Organizing Unstructured Image Collections using Natural Language

## Abstract

Abstract Organizing unstructured visual data into semantic clusters is a key challenge in computer vision. Traditional deep clustering (DC) approaches focus on a single partition of data, while multiple clustering (MC) methods address this limitation by uncovering distinct clustering solutions. The rise of large language models (LLMs) and multimodal LLMs (MLLMs) has enhanced MC by allowing users to define clustering criteria in natural language. However, manually specifying criteria for large datasets is impractical. In this work, we introduce the task Semantic Multiple Clustering (SMC) that aims to automatically discover clustering criteria from large image collections, uncovering interpretable substructures without requiring human input . Our framework, Te xt D riv e n S emantic Multiple C lustering (TeDeSC), uses text as a proxy to concurrently reason over large image collections, discover partitioning criteria, expressed in natural language, and reveal semantic substructures. To evaluate TeDeSC, we introduce the COCO-4c and Food-4c benchmarks, each containing four grouping criteria and ground-truth annotations. We apply TeDeSC to various applications, such as discovering biases and analyzing social media image popularity, demonstrating its utility as a tool for automatically organizing image collections and revealing novel insights. Disclaimer: Potentially sensitive content.

## 1 Introduction

Organizing large volumes of unstructured visual data into semantic clusters is a crucial problem in computer vision and has traditionally been addressed through the lens of unsupervised deep clustering (DC) (Caron et al., ; Van Gansbeke et al., ). Despite the advancements and improved performance, DC remains limited due to its inherently ill-posed nature (Estivill-Castro, ), as a dataset can be clustered in multiple ways (e.g., a dataset of a standard deck of cards can be grouped by suit or rank). Furthermore, the clusters discovered by DC rely on factors such as the inductive biases of the network, augmentations, and pretext tasks; and do not necessarily adhere to the a particular partitioning criteria that a user may have in mind (e.g., suit).

The limitation of DC in exploring visual data only along a single partition is addressed by multiple clustering (MC) methods (Yu et al., ), which uncover distinct clustering solutions. Multiple partitions reveal hidden patterns in the data and allow for analysis from different perspectives. The recent advent of large language models (LLMs) and multimodal LLMs (MLLMs) has further enhanced MC by enabling users to specify the clustering criterion (e.g., group by suit) in natural language (Kwon et al., ; Yao et al., ). While incorporating a human in the loop is appealing, as it grants the user control over the clustering results, specifying a meaningful text criterion still requires prior understanding of the image collections. This task becomes cumbersome, especially due to the proliferation and high scene complexity inherent in large volumes of visual data.

**Table 1: Overview of clustering methods and their key differences. Unlike Deep Clustering (Caron et al., ) and Multiple Clustering methods (IC$\mid$TC (Kwon et al., ) and MMaP (Yao et al., )), the proposed TeDeSC (Ours) requires no auxiliary prior knowledge, while offering interpretable outputs.**
|  |  | DC | MMaP | IC$\mid$TC | Ours |
| --- | --- | --- | --- | --- | --- |
| Prior | User-provided Criteria | ✗ | ✓ | ✓ | ✗ |
| Knowledge # Clusters | ✓ | ✓ | ✓ | ✗ |  |
| Out. | Multiple Clustering | ✗ | ✓ | ✓ | ✓ |
| Interpretability | ✗ | ✗ | ✓ | ✓ |  |

In this work, we propose to ease the burden of specifying text criteria off the user by automatically discovering the clustering criteria, and introduce the task of Semantic Multiple Clustering (SMC), as shown in Fig. 1(top). To tackle SMC, we propose a general two-stage framework Text Driven Semantic Multiple Clustering (TeDeSC), powered by cutting-edge MLLMs and LLMs, that first discovers latent criteria (e.g., Activity and Location) from a given collection of images, and then groups the images into semantic clusters (e.g., “Surfing”,“Skateboarding” under Activity) for every discovered clustering criterion. To reason at a dataset level, TeDeSC first translates the visual data into textual data (e.g., captions), which in turn are then collectively used as a proxy for the LLM to discover the hidden patterns in the image collection. The uniqueness of TeDeSC lies in its: (i) comprehensiveness, as it can exhaustively discover multiple clustering criteria that may not be evident to a user; (ii) interpretability, as it outputs cluster names in natural language as opposed to traditional MC methods; (iii) flexibility, as it can discover clusters at multiple granularities (coarse to fine-grained), without needing to specify the number of clusters a priori; and (iv) generality, as, unlike the existing work (Yao et al., ), it is not limited to object-centric images but can handle complex scenes having fine-grained details. We summarize the key differences among various clustering solutions in Tab. 1 and elaborate in App. A.

Current benchmarks for evaluating multiple clustering either lack realism (Clevr-4c, Fruit-2c, Card-2c) or offer a limited number of criteria (Action-3c), as shown in Fig. 2. To advance research in SMC, we introduce two challenging new benchmarks, COCO-4c and Food-4c, which depict images in daily life contexts and allow the dataset to be clustered as per four distinct criteria. Extensive experimental analyses on both existing and novel benchmarks demonstrate that the proposed TeDeSC can effectively discover meaningful clustering criteria and successfully group semantically similar images (some examples of clustering results by TeDeSC are shown in Fig. 1 (top)).

Lastly, we apply TeDeSC to a variety of applications, including discovering biases in real-world datasets and text-to-image generative models, as well as analyzing the popularity of social media images. For example, as shown in Fig. 1(bottom), TeDeSC can uncover less commonly studied biases (e.g., Hair color) in DALL·E3-generated (Betker et al., ) images, beyond the well-known biases (e.g., Gender) that may have already been corrected for. It achieves this by discovering various human-interpretable semantic clusters (e.g., “Dark Hair”, “Grey Hair”) across different discovered criteria and identifying overpopulated clusters. Similarly, it can identify the semantic visual elements that contribute to the popularity of social images, offering valuable insights to related practitioners. These results suggest that TeDeSC is an automatic, versatile, and highly practical tool, opening up numerous new application opportunities for future research and providing the potential to generate insights from unstructured visual data at scale across various domains.

## 2 Semantic Multiple Clustering

In this section, we first formally define the task of Semantic Multiple Clustering (SMC), and then introduce the existing and newly proposed benchmarks for SMC.

Task Definition:
Given a collection of $N$ unlabeled images $\mathcal{D}=\{\mathbf{x}_{n}\}_{n=1}^{N}$, the goal of SMC is to categorize $\mathcal{D}$ into semantic clusters based on multiple criteria $\mathcal{R}=\{R_{l}\}_{l=1}^{L}$, where $L$ is the total number of criteria. In detail, a criterion $R_{l}$ refers to the grouping theme according to which a set of images can be organized (or partitioned), such as Activity, Location, Mood, or Time of Day.
All semantic clusters $\mathcal{C}_{l}$ under a given criterion $R_{l}$ should align with the theme of that criterion.
For instance, the semantic clusters under the criterion Activity should reflect activities depicted in the images (e.g., “Kayaking”, “Cooking”). The same dataset $\mathcal{D}$, when grouped by a different criterion such as Location, could be clustered into categories like “Outdoor”, “Indoor”, and so on.

