9 DynaMath 72.4 70.0 71.9 71.5 70.3 70.9 74.0 75.0 72.4 75.8 73.4 74.4 76.1 77.7 We-Math 71.1 69.0 70.4 70.6 70.4 71.1 74.4 73.0 66.7 74.5 73.5 70.2 74.2 76.5 LogicVista 66.7 61.6 63.1 66.0 65.6 68.0 69.4 67.3 64.7 65.5 67.1 63.1 70.2 73.4 MMMU 72.6 68.7 71.3 71.7 70.5 72.2 73.8 74.7 70.0 72.6 74.7 71.1 74.1 75.8 MMMU-Pro 57.6 53.6 56.3 57.3 55.9 59.2 58.5 62.7 55.1 59.5 59.9 58.0 64.1 64.7 Perception Tasks V* Bench 81.7 76.4 83.8 84.3 80.1 84.3 88.5 82.2 84.3 83.8 84.3 82.2 86.9 84.8 HR-Bench 4K 81.5 80.4 83.6 81.6 78.0 80.3 85.0 82.7 80.9 82.3 82.4 80.0 81.3 84.0 HR-Bench 8K 75.1 72.4 76.1 76.9 73.3 76.0 80.5 77.6 75.8 78.0 76.9 77.5 79.6 78.4 Document Understanding ChartQA 84.2 80.4 83.9 76.4 80.2 84.4 85.1 85.4 81.7 84.6 84.8 83.6 84.0 93.7 CharXiv (DQ) 88.0 81.3 88.6 85.6 87.6 88.9 88.0 91.1 85.9 89.8 88.0 90.0 90.7 91.8 CharXiv (RQ) 65.9 62.8 67.6 62.5 62.2 64.5 68.8 69.0 63.1 68.6 67.7 68.2 68.6 71.2 DocVQA 95.1 94.2 95.3 94.7 94.9 95.0 95.5 94.9 95.4 94.9 94.9 95.0 95.0 95.4 OCRBench 87.1 81.3 87.4 86.5 86.4 87.6 87.8 85.9 84.0 87.3 86.4 86.7 86.0 87.0 OCRBench v2 (EN) 53.9 48.9 53.8 55.0 52.0 52.5 55.1 56.3 47.5 56.5 56.4 56.8 56.3 57.2 Total Average 73.7 70.3 73.9 72.9 71.9 73.6 75.6 75.3 72.0 74.6 74.6 74.2 75.8 77.4 Broad and consistent gains across capabilities. As shown in Table 1, M-OPD achieves the highest average score at both model scales, outperforming the Qwen3.5-4B and Qwen3.5-9B baselines by 1.91.9 and 2.12.1 points, respectively. More importantly, it improves performance in 3838 of the 4040 model–benchmark settings, covering general VQA, multimodal reasoning, fine-grained perception, and document understanding. These results demonstrate that the benefits of M-OPD extend consistently across capabilities rather than concentrating on a single task family. Stronger and more balanced than SFT and RLVR. With the same training data and backbones, SFT reduces the average score by 3.43.4 points at 4B and 3.33.3 points at 9B. GRPO, GSPO, and DAPO obtain gains on individual benchmarks but regress substantially on others; for instance, GSPO decreases ChartQA by 7.87.8 points at 4B, while GRPO decreases MathVerse-mini by 6.26.2 points at 9B. In contrast, M-OPD surpasses the best average among the RLVR baselines by 1.71.7 points at 4B and 2.82.8 points at 9B. Thus, M-OPD avoids trading gains in one capability for degradation in another. Benefits over vanilla OPSD. Vanilla OPSD shares the on-policy sampling procedure and frozen self-teacher with M-OPD, but differs in both the privileged supervision and the distillation target: it directly distills an answer-conditioned teacher, whereas M-OPD constructs a residual correction from the symbolic view. M-OPD improves the average over vanilla OPSD by 2.02.0 points at 4B and 1.61.6 points at 9B, including a 5.05.0-point gain on MathVerse-mini and a 9.79.7-point gain on ChartQA at 9B. These results support the combined benefit of symbolic supervision and residual target construction for multimodal on-policy self-distillation. 4.3 Ablation Study We conduct all ablations with Qwen3.5-4B on six benchmarks covering general VQA, multimodal reasoning, and fine-grained perception. Each experiment varies one factor while keeping the remaining settings at their defaults. We report individual benchmark scores and their unweighted average. Table 2: Effect of the distillation objective on Qwen3.5-4B. Forward and reverse KL denote DKL(qt⋆∥S~t)D_KL(q_t \| S_t) and DKL(S~t∥qt⋆)D_KL( S_t\|q_t ), respectively. The residual target construction is unchanged. Divergence V* Bench HR-Bench 4K HR-Bench 8K MMStar MathVistamini LogicVista Average Forward KL 84.3 84.8 79.5 74.4 82.0 67.6 78.8 Reverse KL 86.4 85.3 79.6 74.5 82.7 70.0 79.8 JSD 88.5 85.0 80.5 74.6 82.2 69.4 80.0 Distillation objective. As shown in Table 2, we compare forward KL, reverse KL, and JSD as the token-wise divergence measure while keeping the residual target construction unchanged. All three objectives improve over the baseline on every benchmark, showing that the benefits of M-OPD are not specific to a single divergence function. JSD and reverse KL each lead on three benchmarks, indicating different preferences across tasks. JSD achieves the highest overall average and is therefore adopted as our default. Table 3: Effect of the teacher update rule on Qwen3.5-4B. Current uses the latest student weights, EMA tracks their exponential moving average, and Frozen retains the initial weights. Teacher Update V* Bench HR-Bench 4K HR-Bench 8K MMStar MathVistamini LogicVista Average EMA 81.1 85.8 79.8 75.0 81.6 67.1 78.4 Frozen 88.5 85.0 80.5 74.6 82.2 69.4 80.0 Teacher update rule. We examine how updating the self-teacher affects distillation (Table 3). Both EMA and