Reasoning Limitations of Multimodal Large Language Models. A case study of Bongard Problems

## Abstract

Abstract Abstract visual reasoning (AVR) encompasses a suite of tasks whose solving requires the ability to discover common concepts underlying the set of pictures through an analogy-making process, similarly to human IQ tests.
Bongard Problems (BPs), proposed in 1968, constitute a fundamental challenge in this domain mainly due to their requirement to combine visual reasoning and verbal description.
This work poses a question whether multimodal large language models (MLLMs) inherently designed to combine vision and language are capable of tackling BPs.
To this end, we propose a set of diverse MLLM-suited strategies to tackle BPs and examine four popular proprietary MLLMs: GPT-4o, GPT-4 Turbo, Gemini 1.5 Pro, and Claude 3.5 Sonnet, and four open models: InternVL2-8B, LLaVa-1.6 Mistral-7B, Phi-3.5-Vision, and Pixtral 12B.
The above MLLMs are compared on three BP datasets: a set of original BP instances relying on synthetic, geometry-based images and two recent datasets based on real-world images, i.e., Bongard-HOI and Bongard-OpenWorld.
The experiments reveal significant limitations of MLLMs in solving BPs.
In particular, the models struggle to solve the classical set of synthetic BPs, despite their visual simplicity.
Though their performance ameliorates on real-world concepts expressed in Bongard-HOI and Bongard-OpenWorld, the models still have difficulty in utilizing new information to improve their predictions, as well as utilizing a dialog context window effectively.
To capture the reasons of performance discrepancy between synthetic and real-world AVR domains, we propose Bongard-RWR, a new BP dataset consisting of real-world images that translates concepts from hand-crafted synthetic BPs to real-world concepts.
The MLLMs’ results on Bongard-RWR suggest that their poor performance on classical BPs is not due to domain specificity but rather reflects their general AVR limitations.

## 1 Introduction

Analogy-making is a critical aspect of human cognition, tightly linked with fluid intelligence, the capacity to apply learned skills in novel settings (Lake et al., ).
Several approaches have been proposed to build systems capable of making analogies.
Notably, the structure-mapping theory explores methods for discovering structural correspondences between pre-existing object representations (Winston, ; Gentner, ; Carbonell, ; Falkenhainer et al., ; Holyoak & Thagard, ).
However, these approaches often overlook the perceptual aspect, assuming object representations are already given.
Chalmers et al. () highlight that forming useful representations is an intricate challenge.
In particular, perception is not merely a passive reception of sensory data, but rather an active interpretation influenced by prior knowledge.
This process involves the detection of patterns, recognition of analogies, and abstraction of concepts.
The resultant representations may vary significantly depending on the context, which underscores the importance of modeling perception and cognition jointly (Hofstadter, ).

Multiple problems that necessitate combined perception and reasoning have been identified (Hofstadter, ).
Among these tasks are Bongard Problems (BPs), introduced by Bongard (; ).
Initial BPs were designed manually, leading to the formulation of a few hundred task instances by individual contributors (Foundalis, ).
A typical BP consists of two sides, left and right, each comprising six image panels arranged in a grid.
All images on one side illustrate a shared concept absent in the images on the opposite side.
The task is to identify the underlying rule that differentiates the sides and articulate it in natural language.
Initial BPs (Bongard, ), akin to human IQ tests, featured abstract 2D geometric shapes, putting the focus on abstract reasoning.
However, recent works have expanded the set of BPs to include real-world images, which broadens the scope of presented objects, attributes and relations.
Specifically, the matrices in Bongard HOI (Jiang et al., ) depict human-object interactions, while Bongard-OpenWorld (Wu et al., ) employs open-world free-form concepts, increasing the diversity of featured scenes.
Figs. 1(a), 1(c), 1(d) illustrate examples of problems from the three above-mentioned datasets.

A central theme in BPs is recognition of concepts in a context-dependent manner, as object representations need to be formed specifically for the presented matrix, rather than described a priori (Linhares, ).
For example, consider the matrix in Fig. 1(a) – an analysis restricted to its left side may yield multiple concepts, such as the presence of curves or an object centered in the image.
Only through a comprehensive understanding of both matrix sides one can recognize that the left side depicts a single line, while the right side presents two lines.
Such concept-based tasks were argued to promote a more accurate evaluation of a system’s generalization ability and its capacity for abstraction (Mitchell, ; Odouard & Mitchell, ).
Moreover, the concepts in BPs are illustrated with several image examples, which positions the task within a few-shot learning setting (Fei-Fei et al., ; Wang et al., ).
In contrast to other abstract reasoning problems, such as Raven’s Progressive Matrices (RPMs) (Raven, ; Raven & Court, ; Małkiński & Mańdziuk, ) that have recently witnessed the development of large-scale benchmarks (Barrett et al., ; Zhang et al., ), BPs allow to assess system’s ability to derive concepts from a limited set of examples (typically six images per matrix side).
The above aspects make BPs a valuable testbed for assessing abstract reasoning abilities of AI models.

#### Motivation.

The quest to build systems capable of forming abstract concepts dates back to the 1950s (McCarthy et al., ).
The advent of Deep Learning (DL) opened new possibilities to tackle BPs (Kharagorgiev, ; Nie et al., ).
However, despite significant advancements, methods for consistently solving BPs (and other problems that involve abstract reasoning) are still lacking (Mitchell, ; van der Maas et al., ; Stabinger et al., ).
Typically, DL approaches omit the generation of natural language answers by casting BP into a binary classification task, in which a test image had to be assigned to the matching side of the matrix.
Conversely, a parallel stream of research on large language models (LLMs) demonstrated promising results in open-ended language generation (Brown et al., ).
In particular, LLMs were applied to selected AVR tasks (Webb et al., ), though, lately Xu et al. () pointed certain LLM limitations in solving AVR problems represented as text despite using information lossless translation through direct-grid encoding.
Recent works have combined the vision and language modalities into multimodal large language models (MLLMs) (Achiam et al., ; Reid et al., ; Anthropic, ), inviting their application to diverse tasks (Yin et al., ; Wu et al., ).
Motivated by these recent developments we examine the reasoning capabilities of MLLMs in solving BPs.

#### Contributions.

The main contribution of this paper is four-fold.

(1) For the first time in the literature, we consider BPs in the context of MLLMs and propose a diverse set of strategies to solve BP instances in two setups: open-ended language generation and binary classification.

(2) We evaluate $4$ state-of-the-art proprietary MLLMs and $4$ open MLLMs on both synthetic and real-world BPs, and identify their severe abstract reasoning limitations.

(3) To further examine the main difficulties faced by MLLMs in solving both types of BPs (synthetic and real world ones) we introduce a focused dataset of BPs (Bongard-RWR) comprising real-world images that represent concepts from synthetic BPs using real world images.
Thanks to relying on the same abstract concepts as synthetic BPs, Bongard-RWR facilitates direct comparisons of the MLLMs performance in both domains.

(4) We perform a detailed comparative analysis of $8$ MLLMs on Bongard-RWR vs. synthetic BPs, shedding light on the reasons of their generally poor performance.

## 2 Related Work

#### AVR tasks.

The AVR field encompasses a broad set of problems aimed at studying various aspects of visual cognition (Gardner & Richards, ; Małkiński & Mańdziuk, ).
Recent DL research in this domain gravitated towards utilizing certain well-established datasets, e.g. with visual analogies (Hill et al., ; Webb et al., ) or RPMs (Zhang et al., ; Barrett et al., ), to measure the progress of DL models.
However, such benchmarks evaluate system performance in learning a particular task, rather than assessing its general ability to acquire new AVR skills.
To address this limitation, certain tasks have adopted few-shot learning setups, requiring models to learn from a few demonstrations, as exemplified by SVRT (Fleuret et al., ) or Bongard-LOGO (Nie et al., ).
Nonetheless, these benchmarks follow a discriminative setting where a set of possible answers is provided.
Conversely, other datasets such as ARC (Chollet, ) or PQA (Qi et al., ) pose a generative challenge, which may be considered more difficult due to its open-ended nature.
In addition to synthetic tasks featuring 2D geometric shapes, certain datasets present analogous reasoning tasks using real-world images (Teney et al., ; Ichien et al., ; Bitton et al., ).
This approach extends the range of concepts that can be expressed and, above all, allows employing models pre-trained on large image datasets.
In this work, we concentrate on several BP datasets that present a few-shot learning challenge, cover both synthetic and real-world images, and consider settings involving both binary classification and answer generation in natural language.