Unlike IC$\mid$TC (Kwon et al., ) and MMaP (Yao et al., ), where a human operator pre-defines the clustering criteria and the number of clusters $K_{l}$, both the criteria names and the cluster counts are unknown in SMC. A SMC framework must automatically discover both the criteria and the corresponding clusters from $\mathcal{D}$. In contrast to classic MC setting, both the criteria and cluster names in SMC are described in natural language, making the discovered substructure human-interpretable.

Figure: Figure 2: Overview of the SMC benchmarks. We show all clustering criteria and the corresponding ground-truth labels for the example images. We introduce two new challenging benchmarks: COCO-4c and Food-4c.
Refer to caption: x2.png

Benchmarks:
Evaluating SMC methods requires benchmarks that can be partitioned under multiple valid criteria. Currently, only a few benchmarks (Yu et al., ) support the evaluation of SMC methods: Fruit-2c (Muresan & Oltean, ), Card-2c (Kaggle, ), Action-3c (Kwon et al., ), and Clevr-4c (Vaze et al., ). As shown in Fig. 2, these benchmarks are limited by their object-centric nature with simple backgrounds (e.g., Fruit-2c), an insufficient number of criteria (e.g., up to three in Action-3c), and a lack of photorealism due to synthetic generation (e.g., Clevr-4c).

Given that the data encountered in real-world applications is more complex, we propose two new benchmarks for SMC: Food-4c and COCO-4c. Food-4c is sourced from Food-101 (Bossard et al., ), which includes 101 Food type (original annotations), along with new annotations for 15 Cuisine types, 5 Courses types, and 4 Diet preferences, totaling four clustering criteria. Additionally, we constructed COCO-4c using images from COCO-val (Lin et al., ), where we annotated four criteria with varying number of clusters: 64 Activity, 19 Location, 20 Mood, and 6 Time of day.
Examples of these newly constructed benchmarks are shown in Fig. 2. Further details, including the full list of cluster names and the annotation pipeline, are provided in App. B.

## 3 Methodology: Text Driven Semantic Multiple Clustering

Partitioning an unstructured image collection into semantic clusters based on different (unknown) criteria is challenging, as it requires reasoning over the visual contents of all the images concurrently. Specifically, the system needs to first find commonalities among the images for discovering the partitioning criterion (or theme) and then group the images into semantic clusters according to the discovered criterion. To tackle the challenging SMC task, we propose a two-stage framework, named Text Driven Semantic Multiple Clustering (TeDeSC), that significantly deviates from the commonly used technique of deep feature-based clustering, and instead uses text descriptions as a proxy to reason over the images and uncover hidden patterns in $\mathcal{D}$. We elaborate the key design differences between TeDeSC and related work in App. A.

System overview: As illustrated in Fig. 3, the proposed TeDeSC consists of two modules: Criteria Proposer and Semantic Grouper. The Criteria Proposer (or Proposer in short) processes the entire image set $\mathcal{D}$ to discover diverse common themes among the images and proposes grouping criteria $\mathcal{R}$ in natural language (e.g., Location). Once the criteria are proposed, the Semantic Grouper (or Grouper in short) discovers distinct semantic clusters that adhere to each criterion $R_{l}$ at varying levels of semantic granularity and assigns images to their respective clusters (e.g., “Climbing gym”). In this work, we explore various design choices for both the Proposer and Grouper, detailed in the following subsections. Full implementation details, including exact prompts, are provided in App. C.

Figure: Figure 3: TeDeSC is composed of a Criteria Proposer and a Semantic Grouper. (Left) The Proposer processes the entire image set to discover and propose diverse grouping criteria expressed in natural language, which are accumulated in the Criteria Pool. (Middle) The Grouper takes these proposed criteria from the pool, discovers semantic clusters linked to the criteria at three different levels of granularity, and assigns images to their respective clusters. (Right) Multiple substructures of the image set, indicated by the discovered criteria, are revealed across different granularities by combining the cluster assignment results. We explore various design choices, and set the best-performing methods from our experiments as the main configuration (marked with ).
Refer to caption: x3.png

### 3.1 Criteria Proposer

As shown in Fig. 3(left), the Proposer takes the target image collection as input and outputs a set of discovered grouping criteria, expressed in natural language. The core of the Proposer design lies in its ability to concurrently analyze and reason over the visual content of a large set of images. With this in mind, we explore three systematic approaches, which we describe below.

Image-based Proposer: We start with a baseline that leverages a state-of-the-art MLLM (Li et al., ) designed for multi-image reasoning out-of-the-box to directly infer the criteria given a set of images. To reason over a set of images, which is crucial for discovering the criterion, we stitch a batch of images into a $8\times 8$ image grid and input it to the MLLM as a single image. We then prompt the MLLM to propose grouping criteria for the images in the grid. All the resulting criteria from all such image grids are accumulated in a criteria pool, denoted as $\widetilde{\mathcal{R}}$.

Tag-based Proposer: Next, we explore a tag-based approach that uses an open-vocabulary tagger (Radford et al., ) to assign 10 tags to each image in $\mathcal{D}$, using the vocabulary from WordNet (Miller, ). These tags serve as semantic descriptors, translating the visual content of each image into textual form. We then gather all the assigned tags from the images, input them into a LLM, and prompt it to discover grouping criteria based on these tags.

Caption-based Proposer (Main):
While image tags effectively capture certain visual semantics, we found that they predominantly reflect object-related content. To encompass a broader spectrum of visual information—such as environmental settings or interactions—we instead use a MLLM to generate captions for each image in $\mathcal{D}$. Descriptive captions provide a richer and more holistic semantic context.
Staying within the 128k token limit of modern LLMs (Meta, ; OpenAI, ), we feed a subset of captions into a LLM, which we prompt to elicit partitioning criteria. The criteria generated for each subset are accumulated in $\widetilde{\mathcal{R}}$. Experiments in Sec. 4.1 show that the Caption-based Proposer is the most effective; so we use it as our main method and consider the others as baselines.

Criteria refinement:
Since the Proposers operate on subsets, the criteria accumulated in $\widetilde{\mathcal{R}}$ may include redundant or noisy entries. To address this, we input all initially proposed criteria from $\widetilde{\mathcal{R}}$ into a LLM (Meta, ), prompting it to consolidate similar criteria and discard noisy ones. This step refines and updates the criteria pool into $\mathcal{R}$, which is ready to be used in the subsequent stage.

### 3.2 Semantic Grouper

The automatically discovered criteria $\mathcal{R}$ serve as thematic indicators for revealing the semantic substructures (or clusters) within the image set $\mathcal{D}$. To uncover these substructures, as shown in Fig. 3(right), the Grouper takes $\mathcal{D}$ and each criterion $R_{l}$ as inputs. It then discovers cluster names $\mathcal{C}_{l}=\{s_{k}^{l}\}_{k=1}^{K_{l}}$ conditioned on $R_{l}$ and assigns each image to its corresponding cluster. The core design of the Grouper focuses on aligning semantic substructure discovery with a specified partitioning criterion. Similar to the Proposer, we also explore three distinct approaches for the Grouper.