frozen teachers improve over the baseline on average. EMA performs better on HR-Bench 4K and MMStar, whereas the frozen teacher leads on the remaining four benchmarks and achieves a 1.61.6-point higher average. We therefore keep the teacher parameters frozen at initialization during training. Table 4: Effect of the maximum on-policy response length. We vary the response length on Qwen3.5-4B while fixing the other settings as default. Response Length V* Bench HR-Bench 4K HR-Bench 8K MMStar MathVistamini LogicVista Average 1024 84.3 83.5 78.6 75.0 81.4 66.2 78.2 2048 84.8 84.1 79.1 75.4 81.7 66.4 78.6 4096 86.4 84.2 79.9 73.9 82.1 69.6 79.4 8192 88.5 85.0 80.5 74.6 82.2 69.4 80.0 16384 86.9 85.2 80.5 74.3 82.7 68.1 79.6 Maximum response length. As shown in Table 4, we vary the maximum length of on-policy training responses from 10241024 to 1638416384 tokens. Different benchmarks favor different length limits, and increasing the limit does not consistently improve performance on every task. Nevertheless, all tested limits outperform the baseline on average, demonstrating robust gains across the evaluated range. Average performance peaks at 81928192 and declines slightly at 1638416384; we therefore adopt 81928192 as the default. Table 5: Effect of the number of on-policy rollouts. We vary the number of rollouts per prompt on Qwen3.5-4B while keeping all other settings at their default values. Rollout Number V* Bench HR-Bench 4K HR-Bench 8K MMStar MathVistamini LogicVista Average 1 84.3 83.5 81.0 74.1 82.9 68.9 79.1 2 88.5 85.0 80.5 74.6 82.2 69.4 80.0 4 86.4 85.5 79.3 74.4 82.2 69.1 79.5 8 86.9 85.0 79.1 74.5 82.0 68.7 79.4 Number of rollouts. Keeping all other settings at their default values, we vary the number of on-policy trajectories per prompt (Table 5). All tested rollout counts outperform the baseline on every benchmark. Increasing the count from one to two improves the average by 0.90.9 points, while further increases to four or eight yield slightly lower averages. The gains therefore persist across rollout counts, with two rollouts per prompt achieving the highest average score and serving as our default. 4.4 Effectiveness of Symbolic-to-Visual Correction M-OPD aims to transfer the evidence-use advantage of symbolic conditioning to image-conditioned reasoning. We examine this transfer in Qwen3.5-4B by comparing answer-to-evidence attention and the Symbolic Visual Gap before and after training. Evidence preference shifts toward correct evidence. We compare image-conditioned answer-to-evidence attention before and after training using the measure in Section 2.2. As shown in Figure 5 (left), the base model favors distracting evidence at every observed full-attention layer. In contrast, M-OPD increases the relative attention to correct evidence across all observed layers, with correct evidence receiving more attention than distracting evidence from layer 1212 onward. These results show that M-OPD reduces the attention bias toward distracting evidence and strengthens the association between answer generation and the premises supporting a correct derivation. Figure 5: Effectiveness of Symbolic-to-Visual Correction. (Left) Layer-wise answer-to-evidence preference F=log2(C/X)F= _2(C/X) under image conditioning, where positive values favor correct evidence. (Right) The Symbolic Visual Gap before and after training across three task families. The Symbolic Visual Gap narrows across tasks. We compare image-conditioned performance before and after training against the base model’s symbolic-conditioned accuracy, keeping this reference fixed for each task family. As shown in Figure 5 (right), M-OPD reduces the gap on Chart, Math, and General VQA. Chart shows the largest absolute reduction, while Math and General VQA close a larger proportion of their initial gaps. These results show that M-OPD transfers part of the advantage provided by symbolic views to image-conditioned performance across all three task families. Together, the two diagnostics show that M-OPD shifts evidence preference toward correct evidence while consistently narrowing the performance gap between image and symbolic conditioning, transferring part of the symbolic-view advantage to image-only inference. 