#### Approaches to solve BPs.

Initial approaches to tackle BPs involved cognitive architectures (Foundalis, ), program synthesis coupled with inductive logic programming (Saito & Nakano, ; Sonwane et al., ), and the application of Bayesian inference within a visual language framework (Depeweg et al., ; ).
Kharagorgiev () trained a convolutional network on a generated synthetic dataset with geometric shapes and applied a one-level decision tree to solve BPs framed as a binary classification task.
Nie et al. () introduced Bongard-LOGO with synthetically generated BPs and used it to evaluate CNN-based models focused on meta-learning (Snell et al., ; Mishra et al., ; Lee et al., ; Raghu et al., ; Chen et al., ) and relational reasoning (Barrett et al., ).
Jiang et al. () applied the Relation Network (Santoro et al., ) to objects detected with Faster R-CNN (Ren et al., ) and employed the model to solve matrices from the real world Bongard HOI dataset.
Despite high diversity of approaches, none of them has fully addressed the abstract and open-ended nature of BPs.
Most related to our work, Wu et al. () considered hybrid approaches that caption each image panel with an image-to-text model and applied LLMs for processing these text descriptions.
Differently, in this work we focus on MLLMs that are inherently capable of jointly processing images and text.

#### Abstract reasoning of MLLMs.

MLLMs haven’t been yet applied to tackle BPs, though they were applied to several related tasks.
Initial works focused on LLMs and evaluating their abstract reasoning performance in simplified analogy tasks.
Webb et al. () showed that GPT-3 and GPT-4 (text-only variants) performed on the human level, or even outcompeted humans, in certain RPM-like tasks in a zero-shot manner without additional fine-tuning.
However, they represented the image objects as text using a fixed small vocabulary, thus omitting the need for identifying concepts from open-ended shapes, a key challenge of BPs.
Recent research concerning the evaluation of abstract reasoning skills of LLMs concentrates around the Abstraction and Reasoning Corpus (ARC) task (Chollet, ).
It was demonstrated that LLMs can solve certain ARC problems transformed to the text domain (Moskvichev et al., ; Mirchandani et al., ; Camposampiero et al., ; Xu et al., ).
Despite these important stepping stones, the text-based representation taken in these works simplifies the perception task by presenting the model with pre-existing higher level representations.
Only recently, thanks to the appearance of MLLMs, vision and text started to be treated jointly in a unified manner.
Cao et al. () proposed a suite of AVR tasks to compare MLLM and human performance.
Jiang et al. () assessed AVR skills of MLLMs on an introduced multidimensional benchmark combining AVR and perceptual questions.
Our work complements this stream of research by exploring BPs, a fundamental task in the field, and providing insights into MLLM analogy-making performance in synthetic and real-world domains.

Figure: Figure 2: Generation strategies. Direct (a) feeds the image of the whole matrix to the model. Descriptive (b), Contrastive (d), and their iterative variants, (c) and (e), present individual image panels to the model in a fixed order. Their direct variants, (b) and (d), additionally include the image of the whole matrix. Grey background marks a sequence of requests run in a single context window.
Refer to caption: extracted/5933722/images/bp31/whole.png

## 3 Solving BPs with MLLMs

In this paper, we propose a set of novel strategies for solving BPs using MLLMs.
Definition of each strategy includes the input on which the model operates and the sequence of reasoning steps performed by the model.
A high-level overview of these methods is provided in Fig. 2.
In the main tested setting, we follow the initial BP formulation that requires providing an answer in natural language, and propose a model-based approach to automatically evaluate such model predictions.
In addition, we consider simpler formulations of the problem, casting it into a binary classification framework that enables detailed evaluation of AVR abilities of the tested MLLMs.
An illustration of these evaluation settings is presented in Fig. 3.
In what follows, let ${\cal BP}^{X}=\{{\cal L}^{X},{\cal R}^{X},y^{X}\}$ denote a BP instance ($X\in\cal N$ is an index), composed of ${\cal L}^{X}=\{L^{X}_{1},\ldots,L^{X}_{6}\}$ left and ${\cal R}^{X}=\{R^{X}_{1},\ldots,R^{X}_{6}\}$ right panels, resp., and its concept $y^{X}$ expressed in natural language.

### 3.1 Prompting Strategies for Natural Language Answer Generation

We start by defining the strategies for generating answers in natural language.
In each strategy, the model receives a general description of Bongard Problem with two BP examples with correct answers.
Additionally, besides this generic introductory information, a given task ${\cal BP}^{X}$ to be solved is presented in a strategy-specific way. Appendix A.4 presents the exact prompt formulations.

Direct (Fig. 2a). The model receives an image presenting ${\cal BP}^{X}$ and is asked to directly formulate an answer (i.e., describe the difference between ${\cal L}^{X}$ and ${\cal R}^{X}$ panels in natural language).

Descriptive (Fig. 2b). Defines a more granular approach in which the model is first requested to generate a textual description of each image panel of the matrix.
Each description is generated in a separate context, such that the model doesn’t have access to the prior panels nor to their descriptions.
Next, the model is requested to provide an answer to the problem based only on the generated textual descriptions of all image panels.

Descriptive-iterative (Fig. 2c). Evaluates the role of the reasoning context and utilizes a context window comprising the dialog history concerning all images in the given side of the problem.
After generating the description of the first image, the model iteratively refines its output based on subsequent images from the same side.
Based on the textual descriptions of both sides of the problem, the model is requested to provide the final answer.

Descriptive-direct (Fig. 2b with a dashed element). In both above Descriptive strategies, the model is never presented with the image of the whole matrix ${\cal BP}^{X}$. Descriptive-direct strategy extends Descriptive by providing the image of ${\cal BP}^{X}$ along with the textual panel descriptions.

Contrastive (Fig. 2d).
A critical aspect of BPs is the focus on forming concepts within the specific context of the matrix ${\cal BP}^{X}$.
It’s often the case that correct identification of the concept governing one side requires analysis of the other side to identify their key differences.
In Descriptive strategies, the model provides image descriptions concerning a single problem side
${\cal L}^{X}$ or ${\cal R}^{X}$
without taking into account the images from the other side.
Conversely, in the Contrastive strategy, the model is tasked with describing the difference between a pair of corresponding images from both sides of the problem $(L^{X}_{1},R^{X}_{1}),\ldots,(L^{X}_{6},R^{X}_{6})$.
After describing the differences between all six image pairs in separate contexts, the model generates its final answer based on these textual descriptions.

Contrastive-iterative (Fig. 2e).
Extends Contrastive by performing all reasoning steps in a single context window, enabling the model to gradually improve its understanding of the rule separating both sides.

Contrastive-direct (Fig. 2d with a dashed element).
Extends Contrastive by including the image of the whole matrix together with textual descriptions of differences within each panel pair.