Furthermore, as clusters under a given criterion can be formed at varying semantic granularities, depending on user preferences, we have designed our Grouper to cluster $\mathcal{D}$ at three levels of granularity: coarse, middle, and fine-grained. This design enables TeDeSC to provide new insights into the data at different granularities.
For example, for the criterion food Cuisine, TeDeSC can organize images at a coarse-grained continental level (e.g., “European” or “Asian”), a middle-grained regional level (e.g., “Mediterranean” or “Southeast Asian”), or a fine-grained national level (e.g., “Italian” or “Thai”).

Image-based Grouper:
Given a target criterion $R_{l}\in\mathcal{R}$, we first prompt a LLM to generate a question $q_{l}$ specific to $R_{l}$-i.e., for criterion Mood the generated question is: “What mood is conveyed by this image? Answer with an abstract, common, and specific category name, respectively.” We then use $q_{l}$ to guide a visual question answering (VQA) model to infer semantic cluster names for each image as $\left(s_{\text{coarse}}^{l},s_{\text{mid}}^{l},s_{\text{fine}}^{l}\right)=
\text{VQA}(\mathbf{x}_{n},q_{l})$. Consequently, by aggregating the cluster assignment results at each granularity level across $\mathcal{D}$, we can derive multi-granularity semantic substructures.

Tag-based Grouper:
Given a criterion, we prompt a LLM to generate a list of common, middle-grained tags specific to that criterion (e.g., “Recreational facility”). Following Liu et al. (), we then obtain coarse- and fine-grained tags by querying the LLM to generate super- and sub-categories (e.g., “Indoor” and “Climbing gym”) for each middle-grained tag. Unlike lexical databases such as WordNet or ConceptNet (Speer et al., ), which do not support free-form input and may be limited in accommodating certain criteria, tag synthesis using a LLM provides a flexible and reliable alternative. Subsequently, we use an image tagger to assign the most relevant tag from the candidate tags at each granularity to each image, resulting in multi-granularity substructures after aggregation.

Caption-based Grouper (Main):
We prompt a MLLM to generate captions that specifically focus on the target criterion for each image, as $e_{n}^{l}=\text{MLLM}(\mathbf{x}_{n},R_{l})$. Next, we use a LLM in a three-step process to assign images to clusters at multiple granularity levels: i) Initial Naming: First, we prompt the LLM to assign a class name to each caption as $s_{n}^{l}=\text{LLM}(e_{n}^{l},R_{l})$, resulting in an initial set of names $\mathcal{S}_{\text{init}}^{l}$ of size $N$; ii) Multi-granularity Cluster Refinement: Using these initial names as basis, we prompt the LLM to refine them into three structured granularity levels: $\left(\mathcal{S}_{\text{coarse}}^{l},\mathcal{S}_{\text{mid}}^{l},\mathcal{S}
_{\text{fine}}^{l}\right)=\text{LLM}(\mathcal{S}_{\text{init}}^{l},R_{l})$. These structured names serve as candidates for cluster assignment; iii) Final Assignment: Each image is then assigned a class name from each granularity level based on its caption, as $\left(s_{\text{coarse}}^{l},s_{\text{mid}}^{l},s_{\text{fine}}^{l}\right)=
\text{LLM}(e_{n}^{l},\mathcal{S}_{\text{coarse}},\mathcal{S}_{\text{mid}},
\mathcal{S}_{\text{fine}})$. Experiments in Sec. 4.2 show that the Caption-based Grouper performs the best; thus we use it as our main method.

## 4 Experiments

Implementation details:
For all experiments, we run with our proposed TeDeSC framework, using the following configuration: i) CLIP ViT-L/14 (Radford et al., ) as the Tagger, ii) LLaVA-NeXT-7B (Liu et al., ) as the MLLM, iii) Llama-3.1-8B (Meta, ) as the LLM, and iv) BLIP-2 Flan-T5${}_{\text{XXL}}$ (Li et al., ) as the VQA model. For the Image-based Proposer, however, we use LLaVA-NeXT-Interleave-7B (Li et al., ) as the MLLM due to its strong multi-image reasoning capability. Additionally, we explore a variant of the Image-based Grouper using LLaVA-NeXT-7B as the VQA model. Further implementation details, including exact prompts, are provided in App. C.

Evaluation metrics for Criteria Discovery:
Given the discovered criteria set $\mathcal{R}$ of the proposer, we assess its quality from two dimensions: i) Comprehensiveness: We compute True Positive Rate (TPR) (Csurka et al., ) for the predicted criteria relative to the annotated ones as $\text{TPR}=\frac{\mid\mathcal{R}\cap\mathcal{Y}\mid}{|\mathcal{Y}|}$, to assess to what extent the predicted set covers the ground-truth set $\mathcal{Y}$; ii) Diversity: We compute the pairwise semantic similarity between the predicted criteria $\mathcal{R}$, using Sentence-BERT (Reimers & Gurevych, ), and convert it into a diversity measure by subtracting the similarity from 1. The final score is the average of these pairwise values, reflecting how well the proposed criteria avoid redundancy and capture distinct aspects of the data—i.e., criteria such as Location and Place are nearly identical and provide little additional insight. A higher score indicates better diversity. It is important to note that the number of valid grouping criteria is subjective and potentially unlimited, making False Positives difficult to define. Thus, we use TPR as the primary evaluation metric.

Evaluation metrics for substructure uncovering:
Following Conti et al. () and Liu et al. (), for each criterion and its substructure uncovered by the grouper, we evaluate its alignment with the substructure defined by the ground-truth labels along two dimensions: i) Semantic Consistency: For each image, we measure the semantic similarity between its assigned cluster name and the ground-truth label under the current criterion using Sentence-BERT. The average similarity across the dataset is reported as Semantic Accuracy (SAcc), reflecting how well the predicted substructure semantically aligns with the ground-truth. ii) Structural Consistency: We compute the clustering accuracy (CAcc) between the predicted and ground-truth substructures (clusterings) to evaluate how accurately the predicted structure groups images. By combining CAcc and SAcc, we evaluate the overall alignment of the predicted substructure with the ground-truth across various criteria.

Evaluation strategy:
Since the granularity of the ground-truth annotations is unknown during evaluation, we choose the substructure from the three predicted granularities that achieves the highest CAcc relative to the ground-truth for assessing our TeDeSC. Unlike methods (Kwon et al., ; Yao et al., ), which rely on the ground-truth number of clusters to create flat clusterings that perfectly match the ground-truth granularity, we believe our approach offers a fair and practical evaluation strategy for systems capable of providing multi-granularity output.

