Investigating Inference-time Scaling for Chain of Multi-modal Thought: A Preliminary Study
Authors: Yujie Lin, Ante Wang, Moye Chen, Jingyao Liu, Hao Liu, Jinsong Su, Xinyan Xiao
Accepted at: acl25

Investigating Inference-time Scaling for Chain of Multi-modal Thought: A Preliminary Study

Yujie Lin1,3*, Ante Wang1,3*, Moye Chen2, Jingyao Liu1, Hao Liu2
Jinsong Su1,3,4† and Xinyan Xiao2
1School of Informatics, Xiamen University, China 2Baidu Inc., Beijing, China
3Key Laboratory of Digital Protection and Intelligent Processing of Intangible Cultural Heritage of Fujian and Taiwan (Xiamen University), Ministry of Culture and Tourism, China
4Shanghai Artificial Intelligence Laboratory
{yjlin,wangante}@stu.xmu.edu.cn jssu@xmu.edu.cn

Abstract

Recently, inference-time scaling of chain-of-thought (CoT) has been demonstrated as a promising approach for addressing multi-modal reasoning tasks. While existing studies have predominantly centered on text-based thinking, the integration of both visual and textual modalities within the reasoning process remains unexplored. In this study, we pioneer the exploration of inference-time scaling with multi-modal thought, aiming to bridge this gap.

To provide a comprehensive analysis, we systematically investigate popular sampling-based and tree search-based inference-time scaling methods on 10 challenging tasks spanning various domains. Besides, we uniformly adopt a consistency-enhanced verifier to ensure effective guidance for both methods across different thought paradigms. Results show that multi-modal thought promotes better performance against conventional text-only thought, and blending the two types of thought fosters more diverse thinking. Despite these advantages, multi-modal thoughts necessitate higher token consumption for processing richer visual inputs, which raises concerns in practical applications. We hope that our findings on the merits and drawbacks of this research line will inspire future works in the field.1

1 Introduction

The remarkable performance of OpenAI’s o1 in tackling reasoning tasks has sparked widespread research interest in studying inference-time scaling across various communities (Chen et al., 2025). This technique is built upon the success of Chain-of-Thought (CoT, Wei et al. 2022), which enables large language models (LLMs) to solve a problem through step-by-step reasoning. It makes use of additional computation at inference time to conduct “slow thinking” (Kahneman, 2011) to further improve the accuracy of responses. Taking the rich experience of pioneering research in language-only approaches (Xu, 2023; Yao et al., 2024b; Snell et al., 2024; Wu et al., 2024; Luo et al., 2024; Xie et al., 2024; Wang et al., 2024b,a; Li et al., 2025; Wang et al., 2025; Bi et al., 2025), rapid progress has been made in addressing multi-modal reasoning tasks leveraging typical methods such as Best-of-N, Beam Search, and Monte Carlo Tree Search (MCTS) (Xu et al., 2024; Yao et al., 2024a).

Although effective, these methods mostly follow the practice of text-based thinking, overlooking the crucial role of thinking in the visual modality in multi-modal scenarios. This oversight leads to sub-optimal performance, thus highlighting the need for new approaches that integrate both modalities. Consider the process of solving geometric problems as an example: humans often utilize auxiliary lines to facilitate problem-solving. Analogously, rich and intuitive visual information, e.g., drawn auxiliary lines, can enhance the model’s ability to generate improved solutions, as shown in Figure 1. Recent studies (Lu et al., 2022, 2023; Zhou et al., 2024; Hu

![Solving the problem using text-only thought vs. multi-modal thought. Additional visual information from the latter offers richer and more intuitive features, making it easier to yield better subsequent steps.](page_768_370_393_246.png)

Figure 1: Solving the problem using text-only thought vs. multi-modal thought. Additional visual information from the latter offers richer and more intuitive features, making it easier to yield better subsequent steps.
et al., 2024; Zhang et al., 2024b; Chen et al., 2024b; Cheng et al., 2025) have also demonstrated the benefits of incorporating supplementary visual information at each reasoning step compared with conventional text-based methods (Zhang et al., 2023; Zheng et al., 2023; Mitra et al., 2024). Therefore, an important yet under-explored question arises: What is the potential of inference-time scaling of multi-modal thinking?

To this end, we conduct the first study on this problem, shedding light on the merits and constraints of this new research line. We follow Wei et al. (2022) and Hu et al. (2024) to elicit text-only and multi-modal thought, respectively. For inference-time scaling, we investigate popular sampling-based and tree search-based methods. Sampling-based method generates multiple independent samples in parallel, applying techniques like Self-Consistency (Wang et al., 2023) or Best-of-N (Chen et al., 2024a; Wan et al., 2024) to select the most reliable reasoning trails. However, this approach is inefficient because it requires exploring full solution paths, even if a mistake has occurred early. Tree search-based method tackles this issue by utilizing sophisticated search algorithms, such as Beam Search (Yao et al., 2024b) and MCTS (Tian et al., 2024a). Both these methods ask for a critic to discriminate the promising samples or search steps. We consistently employ an advanced Large Vision Language Model (LVLM) as a verifier to infer critic scores and, alternatively, enhance this method by aggregating results from multiple trials. In this way, it effectively provides reliable feedback without the need for specific training.

We conduct a comparison of inference-time scaling using multi-modal and text-only thought across 10 datasets, encompassing tasks related to geometric reasoning, mathematical reasoning, and visual question answering. The main findings are as follows:

• The use of multi-modal thought achieves significantly better performance and higher upper bounds compared to text-only thought on average, demonstrating the potential of this line of research.

• Although effective, it requires higher token consumption to process richer visual inputs. This result calls for more efficient reasoning mechanisms, especially for practical concerns.

• Further analyses show that tree search-based methods effectively mitigate reasoning errors, such as invalid processed images. However, their success heavily relies on verifier performance, highlighting the need to develop more effective multi-modal verifiers.

We hope that these findings can inspire future research to develop more advanced and robust methods for multi-modal reasoning.

