Visual Sketchpad: Sketching as a Visual Chain of Thought for Multimodal Language Models

Thank you for your insightful and constructive review! We are honored that you believe visual sketchpad is interesting and effective. We address each question as follows. Hope that our response clarified your concerns, and we would be grateful if you could consider improving the rating after seeing our responses!

1. As the proposed visual sketchpad attempts to generate code to draw the images. I wonder if it is possible that sometimes code has issues and cannot generate images properly. If so, how to deal with such issues.

Answer: We thank the reviewer for pointing this out. Sometimes, LMs generate incorrect code that results in execution errors. Our framework addresses this problem by feeding the error message back to the model and prompting it to generate a revised version of the code. This idea was developed by a long line of prior work, for example, self-debug [1] and AutoGen[51]. We will add more discussions in the final version.

[1] Chen, Xinyun, Maxwell Lin, Nathanael Schärli, and Denny Zhou. "Teaching large language models to self-debug." arXiv preprint arXiv:2304.05128 (2023).

2. For the geometry problem, can the visual sketchpad support geometry image (e.g., in jpg) as input? If so, how does the visual sketchpad overlay lines on the image?

Answer: This is a great question. We experimented with many multimodal LLMs (e.g., GPT-4o) and diffusion-based image editing models (e.g., SDXL-edit), but found that these models were unable to accurately add the required line to the geometry image. As a result, our current framework does not support using only the geometry image as input. Instead, we provide the matplotlib code for the geometry diagrams, enabling the LLM to add a line programmatically. Future work would be to develop or fine-tune an image-editing model specifically for overlaying precise lines on geometric images. We appreciate your question and will include this discussion in our future work section.

3. Currently, the visual sketchpad is a set of different prompts that tackle specific problems with a corresponding set of tools. Can the visual sketchpad be a single prompt to call tools and tackle all the problems listed in the evaluation? If so, that would be useful as the prompt can be integrated into the system prompt for MLMs as an enhanced version.

Answer: Thanks for your suggestion! Visual sketchpad uses a single unified prompt for all vision tasks and similarly, a single unified prompt for all math tasks. These prompts can be directly integrated into the system prompt of any MLMs.

4. The evaluation misses an important set of comparisions: There is no comparison between the proposed approach and the existing chain-of-thought frameworks.

Answer: Thanks for your feedback. We'd like to clarify that our GPT-4-turbo and GPT-4 baselines already incorporate chain-of-thought reasoning. These models produce multiple reasoning steps before outputting a final answer. It is widely believed that OpenAI trains their models to output chain-of-thought reasoning during the instruction-tuning and alignment processes. Here is a sample output from the baseline methods. As you can see, the baseline already employs a chain-of-thought approach:

Query: You are given an adjacency matrix of a graph and two query nodes. \n\nYOUR TASK is to find if there is a path between the two nodes.\n\n Example:\nAdjacency Matrix: [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]....

Baseline GPT-4 output: The adjacency matrix provided represents an undirected graph where each row and column corresponds to a node, and the value at a given position (i, j) indicates whether there is a direct edge between node i and node j. A value of 1 represents an edge, and a value of 0 represents no edge.\n\nFrom the adjacency matrix, we can see that most nodes have no edges connecting them to any other nodes, except for nodes 8 and 10 which are connected to each other (as indicated by the 1s at positions (8, 10) and (10, 8)).\n\nThe query is asking whether there is a path between node 9 and node 4. Looking at the adjacency matrix:\n- Node 9 has no edges connecting it to any other nodes (the entire row and column corresponding to node 9 are zeros).\n- Similarly, node 4 has no edges connecting it to any other nodes (the entire row and column corresponding to node 4 are zeros).\n\nSince neither node 9 nor node 4 has any connections to other nodes, and there are no intermediate nodes that connect these two nodes, there is no path between node 9 and node 4.\n\nFINAL ANSWER: no\n

5. Although most benchmarks in the evaluation show that the additional context from visual sketchpad brings benefits, I wonder if there are some cases that the additional context introduces noises and causes errors compared with the baseline model.