Figure: Figure 4: Comparison of Criteria Proposers. (a) Comprehensiveness: TPR performance of each proposer evaluated on Basic and Hard ground-truth criteria. (b) Diversity: Diversity scores of the proposed criteria for each proposer. (c) Influence of Image Quantity: TPR performance of the caption-based proposer on Hard ground-truth criteria across varying image scales used for criteria discovery. See expanded results in App. E.1.
Refer to caption: x6.png

### 4.1 Study of the Criteria Proposer

Expanding ground-truth criteria for comprehensive evaluation:
The newly introduced benchmarks provide up to four ground-truth criteria to evaluate the predicted criteria, but for image collections with high scene complexity (e.g.,, COCO-4c), these are still insufficient to cover all valid grouping options. To address this, we expanded the ground-truth criteria for each of the six benchmarks in Sec. 2 by using human annotators to identify additional criteria. This resulted in expanded sets that have: {10, 4, 11, 7, 17, 11} distinct criteria for {Fruit-2c, Card-2c, Action-3c, Clevr-4c, COCO-4c, Food-4c}.
We refer to the per-image annotated criteria set (see Fig. 2) as Basic ground truth and the expanded set as Hard.
See App. B.2 for the exact criteria and annotation details.

Which Criteria Proposer is best?
Our comparative results, presented in Fig. 4(a-b), show that the Caption-based Criteria Proposer consistently outperforms
its counterparts
by a significant margin across all six benchmarks.
As shown in Fig. 4(a), the caption-based proposer achieves an average of 100% TPR on the Basic criteria set and 75.1% TPR on the Hard set across the benchmarks.
Its superior performance is particularly evident under the Hard criteria, where it surpasses the second-best tag-based proposer by +32.2% TPR.
Meanwhile,
the criteria predicted by the caption-based proposer also show greater diversity in Fig. 4(b), coming closest to the diversity of human-annotated criteria.

Although the tag-based proposer performs well on object-centric benchmarks like Clevr-4c or Food-4c, it significantly lags behind the caption-based proposer on more challenging benchmarks such as COCO-4c and Action-3c, which feature more complex, realistic images. This discrepancy arises because image tagging is a more object-centric way of representing image semantics, potentially missing the rich context depicted in images.
Conversely, while the image-based proposer outperforms the tag-based proposer on COCO-4c and Action-3c, it is less effective overall because it is limited to reasoning over a small subset of images and loses visual details when combining images into a grid.

Studying the influence of image quantity on Criteria Discovery:
Fig. 4(c) shows the TPR performance of the caption-based proposer across varying image scales (100% to only 1 image) used for criteria proposing, tested on the Hard criteria sets of six benchmarks. Interestingly, satisfactory performance is achieved with just a few images in object-centric benchmarks like Card-2c and Clevr-4c. In fact, even a single image often provides sufficient information for reasonable criteria discovery in these object-centric datasets, where a brief glimpse often represents the entirety adequately. For example, seeing one playing card allows the proposer to easily suggest criteria like “Rank” and “Suit” in the Card-2c dataset. However, this does not hold for more complex datasets like COCO-4c, Food-4c, and Action-3c, which contain diverse and realistic scenarios. Here, a reduction in image scale leads to a clear drop in TPR performance, as these datasets require a larger set of images to capture their intricate and varied thematic criteria. Since TeDeSC operates without prior knowledge of the dataset, we default to using the entire dataset to ensure comprehensive criteria discovery.

Figure: Figure 5: Comparison of the Semantic Groupers. We show CAcc, SAcc, their Harmonic Mean (HM) evaluated on the basic criteria. The Caption-based Proposer is used by all groupers. See expanded results in App. E.2.
Refer to caption: x7.png

### 4.2 Study of the Semantic Grouper

Which Semantic Grouper is best?
To determine which grouper best uncovers the substructures indicated by the discovered criteria and aligns most closely with the ground truth, we use the Harmonic Mean (HM) of the CAcc and SAcc for each criterion. This allows us to identify the best overall performer for each criterion.
In the comparison, to further illustrate the relative performance position of our framework, we first establish a pseudo upper-bound reference by leveraging the zero-shot classification capabilities of CLIP ViT-L14 (Radford et al., ) with ground-truth labels for each criterion, where the grouping criteria, cluster names, and number of clusters are all known. Additionally, we apply KMeans (Ahmed et al., ) with the ground-truth number of clusters, using robust visual features from CLIP ViT-L14, DINOv1-B/16 (Li et al., ), and DINOv2-G/14 (Oquab et al., ) to establish baseline positions for clustering performance.

Our comparative analysis, presented in Fig. 5, shows that the Caption-based Semantic Grouper performs best, ranking first in 12 out of 19 tested criteria based on the HM, across six benchmarks.
Specifically, in terms of CAcc, the caption-based grouper achieves an average of 59.9% across all tested criteria, closely aligning with the pseudo-upper-bound average of 58.1% and significantly outperforming feature representation-driven baselines, with the highest being DINOv2 at 40.6% CAcc. This demonstrates the effectiveness of our text-driven approach, as the cluster names inferred by the caption-based provide robust guidance for grouping. For SAcc, while the caption-based grouper falls short of the upper-bound reference average of 74.2%, where exact ground-truth class names are used, it still achieves a notable average of 60.5% across all tested criteria, surpassing its counterparts. To some extent, this gap in semantic consistency is expected due to the open nature of the semantic space—i.e., names like “Joyful”, “Happy”, and “Cheerful” are often used to describe the same Mood, yet they do not exhibit full semantic equivalence.
The BLIP-2 image-based grouper also shows commendable performance, ranking first in 5 of the 19 tested criteria. This suggests that the criterion-customized prompts generated by LLM help BLIP-2 accurately label relevant visual content. However, its per-image labeling approach may lead to noisy clusters due to a lack of overall alignment between them.
The tag-based grouper lags behind in all benchmarks likely due to a mismatch between the generated tags and the concepts in the dataset.

**Table 2: Comparison with criterion-conditioned clustering methods. For each benchmark, we report the average CAcc (%) and SAcc (%) across all criteria. We provide CLIP ViT-L/14 zero-shot performance as the pseudo upper-bound reference (UB). See expanded per-criterion results in App. E.3.**
|  | COCO-4c | Food-4c | Clevr-4c | Action-3c | Card-2c | Fruit-2c | Avg |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
|  | CAcc | SAcc | CAcc | SAcc | CAcc | SAcc | CAcc | SAcc | CAcc | SAcc | CAcc | SAcc | CAcc | SAcc |
| UB | 40.1 | 60.6 | 64.1 | 80.2 | 56.7 | 72.5 | 79.8 | 82.3 | 41.4 | 66.9 | 69.4 | 88.3 | 50.2 | 64.4 |
| IC$\mid$TC | 48.9 | 53.2 | 50.5 | 61.7 | 58.3 | 36.8 | 76.4 | 56.3 | 74.8 | 81.2 | 63.3 | 55.1 | 53.1 | 49.2 |
| MMaP | 33.9 | - | 43.8 | - | 62.8 | - | 60.6 | - | 36.9 | - | 51.0 | - | 41.3 | - |
| TeDeSC (Ours) | 51.2 | 48.4 | 48.1 | 64.9 | 64.9 | 54.3 | 68.3 | 60.6 | 73.3 | 84.3 | 65.1 | 61.1 | 53.0 | 53.4 |