2 Preliminaries

In this section, we firstly establish the formulation for both text-only and multi-modal thought (\S2.1), and then provide a detailed explanation of two inference-time scaling paradigms (\S2.2): sampling-based and tree search-based methods. In addition, we present a prompting-based verifier equipped with a consistency-enhanced mechanism to effectively guide these inference-time scaling methods (\S2.3).

2.1 Thought Formulation

Chain-of-Thought (CoT, Wei et al. 2022) is a technique that encourages the model to generate intermediate reasoning steps \( \mathbf{S} = (s_1, ..., s_n) \) before reaching the final answer \( a \). In the context of multi-modal reasoning tasks, given a problem \( q \) and images \( I \), each reasoning step \( s_i \) is sampled from an LVLM \( \mathcal{M} \):

\[
s_i \sim \mathcal{M}(q, I, s_{1:i-1}).
\]

This expansion allows for more computations to be deployed and can unlock the ability to solve more complex problems (Li et al., 2024b).

Following the success on language-only reasoning tasks, most previous works (Zhang et al., 2023; Zheng et al., 2023; Mitra et al., 2024) study text-only thought, where \( \mathbf{S} \) is defined as a text string. In this work, we aim to explore the potential of multi-modal thought, where any reasoning step \( s_i \) can blend multi-modal information, e.g., both text and image.

However, as most prevalent LVLMs still struggle to generate reliable images, we follow Hu et al. (2024) to allow the LVLM to generate executable code for visual manipulation instead. Implementation details can be found in Appendix A.
2.2 Inference-Time Scaling

2.2.1 Sampling-based Methods
These methods scale inference-time computation by generating multiple reasoning chains in parallel, and then determining the most promising answer from them. Here we investigate two widely used techniques, Self-Consistency (Wang et al., 2023) and Best-of-N (Chen et al., 2024a; Wan et al., 2024).

Self-Consistency  This method leverages the intuition that the correct answer typically can be reached using multiple different ways of thinking (Wang et al., 2023). Given \( N \) sampled reasoning chains \( S_1, ..., S_N \) generated from the LVLM, it selects the most consistent answer via majority voting over their corresponding answers \( a_1, ..., a_N \):

\[
\mathbf{a}^* = \arg \max_{\mathbf{a} \in \{a_1, ..., a_N\}} \sum_{i=1}^N \mathbb{I}(a_i = \mathbf{a}),
\]

where \( \mathbb{I}(\cdot) \) denotes the indicator function and \( \mathbf{a}^* \) represents the selected answer.

Best-of-N  This approach utilizes trained verifiers to evaluate the correctness of model generated solutions. Compared to Self-Consistency based on voting, it can be more efficient when a strong verifier is available. Formally, given \( N \) sampled reasoning chains and a verifier \( \mathcal{F}(\cdot) \), we have

\[
S^* = \max_{S \in \{S_1, ..., S_N\}} \mathcal{F}(S),
\]

where \( S^* \) is the reasoning chain with the highest verifier score, from which the final answer \( \mathbf{a}^* \) is derived.

2.2.2 Tree Search-based Methods
Sampling-based methods are easy to implement due to their simplicity. However, they are inefficient because they require exploring full solution paths, even if a mistake occurs early (Xiang et al., 2025). To address this challenge, tree search-based methods are later explored. They model the problem-solving as a tree search process, where each node represents a reasoning step. Here, we investigate the most prevalent Beam Search (Welleck et al., 2022; Xie et al., 2023; Yao et al., 2024b; Wu et al., 2024) and MCTS (Xu, 2023; Ding et al., 2024; Luo et al., 2024; Xie et al., 2024; Liu et al., 2024a; Tian et al., 2024a; Yao et al., 2024a) algorithms in both language-only and multi-modal tasks.

Beam Search  Adapted from classical beam search algorithms used in sequence generation tasks (e.g., machine translation (Sutskever, 2014; Wu, 2016)), this method dynamically explores and prunes reasoning paths at each step for deductive reasoning. The algorithm operates with a beam width \( B \) (number of retained reasoning chains per step) and an expansion size \( N \) (new thoughts generated per candidate). Starting with \( N \) initial candidate thoughts sampled from a question \( q \) via Equation 1, a verifier \( \mathcal{F}(\cdot) \) scores all candidates, retaining only the top-\( B \) chains. Each retained chain is then expanded by sampling \( N \) new thoughts, producing \( B \times N \) candidates, after which the verifier reevaluates and prunes the pool to the top-\( B \) chains. This cycle of scoring and pruning repeats iteratively until all active chains reach finished states (final answers), at which point the highest-scoring finished chain across all iterations is selected as the final answer \( \mathbf{a}^* \).

MCTS  It is a decision-making algorithm that is powerful for solving complex problems, as demonstrated by AlphaGo (Silver et al., 2016, 2017). MCTS operates by iteratively exploring the most promising reasoning paths through four key phases: selection, expansion, evaluation, and backpropagation.

In the selection phase, the algorithm traverses the tree from the root node, recursively choosing child nodes using the Upper Confidence Bound (UCB) metric (Kocsis and Szepesvári, 2006). This metric strategically balances the exploitation of high-value paths and the exploration of under-visited paths. The UCB formula is defined as:

\[
\text{UCB}(s_i) = \frac{V(s_i)}{C(s_i)} + w \times \sqrt{\frac{\ln C(s_{i-1})}{C(s_i)}},
\]

where \( V(s_i) \) and \( C(s_i) \) denotes the accumulated value and count of being visited of \( s_i \). \( w \) is a weighting parameter that adjusts the exploration-exploitation balance. During expansion, the algorithm extends the selected node by generating a new thought through Equation 1. The evaluation phase then estimates the value of this newly expanded node using a verifier \( \mathcal{F}(\cdot) \). Finally, backpropagation updates the values of all ancestors, propagating the evaluation results back to the root.

After multiple iterations, the finished reasoning chain with the highest accumulated value is selected, yielding the optimal final answer \( \mathbf{a}^* \).
Figure 2: Three types of verifiers investigated in this work, where the classification-based verifier outputs sparse binary scores (0 or 1) and the regression-based verifier provides dense but inaccurate scores. We introduce the consistency-enhanced verifier to compute dense and accurate scores by aggregating multiple evaluations sampled from the classification-based verifier.