Figure: Figure 3: Evaluation settings. We consider the three settings to solve BPs: (a) the ground-truth answer $y$ is paired with a description $\widehat{y}$ generated by the MLLM and the model needs to verify if they describe the same concepts; (b) given a possible solution $\overline{y}$ the model needs to assess whether it’s correct; (c) two test images corresponding to the left (L) and right (R) sides, resp., are randomly shuffled, and the model needs to assign each image from the pair to the proper side of the problem.
Refer to caption: extracted/5933722/images/bp31/whole.png

### 3.2 Evaluation of Solutions Expressed in Natural Language

The correct answer to a BP may be formulated in natural language in many different ways.
To account for this inherent variability, we utilize a model-based approach to assess whether the generated answer $\widehat{y}$ matches the ground-truth $y$.
In the proposed setting, an MLLM ensemble receives both $\widehat{y}$ and $y$ and is requested to output a binary yes/no answer whether both descriptions refer to the same concept (see Fig. 3a).
Specifically, we assess the correctness of $\widehat{y}$ using all four considered proprietary MLLMs and count it as correct if at least two models agree with this class (see details in Appendix B).
In contrast to solving the BP task, which requires abstract reasoning abilities, the task of determining whether two answers refer to the same concept boils down to assessing the semantic similarity between two texts, and MLLMs are known to excel in such setup (Lu et al., ).

### 3.3 Binary classification formulations

To dive deeper into the AVR capabilities of the studied models, we cast the BP task into three binary classification settings, reducing the task’s difficulty.
Firstly, we provide the model with the image of the whole matrix ${\cal BP}^{X}$ along with a possible solution, and the model is prompted to generate a binary score assessing the correctness of the provided answer (Fig. 3b).
Two settings are considered, in which the solution is formed by either the actual ground-truth answer (the expected answer is yes), or by an incorrect answer taken from a different BP matrix (the expected answer is no).
Secondly, we follow a setting exemplified in the Bongard-LOGO dataset (Nie et al., ) in which two test images have to be classified to different sides of the problem (Fig. 3c).
To this end, we take two test images corresponding to the respective sides of the matrix, randomly shuffle the images, and request the model to determine the side to which each image belongs.
In synthetic BPs we create the test set by removing the 6th image from each side of the matrix, while in BPs from Bongard HOI, Bongard-OpenWorld and Bongard-RWR we use the additional test images.
We refer to these three formulations as Ground-truth, Incorrect Label, and Images to Sides (see prompts in Appendix A.3).

## 4 Bongard-RWR: Synthetic BPs expressed in real-world images

One of the interesting research avenues is to compare the MLLMs performance on synthetic BPs vs. real-world ones. Note, however, that a direct performance comparison on synthetic Bongard dataset vs. real-world Bongard HOI and Bongard-OpenWorld datasets is not meaningful, as these datasets depict different concepts. To enable a meaningful comparison and additionally determine whether the MLLMs performance score is domain-related, we introduce Bongard Real-World Representations, a focused dataset that expresses concepts present in synthetic BPs using real-world images, thus creating their real-life equivalents, as illustrated in Fig. 1(b).
Appendix C contains additional examples.
The dataset is available at: [https://github.com/pavonism/bongard-rwr](https://github.com/pavonism/bongard-rwr).

### 4.1 Bongard-RWR dataset generation

For a given instance ${\cal BP}^{X}$, we first use GPT-4o to describe its underlying concept $y^{X}$ in $N=10$ different ways using the prompt listed in Prompt 4.1.
We obtain $N$ real-world textual descriptions $D^{X}_{i}=\{D^{XL}_{i},D^{XR}_{i}\},$
$i=0,\ldots,N-1$, of each side $S\in\{L,R\}$.
Then, we use image search engine Pexels API (Pexels, ) to download $M=15$ images per each described side $D^{XS}_{i}$.
We employ GPT-4o (see Prompt  A.1 in Appendix  A.1) to select only those images that properly illustrate the concept of the respective side and are indeed distinguishable from the alternative concept.
We stop the selection procedure after having a set of $T=3$ descriptions $\{D^{X}_{i_{1}},D^{X}_{i_{2}},D^{X}_{i_{3}}\}$, each with $2$ appropriate images: $I^{XS}_{k}(1),I^{XS}_{k}(2)$, $k=i_{1},i_{2},i_{3}$ per each side $S$ ($6$ left and $6$ right ones).

The corresponding real-world problem instance ${\cal RWR}^{X}=\{{\cal L}^{X},{\cal R}^{X}\}$ is constructed as follows (see Algorithm 1 in Appendix C): ${\cal S}^{X}=\{I^{XS}_{i1}(1),I^{XS}_{i2}(1),I^{XS}_{i3}(1),I^{XS}_{i1}(2),I^{
XS}_{i2}(2),I^{XS}_{i3}(2)\}$, $S\in\{L,R\}$ so as to decrease the possibility of generating a problem with a trivial answer, which is highly probable if the images from a singular textual description $D^{X}_{i}$ are taken.

We run Algorithm 1 for the first 100 synthetic BPs.
After applying the exclusion criteria, this lead to the generation of
$50$ instances ${\cal RWR}^{X}$. However, as we noticed through a manual inspection, some of them were not well depicting the respective problem concept. Hence, we modified the dataset in the following way: $14$ problems were entirely removed and, out of the remaining $36$, $24$ were adjusted through a manual selection of the images that well represent the considered concept. Furthermore, we extended the dataset by adding $17$ problems with manually translated concepts (i.e., with no use of GPT-4o), for which images were also selected manually, and $7$ constructed by hand, i.e., by means of making photos of manually-built scenes reflecting the respective concepts.

All in all, we obtained a real-world Bongard-RWR dataset containing $60$ problems, out of which $12$ were generated fully automatically, $24$ were generated automatically and adjusted manually afterward (manual selection of the images), $17$ were composed manually (manual translation of the concept and manual selection of the images), $7$ were constructed entirely manually (photos of manually-built scenes).
The details are provided in Appendix C.

## 5 Experiments

To evaluate the AVR capabilities of MLLMs, we conduct experiments in two main settings, involving $3$ binary classification setups and $7$ proposed generation methods.
Our evaluation spans a range of MLLMs, including $4$ proprietary models accessible via API: GPT-4o, GPT-4 Turbo (Achiam et al., ), Gemini 1.5 Pro (Reid et al., ), and Claude 3.5 Sonnet (Anthropic, ), alongside $4$ open-access models run locally on an NVIDIA DGX A100 node: InternVL2-8B (Chen et al., ; ), LLaVa-1.6 Mistral-7B (Liu et al., ; ; Jiang et al., ), Phi-3.5-Vision (Abdin et al., ), and Pixtral 12B (MistralAI, ).
We consider four BP datasets covering both synthetic and real-world images. Specifically, we use the first 100 manually constructed (synthetic) BPs from (Bongard, ), 100 problem samples from Bongard HOI and Bongard-OpenWorld, and all 60 instances from Bongard-RWR.
Table 1 presents the results.

Binary classification (Ground-truth).
We first assess whether MLLMs can determine if a given concept matches a problem instance.
On synthetic BPs, $3$ proprietary (GPT-4o, Gemini 1.5 Pro, Claude 3.5 Sonnet) and $2$ open-access (LLaVa-1.6 Mistral-7B, Pixtral 12B) models outperform a random classifier by a notable margin.
On Bongard HOI, $3$ proprietary (GPT-4o, GPT-4 Turbo, Gemini 1.5 Pro) and the same $2$ open-access models also surpass random guessing.
Notably, Pixtral 12B attained a perfect score on this dataset.
On Bongard-OpenWorld GPT-4o, Gemini 1.5 Pro, LLaVa-1.6 Mistral-7B, and Pixtral 12B achieve reasonable results.
Again, the leading model is Pixtral 12B with the outstanding $99\%$ outcome.
Model accuracy drops significantly on Bongard-RWR, where only LLaVa-1.6 Mistral-7B and Pixtral 12B outperform a random classifier.
This suggests that correctly identifying concepts expressed in Bongard-RWR likely requires more advanced reasoning abilities, even in the relatively simpler binary classification setting.

Binary classification (Incorrect Label). Rejecting a possible solution is intuitively simpler than confirming its correctness, as it boils down to finding at least one image that doesn’t match the provided concept.
Accordingly, $6$ models perform better in the Incorrect Label setting than in Ground-truth, with $7$ perfect scores, $2$ of them on Bongard-RWR.
The exceptions are LLaVa-1.6 Mistral-7B, and Pixtral 12B which are below a random guessing threshold for all four datasets, despite being above this threshold in Ground-truth.
This suggests that their strong performance in the Ground-truth setting may be due to a potential bias toward agreeing with the provided concept.