Comparison with criterion-conditioned clustering methods:
We compare our top-performing Caption-based Grouper with recent methods that support text-conditioned clustering: i) IC$\mid$TC (Kwon et al., ), which uses LLaVA (Liu et al., ) and GPT-4 (OpenAI, ) to cluster images based on user-specified text criteria, and ii) MMaP (Yao et al., ), which generates cluster names with GPT-4 for user-specified criteria as pseudo prototypes, then uses these prototypes to derive proxy word embeddings for each image via prompt tuning CLIP (Radford et al., ) before applying KMeans clustering. It is important to note that both IC$\mid$TC and MMaP require user-provided (ground-truth) criteria and the number of clusters ($K_{l}$) as auxiliary prior input to work. . In stark contrast, our grouper uses the criteria discovered by the proposer and requires no pre-set cluster counts to forge high-quality clusters, operating entirely automatically. As shown in Tab. 2, our caption-based grouper not only outperforms MMaP but also achieves performance comparable to IC$\mid$TC across the six tested benchmarks. This highlights that our framework can deliver equally satisfactory results on the SMC task without requiring users to pre-define grouping criteria or cluster counts in their large image collections. We provide implementation details of IC$\mid$TC and MMaP in App. D.

Figure: Figure 6: Ablation study of multi-granularity refinement. For each benchmark, we show average CAcc and SAcc across all criteria. See expanded per-criterion numerical results in App. E.4.
Refer to caption: x8.png

Necessity of multi-granularity cluster refinement:
To validate the effectiveness of the multi-granularity cluster refinement design, we design control experiments with our Caption-based Grouper, using three different methods for constructing cluster names to organize images: i) Initial Names: using the initially assigned names as the final output, ii) Flat Refinement: prompting the LLM to refine the initial names into a flat list with a unified granularity, and our iii) Multi-granularity Refinement. We then compare the performance of these approaches in Fig. 6. We observe that both refinement methods significantly improve clustering accuracy compared to using noisy initial names, highlighting the importance of having granularity-consistent cluster names for accurately revealing substructures. Additionally, our proposed multi-granularity method surpasses flat refinement, as it enables the grouper to generate clustering results at different granularities, providing greater flexibility in aligning with the label granularity-the user-preferred level of detail.

Additional studies:
In App. F, we provide further studies on: i) Fine-grained Scenario: We examine how to integrate our framework with more advanced cross-modal Chain-of-Thought prompting strategies to better handle fine-grained criteria. ii) Sensitivity Analysis: We analyze the system sensitivity to various MLLMs and LLMs. Additionally, Sec. G offers a Qualitative Analysis by visualizing clustering results for different criteria, and Sec. H includes a Failure Case Analysis.

## 5 Applications

Discovering and mitigating dataset bias: Given an image collection that contains spurious correlations (Geirhos et al., ), we are curious whether we can proactively find this issue caused by data bias directly from the training images without relying on either the annotations (Sagawa et al., ) or post hoc misclassified images (Kim et al., ).

Figure: Figure 7: Results of dataset bias discovery and mitigation. Worst group and average accuracies(%) are reported.
Refer to caption: x9.png

As a case study, we applied the proposed TeDeSC framework to the 162k training images of the CelebA (Liu et al., ) dataset—a binary hair color classification dataset where the target label “Blond” is spuriously correlated with the demographic attribute “Female” in its training split. Additional details are provided in App. I.1.

Findings: As expected, our method identified the grouping criteria Hair color and Gender.
Next, we analyzed the predicted gender distributions within the “Blond” and “Not Blond” (all other colors) clusters. As shown in Fig. 7(a), we observed that the gender distribution within the “Blond” cluster is highly skewed, with 86.5% of the images representing females, closely matching the ground-truth distribution (94.3%).
Such an imbalance confirms the potential issue of spurious correlations between “Blond” and “Female”.
To further validate this observation, following B2T (Kim et al., ), we used our predicted distributions to train a debiased model with GroupDRO (Sagawa et al., ) and compared it with other unsupervised bias mitigation methods, including JTT (Liu et al., ), CNC (Zhang et al., ), B2T, and GroupDRO trained with ground-truth labels.
As shown in Fig. 7(b), our debiased model achieved robust performance, comparable to that of B2T, demonstrating the reliability of its discovered distributions.

Figure: Figure 8: Bias discovery results in T2I models. Bias evaluation results are shown for the associated occupations.
Refer to caption: x10.png

Discovering novel bias in Text-to-Image Diffusion Models:
Stereotypical biases related to gender or race (Naik & Nushi, ) in images generated by widely accessible text-to-image (T2I) models like Stable Diffusion XL (SDXL) (Podell et al., ) and DALL·E3 (Betker et al., ) have sparked intense discussions (Nicoletti & Bass, ) and significant research (Bianchi et al., ). However, beyond these well-known biases extensively studied in social science, we wonder: Are there other biases present in T2I-generated images?
To explore this question, we selected nine occupations (e.g.,, Nurse or CEO) from prior studies (Bianchi et al., ; Bolukbasi et al., ) as subjects for our case study on bias.
For each occupation, we generated 100 images using the prompt “A portrait photo of a $<$OCCUPATION$>$” with both DALL-E3 and SDXL, resulting in a total of 1.8k images (see Fig. 20 and Fig. 21 for examples).
We applied TeDeSC to these images and automatically discovered 10 grouping criteria (possible bias dimensions) along with their predicted distributions for each occupation image set. To inspect the biases, we calculated the normalized entropy of each distribution to quantify the bias intensity, as proposed by D’Incà et al. (), and identified the dominant cluster—the one containing the most images—as the possible bias direction.
Furthermore, we conducted a user study with 54 anonymous participants to assess how well our bias discovery results align with human judgment. We found that our system’s bias intensity scores closely matched human ratings—with an Absolute Mean Error (AME) of 0.1396 on a scale from 0 to 1—and that its predicted bias directions agreed with human evaluations 72.3% of the time. We highlight some key findings below and provide complete results and evaluations in App. I.2.

Findings:
In Fig. 8, we present some of our notable findings.
Without any predefined biases, our method successfully identifies well-known social biases associated with certain occupations.
As shown in Fig. 8(a–c), the SDXL-generated images exhibit near-total social bias for occupations like Nurse, Firefighter, and Basketball Player, displaying gender and racial imbalances that exceed official statistics such as those from U.S. Bureau of Labor Statistics ().
In contrast, DALL·E3 shows markedly improved performance in mitigating social biases—likely due to its bias mitigation “guardrails” (OpenAI, ).
More importantly, as shown in Fig. 8(d–f), our method revealed previously unnoticed novel bias dimensions where both models exhibit moderate biases. For example, we found that SDXL strongly associates CEOs with “Grey” hair color, while DALL·E3 favors “Dark” hair. Interestingly, and contrary to trends observed in well-known social biases, DALL·E3 shows stronger biases than SDXL in Hair style and Grooming for Nurse and Teacher. For instance, 91% of the Teacher images generated by DALL·E3 depict individuals who are clean-shaven (Fig. 8(f)).
The gap in DALL·E3’s performance between addressing well-known and novel biases suggests that even industrial T2I models with guardrail systems may overlook some novel biases, underscoring the importance of thoroughly examining biases beyond the commonly recognized ones.