2.3 Verifiers for Inference-Time Scaling

The verifier \( \mathcal{F} \) is pivotal in inference-time scaling, tasked with evaluating the validity of reasoning chains. Existing approaches fall into two categories: training-based (Xiong et al., 2024; Wang et al., 2024c) and prompting-based (Tian et al., 2024b; Shinn et al., 2024; Jones et al., 2024). Training-based approaches hold theoretical promise by optimizing verifiers on corresponding labeled data. However, acquiring such annotations is challenging, resulting in datasets limited in scale and diversity, thereby restricting the generalizability of trained verifiers. Thus, this work focuses on prompting-based approaches, capitalizing on the strong instruction-following capabilities of LVLMs to assess reasoning chains.

Formally, given a reasoning chain \( s_{1:i} \), the verifier \( \mathcal{F} \) operates as: \( r = \mathcal{M}(P, s_{1:i}) \), where \( P \) represents the verification instruction, and \( r \) is the evaluation output, which includes a scalar score. Particularly, we investigate two instruction designs for \( P \):

• Classification-Based (Tian et al., 2024b; Zhang et al., 2024a; Shinn et al., 2024): It prompts the verifier to classify the reasoning chain as “correct” or “incorrect.” While intuitive, this binary output provides sparse feedback, offering limited granularity to guide searching.

• Regression-Based (Jones et al., 2024; Xiong et al., 2024): Here, the verifier is prompted to output a continuous score \( \in [0, 1] \) reflecting the quality of chains. However, directly predicting precise scores is error-prone, often yielding high-variance results that degrade performance.\footnote{The prompts used for these two designs are in Appendix B.}

To address these limitations, we introduce the Consistency-Enhanced Verifier, compared with the above two in Figure 2. This method aggregates \( N_v \) independent evaluations using classification-based instructions, computing the proportion of “correct” classifications across trials. In this way, it not only avoids variance in regression-based outputs but also overcomes the sparsity of single-trail classification, enabling more reliable guidance for inference-time scaling.

3 Experiments

3.1 Setup

Datasets  We conduct experiments on 10 datasets spanning three distinct domains:

• Geometric Reasoning: To assess geometry problem-solving capabilities, we utilize the Geometry3K dataset (Lu et al., 2021) and three tasks from IsoBench (Fu et al., 2024), including Connectivity, Maxflow, and Isomorphism.

• Mathematical Reasoning: We evaluate mathematical reasoning performance using the Parity, Convexity, and Winner ID tasks from IsoBench (Fu et al., 2024).

• Visual Question Answering (VQA): To test generalizability, we also employ three challenging VQA benchmarks: V* Bench (Wu and Xie, 2024), MMVP (Tong et al., 2024), and BLINK (Fu et al., 2025).

More detailed introduction to these datasets can be found in Appendix C.

Baselines  CoT (Wei et al., 2022) and Visual Sketchpad (Hu et al., 2024) are employed in our experiments to implement text-only thought and multi-modal thought, respectively. Both of them are further compared under four inference-time scaling methods: Self-Consistency, Best-of-N, Beam Search, and MCTS. Additionally, the following latest multi-modal reasoning frameworks are also compared in our main experiment, including Multimodal-CoT (Zhang et al., 2023), DD-CoT (Zheng et al., 2023), and CCoT (Mitra et al., 2024). Detailed baseline descriptions are provided in Appendix D.
<table>
  <tr>
    <th rowspan="2">Methods</th>
    <th colspan="3">Geometry</th>
    <th colspan="4">Math</th>
    <th colspan="3">VQA</th>
  </tr>
  <tr>
    <th>Geometry3K</th>
    <th>Maxflow</th>
    <th>Isomorphism</th>
    <th>Connectivity</th>
    <th>Convexity</th>
    <th>Parity</th>
    <th>Winner ID</th>
    <th>V* Bench</th>
    <th>MMVP</th>
    <th>BLINK</th>
  </tr>
  <tr>
    <td>Direct</td>
    <td>35.4</td>
    <td>28.9</td>
    <td>50.8</td>
    <td>52.3</td>
    <td>90.2</td>
    <td>72.1</td>
    <td>51.8</td>
    <td>51.7</td>
    <td>64.0</td>
    <td>60.7</td>
  </tr>
  <tr>
    <td>Multimodal-CoT</td>
    <td>43.8</td>
    <td>25.8</td>
    <td>50.0</td>
    <td>71.1</td>
    <td>91.8</td>
    <td>75.8</td>
    <td>57.6</td>
    <td>49.2</td>
    <td>65.3</td>
    <td>63.3</td>
  </tr>
  <tr>
    <td>DDCoT</td>
    <td>29.2</td>
    <td>25.8</td>
    <td>51.6</td>
    <td>60.2</td>
    <td>77.3</td>
    <td>82.1</td>
    <td>43.2</td>
    <td>47.9</td>
    <td>49.3</td>
    <td>64.0</td>
  </tr>
  <tr>
    <td>CCoT</td>
    <td>25.0</td>
    <td>26.6</td>
    <td>35.9</td>
    <td>12.5</td>
    <td>87.5</td>
    <td>56.5</td>
    <td>39.3</td>
    <td>53.4</td>
    <td>54.0</td>
    <td>64.4</td>
  </tr>
  <tr>
    <th colspan="11">Text-only Thought + Inference-time Scaling</th>
  </tr>
  <tr>
    <td>CoT</td>
    <td>39.6</td>
    <td>30.9</td>
    <td>43.0</td>
    <td>53.9</td>
    <td>91.0</td>
    <td>77.9</td>
    <td>56.4</td>
    <td>46.2</td>
    <td>65.7</td>
    <td>62.2</td>
  </tr>
  <tr>
    <td>+Self-Consistency</td>
    <td>37.5</td>
    <td>35.9</td>
    <td>51.6</td>
    <td>62.5</td>
    <td>93.4</td>
    <td>76.0</td>
    <td>57.2</td>
    <td>52.1</td>
    <td>62.3</td>
    <td>64.6</td>
  </tr>
  <tr>
    <td>+Best-of-N</td>
    <td>43.8</td>
    <td>39.8</td>
    <td>53.1</td>
    <td>60.9</td>
    <td>93.4</td>
    <td>81.0</td>
    <td>56.0</td>
    <td>53.4</td>
    <td>67.3</td>
    <td>65.5</td>
  </tr>
  <tr>
    <td>+Beam Search</td>
    <td>41.7</td>
    <td>54.7</td>
    <td>59.4</td>
    <td>65.6</td>
    <td>94.5</td>
    <td>85.2</td>
    <td><b>61.1</b></td>
    <td>37.8</td>
    <td>70.0</td>
    <td>59.8</td>
  </tr>
  <tr>
    <td>+MCTS</td>
    <td>45.8</td>
    <td>51.6</td>
    <td>62.5</td>
    <td>64.8</td>
    <td>94.9</td>
    <td>81.0</td>
    <td>58.4</td>
    <td>53.4</td>
    <td>66.7</td>
    <td><u>66.2</u></td>
  </tr>
  <tr>
    <th colspan="11">Multi-modal Thought + Inference-time Scaling</th>
  </tr>
  <tr>
    <td>Visual Sketchpad</td>
    <td>33.3</td>
    <td>81.3</td>
    <td>86.1</td>
    <td>85.9</td>
    <td>93.0</td>
    <td>81.0</td>
    <td>53.7</td>
    <td>49.1</td>
    <td>66.3</td>
    <td>58.2</td>
  </tr>
  <tr>
    <td>+Self-Consistency</td>
    <td>39.6</td>
    <td>85.2</td>
    <td>88.3</td>
    <td>87.5</td>
    <td>96.5</td>
    <td>83.6</td>
    <td>54.1</td>
    <td>51.3</td>
    <td>68.3</td>
    <td>61.5</td>
  </tr>
  <tr>
    <td>+Best-of-N</td>
    <td>43.8</td>
    <td>91.4</td>
    <td>89.8</td>
    <td>91.4</td>
    <td>94.1</td>
    <td>82.8</td>
    <td>54.9</td>
    <td>55.0</td>
    <td>67.7</td>
    <td>66.1</td>
  </tr>
  <tr>
    <td>+Beam Search</td>
    <td><b>54.2</b></td>
    <td><b>95.3</b></td>
    <td><b>92.2</b></td>
    <td><b>99.2</b></td>
    <td><b>96.5</b></td>
    <td><b>87.2</b></td>
    <td>58.4</td>
    <td><b>64.3</b></td>
    <td>71.3</td>
    <td>64.8</td>
  </tr>
  <tr>
    <td>+MCTS</td>
    <td>52.1</td>
    <td>94.5</td>
    <td>93.0</td>
    <td>99.2</td>
    <td>96.9</td>
    <td>86.7</td>
    <td>60.3</td>
    <td>62.2</td>
    <td><b>74.0</b></td>
    <td><u>68.7</u></td>
  </tr>
</table>