Answer: This is a good point. Yes. There are instances where the additional context from the visual sketchpad can introduce errors. For example, the vision expert in our framework such as GroundingDINO, may wrongly annotate or miss bounding boxes. We found that GPT-4o is really good at figuring out if these vision experts are making mistakes, and correcting them during reasoning, as we write in L 288-289. But there are times where GPT-4o is still misled by these noises. We appreciate your feedback and will include this point in the limitations section of the final version.

6. Typos Line 64: jigwaw -> jigsaw

Answer: Thanks for pointing out the typo. We will fix it in the final version.

We appreciate your constructive feedback! We are encouraged that you acknowledge the originality, quality, clarity, and significance of our work. We address your concerns as follows, and hope that they can clarify your concerns, and hope that you can improve the rating after seeing the responses!

1. Clarity: The reviewer found the title and general positioning of this work slightly misleading. Visual SKETCHPAD naturally would refer to chain of thought framework with that includes generalised sketching capabilities. Troughout this work sketching soley refers to drawing of auxiliary lines for geometric problems and is only one of the multiple tools that the proposed framework makes use of for visual artefact generation.

Answer: We respectfully point out that this is a false statement. For vision problems, our work draws numbers and bounding boxes on objects. This is similar to the human sketching process. We circle things on an image and put numbers on it to help reasoning. Even for math problems, we believe that drawing out math functions and graphs is also a sketching process. We as humans often do that on our sketchpad during math examples.

2. Origniality: the main concern of the reviewer is with the extent of the novelty of this work. The single differentiating factor compared to standard pipelines is the incorporation of visual artefacts on intermediate CoT steps. Incoorporation of visual reasoning information for LLM reasoning cannot be considered a purely novel proposition (for example [a] or [60]). Even though the proposed approach departs from these methods by iteratively updating the context with newly formed visual artefacts, the reviewer is still skeptical w.r.t the extent of the contribution for NeurIPS standards.

Answer: We again respectfully disagree with the reviewer. Updating the visual context during reasoning is the key novelty unique to our work, which brings significant performance gain. Prior works, for example [a], [60], VisProg, and ViperGPT, only do reasoning on text, and the performance is not great. For example, [a] uses GPT-3 and gets 44.6% on OK-VQA. An earlier work, [b], directly prompt GPT-3 with image captions, get 48% by directly prompting GPT-3 with image captions. In ViperGPT, the work that gets the best zero-shot result, but are still far from supervised state of the art. We have been following this line of work, and find the key thing missing is that the LLM cannot make new plans based on new visual contexts. Our method is the first work in this line of research that greatly outperforms all existing state of the art and unleashes the power of the best multimodal LLMs.

Sidenote: Thanks for bringing up [a]. We will cite it in our final version.

[b] Yang, Z., Gan, Z., Wang, J., Hu, X., Lu, Y., Liu, Z., & Wang, L. (2022). An Empirical Study of GPT-3 for Few-Shot Knowledge-Based VQA. AAAI.

Thanks for your valuable feedback! We are honored that you believe the pipeline is reasonable, achieving good results, and the paper well-written. We address your questions below. Hope that we addressed your concerns, and we would be grateful if you could consider improving the rating after seeing our responses!

1. The idea is not new. VisProg is a similar work. Personally, this work could be an incremental work based on VisProg by introducing chain-of-thought and applying multimodal reasoning.

Answer: Great to hear that you are also following this direction! We have also followed this direction for a long time, and believe Sketchpad fixes the key pain point of VisProg/ViperGPT. The huge performance gain demonstrates the significance of our work. This work actually starts with the authors carefully investigating ViperGPT's trajectories when solving OK-VQA. We find that many LLM-generated programs are wrong, and the vision tools break frequently. We realize that the LLM can be much more powerful if it can investigate the intermediate visual artifacts during the execution of the programs. We further develop this idea and find that it also applies to math and geometry problems. The key innovation is not about vision tool-use, but about multimodal reasoning: LLMs should think step by step across modalities, just like humans do when they are drawing on sketchpads.

2. It is very confusing to use the word "sketches" since the drawings are straight lines, boxes, or marks, which are in fact irrelevant to sketches from my view.