Binary classification (Images to Sides). We also evaluate the models’ ability to correctly assign two test images to the appropriate sides of the problem.
A problem is considered solved if both images are correctly assigned to the respective sides.
Proprietary models perform well in this task across synthetic BPs, Bongard HOI and Bongard-OpenWorld.
Conversely, among open-access models, only Pixtral 12B consistently achieves strong results.
Notably, on Bongard-RWR Pixtral 12B solves 26/60 problems, outperforming all proprietary models, however, all models perform below the level of random guessing.
The remaining open-access models show poor results in this setting.
Notably, weak results of LLaVa-1.6 Mistral-7B on real-world datasets are primarily attributed to its incorrect generation of JSON output required to format the result.

Generative capabilities in the Direct setting.
Model performance using the Direct generation strategy is generally weak on synthetic BPs, with the best model, GPT-4o, solving only 17 out of 100 problems.
This indicates that the models struggle to identify abstract, synthetic concepts and express them in natural language.
The challenge is even more apparent on Bongard-RWR, where the best model, GPT-4o, solves only 5 out of 60 problems.
Nevertheless, performance improves on Bongard HOI and Bongard-OpenWorld, with best results of 35/100 and 40/100, resp.
Notably, while GPT-4o achieves the highest scores on these two datasets, Pixtral 12B ranks second (28/100 and 33/100, resp.), showing that smaller open-access models can still be competitive in this setting.
While the better performance on Bongard HOI and Bongard-OpenWorld may be attributed to a higher ratio of real-world images in the training data, the weak results on Bongard-RWR suggest that the discrepancy is more related to the specific underlying concepts than the visual domain as such (see Figure 7 in Appendix C for the details).

Independent image description.
In the next experiment we analyse whether an iterative reasoning approach, in which the model first generates separate captions for each image and then combines them into a final answer, can improve performance.
In comparison to the Direct strategy, the Descriptive one improves the best results across all datasets:
from 17 to 21 on synthetic BPs,
from 35 to 45 on Bongard HOI,
from 40 to 57 on Bongard-OpenWorld,
and from 5 to 13 on Bongard-RWR. A clear improvement can be observed individually for each proprietary model. The gain is less pronounced (if at all) for individual open-access models.
We hypothesize that this improvement is due to the Descriptive setting being more aligned with the model’s training, where it primarily learns to caption individual images.
However, this strategy doesn’t leverage the additional information present in the joint BP image, and certain context-dependent visual features may be missed in captioning.
We believe that with further advancements in reasoning over multi-part compositional images, models in the Direct setting should eventually outperform the Descriptive strategy.

Contrastive reasoning.
Correct identification of concepts in BPs requires a joint processing of the images from both sides of the problem.
The Contrastive strategy evaluates the model ability to extract underlying differentiating concepts within such image pairs.
Across all datasets, the models evaluated under the Contrastive strategy perform worse than with the Descriptive strategy.
This points to the fundamental difference between human and machine approaches to solving AVR tasks.
Humans often rely on direct comparisons between image panels from different categories to highlight differences (Nüssli et al., ), whereas the tested methods perform better when making comparisons on text-based image descriptions, potentially disregarding critical visual details missed during image captioning.
This discrepancy indicates the need for further modeling improvements to fully leverage the Contrastive strategy.

Iterative reasoning.
Next, we tested whether preserving responses from past turns in the dialog context could improve concept identification in both Descriptive and Contrastive settings.
The Descriptive-Iterative strategy visibly worsens the results compared to its non-iterative counterpart across all datasets and models, except for negligible improvement of InternVL2-8B on synthetic BPs and several cases of a complete failure (accuracy of 0 0) for both strategies.
In contrast, Contrastive-Iterative brings no improvement over Contrastive strategy in only $5$ cases, $2$ for synthetic BPs, and $3$ regarding Bongard-OpenWorld.
Despite these improvements, Contrastive-iterative strategy generally performs worse than Descriptive.
This indicates that contemporary models have difficulties to effectively use additional information from the context window.

Multimodal answer generation.
In the final experiment, we assessed whether incorporating an image of the entire matrix at the answer generation step would improve the performance of Descriptive and Contrastive strategies.
Descriptive-Direct shows performance improvements over Descriptive in $12$ out of $32$ (dataset, model) cases.
Contrastive-Direct improves upon Contrastive in all (dataset, proprietary model) configurations, and additionally improves in certain (dataset, open-access model) settings.
However, despite these gains, Contrastive-Direct overall performs worse than Descriptive, except for GPT-4o and InternVL2-8B on synthetic BPs, and InternVL2-8B on Bongard HOI.
This suggests that contemporary models are to some extent capable of utilizing additional visual inputs to improve reasoning performance, in particular the newest GPT-4o, which displays improvement from incorporating the -direct extension in 7 out of 8 cases.
Nevertheless, further work is needed to improve consistency across all models.