Table 1: Accuracy across 10 datasets from three domains. For each dataset, the best result is highlighted in bold, and the second-best is emphasized with underlining.

Metrics We evaluate the performance using two metrics: Accuracy and Pass@K. Accuracy measures whether the highest-ranked answer is correct, while Pass@K represents whether the correct answer can be recalled within \( K \) answers.

Implementation Details We employ GPT-4o-mini\(^3\) as the policy and verifier by default. For all experiments, we set the temperature to 1.0 during generation. For Self-Consistency and Best-of-N, the number of samples \( N \) is set to 5. For Beam Search, we set both the beam width \( B \) and expansion size \( N \) to 4. For MCTS, we set the maximum expansion per node to 4, the maximum number of iterations to 30, and the exploration constant \( w \) in UCB to 1.4. We adopt the consistency-enhanced verifier by default and set the number of samples \( N_v \) to 5.

3.2 Multi-modal vs. Text-only Thought

Multi-modal thought shows greater advantages compared with text-only thought. Table 1 presents compelling experimental results that highlight the superiority of multi-modal thought over both text-only thought and the latest multi-modal reasoning frameworks, particularly when enhanced by inference-time scaling.

A closer analysis reveals notable performance variations across different domains. In geometric reasoning, multi-modal thought consistently outperforms text-only thought under single-chain reasoning, with the exception of Geometry3K, where it initially lags but surpasses text-only thought when inference-time scaling is applied. In mathematical reasoning, the advantages of multi-modal thought become even more evident. For example, while text-only thought initially excels on Winner ID due to the problem’s rich textual context, multi-modal thought progressively closes the gap under inference-time scaling. The similarly superior performance observed across VQA tasks further underscores the adaptability and effectiveness of multi-modal thought, strengthening its potential for broader applications.

Multi-modal thought exhibits a higher performance upper limit. To further investigate the potential of text-only and multi-modal thought, we compare their performance upper limits on the Maxflow dataset using Best-of-N and MCTS methods. As shown in Figure 3, within Best-of-N, accuracy consistently improves as \( N \) increases, with multi-modal thought achieving a significantly

![Performance comparison between text-only thought and multi-modal thought on the Maxflow dataset under Best-of-N (left) and MCTS (right).](page_1012_1202_410_282.png)

Figure 3: Performance comparison between text-only thought and multi-modal thought on the Maxflow dataset under Best-of-N (left) and MCTS (right).
Figure 4: Performance comparison between text-only thought and multi-modal thought varies with the maximum token consumption on the Maxflow dataset under Self-Consistency.

Figure 5: Performance of Self-Consistency on the Maxflow dataset as the number of samples increases, comparing text-only thought, multi-modal thought, and the hybrid form.

higher upper limit. This trend is further validated by the MCTS results, which exhibit a similar pattern, reinforcing the superior potential of multi-modal thought.

The effectiveness of multi-modal thought relies on higher token consumption. Given the substantial difference in token cost between processing text and image information in LVLMs, it is crucial to understand the trade-off between performance and token usage for text-only and multi-modal thought. To this end, we conduct experiments on the Maxflow dataset using Self-Consistency to analyze their performance under inference-time scaling with varying token limits per sample.

Figure 4 illustrates the relationship between token limits and performance for both text-only and multi-modal thought. Under strict token constraints, multi-modal thought underperforms compared to text-only thought. This is likely due to the limited number of reasoning steps multi-modal thought can sample when the token budget is severely restricted, preventing the model from effectively processing visual information.