Figure: Figure 9: Analysis of social media photo popularity on SPID dataset. We show the viral and major popular clusters along with the popularity distribution of data points within these clusters across five criteria (in Grey).
Refer to caption: x11.png

Analyzing Social media image popularity:
Given a set of social media photos with significantly varying popularity for each photo, it is natural to ask: What visual element makes a photo popular?
As a case study, we applied TeDeSC to 4.1k Flickr photos from the SPID dataset (Ortis et al., ), each accompanied by a popularity score based on the number of views.
After our method grouped the photos into semantic clusters based on 10 discovered criteria, we calculated two scores for each cluster: i) $\bar{P}$: the average popularity of photos within the cluster, and ii) $\bar{P}_{w}$: the average popularity $\bar{P}$ weighted by the cluster’s proportion relative to the entire dataset.
Here, we consider the cluster with the highest $\bar{P}$ as viral, meaning its photos are highly popular but may be few in number, and the cluster with the highest $\bar{P}_{w}$ as major popular, where the majority of popular photos are concentrated.
We discuss the key findings below and provide complete results in App. I.3.

Findings:
As shown in our analysis in Fig. 9, by combining the interpretable groupings from our method with popularity scores, the visual elements that drive virality (clusters with the highest $\bar{P}$) and the common traits shared among widely popular images (clusters with the highest $\bar{P}_{w}$) across different dimensions clearly emerged.
Interestingly, we further observe that viral visual elements often exhibit sharp semantic contrast with those of the majority of popular images, such as Musical activities vs. Rest and relaxation, and High-intensity expressions vs. Neutral emotion. This suggests that viral content is more attention-grabbing, likely due to novel, unexpected, or intense visuals that stand out, especially in an era where the average attention span is less than 9 seconds (McSpadden, ; Farid, ).
During our analysis, as shown in Fig. 9, we unexpectedly found that some of the most popular images in certain clusters contained not safe for work (NSFW) content, which had not been previously identified in the SPID dataset. This suggests that some images gain popularity due to negative or provocative visuals. It also highlights the need for more thorough inspection of visual datasets to avoid harm, and our proposed framework can be a useful tool for this purpose.

## 6 Conclusion

In this work, we introduce the task of semantic multiple clustering and propose TeDeSC, a system that automatically discovers grouping criteria in natural language from large image collections and uncovers interpretable data substructures based on these criteria. We rigorously evaluate various design choices of TeDeSC on four existing and two newly proposed benchmarks, and demonstrate its ability to reveal valuable insights that might otherwise go unnoticed in various real-world applications.

#### Acknowledgments

This work was supported by the MUR PNRR project FAIR - Future AI Research (PE00000013), funded by NextGenerationEU. E.R. acknowledges partial support from the PRECRISIS project, funded by the EU Internal Security Fund (ISFP-2022-TFI-AG-PROTECT-02-101100539), the EU project SPRING (No. 871245), and the PRIN project LEGO-AI (Prot. 2020TA3K9N). This work was conducted within the Vision and Learning joint laboratory of FBK and UNITN.
We extend our gratitude to Feng Xue for his valuable suggestions on plot creation. M.L. would like to thank Margherita Potrich for her unwavering support.

## Ethics Statement

We do not anticipate any immediate negative societal impacts from our work. However, we encourage future researchers building on this work to remain vigilant, as we have, about the potential for TeDeSC, which integrates LLMs and MLLMs–particularly their human-like reasoning abilities– to be used both for good and for harm.

The motivation behind our studies on biases in existing datasets and text-to-image (T2I) generative model outputs, as well as our exploration of social media image popularity, is to reveal and address these biases and the presence of sensitive or not-safe-for-work (NSFW) content that objectively exist in the datasets and models. We emphasize that our aim is to study and mitigate these issues, and in doing so, we do not create any new biases or disturbing content. Specifically, in Sec. 5, we use well-established benchmarks, such as CelebA (Liu et al., ), for our study of dataset bias, and for bias discovery in T2I generative models, we select occupation-related subjects known to be associated with biases from prior studies (Bianchi et al., ; Bolukbasi et al., ). Furthermore, our framework reveals previously undisclosed sensitive and sexual content in the SPID dataset (Ortis et al., ). We responsibly present these findings in Sec. 5, applying significant blurring to disturbing content, with the intention of raising community awareness about the need to further scrutinize NSFW content in existing benchmarks. However, we acknowledge that our methodology and findings could potentially be misused by malicious actors to promote harmful narratives or discrimination against certain groups. We strongly oppose any such misuse or misrepresentation of our work. Our research is conducted with the aim of advancing technology while prioritizing public welfare and well-being.

For the creation of our two new benchmarks, COCO-4c and Food-4c, we sourced images exclusively from the COCO-val-2017 (Lin et al., ) and Food-101 (Bossard et al., ) datasets, strictly adhering to their licensing agreements. Additionally, we utilized voluntary human annotators for proposing valid grouping criteria and creating annotations along these criteria, rather than employing annotators from crowdsourcing platforms. This decision was made to ensure sustainability, fair compensation, and high-quality work, as well as to safeguard the psychological well-being of participants. Similarly, for our user study on T2I model bias evaluation, we recruited voluntary participants via questionnaires to collect human evaluation results. The user study was conducted entirely anonymously, with participants providing informed consent. Our project, including data annotation and the user study involving human subjects, was approved by the Ethical Review Board of our university.

Lastly, we emphasize that our proposed framework, TeDeSC, relies on open-source LLMs and MLLMs, allowing full deployment on local machines. We refrain from using APIs from industrial LLMs or MLLMs, both to ensure reproducibility and to protect data privacy.

## Reproducibility Statement

We will release all essential resources required to reproduce the experimental results presented in this project, including source code, exact prompts, benchmarks with their data splits, and generated images, upon publication. Our proposed framework, TeDeSC, is built on open-source, publicly accessible models to ensure reproducibility. In Sec. 3, we provide a detailed description of how our framework is constructed. Additionally, App. C contains further implementation details, including exact prompts, to help practitioners easily reproduce our method. Details regarding the implementation of the compared methods are also provided in App. D. Moreover, we present extended numerical experimental results in App. E, alongside comprehensive findings for the application study in App. I. We believe that the thorough descriptions of our methodology, the extensive presentation of experimental results, and the open-source nature of our framework ensure that this work is highly reproducible, enabling future researchers and practitioners to readily apply our method to various domains.

## Appendix

[chapters]
\printcontents[chapters]1

This appendix provides detailed supplementary information supporting the implementations, experiments, and findings presented in the paper. First, in App. A, we offer an extensive discussion of Related Work, covering tasks and methods pertinent to our study.
In App. B, we describe the benchmarks used in our study, including the construction of the newly proposed COCO-4c and Food-4c datasets, along with the process for creating hard ground-truth criteria for evaluating different proposers. App. C outlines the prompts and implementation details for our proposed framework, including both Criteria Proposers and Semantic Groupers. App. D provides a deep dive into the implementation specifics of the compared methods used in our experiments. In App. E, we present additional quantitative results that supplement the findings reported in the main paper, covering evaluations of the Criteria Proposer, Semantic Grouper, and comparisons with other clustering methods. App. F extends our analysis of the proposed framework, including system sensitivity and studies on fine-grained image collections. App. G presents further qualitative results for the predicted clusters, while App. H offers a more detailed analysis of the failure cases encountered by our method. App. I provides additional findings, along with implementation details and user study results for the three applications explored in this work. Finally, App. J presents a deeper discussion of related settings pertinent to our research.