**Table 1: Evaluation results. The number of correct answers to the first 100 synthetic BPs, 100 selected BPs from Bongard HOI and Bongard-OpenWorld, and all 60 BPs from Bongard-RWR. The best result for a given strategy is marked in bold, and the second best is underlined.**
| Synthetic BPs | GPT-4 | GPT-4 | Gemini | Claude | InternVL2 | LLaVa-1.6 | Phi | Pixtral |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Omni | Turbo | 1.5 Pro | 3.5 Sonnet | 8B | Mistral 7B | 3.5V | 12B |  |
| Ground-truth | $\underline{87}$ | $48$ | $78$ | $84$ | $30$ | $70$ | $22$ | 92 |
| Incorrect label | $\underline{79}$ | 89 | $70$ | $74$ | $78$ | $24$ | $\underline{79}$ | $27$ |
| Images to sides | $\underline{72}$ | $56$ | $69$ | 75 | $32$ | $33$ | $4$ | $57$ |
| Direct | 17 | $6$ | $7$ | $\underline{13}$ | 0 0 | 0 0 | 0 0 | $1$ |
| Descriptive | $17$ | $15$ | 21 | $\underline{19}$ | 0 0 | $1$ | $2$ | $4$ |
| Descriptive-iter. | 9 | $7$ | $4$ | $\underline{8}$ | $1$ | 0 0 | $1$ | $2$ |
| Descriptive-direct | 22 | $13$ | $20$ | 22 | $1$ | 0 0 | $1$ | $5$ |
| Contrastive | $10$ | $8$ | 17 | $\underline{15}$ | 0 0 | 0 0 | 0 0 | $1$ |
| Contrastive-iter. | 20 | $9$ | $\underline{12}$ | $11$ | $1$ | 0 0 | 0 0 | $4$ |
| Contrastive-direct | $\underline{19}$ | $9$ | 20 | $18$ | $1$ | 0 0 | $1$ | $1$ |
| Bongard HOI | GPT-4 | GPT-4 | Gemini | Claude | InternVL2 | LLaVa-1.6 | Phi | Pixtral |
| Omni | Turbo | 1.5 Pro | 3.5 Sonnet | 8B | Mistral 7B | 3.5V | 12B |  |
| Ground-truth | $73$ | $\underline{74}$ | $60$ | $32$ | $41$ | $70$ | $49$ | 100 |
| Incorrect label | 100 | 100 | $96$ | 100 | $90$ | $32$ | $67$ | $33$ |
| Images to sides | 99 | $92$ | $95$ | 99 | $13$ | 0 0 | $7$ | $86$ |
| Direct | 35 | $22$ | $23$ | $5$ | $12$ | $5$ | $1$ | $\underline{28}$ |
| Descriptive | $42$ | 45 | $40$ | $\underline{44}$ | $2$ | $4$ | $4$ | $27$ |
| Descriptive-iter. | 32 | $\underline{23}$ | $6$ | $6$ | 0 0 | $1$ | $2$ | $11$ |
| Descriptive-direct | 45 | $\underline{40}$ | $30$ | $29$ | $7$ | $3$ | $7$ | $25$ |
| Contrastive | 18 | $5$ | $\underline{15}$ | $13$ | $2$ | $1$ | $2$ | $7$ |
| Contrastive-iter. | 22 | $20$ | $15$ | $\underline{21}$ | $2$ | $1$ | $3$ | $14$ |
| Contrastive-direct | $\underline{25}$ | $12$ | 27 | $15$ | $7$ | 0 0 | $1$ | $7$ |
| Bongard-OpenWorld | GPT-4 | GPT-4 | Gemini | Claude | InternVL2 | LLaVa-1.6 | Phi | Pixtral |
| Omni | Turbo | 1.5 Pro | 3.5 Sonnet | 8B | Mistral 7B | 3.5V | 12B |  |
| Ground-truth | $\underline{80}$ | $52$ | $59$ | $37$ | $49$ | $72$ | $31$ | 99 |
| Incorrect label | 100 | 100 | $98$ | $99$ | $86$ | $44$ | $83$ | $29$ |
| Images to sides | $94$ | $86$ | 96 | 96 | $19$ | $2$ | $9$ | $87$ |
| Direct | 40 | $21$ | $13$ | $10$ | $11$ | $12$ | $7$ | $\underline{33}$ |
| Descriptive | $46$ | 57 | $32$ | $\underline{53}$ | $18$ | $16$ | $12$ | $34$ |
| Descriptive-iter. | 31 | $\underline{24}$ | $6$ | $13$ | $4$ | $2$ | $2$ | $11$ |
| Descriptive-direct | 52 | 52 | $25$ | $46$ | $24$ | $8$ | $9$ | $38$ |
| Contrastive | $\underline{19}$ | $12$ | $11$ | 21 | $7$ | $1$ | $5$ | $14$ |
| Contrastive-iter. | $\underline{25}$ | $21$ | $8$ | 34 | $5$ | $1$ | $3$ | $18$ |
| Contrastive-direct | 35 | $25$ | $17$ | $22$ | $12$ | $4$ | $4$ | $\underline{27}$ |
| Bongard-RWR | GPT-4 | GPT-4 | Gemini | Claude | InternVL2 | LLaVa-1.6 | Phi | Pixtral |
| Omni | Turbo | 1.5 Pro | 3.5 Sonnet | 8B | Mistral 7B | 3.5V | 12B |  |
| Ground-truth | $22$ | $5$ | $26$ | $10$ | $13$ | $\underline{38}$ | $21$ | 58 |
| Incorrect label | $59$ | 60 | $52$ | 60 | $53$ | $21$ | $47$ | $9$ |
| Images to sides | $15$ | $17$ | $19$ | $\underline{24}$ | $16$ | 0 0 | $1$ | 26 |
| Direct | 5 | $1$ | $\underline{3}$ | $1$ | 0 0 | 0 0 | 0 0 | $1$ |
| Descriptive | $\underline{8}$ | $5$ | $7$ | 13 | 0 0 | 0 0 | 0 0 | $1$ |
| Descriptive-iter. | 4 | $1$ | 0 0 | $\underline{3}$ | 0 0 | 0 0 | 0 0 | 0 0 |
| Descriptive-direct | $5$ | 7 | $5$ | $\underline{6}$ | 0 0 | 0 0 | 0 0 | $2$ |
| Contrastive | 2 | 0 0 | $1$ | 2 | 0 0 | 0 0 | 0 0 | 0 0 |
| Contrastive-iter. | 5 | $3$ | $3$ | $\underline{4}$ | 0 0 | 0 0 | 0 0 | $1$ |
| Contrastive-direct | $\underline{4}$ | $1$ | 5 | $\underline{4}$ | 0 0 | 0 0 | 0 0 | 0 0 |

Comparison of prompting strategies.
Across all models, the Descriptive strategy achieves the highest scores on Bongard-RWR and Bongard-OpenWorld.
In Bongard HOI, it ties with Descriptive-direct, while in synthetic BPs, it ranks just behind its -direct extension.
As shown in Appendix D, altogether Descriptive strategies solve the same number of synthetic BPs as Contrastive strategies (44; Fig. 9), but lead in Bongard HOI (82 vs. 63; Fig. 11), Bongard-OpenWorld (90 vs. 76; Fig. 13), and Bongard-RWR (20 vs. 11; Fig. 15).
This overall advantage of Descriptive over Contrastive strategies indicates that current MLLMs perform better with prompting strategies focused on processing single images.
This also highlights the need to improve multi-image reasoning capabilities of MLLMs for tasks that require reasoning across multiple images.
Figs. 9 – 16 in Appendix D further show that altogether the considered approaches solved 54, 89, 93, and 23 problems from synthetic BPs, Bongard HOI, Bongard-OpenWorld, and Bongard-RWR, resp.
This raises the question of whether an ensemble combining all proposed strategies could further enhance model reasoning performance.
We leave the exploration of this emerging direction for future work.

Proprietary vs. open-access models.
Proprietary models generally outperform open-access ones, leading in 35 out of 40 (dataset, strategy) pairs.
The black-box nature of proprietary models makes it challenging to attribute their advantage to specific aspects, whether it be the number of parameters, the size and composition of training data, or the pre- and post-processing methods.
However, the recently released Pixtral 12B model performs competitively in multiple settings, occasionally surpassing proprietary models.
This highlights the viability of developing competitive MLLMs without sacrificing accessibility. At the same time, a clear performance drop of Pixtral 12B on synthetic BPs and Bongard-RWR instances suggests its intrinsic weakness in reasoning about abstract concepts, whether reflected in synthetic or real-world manner, similarly to other open models.

Comparison with state-of-the-art.
A direct comparison with the results from (Wu et al., ) is challenging due to the different ranges of test problems used in each study.
With this caveat, we concentrate on key high-level observations from both works.
Wu et al. () primarily focus on a binary classification setting corresponding to the Images to Sides setup in our work.
On Bongard-OpenWorld, our best performing models, Gemini 1.5 Pro and Claude 3.5 Sonnet, achieved 96% accuracy, while their top method, SNAIL—a meta-learning approach leveraging pre-trained OpenCLIP image representations—achieved 64%.
This suggests that MLLMs, which uniformly process images and text, outperform decoupled two-stage approaches, which handle image captioning and text-based reasoning with different models.
They also briefly consider a natural language generation task, where models describe concepts presented in the BP instance (Wu et al., , Appendix E).
They again use a two-step approach comprising fine-tuned BLIP-2 for image captioning and ChatGPT for concept generation.
In contrast, we employ a single MLLM for both tasks.
For evaluating free-form concept generation, they use automated text-based metrics, which provide a general measure of text similarity.
We, however, employ a voting MLLM ensemble, offering a more direct assessment of solution correctness.

## 6 Conclusions

In this paper, we investigate the reasoning capabilities of proprietary and open-access MLLMs using BPs as a case study.
Despite rapid progress, MLLMs still exhibit significant reasoning limitations.
Across all proposed answer generation strategies, the best-performing model managed to solve only 22 out of 100 synthetic BPs.
Performance moderately improves when dealing with real-world concepts, as demonstrate the results on the Bongard HOI and Bongard-OpenWorld datasets.
However, the models still struggle to leverage additional multimodal data and effectively utilize the dialog context window.
To delve deeper into the performance discrepancies between synthetic and real-world domains, we introduced Bongard-RWR, a new BP dataset designed to represent concepts from synthetic BPs via real-world images.
Focused experiments with this dataset suggest that the models’ weak performance on synthetic BPs is not domain-specific but rather indicative of broader limitations in their reasoning abilities.
On a positive note, experiments conducted in three binary classification settings show that some models achieve encouraging results, suggesting that current limitations may be overcome with future advancements.