However, as the token limits are relaxed, the performance of multi-modal thought improves rapidly. With a more generous token budget, the model can fully leverage visual information, leading to significant performance gains. This highlights a key trade-off: while multi-modal thought enables more complex reasoning, it requires significantly more tokens to process visual inputs effectively. This suggests that future research should prioritize developing methods for compressing or optimizing the token consumption associated with image processing in LVLMs, enabling more efficient utilization of multi-modal thought.

Multi-modal and text-only thought are complementary. While our results demonstrate the overall effectiveness of multi-modal thought, we further examine whether text-only thought retains value in certain scenarios. We hypothesize that the two approaches may be complementary, each leveraging different aspects of the input. To test this, we conduct experiments on the Maxflow dataset using the Self-Consistency method, comparing text-only thought, multi-modal thought, and a hybrid form, i.e., voting from both text-only thought and multi-modal thought.

As presented in Figure 5, the hybrid form outperforms both text-only and multi-modal thought individually, suggesting that text-only thought provides valuable insights that enhance reasoning, even in cases where multi-modal reasoning alone may fall short. This performance boost underscores the complementary nature of the two approaches and highlights the potential of a balanced integration of them for more robust multi-modal reasoning.

3.3 Ablation Study on the Verifier

Consistency-enhanced verifier outperforms naive prompting-based alternatives. To evaluate the superiority of our proposed consistency-enhanced verifier, we compare its performance against classification-based and regression-based verifiers, as described in §2.3. We conduct this comparison on the Geometry3K, Maxflow, and Isomorphism datasets using MCTS with multi-modal thought. As shown in Figure 6, our verifier consistently outperforms both naive prompting-based
Figure 6: Performance comparison of Classification-Based, Regression-Based, and Consistency-Enhanced Verifiers using MCTS with multi-modal thought across three datasets.

Figure 7: Error statistics on four inference-time scaling methods with multi-modal thought.

approaches across all three datasets, demonstrating its effectiveness in addressing the limitations of existing approaches and providing more reliable guidance for inference-time scaling.

Consistency-enhanced verifier performance scales with \( N_v \). Our consistency-enhanced verifier is designed based on the hypothesis that aggregating multiple verifications enhances robustness and performance. Specifically, we expect accuracy to improve as the number of sampled verifications increases. To validate this, we conduct experiments using MCTS on the Geometry3K, Maxflow, and Isomorphism datasets, systematically varying \( N_v \). From the results in Table 2, we observe a clear trend: increasing \( N_v \) consistently improves performance. This finding strongly supports our hypothesis, confirming the effectiveness of the design rationale for the verifier.

<table>
  <tr>
    <th></th>
    <th>Geometry3K</th>
    <th>Maxflow</th>
    <th>Isomorphism</th>
  </tr>
  <tr>
    <td>\( N_v = 3 \)</td>
    <td>41.7</td>
    <td>89.8</td>
    <td>91.4</td>
  </tr>
  <tr>
    <td>\( N_v = 5 \)</td>
    <td>52.1</td>
    <td>94.5</td>
    <td>93.0</td>
  </tr>
  <tr>
    <td>\( N_v = 7 \)</td>
    <td>58.3</td>
    <td>97.7</td>
    <td>96.1</td>
  </tr>
</table>

Table 2: Performance variants with \( N_v \) under MCTS method with multi-modal thought.

3.4 Error Analysis

To gain deeper insights into the behavior of multi-modal thought under different inference-time scaling methods, we conduct a detailed error analysis. We identify four primary sources of error: Wrong Decision, Execution Error, Ineffective Operation, and Invalid Reasoning (detailed explanations are provided in Appendix E) and then randomly sample 100 error cases from each method across all datasets, manually classifying the underlying causes.

Tree search-based methods significantly reduce intermediate errors. Figure 7 presents the distribution of error types for various inference-time scaling methods. We can find that sampling-based methods exhibit a predominance of intermediate reasoning errors (Execution Error, Ineffective Operation, Invalid Reasoning). Among these, Execution Error is the most prevalent, which mostly occurs in VQA tasks. This is likely due to the difficulty expert models face in accurately operating images, coupled with a lack of error-handling logic in the code. Consequently, simple sampling methods often continue exploring flawed paths after encountering such errors, leading to the failure. In contrast, tree search-based methods significantly mitigate intermediate reasoning errors. By incorporating verifiers at each step, these methods strategically select optimal reasoning paths, effectively preventing the exploration of erroneous reasoning steps.

Effective verifiers are crucial for further error reduction. The reduction in intermediate errors leads to a relative increase of Wrong Decision, highlighting this error type as the new primary challenge. Further manual observation reveals that these errors primarily stem from limitations in the verifier. While effective at identifying blatant errors, the verifier struggles with more nuanced or complex reasoning steps. This underscores the critical importance of improving verifier effectiveness, particularly in discerning subtle errors, to fully unlock the potential of multi-modal thought.
<table>
  <tr>
    <th>Methods</th>
    <th>Geometry3K</th>
    <th>Maxflow</th>
    <th>Connectivity</th>
  </tr>
  <tr>
    <th colspan="4">Qwen2-VL-72B-Instruct</th>
  </tr>
  <tr>
    <td>Direct</td>
    <td>43.8</td>
    <td>10.4</td>
    <td>85.4</td>
  </tr>
  <tr>
    <td>CoT</td>
    <td>31.3</td>
    <td>35.4</td>
    <td>64.6</td>
  </tr>
  <tr>
    <td>+Best-of-N</td>
    <td>31.3</td>
    <td>35.4</td>
    <td>66.7</td>
  </tr>
  <tr>
    <td>Visual Sketchpad</td>
    <td>41.7</td>
    <td>12.5</td>
    <td>93.8</td>
  </tr>
  <tr>
    <td>+Best-of-N</td>
    <td>45.8</td>
    <td>31.3</td>
    <td>98.4</td>
  </tr>
  <tr>
    <th colspan="4">OPENAI-gpt-4o-mini</th>
  </tr>
  <tr>
    <td>Direct</td>
    <td>35.4</td>
    <td>28.9</td>
    <td>52.3</td>
  </tr>
  <tr>
    <td>CoT</td>
    <td>39.6</td>
    <td>30.9</td>
    <td>53.9</td>
  </tr>
  <tr>
    <td>+Best-of-N</td>
    <td>43.8</td>
    <td>39.8</td>
    <td>60.9</td>
  </tr>
  <tr>
    <td>Visual Sketchpad</td>
    <td>33.3</td>
    <td>81.3</td>
    <td>85.9</td>
  </tr>
  <tr>
    <td>+Best-of-N</td>
    <td>43.8</td>
    <td>91.4</td>
    <td>91.4</td>
  </tr>
  <tr>
    <th colspan="4">OPENAI-gpt-4o</th>
  </tr>
  <tr>
    <td>Direct</td>
    <td>52.1</td>
    <td>50.0</td>
    <td>71.1</td>
  </tr>
  <tr>
    <td>CoT</td>
    <td>54.2</td>
    <td>55.5</td>
    <td>76.6</td>
  </tr>
  <tr>
    <td>+Best-of-N</td>
    <td>70.8</td>
    <td>67.2</td>
    <td>90.6</td>
  </tr>
  <tr>
    <td>Visual Sketchpad</td>
    <td>62.5</td>
    <td>93.8</td>
    <td>98.4</td>
  </tr>
  <tr>
    <td>+Best-of-N</td>
    <td>77.1</td>
    <td>96.9</td>
    <td>99.2</td>
  </tr>
</table>