We will release all essential resources for reproducing this work, including code, prompts, benchmarks, and annotations, upon publication.

## Appendix A Related Work

Image Clustering.
Image clustering (Xu & Wunsch, ) discovers hidden grouping structures within large, unstructured, and unlabeled image collections, serving as a tool for various data-driven applications (Wazarkar & Keshavamurthy, ). To achieve this, deep clustering (DC) methods such as DEC (Xie et al., ) and SCAN (Van Gansbeke et al., ) focus on simultaneously learning feature representations and cluster assignments using deep neural networks via self-supervised techniques (Caron et al., ; Zhong et al., ; Ren et al., ). Furthermore, large-scale pre-trained feature representations like DINOv1 (Caron et al., ), DINOv2 (Oquab et al., ), and CLIP (Radford et al., ) have also been shown to be effective at clustering image collections in a zero-shot fashion with the help of KMeans (Vaze et al., ; Liu et al., ; Han et al., ).

However, it is well-known that “clusters are in the eye of the beholder” (Estivill-Castro, ); there often exist multiple ways to partition the same image collection into clusters, and what constitutes a cluster depends on the user’s needs. This insight has led to the study of Multiple Clustering (MC) (Ren et al., ; Yao et al., ; Yu et al., ), which aims to simultaneously learn feature representations and cluster assignments from different perspectives to find various ways of grouping the same data, enabling alternative interpretations from different viewpoints. Although existing MC methods have achieved impressive results (Yao et al., ) on some benchmarks, they share similar limitations with deep clustering approaches (Xie et al., ; Van Gansbeke et al., ). Their results require intensive manual post-analysis, and they also hold strong assumptions: users must specify (i) the number of potential clusterings and (ii) the number of clusters within each clustering. However, when dealing with millions of unstructured images, it is infeasible for users—who are trying to understand the data—to know this information a priori.

To address this challenge, recent works such as IC$\mid$TC (Kwon et al., ) and MMaP (Yao et al., ) propose a relaxed assumption: users may have certain criteria and corresponding cluster counts in mind for grouping images. They leverage these user-provided priors as auxiliary information to generate multiple criteria-conditioned clusterings through the cooperation of large language models (e.g.,, GPT-4 (OpenAI, )), multimodal large language models (e.g.,, LLaVA (Liu et al., )), or vision-language models (e.g.,, CLIP (Radford et al., )). However, as image collections—like those from social media platforms (Ortis et al., )—continue to diversify, the complexity of the data structure grows. It is impractical to expect the user to specify grouping criteria for a large image collection that they are not familiar with. Moreover, relying solely on human-defined criteria limits our ability to discover novel patterns and insights that might otherwise remain unnoticed. Besides, data analysis tools such as REVISE (Wang et al., ) and Know Your Data (Google People + AI Research, ) also allow users to explore visual data through multiple dimensions. However, they require human annotations to function and are thus limited to existing annotated datasets only.

In stark contrast to prior work, we introduce and study the task of semantic multiple clustering (SMC). Instead of requiring users to specify the grouping criteria, SMC seeks to actively and automatically discover criteria expressed in natural language from large visual data and uncover the corresponding semantic substructures, without access to any of the aforementioned human priors. As demonstrated in Sec. 5, the flexibility provided by our proposed SMC framework adds significant value to various data-driven applications, unveiling novel insights about the data that might not have been noticed before.

Topic Discovery.
The setting of semantic multiple clustering (SMC) is also related to the field of Topic Discovery (Blei et al., ; Wang et al., ; Eklund & Forsman, ) in natural language processing, which aims to identify textual themes from large text corpora (e.g.,, documents). Our work shares motivational similarities with topic discovery because both tasks seek to find common, thematic concepts from large volumes of data. In contrast, our work focuses on discovering thematic criteria from large visual content. However, indeed, the core challenges of SMC and topic discovery are highly similar: they both require systems that can concurrently reason over large volumes of data. Nevertheless, SMC is an even more challenging task than topic discovery for two reasons: i) semantics are not explicitly expressed in images, whereas they are in text; ii) there is currently no vision model that can encode large sets of images and reliably reason over them. Thus, in this work, we translate images to text and use text as a proxy to elicit the large-scale reasoning capability of large language models (Meta, ).

Multimodal Large Language Model. Recent advancements in multimodal large language models (MLLMs) have been driven by the availability of large-scale vision-language aligned training data. The typical paradigm (Liu et al., ) involves using a pre-trained large language model (LLM) (Meta, ; Chiang et al., ; Jiang et al., ; Meta, ) alongside a pre-trained vision encoder (Radford et al., ). A projector is learned to align visual inputs with the LLM in the embedding space, which enhances visual understanding by utilizing the reasoning capabilities of LLMs. Several models have achieved significant success in zero-shot image captioning and visual question answering (VQA), including BLIP-2 (Li et al., ), BLIP-3 (Xue et al., ), Kosmos-2 (Peng et al., ), and the LLaVA series (Liu et al., ; ; Li et al., ). In our proposed TeDeSC framework, we employ MLLM primarily as a zero-shot image parser, converting visual information into text and using this text as a proxy to elicit LLMs for reasoning over large image collections and discovering grouping criteria. Additionally, we leverage the multi-image reasoning capability of LLaVA-NeXT-Interleave (Li et al., ) to establish a baseline image-based proposer for the SMC task, while utilizing BLIP-2 with customized prompts in a VQA style (Shao et al., ; Zhu et al., ) as the image-based grouper to form semantic clusters linked to specific visual content within the images.

Large Language Model. In the era of large language models (LLMs) advancement (Ouyang et al., ), modern LLMs, such as the Llama series (Touvron et al., ; Meta, ; ), Vicuna (Chiang et al., ), Mistral-7B (Jiang et al., ), and the GPT series (Brown et al., ), have demonstrated remarkable zero-shot capabilities in tasks involving text analysis, completetion, generation, and summarization. With advanced prompting techniques like Chain-of-Thought (CoT) (Wei et al., ), the reasoning abilities of LLMs can be further enhanced. In the proposed TeDeSC framework, we design CoT prompts (see App. C) to harness the text generation and summarization capabilities of Llama-3.1 as a reasoning engine. This aids TeDeSC in several key areas: discovering grouping criteria from large sets of image captions, automatically prompting VQA models, generating criterion-specific tags, uncovering cluster semantics, and grouping images based on their captions. Unlike prior works (Zhuge et al., ) that focus on set difference captioning (Dunlap et al., ), fine-grained concept discovery (Liu et al., ), or video understanding (Wang et al., ), we leverage LLMs to tackle the challenging semantic multiple clustering task. While IC$\mid$TC (Kwon et al., ) also uses the LLM (GPT-4 (OpenAI, )) for grouping visual data, our proposed TeDeSC differs in two key aspects: i) TeDeSC does not require user-defined grouping criteria or the number of clusters, and ii) TeDeSC provides multi-granularity outputs to meet various user preferences.