## Appendix A MLLM prompts

### A.1 Prompts for Bongard-RWR generation

Prompt A.1 was used to select those images that correctly represent given concept translation. In addition to the left and right concepts, we also provided prompts briefly explaining the context that the image should match. These prompts were generated during the translation stage of our algorithm
(see the fourth line in Algorithm 1).

### A.2 Prompt describing the Bongard problem

Prompt A.2 describing the BP task has been placed at the beginning of each solving strategy introduced in Section 3.1.

### A.3 Prompts for Classification Strategies

Prompt A.3 was used to assess solution correctness (see Section 3.2).
Prompt A.3 was used to assign images to sides (see Section 3.3).

### A.4 Prompts for Natural Language Answer Generation Strategies

Prompts A.4–A.4 were used for natural language answer generation (see Section 3.1).

## Appendix B Evaluation of MLLMs answers

Preliminary experiments revealed that proprietary MLLMs are generally much more effective in solving Bongard Problems than open, publicly-available MLLMs. Therefore, all efforts devoted to optimizing the final scores, in particular tuning the evaluation prompt were performed using these $4$ commercial MLLMs.

Open-ended characteristics of BPs stemming from a textual form of an answer, and the number of considered models (8), generation strategies (7), datasets (4), and BP instances per dataset (60 in Bongard-RWR and $100$ in the remaining cases) require the use of an automated NLP-based evaluation of the model’s answers. For this task we employed MLLMs with a specially designed prompt. The initial version of the evaluation prompt (see Prompt B) was intentionally relatively simple – a model received an answer to be evaluated as well as the ground-truth labels, and was requested to output a binary yes/no answer.
This prompt formulation turned out to be too simplistic.
While the level of agreement between all models was relatively high ($87\%$ of responses were rated unanimously by all models), as illustrated in Fig. 4(a), manual inspection of the selected answers revealed that the assessment was generally too optimistic and relatively many evaluations wrongly pointed to correct answers.

Figure: (a) Results with the initial evaluation prompt.
Refer to caption: extracted/5933722/images/bongard-solved-by-gpt-4o-with-descriptive-prompting-and-initial-prompt.png

### B.1 Evaluation prompt optimization

Due to the above evaluation disagreement, we made an attempt to optimize the prompt based on the GPT-4o solutions for the additional $20$ BPs (#101 – #120) that were not used in the main experiments.
First, following the few-shot prompting technique, we expanded the prompt to include two examples showing a possible logical difference between correct and incorrect answers. Furthermore, we added a sentence which requested a strict logical compliance with the provided labels. However, this refinement appeared to be too strong, as $2$ (out of $4$) models didn’t evaluate any of the solutions as correct.

To impose some flexibility, we changed the word strictly to logically, but this resulted in an increased rate of false-positive evaluations.
Finally, we combined these two prompts, obtaining the outcome closest to the manual (our human) evaluation. The final version of our evaluation prompt is listed in Prompt B.1. Additionally, we attempted to attach the image of the evaluated BP instance to each version of our prompt, but this actually confused the models rather than improving their results, so we ultimately abandoned this option and stuck with the fully text-based prompt.

Although the consistency of results regarded as the number of unanonimous assessments stayed at the same level ($87\%$) (see Fig. 4(b)), the number of answers rated as correct significantly decreased, which was in accordance with our random manual verification.

Despite lowering the results variation, there were still BPs for which the assessment varied. Therefore, we eventually decided to use hard voting to ensemble all models’ evaluations. We marked a solution as correct if at least $2$ of the $4$ models evaluated it as correct. This approach brought better results than the majority voting.

### B.2 Manual verification of the evaluation performance of MLLMs

In order to finally assess the efficacy of Prompt B.1 we manually checked the models’ evaluation performance on the $100$ BPs solved by GPT-4o using the Descriptive strategy. As shown in Table 1 in the main paper, all proprietary models achieved better scores on incorrect labels classification. For this reason, we decided to manually verify only the problems evaluated as correct by at least one MLLM, assuming that those incorrect are generally evaluated properly. The comparison between the evaluation performance of the initial and final prompts and our manual evaluation is presented in Table 2. All models denotes evaluations where a solution is marked as correct only if all models evaluate it as correct. Similarly, any model refers to the cases where a solution is marked as correct if at least one model evaluates it as correct. Voting refers to the hard-voting scheme described in section B.1. It is important to observe that the chosen voting evaluation method differed from the manual evaluation in only one specific problem, which is depicted in Fig. 5.

In addition, we checked the performance of our enhanced evaluation prompt on $20$ new, not used in other experiments, manually evaluated Bongard-OpenWorld problems solved by GPT-4o using the Descriptive strategy. Again, the use of Prompt B.1 visibly increased the consensus with manual evaluation (see Table 3). The difference between our manual evaluation and the voting scheme occurred only in 2 problem solutions whose correctness is disputable (see Fig. 6).

Obviously, the choice of examples shown in the prompt may additionally impact the evaluation performance. Nevertheless, the finally proposed evaluation prompt seems to well suit both domains: synthetic and real-world, and should potentially be effective in other similar datasets and solving strategies.

**Table 2: Consensus with manual evaluation on synthetic BPs. The percentage of the solutions evaluated the same as in our manual evaluation in BP instances $\#1-\#100$ (Bongard, ). The assessed solutions were obtained by GPT-4o using the *Descriptive* prompting strategy.**
| initial prompt | final prompt |  |  |  |  |
| --- | --- | --- | --- | --- | --- |
| All models | Any model | voting | All models | Any model | voting |
| 0.93 | 0.9 | 0.94 | 0.9 | 0.96 | 0.99 |

Figure: Figure 5: Synthetic BP #85. This is the only BP instance for which the voting-based evaluation of MLLM solutions differed from our manual evaluation. Left: Three parts. Right: Five parts. GPT-4o answer: Left: All images are composed of exactly three lines. Right: All images are composed of more than three lines. Voting marked it as incorrect, whereas in manual evaluation it was marked as correct. The first difference lies in the meaning of the words lines and parts, which, in this visual context, seems identical. The second difference stems from the number of the parts on the right side of the problem. The answer seems to be correct, as obviously, five is more than three. However, one could argue that the answer is incomplete, as each of the squares on the right side clearly depicts exactly five parts.
Refer to caption: extracted/5933722/images/bongard-85.png

**Table 3: Consensus with manual evaluation on Bongard-OpenWorld. The percentage of the solutions evaluated the same as in our manual evaluation in the additional 20 Bongard-OpenWorld instances $\#101-\#120$ (Wu et al., ), not used in the main experiment. The solutions were obtained by GPT-4o using the *Descriptive* prompting strategy.**
| initial prompt | final prompt |  |  |  |  |
| --- | --- | --- | --- | --- | --- |
| All models | Any model | voting | All models | Any model | voting |
| 0.75 | 0.7 | 0.7 | 0.65 | 0.85 | 0.9 |

Figure: (a) Left: Underground tunnels beneath the city. Right: NOT Underground tunnels beneath the city. GPT-4o solution: Left: All images depict scenes that are primarily indoors or underground. Right: All images depict scenes that are primarily outdoors. We evaluated it as correct, while the voting marked it as incorrect. The difference arises from how the left concept is perceived. Although the images on the left depict an underground setting, they do not appear to represent an indoor scene. Nevertheless, one of the statements is still true.
Refer to caption: extracted/5933722/images/bongard-openworld-110.png

## Appendix C Bongard-RWR dataset

Bongard-RWR dataset developed in this work is attached in the technical appendix and will also be released for the reserach community under the MIT license.
The dataset generation algorithm is presented in Algorithm 1 using notation introduced in Section 4.1.

Figure: Algorithm 1 The Bongard-RWR dataset generation.