Table 3: Accuracy on three datasets by employing different policy models.

3.5 Policy Model Impact

To assess the impact of the underlying policy model on the effectiveness of multi-modal thought, we extended our experiments beyond the previously used GPT-4o-mini to include a representative open-source LVLM Qwen2-VL-72B-Instruct (Wang et al., 2024d) and a more advanced closed-source LVLM GPT-4o\footnote{gpt-4o-2024-08-06}. The experiments are conducted on the Geometry3K, Maxflow, and Connectivity datasets, using Best-of-N as the inference-time scaling method.

Performance of multi-modal thought generalizes across models. As shown in Table 3, multi-modal reasoning consistently improves performance across all three evaluated LVLMs, suggesting that the benefits of multi-modal thought are not model-specific but rather a generalizable advantage across different architectures and training paradigms.

The stronger the model, the greater the performance gains. An intriguing trend also emerges from the results, i.e., the performance gains from multi-modal thought correlate with the strength of the policy model. Weaker models, such as Qwen2-VL, exhibit modest improvements, whereas the more powerful GPT-4o achieves significantly larger gains. This suggests that a model’s capacity to effectively extract and integrate visual information is contingent upon its inherent capabilities. Stronger models, possessing superior reasoning abilities, are able to leverage multi-modal cues more efficiently, resulting in greater performance improvements under inference-time scaling.

4 Discussion

The necessity of multi-modal thought. In this study, we empirically demonstrate that multi-modal thought possesses unique potential in representing cognitive processes that transcend the limitations of text alone. We argue that this approach can convey richer cognitive features, a perspective that aligns with the opinions from Chen et al. (2025). A representative example, illustrated in Figure 1, involves geometric reasoning. Here, visual-spatial elements (e.g., the use of auxiliary lines) provide critical insights that are inherently difficult to articulate through textual descriptions, thereby enhancing conceptual clarity. By integrating such multi-modal thought, the policy can engage in more informed decision-making processes, systematically improving problem-solving performance.

Reducing token costs for multi-modal thought to achieve efficient inference. Our analysis of token computations (Figure 4) demonstrates that multi-modal thought, while effective, incurs substantial token costs. This underscores the need for efficient compression techniques specifically designed for processing visual information in LVLMs. While prior works (Wang and Xuan, 2024; Huang et al., 2024; Zhu et al., 2024) have explored visual token compression, they have largely overlooked the unique challenges of multi-modal thought reasoning. Thus developing methods for efficient visual information handling in this context becomes a key direction for future research.

Constructing stronger multi-modal verifiers for better performance. Our error analysis (\S3.4) highlights the critical role of the verifier in inference-time scaling, where its effectiveness directly influences error reduction and performance gains. However, research on multi-modal verifiers (Ouali et al., 2024; Xiyao et al., 2024; Yu et al., 2024; Zang et al., 2025) remains in its early stages, limiting the potential of multi-modal thought. Advancing more robust and accurate verifiers is therefore crucial for fully unlocking the benefits of inference-time scaling.

Exploring inference-time scaling for the chain of any-modal thought reasoning. Recent works
have extended CoT reasoning beyond text and images to more modalities, such as audio (Ma et al., 2025) and video (Fei et al., 2024). However, the effectiveness of inference-time scaling for these modalities remains unexplored. While our findings confirm the benefits of scaling for text-image reasoning, whether these advantages extend to other modality combinations remains an open question.

5 Conclusion

In this work, we present a systematic investigation of inference-time scaling with multi-modal thought. We conduct comprehensive experiments across 10 challenging tasks spanning diverse domains, investigating both sampling-based and tree search-based scaling methods. We demonstrate that multi-modal thought consistently outperform text-only reasoning, achieving progressively stronger performance with increased computational budgets. This empirical evidence positions multi-modal thought scaling as a promising direction for enhancing complex reasoning capabilities in multi-modal scenarios. However, we notice that performance gains are accompanied by higher computational costs and depend heavily on the effectiveness of the verifier, thus hindering real-world deployment. We hope this work will serve as a springboard for studying inference-time scaling with multi-modal thought, thereby advancing multi-modal reasoning.

Limitations

Due to the inability of current LVLMs to generate fine-grained images directly, we rely on generating image operation codes as a substitute, preventing a fully end-to-end multi-modal thought process. Additionally, we do not explore smaller-scale models, such as 7B, as their limited visual processing, instruction-following, and code generation abilities make them unsuitable for objectively evaluating multi-modal thought under inference-time scaling. Another limitation is the exclusion of training-based methods that require long CoT data, as current LVLMs struggle to generate high-quality long reasoning chains over multi-modal datasets, making data construction a significant challenge. Lastly, our study focuses solely on text and image modalities, leaving the generalizability of our findings to other modalities, such as audio and video, an open question.