Answer: We understand your concerns about our terminology. We use the term ‘sketch’ as a metaphor for the process of humans drawing things on a sketchpad while thinking. We are also open to advice on new terminology!

3. Is there any evidence that LMs can change the plan given the intermediate visual outcomes during reasoning?

Answer: Yes, there is substantial evidence supporting this. For example, in the dataset V*,for 26% of the examples, GPT-4o find that GroundingDINO fails to detect small objects, and decides to use a sliding window to do a more careful search. Figure 1 (d) is another good example. After using segmentation, GPT-4o decides to use depth estimation to further confirm the answer. Furthermore, the performance gap between VisProg and our method in table 3 quantitatively shows the difference. VisProg can be viewed as a version in which the plan cannot be changed. And its performance is much lower than ours (e.g., 17% v.s. 86% on MMVP).

4. Is there an in-context learning for LM-based code generator?

Answer: Yes. For computer vision tasks, all tasks share the same prompt, and the prompt contains 6 in-context examples. For math tasks, there are 5 in-context examples.

5. Is that possible to equipt CoT to VisProg (using the same specialist vision models of this work), thus achieving similar performances on math and vision problems?

**Answer: ** In our VisProg experiment, to make a fair comparison, we replaced the LLM to GPT-4o/turbo, and then replaced the vision experts with the ones used by our method. It is way worse than our method, as shown in Table 3. So, the short answer is no, VisProg cannot achieve similar performance. The key difference is that in VisProg, the LLM makes the plan after seeing the textual query, without any visual context. We manually inspect VisProg’s traces, and find that many plans are not reasonable and not robust. For example, GroundingDINO often makes mistakes, and the wrong bounding boxes destroy the VisProg programs.

6. To solve the geometry problem, the proposed model is going to generate auxiliary lines. Is there GT that can be used to quantitatively assess the correctness of the lines?

Answer: Good question! The short answer is no because it is really hard to generate GT for a geometry problem. There are often multiple solutions for the same question, using different auxiliary lines that get the same correct answer. To evaluate the correctness of the lines, we have to show the reasoning trajectory of GPT-4o to humans and let them decide. As shown in L293-297, humans find that for 80% of the cases, the auxiliary line is reasonable.

7. In Table 3, VisProg performs poorly and the reason claimed is the errors from vision modules. Why Sketchpad did not suffer from this issue?

Answer: Great question! The reason is that Sketchpad includes visual results as part of the reasoning process, allowing GPT-4 to inspect the results and find the errors from vision modules. For example, GroundingDINO may make mistakes for object detection. In VisProg, since the plan is not changed, there is no way to fix it. For Sketchpad, GroundingDINO will also visualize its results, with bounding boxes drawn around the objects. GPT-4 can easily figure out which boxes are wrong by inspecting the visualized results.

Thanks for your kind and insightful feedback! We are honored that you believe Sketchpad is a great idea. We address your questions as follows:

1. More discussion about the robustness (repeatibility) is needed, since a common problem for these commercial LVLMs is the instability. Does the method alleviate the invalid responces? How robust is it? Does multiple re-try helps to improve the performance?

Answer: This is a great question. Regarding invalid responses, we observe that GPT-4-turbo and GPT-4o rarely produce invalid responses for our datasets. There are a few (<5) examples per dataset blocked by safety shields. For robustness, we set the temperature of decoding to 0 to reduce randomness, but still notice some instability in the OpenAI API. To address this, we conducted 3 runs per task. For instance, on BLINK depth, the GPT-4o baseline has a standard deviation of 1.5%, while with visual sketchpad, it's 1.2%. We will update the final version with mean and variance for 3 runs for each task.

2. More explaination about the human evaluation is needed. I noticed the author have included the user study. How exactly the user study is conducted? The author is suggested to elablorate this.

Answer: For human evaluation, we present the reasoning steps of GPT-4o (interleaved between text and images) to two human subjects. In the geometry task, we ask the annotators to respond with "yes" or "no" to the question: "Would you draw the same auxiliary lines to answer the question?" For computer vision tasks, we ask: "Are the visual reasoning steps reasonable?" We will include an additional human evaluation section in the appendix to provide more comprehensive details.