Furthermore, Fig. 8 provides additional examples of the proposed Bongard-RWR dataset. Each subfigure presents a comparison between the synthetic Bongard problem and its respective real-world translation in Bongard-RWR. Examples 8(a) and 8(b) were translated automatically, whereas 8(c) and 8(d) were constructed fully manually, including building an appropriate scene and taking a picture. Additionally, Fig. 7 shows a particular approach taken when translating a given synthetic BP to its Bongard-RWR counterpart (problems not translated and those rejected after translation are combined into one category).

Figure: Figure 7: The structure of the Bongard-RWR dataset. Each color denotes the genesis of the translation of the respective problem. Problems not translated and those rejected after translation are combined into one category. Red color outlines denote problems which were solved by any model using any strategy. There is no visible correlation between the set of solved problem and the methods used for their generation.
Refer to caption: extracted/5933722/images/bongard_rwr_colormap.png

Figure: (a) Synthetic BP #8 with its automatically translated Bongard-RWR version. Left: Ends of the curve are far apart. Right: Ends of the curve are close together.
Refer to caption: extracted/5933722/images/bongard-8.png

## Appendix D Coverage of Bongard-RWR instances

Even though the final results of individual models and strategies solving Bongard-RWR are somewhat unsatisfactory, especially in the case of open language response generation, it is worth to examine the degree of overlap of correct answers across the tested models. On the one hand, the results of ground-truth classification and model’s disagreement on the solution evaluation clearly confirm inability of any single model to solving all problems from the Bongard-RWR datatset. On the other hand, it is likely that the overlap is not complete, and it is posible to expand the solution coverage by appropriate mixture-of-experts approach.
This is indeed the case in our experiments, as illustrated in Figures 9 - 16. While single proprietary MLLMs solved between $9$ and $14$ instances, the number of instances solved by any MLLM equaled $23$.
We leave exploration of this path for future research.

Figure: Figure 9: Overall result of each strategy on synthethic BPs. Colormaps depict all problems solved by any tested model using the respective prompting strategy. The right figure aggregates strategies into corresponding groups for better coverage exposure.
Refer to caption: extracted/5933722/images/synthetic-solved-colormap-strategies.png

Figure: Figure 10: Final summary of all experiments on the synthetic Bongard Problems dataset. The colormap aggregates all problems solved by any tested model using any generation prompting strategy. Overall, the models collectively managed to solve 53 problems.
Refer to caption: extracted/5933722/images/synthetic-solved-colormap.png

Figure: Figure 11: Overall result of each strategy on Bongard HOI. Colormaps depict all problems solved by any tested model using the respective prompting strategy. The right figure aggregates strategies into corresponding groups for better coverage exposure.
Refer to caption: extracted/5933722/images/hoi-solved-colormap-strategies.png

Figure: Figure 12: Final summary of all experiments on the Bongard HOI dataset. The colormap aggregates all problems solved by any tested model using any generation prompting strategy. Overall, the models collectively managed to solve 88 problems.
Refer to caption: extracted/5933722/images/hoi-solved-colormap.png

Figure: Figure 13: Overall result of each strategy on Bongard-OpenWorld. Colormaps depict all problems solved by any tested model using the respective prompting strategy. The right figure aggregates strategies into corresponding groups for better coverage exposure.
Refer to caption: extracted/5933722/images/openworld-solved-colormap-strategies.png

Figure: Figure 14: Final summary of all experiments on the Bongard-OpenWorld dataset. The colormap aggregates all problems solved by any tested model using any generation prompting strategy. Overall, the models collectively managed to solve 93 problems.
Refer to caption: extracted/5933722/images/openworld-solved-colormap.png

Figure: Figure 15: Overall result of each strategy on Bongard-RWR. Colormaps depict all problems solved by any tested model using the respective prompting strategy. The right figure aggregates strategies into corresponding groups for better coverage exposure.
Refer to caption: extracted/5933722/images/rwr-solved-colormap-strategies.png

Figure: Figure 16: Final summary of all experiments on the Bongard-RWR dataset. The colormap aggregates all problems solved by any tested model using any generation prompting strategy. Overall, the models collectively managed to solve 23 problems.
Refer to caption: extracted/5933722/images/rwr-solved-colormap.png

## Appendix E Comparison of Synthetic Bongard vs. Bongard-RWR Results

Our research shows that all of the tested models have difficulty solving synthetic concepts when applied to real-world images. Comparing the results for both datasets (see Figures 10 and 16) we identified some discrepancies. Four problems that remained unsolved in the synthetic BPs were successfully solved in the real-world domain of the Bongard-RWR dataset: #56, #87, #88, and #98. However, three of these problems differ slightly from their synthetic counterparts. The images in #56 from Bongard-RWR feature a variety of colors instead of the usual black-and-white figures. Furthermore, in real-world version of problem #87 more images feature disjoint elements instead of multi-part objects, which may have nudged the model toward the correct answer. Additionally, in problem #98, the figures are shown against a hatched texture, which was not accounted for in the real-world translation.

Conversely, 22 problems that were solved in the synthetic BPs were not solved in the Bongard-RWR dataset. In most cases, the models focused on general associations that did not apply to all the images. For example, the concept presented in problem #3 is: ”LEFT: Outline figures, RIGHT: Solid figures.” Claude 3.5 Sonnet, using the Descriptive strategy, responded: ”LEFT: focuses on practical, everyday objects or scenes, RIGHT: emphasizes aesthetic, artistic, or decorative elements that serve more for visual appeal than utility”. Nevertheless, both sides feature a red coffee cup with a saucer, which matches both generated descriptions. The key difference lies in the color of the saucer’s rim, which determines whether it should be considered as an outline or a solid figure.

Figure: (a) Model’s answer: ”Left: All shapes are filled. Right: At least one shape is unfilled”. Evaluated as incorrect.
Refer to caption: extracted/5933722/images/bongard-56.png

Figure: (a) Model’s answer: ”Left: All shapes are composed of straight lines that form only acute or right angles. Right: All shapes contain at least one instance of obtuse angles or curves (e.g., pentagon, ”H” shape, radial pattern)”. Evaluated as incorrect.
Refer to caption: extracted/5933722/images/bongard-87.png

Figure: (a) Model’s answer: ”Left: Each image contains an even number of shapes. Right: Each image contains an odd number of shapes”. Evaluated as incorrect.
Refer to caption: extracted/5933722/images/bongard-88.png

Figure: (a) Model’s answer: ”Left: All images contain geometric shapes or patterns that are oriented or have components that predominantly point to the right. Right: All images contain geometric shapes or patterns that are either static (not pointing in any specific direction) or have components that do not predominantly point to the right”. Evaluated as incorrect.
Refer to caption: extracted/5933722/images/bongard-98.png

## Peer Reviews

confidence: 4
contribution: 2
initial_rating: 5
presentation: 3
questions: It would be nice to show some human score for BPs. Is there any attempt toward that?
soundness: 3
strengths: The paper provides a comprehensive evaluation of the capabilities of vision language models on Bongard Problems (BPs). The paper includes eight models and 10 metrics to evaluate them on 4 types of BPs, including one created by the authors. I believe it will be very helpful for future study of BPs.
summary: The paper focuses on the capability of multimodal large language models (MLLM) to solve Bongard Problems (BP). The authors propose a new BP dataset, where the two sides of the images are distinguished by abstract visual concepts. The authors design a set of evaluation methods for MLLMs, including binary classifications and solving BP using different generation strategies. The results on the proposed BP dataset and three other BP datasets show that the abstract visual reasoning capabilities of MLLMs are limited in solving BP, especially in the proposed ones.
weaknesses: - The presentation of the paper needs to be improved. Despite numerous settings, new generation strategies and new dataset, the authors choose to present the results in just one table. It is almost impossible to interpret the table and verify the claims made by the authors without checking back and forth. I suggest reviewer break down the table into small ones, where each of them provides a clear message to the readers. If that takes more space than the current version, some of the experiment results can be moved to appendix.
- The observation from the results is currently not very interesting. The major claim made by the authors is that the capability of the VLMs on BPs are limited. Not many intuitions behind are obtained, part of it is because of the poor presentation, and the other part is probably because the observations are not very consistent across different models. I suggest the authors dive deep into the details and conduct additional experiments if necessary. Overall, I believe the contribution of the paper can be improved.
- The new BP dataset created in the paper is quite difficult for the models. I believe a comprehensive human study is necessary in this case to ensure the validity of the dataset. It is great that the dataset is released, but after a quick scan of the dataset, I personally find it very hard to distinguish the left and the right images for some BPs. Therefore, I suggest the authors to report human performance on the tasks and report consistency across human annotators.