Acknowledgments

The project was supported by National Key R&D Program of China (No. 2022ZD0160501), Natural Science Foundation of Fujian Province of China (No. 2024J011001), and the Public Technology Service Platform Project of Xiamen (No.3502ZZ20231043). We also thank the reviewers for their insightful comments.

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A Implementation Details of Multi-modal Thought

Recognizing the limitations of current generative models in fine-grained drawing, we leverage Visual Sketchpad (Hu et al., 2024) to enable multi-modal reasoning. Visual Sketchpad empowers LVLMs to generate sketches as intermediate reasoning artifacts, boosting problem-solving capabilities. It interprets multi-modal queries, devises sketching strategies, synthesizes programs for sketch generation, and analyzes the resulting sketches to formulate responses.

Specifically, at each step \( i \), the model outputs a textual thought \( t_i \) and a visual operation \( o_i \):

\[
t_i, o_i = \mathcal{M}(q, I, s_{1:i-1}),
\]

where \( o_i \) is executable code specifying visual operations.

A code executor \( \mathcal{G} \) then updates the visual contexts by applying \( o_i \) to the previous images \( I \):

\[
I' = \mathcal{G}(I, o_i),
\]
<table>
  <tr>
    <th>Dataset</th>
    <th>Description</th>
    <th>Size</th>
  </tr>
  <tr>
    <td>Maxflow</td>
    <td>Find the maximum flow through a network.</td>
    <td>128</td>
  </tr>
  <tr>
    <td>Isomorphism</td>
    <td>Determine structural equivalence of two graphs.</td>
    <td>128</td>
  </tr>
  <tr>
    <td>Connectivity</td>
    <td>Determine path existence between two graph vertices.</td>
    <td>128</td>
  </tr>
  <tr>
    <td>Convexity</td>
    <td>Determine whether a function is convex or concave.</td>
    <td>256</td>
  </tr>
  <tr>
    <td>Parity</td>
    <td>Determine if a function is even, odd, or neither.</td>
    <td>384</td>
  </tr>
  <tr>
    <td>Winner ID</td>
    <td>Determine chess game outcome from the final board state.</td>
    <td>257</td>
  </tr>
  <tr>
    <td><i>V*</i> Bench</td>
    <td>Questions about small items in an image.</td>
    <td>238</td>
  </tr>
  <tr>
    <td>MMVP</td>
    <td>Visual questions designed to reveal CLIP-based LM shortcomings.</td>
    <td>300</td>
  </tr>
  <tr>
    <td>BLINK</td>
    <td>Visual perception tasks challenging for multi-modal LMs.</td>
    <td>728</td>
  </tr>
</table>

Table 4: The detailed introduction of the datasets in our experiments.

\[
\mathbf{I} = \mathbf{I} \cup \mathbf{I}' ,
\]

where \( \mathbf{I}' \) represents the updated images. Thus the next reasoning step \( s_i = \{ t_i, o_i, \mathbf{I}' \} \).

Visual Sketchpad integrates various tools for sketch generation. For geometric and mathematical tasks, it uses Python libraries like matplotlib and networkx. For VQA, it incorporates specialized vision models and visual manipulations, including:

• **Detection:** Use Grounding-DINO (Liu et al., 2024b) to detect and label objects in images based on textual queries.

• **Segmentation:** Generate segmented images with labeled masks by employing SegmentAnything (Kirillov et al., 2023) and Semantic-SAM (Li et al., 2024a).

• **Depth Estimation:** Leverage DepthAnything (Yang et al., 2024) to produce depth maps from input images.

• **Visual Search:** Implements a sliding window approach to locate small objects based on textual queries.

• **Image Manipulation:** Include zoom/crop (region of interest extraction) and image overlay (alpha blending).

B Prompts for Verifiers

We use the following prompts for two kinds of verifiers:

• **Classification-Based:** *Verify the reasoning process above and provide the final judgment of 'yes' or 'no' on whether the reasoning is valid at last after "Final Decision:"*.

• **Regression-Based:** *Verify the reasoning process above and provide a validation score from 0 (worst) to 1.0 (best) at last after "Final Score:"*.

C Datasets

The detailed introduction of datasets in our experiments are presented in Table 4.

D Baseline Introduction

Here we introduce the latest multi-modal reasoning baselines in our experiments:

• **Multimodal-CoT** (Zhang et al., 2023): A multi-modal extension of CoT that concate-
nates the reasoning process with the problem context for answering.

• DDCoT (Zheng et al., 2023): A method that decouples reasoning and recognition, and then integrate visual capabilities into the reasoning process.

• CCoT (Mitra et al., 2024) A framework that generates a scene graph before answering.

E Error Category Explanation

We define four categories of error of multi-modal thought under inference-time scaling methods as follows:

• Wrong Decision: The correct answer is present within the candidate reasoning chains but is not selected. This indicates an error in the decision-making process.

• Execution Error: The code generated during the reasoning process contains bugs, preventing the reasoning process from proceeding correctly.

• Ineffective Operation: The reasoning process is hampered by ineffective operations that produce unhelpful or misleading visual information.

• Invalid Reasoning: The error stems from a flawed reasoning process, leading to an incorrect conclusion.

Examples of each error category are provided in Figure 8.

F Additional Experiments

F.1 Test Results on M^3CoT

To validate the effectiveness on more challenging datasets, we conduct evaluations on M^3CoT (Chen et al., 2024b) datasets using GPT-4o, as presented in Table 5. These results demonstrate that the scaling of multi-modal thought continues to yield performance improvements in more complex scenarios.

<table>
  <tr>
    <th>Methods</th>
    <th>M^3CoT</th>
  </tr>
  <tr>
    <td>Directly</td>
    <td>64.4</td>
  </tr>
  <tr>
    <td>CoT</td>
    <td>65.0</td>
  </tr>
  <tr>
    <td>+Self-Consistency</td>
    <td>68.2</td>
  </tr>
  <tr>
    <td>+Best-of-N</td>
    <td>68.8</td>
  </tr>
  <tr>
    <td>Visual Sketchpad</td>
    <td>66.4</td>
  </tr>
  <tr>
    <td>+Self-Consistency</td>
    <td>69.0</td>
  </tr>
  <tr>
    <td>+Best-of-N</td>
    <td>70.4</td>
  </tr>
</table>

Table 5: Performance on M^3CoT using GPT-4o.