5 Related Work Multimodal Reinforcement Learning. Reinforcement learning with verifiable rewards (RLVR) (Guo et al., 2025) has become an important post-train recipe to improving multimodal large language models (MLLMs) (Hong et al., 2025). Recent work strengthens visual reasoning by combining supervised cold-start training with RL or scaling RL across diverse multimodal tasks (Huang et al., 2026; Tong et al., 2025). Beyond reasoning over the original visual input, agentic approaches learn to acquire and manipulate visual evidence through operations such as cropping, zooming, and drawing (Hong et al., 2026; Su et al., 2026; Yan et al., 2026). However, final-answer rewards evaluate the completed response without explicitly specifying which intermediate visual evidence should support it. Our work instead uses token-level self-distillation from symbolic views to guide image-conditioned answer generation. On-Policy Self-Distillation. On-policy distillation (OPD) provides dense token-level supervision from a stronger teacher on the student’s own rollouts (Agarwal et al., 2024; Lu and Lab, 2025). Evaluating the teacher on prefixes sampled by the current student alleviates the distribution mismatch inherent in off-policy distillation, making OPD a compelling post-training paradigm (Li et al., 2026). Recent self-distillation methods obtain this supervision from the same model under more informative conditioning, without requiring a separate teacher model. Self-Distilled Reasoner (Zhao et al., 2026) uses reference solutions, SDPO (Hübotter et al., 2026) uses textual environment feedback, and Self-Distillation Zero (He et al., 2026) distills a self-reviser conditioned on the initial response and binary reward. In multimodal settings, Vision-OPD transfers crop-conditioned regional perception to a full-image student (Yuan et al., 2026). RLSD combines self-distilled token-level update magnitudes with reward-based update directions (Yang et al., 2026). Unlike existing multimodal self-distillation methods targeting specific capabilities, such as fine-grained perception in Vision-OPD and mathematical reasoning in RLSD, M-OPD improves a broad range of multimodal abilities through symbolic-to-visual correction. Distillation with Privileged Information. Privileged conditioning can improve self-teacher predictions while also introducing preferences that depend on information unavailable to the student. DOPD routes supervision between privileged teacher and student policies according to token-level advantages and probabilities (Yu et al., 2026b). Purified OPSD discounts reference-induced preferences and applies the remaining question-conditioned correction to a clean base prediction (Shen et al., 2026). M-OPD uses captions and code as privileged symbolic views, applying a residual correction to a clean image-conditioned prediction to improve evidence use. 6 Conclusion In this work, we revisit the assumption of a seamless transition from perception to reasoning. We identify the Symbolic Visual Gap and reveal visual evidence selection as one more bottleneck between perception and reasoning. 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Appendix A Additional Case Studies Figures 6, 7 and 8 provide additional examples of visual evidence selection, supplementing Figure 2 in the main text. Green and red mark correct and distracting evidence, respectively, with darker shading indicating stronger answer-to-evidence attention. As shown in Figure 6, the response contains the relevant chart values, yet associates a distracting value with the queried category and uses it in the derivation. The subsequent calculation is valid given that premise, but yields the wrong answer. Attention is also stronger on the distracting value used in the derivation. This case further distinguishes the availability of visual information from its selection as evidence. Figure 6: Evidence selection in a radial bar chart. Relevant values are available, but distracting evidence is used as the premise for the derivation. A similar pattern appears in Figure 7. The response repeatedly lists “Lack of control” across the three overlaps, but compares only pair-specific factors to conclude that there is no common cause. These distracting factors receive stronger attention, while the shared factor is omitted from the comparison. The required information is therefore already verbalized, but does not guide the final answer. Figure 7: Evidence selection in a Venn diagram. The shared factor is verbalized but omitted from the final comparison. Likewise, in Figure 8, the response lists the required values 2222, 2525, and 3939, yet selects 2222 and 2828 as the two smallest blue values and 5555 as the smallest green value. The resulting comparison, 22+28<5522+28<55, yields “No” instead of the correct “Yes” from 22+25>3922+25>39. Attention also favors the distracting values used in the computation. Together, these examples support the observation in the main text: having task-relevant information available in the trace does not ensure that it is selected as evidence for subsequent reasoning. Figure 8: Evidence selection in a line chart. The required values are listed, but the computation uses incorrectly selected extrema.