------
### Post-rebuttal comments:
- The authors added a human study of the new BP dataset and re-organized the experiment section, which are important improvements for the paper. Therefore, I have raised my score.
- I agree with other reviewers that the dataset and the analysis can be made more rigorous and comprehensive. Therefore, I believe this paper has not reached the bar of NeurIPS.

---

confidence: 4
contribution: 3
initial_rating: 3
presentation: 3
questions: 1. What is your insight on these proposed generation strategies in Figure 2? (Why do you choose these tasks?)

2. There are also some works from the observation in psychological experiments like MindSet [1], which could be the data sources for BP tasks or AVR tasks.

3. As your works show some similar observations to previous benchmark works like VCog-Bench, and François Chollet's book "On the measure of intelligence, you can put some further discussions in the main body of your paper.

Post Rebuttal:

I take a quick view of the authors' reply and other reviews' score, I decide to decrease my final score to 4. Though the authors choose a good topic as motivations, the main pain points (over claiming, lacking data, lacking detailed definition) are difficult to solve. This, we all agree this paper doesn't match the bar of ICLR.
soundness: 2
strengths: 1. This is an important problem for MLLM nowadays. I like the motivation of your paper. As we know, Human IQ test has a long history in psychometrics and only a few of works try to explore the different between MLLM and human in this topic [1].    

2. They have open-sourced their dataset containing 100 samples. I have a quick review of the dataset repo. The data structures and descriptions are easy to follow.  

3. Compare with most of visual reasoning benchmark papers, this paper use less data but it has a solid cognition background. I happen to agree with some viewpoints of the authors, which are also highlighted by Google DeepMind recently.      

References:     
[1] Galatzer-Levy, Isaac R., et al. "The Cognitive Capabilities of Generative AI: A Comparative Analysis with Human Benchmarks." arXiv preprint arXiv:2410.07391 (2024).
summary: This paper focuses on exploring one limitation of MLLM in visual understanding: there is still a big gap between MLLMs and humans in the IQ test / AVR test from psychometrics. They choose Bongard Problems to conduct the case study. Firstly, they build a new benchmark with some Bongard Problem samples. Then, they compare some SOTA MLLMs and VLMs with this multi-image reasoning task. The results suggest that the weak performance of MLLMs on Bongard Problems is not due to the domain specificity, but rather comes from their multi-image reasoning capability.
weaknesses: 1. It is worth to highlight that BP is only a subtask of AVR test. Compared to RAVEN, BP is not widely used by human's IQ test recently. I think you should discuss this limitation and consider exploring a board scope of AVR tasks in the future work.

2. The Evaluation settings in Figure 3 is unclear. It seems that most of the settings proposed by you can only use to test the closed-sourced models like Claude 3.5 and GPT-4o. The multi-image reasoning capbility of most of open-sourced MLLMs are not eligible in these tasks.

3. For a better understanding, the user study between human and MLLM is also important for this task.

4. Lacking an in-detailed analysis of the 100 samples in your datatset, e.g. the difficulty of each image pair.

---

confidence: 4
contribution: 2
initial_rating: 5
presentation: 3
questions: - Can you provide the rationale behind the proposed strategies in the experiments? Does it relate to the theory of AVR from a cognitive science perspective? Can you summarize the high-level idea of the design?
- To further understand the limitations, do you think the same model with different sizes (LLaVA 1.6 7b/13b/70b) will highlight some observations? I think it can reveal how scaling law will help with this problem.
- Can you list the key reasons why MLLMs fail in BPs? This should be provided in the conclusion section. You need to expand "broader limitations in their reasoning abilities" in Line 537-538.
soundness: 2
strengths: 1. The problem of Abstract visual reasoning (AVR) is a popular problem and has gained great attention lately. The perspective of Bongard Problems is novel and meaningful.
2. The experiments of this paper are comprehensive on various MLLMs and 4 datasets (one of them is newly collected by this paper).
3. The dataset is already open-sourced, which may contribute to the research community in the future.
summary: This paper investigates the Bongard Problems (BPs) as a case study in Multimodal LLMs. This problem represents a foundational problem in Abstract visual reasoning (AVR). This paper gathered a new dataset Bongard-RWR and used multiple strategies to test the proprietary and open-sourced MLLMs on both synthetic and real-world BPs. The experiments show that there is still a gap for MLLMs to do AVR, but certain strategies.
weaknesses: 1. The contribution of the proposed Bongard-RWR dataset is not clear enough, although the authors briefly mentioned in Line 311-312. The previous datasets already covered both synthetic and real-world settings. How do the proposed datasets differentiate from these datasets? It is unclear why the authors find previous datasets insufficient or lacking in meaningfulness due to differences in concepts.
2. While the paper evaluates current MLLMs, it fails to offer a clear direction for enhancing their AVR capabilities or to present any new insights beyond highlighting general limitations. The results of different strategies might only reflect the training data (instruction tuning data) for these models. 
3. Since the newly gathered dataset is considered as a main contribution, there are no clear statistics of this dataset provided.

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confidence: 3
contribution: 3
initial_rating: 8
presentation: 3
questions: - Some open-source models like InternVL2 and Phi-3.5V perform well on many benchmarks but struggle, nearing chance-level performance on Bongard Problems, while LLava-1.6 and Pixtral perform okay. What do the authors think causes these discrepancies?
- How closely does abstract visual reasoning (AVR) reflect real-world visual reasoning (VR)? For instance, if a model excels in AVR, can we expect it to perform well in VR, and vice versa? Some potential correlations experiments between AVR and VR performance might give some insights.
soundness: 3
strengths: - The paper studies an interesting topic of Bongard Problems (BPs). It introduces a comprehensive evaluation of MLLMs using BPs, which are notoriously challenging in abstract reasoning. By testing both synthetic and real-world BP datasets, the authors highlight critical weaknesses in these models, providing valuable insight into their current capabilities. This positions BPs as a powerful benchmark for future MLLM advancements.
- This paper creates Bongard-RWR to bridge the gap between abstract synthetic reasoning and real-world tasks. This dataset allows for more meaningful comparisons of MLLM capabilities across domains. Also, this dataset enables future work to pinpoint the source of reasoning failures more precisely.
- The paper is well written and easy to understand.
summary: This paper investigates the abstract reasoning capabilities of multimodal large language models (MLLMs) using Bongard Problems (BPs), which require analogy-making between sets of images. The authors test several MLLMs on both synthetic and real-world BP datasets, highlighting significant limitations in their performance, especially with abstract, synthetic problems. Despite some improvement with real-world images, the models still struggle with effectively incorporating new information and handling complex visual reasoning tasks. To address this, the paper introduces a new dataset, Bongard-RWR, translating synthetic BP concepts into real-world images.
weaknesses: I didn't see major weaknesses.

Meta-review: The AC acknowledges the authors’ efforts in exploring a potential direction for this field and providing dataset statistics. However, the paper's primary contribution, the dataset, lacks sufficient novelty, after careful checking and syncing with reviwers' commets, as it appears to primarily bridge synthetic and realistic Bongard problems through a data augmentation technique, building incrementally on existing datasets like Bongard HOI and Bongard-OpenWorld. Furthermore, the limited sample size of 100 raises methodological concerns regarding potential bias and insufficient statistical power, with no detailed justification provided for its adequacy. While the work has merit, these limitations lead to a reject recommendation for now.

Decision: Reject