<table>
  <tr>
    <th>Methods</th>
    <th>BLINK</th>
  </tr>
  <tr>
    <td>Visual Sketchpad</td>
    <td>58.2</td>
  </tr>
  <tr>
    <td>+α=0.2</td>
    <td>57.1</td>
  </tr>
  <tr>
    <td>+α=0.4</td>
    <td>54.8</td>
  </tr>
  <tr>
    <td>+α=0.6</td>
    <td>47.4</td>
  </tr>
</table>

Table 6: Performance on BLINK using multi-modal thought with varying intermediate image resolution scale factors (α).

larger \( \alpha \) corresponds to lower resolution and poorer quality). The results are reported in Table 6.

These results show that reduced image quality (i.e., increased \( \alpha \)) leads to a clear degradation in reasoning performance and we also observe a qualitative reduction in inference latency with lower-resolution images. This suggests a potential trade-off between reasoning accuracy and computational efficiency, which merits further exploration.

Reviewer paper summaries: This paper investigates inference-time scaling strategies for multi-modal chain-of-thought (CoT) reasoning, comparing text-only and multi-modal approaches across 10 datasets in geometric, mathematical, and visual question-answering tasks. The authors systematically evaluate sampling-based (e.g., Self-Consistency, Best-of-N) and tree search-based (e.g., Beam Search, MCTS) methods, introducing a consistency-enhanced verifier to guide reasoning. Results show that multi-modal reasoning outperforms text-only methods in accuracy (e.g., 52.1% vs. 45.8% on Geometry3K with MCTS, Table 1) but incurs higher token costs. The study highlights the potential of multi-modal CoT while exposing challenges like computational overhead and verifier limitations.

This paper investigates inference-time scaling in multi-modal thought, bridging the gap in research focused on text-only CoT. Through experiments, it evaluates multi-modal thought in geometric, mathematical, and visual reasoning tasks, comparing sampling (e.g., Self-Consistency) and tree search methods (e.g., Beam Search, MCTS). Results show multi-modal thought outperforms text-only thought, especially in complex tasks, but requires more computational resources (e.g., token usage) and depends on verifier quality. The paper proposes a consistency-enhanced verifier to improve scoring reliability, enhancing inference-time scaling.
Summary of strengths: - Comprehensive empirical evaluation : The paper tests methods across diverse domains (geometry, math, VQA) with 10 datasets, providing granular results (e.g., Table 1 shows multi-modal gains in 10 tasks).

- Figure 4 reveals the trade-off between performance and token consumption, offering actionable guidance for deployment, which I personally favor much.

- The consistency-enhanced verifier (§2.3) is rigorously validated against classification/regression baselines (Figure 6), demonstrating its superiority.

- The breakdown of error types (e.g., execution errors, decisive errors, etc) adds depth to the findings.

1. First study on inference-time scaling in multi-modal thought, filling a key research gap.
Introduced the Consistency-Enhanced Verifier, boosting reliability.
2. Tested on 10 datasets (geometric, mathematical, and visual reasoning tasks), validating multi-modal thought’s effectiveness.
Compared methods like Self-Consistency, Best-of-N, Beam Search, and MCTS, offering robust experimental insights.
Summary of weaknesses: - **Incomplete Literature Review**. The paper asserts that "existing studies have predominantly focused on text-based reasoning, with the integration of visual and textual modalities in reasoning remaining unexplored." However, this claim overlooks recent works such as MVoT, VoT, and Mulberry, which explicitly combine visual and textual modalities for multi-modal reasoning—some even incorporate tree search techniques (e.g., MCTS). Since these methods predate the ARR Feb 2025 submission deadline, they undermine the paper’s initial argument regarding the novelty of its research gap.

- The Best-of-N framework introduces a trained verifier, adding unnecessary complexity compared to training-free approaches. Furthermore, the evaluation of the verifier’s robustness is insufficient: its performance on out-of-distribution (OOD) tasks remains untested, raising doubts about the reliability of the method’s dependency on a learned verification component.

- While the paper combines existing inference-time scaling methods (e.g., self-consistency, Best-of-N, beam search, MCTS) with CoT/Visual Sketchpad, it does not propose any novel technical components. This absence of innovation diminishes the work’s originality and restricts its contribution to a mere synthesis of prior techniques.

- The visual sketch pad can only suggest that traditional tasks requiring textual thought might benefit more from multimodal thought. I hope to consider benchmarks that genuinely require multi-step visual thought [1], to determine if consistent results can be achieved.
- The proposed verification performance depends on the quality of the underlying verifier; if the verifier is biased, the results may be unreliable. I am curious whether the conclusions are robustly consistent across fields beyond mathematics, such as multimodal commonsense reasoning and scientific reasoning (e.g., M3CoT [1] and ScienceQA [2] benchmarks).
- Regarding token efficiency, should image tokens be considered? I believe that in multimodal thought, images must inherently be part of the logical output tokens.

* If you can address my concerns, I will increase my score.

- CoMT: A Novel Benchmark for Chain of Multi-modal Thought on Large Vision-Language Models
- Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answering
- M3CoT: A Novel Benchmark for Multi-Domain Multi-step Multi-modal Chain-of-Thought
Comments, suggestions and typos: N/A

Missing Multi-modal Reasoning Reference:
- CoMT: A Novel Benchmark for Chain of Multi-modal Thought on Large Vision-Language Models
- Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answering
- MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts
- MathVerse: Does Your Multi-modal LLM Truly See the Diagrams in Visual Math Problems?
- M3CoT: A Novel Benchmark for Multi-Domain Multi-step Multi-modal Chain-of-Thought

The discussion on inference scaling lacks sufficient references. It would be beneficial to incorporate more literature on inference scaling, such as those in [1], to enhance the related work section.

[1] Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models
Overall assessment scores: 2.5

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