Text-Driven Image Retrieval.
Given a query text (e.g.,, “sofa” or “person wearing a blue T-shirt”), text-driven image retrieval methods (Karthik et al., ; Liu et al., ; Wu et al., ) aim to find images from an image collection that are relevant to the query. In other words, in the scenario we are considering, given the image collection and a list of text queries, one can organize images according to the text using text-driven image retrieval techniques. In this context, the query can be considered as a sort of “cluster name”. However, this differs significantly from the proposed task of semantic multiple clustering (SMC), because SMC requires both discovering the textual criteria and the corresponding textual clusters. Thus, without knowing text queries as prior information, text-driven image retrieval methods are not able to accomplish SMC.

## Appendix B Benchmark Details

### B.1 Benchmark Construction of COCO-4c and Food-4c

**Table 3: Summary of number of classes for the basic criteria annotation across the six benchmarks.**
| Dataset | Basic Criterion | Number of Classes |
| --- | --- | --- |
| COCO-4c | Activity | 64 |
| Location | 19 |  |
| Mood | 20 |  |
| Time of Day | 6 |  |
| Food-4c | Food Type | 101 |
| Cuisine | 15 |  |
| Course | 5 |  |
| Diet | 4 |  |
| Action-3c | Action | 40 |
| Location | 10 |  |
| Mood | 4 |  |
| Clevr-4c | Color | 10 |
| Texture | 10 |  |
| Shape | 10 |  |
| Count | 10 |  |
| Card-2c | Rank | 14 |
| Suit | 5 |  |
| Fruit-2c | Species | 34 |
| Color | 15 |  |

To create high-quality benchmarks for COCO-4c and Food-4c, we designed a four-step annotation pipeline:

(1) Criteria Identification: We first split COCO-val-2017 (Lin et al., ) and Food-101 (Bossard et al., ) images into batches of 100. Each batch was stitched into a 10$\times$10 grid to form a single image. These grid images were then distributed to 5 human annotators, who were tasked with identifying grouping criteria. For each dataset, we selected the 4 most frequently occurring criteria, as shown in Tab. 3, to proceed with per-image annotation.

(2) Label Candidate Generation: To facilitate the annotation process, we used GPT-4V (OpenAI, ) to generate an initial list of candidate labels for each criterion. Specifically, for each criterion of COCO-4c and Food-4c, GPT-4V was prompted to assign a label that reflected the criterion for each image. This resulted in a list of criterion-specific label candidates for each dataset.

(3) Image Annotation: Next, 10 human annotators were tasked with assigning a label from the criterion-specific candidates to each image in COCO-4c and Food-4c for each criterion. The entire annotation process took 25 days to complete.

(4) Label Merging: Image annotation is inherently subjective, with annotators potentially assigning different labels for the same criterion. For example, one annotator might label the Mood criterion as
\sayHappy, while another might label it as \sayJoyful or
\sayDelightful.
To resolve such discrepancies, we used majority voting to determine the final label for each image. Specifically, the most frequently assigned label among the 10 annotators was chosen as the final label for each criterion.

Following these steps, we constructed COCO-4c and Food-4c. Note that we used the official COCO-val-2017 (Lin et al., ) and Food-101 (Bossard et al., ) images for our benchmarks and did not collect any new images. We adhered strictly to the licenses of the datasets during their creation. The exact number of classes is presented in Tab. 3. Additionally, the annotated class names for each criterion of COCO-4c are provided in Tab. 4, and for Food-4c in Tab. 5.

**Table 4: Full class names for COCO-4c across the four basic criteria.**
| Criterion | COCO-4c |
| --- | --- |
| Activity | “repairing a toilet”,<br>“playing volleyball”,<br>“playing guitar”,<br>“haircutting”,<br>“cutting a cigar”,<br>“kayaking”,<br>“applauding”,<br>“tying a tie”,<br>“playing basketball”,<br>“washing dishes”,<br>“gardening”,<br>“texting messages”,<br>“repairing a car”,<br>“peeing”,<br>“cleaning the floor”,<br>“writing on a book”,<br>“feeding a horse”,<br>“singing”,<br>“baking”,<br>“hiking”,<br>“smoking”,<br>“riding an elephant”,<br>“pouring liquid”,<br>“waving hands”,<br>“swimming”,<br>“meditating”,<br>“fixing a bike”,<br>“cutting vegetables”,<br>“walking a dog”,<br>“reading a book”,<br>“celebrating”,<br>“queuing”,<br>“cutting a cake”,<br>“brushing teeth”,<br>“playing soccer”,<br>“jumping”,<br>“snowboarding”,<br>“playing”,<br>“touching animals”,<br>“pushing a cart”,<br>“watching tv”,<br>“rowing a boat”,<br>“taking photos”,<br>“running”,<br>“flying a kite”,<br>“riding a horse”,<br>“playing video games”,<br>“holding up an umbrella”,<br>“throwing a frisbee”,<br>“lying down”,<br>“riding a bike”,<br>“drinking”,<br>“cooking”,<br>“phoning”,<br>“chatting”,<br>“skiing”,<br>“driving”,<br>“surfing”,<br>“skateboarding”,<br>“playing baseball”,<br>“playing tennis”,<br>“using a computer”,<br>“posing”,<br>“eating” |
| Location | “amusement or theme park”,<br>“healthcare facility”,<br>“virtual or digital space”,<br>“educational institution”,<br>“industrial area”,<br>“historical landmark”,<br>“public event or gathering”,<br>“store or market”,<br>“underground or enclosed space”,<br>“transportation hub”,<br>“zoo”,<br>“water body”,<br>“office or workplace”,<br>“park or recreational area”,<br>“restaurant or dining area”,<br>“sports facility”,<br>“natural environment”,<br>“urban area or city street”,<br>“residential area” |
| Mood | “anxious”,<br>“sombre”,<br>“contemplative”,<br>“suspenseful”,<br>“serene”,<br>“nostalgic”,<br>“inspired”,<br>“whimsical”,<br>“romantic”,<br>“mysterious”,<br>“melancholic”,<br>“chaotic”,<br>“humorous”,<br>“vibrant”,<br>“peaceful”,<br>“energetic”,<br>“focused”,<br>“joyful”,<br>“relaxed”,<br>“adventurous” |
| Time of Day | “evening”,<br>“afternoon”,<br>“night”,<br>“morning”,<br>“indoor lighting”,<br>“midday” |

**Table 5: Full class names for Food-4c across the four basic criteria.**
| Criterion | Food-4c |
| --- | --- |
| Food Type | “apple pie”,<br>“baby back ribs”,<br>“baklava”,<br>“beef carpaccio”,<br>“beef tartare”,<br>“beet salad”,<br>“beignets”,<br>“bibimbap”,<br>“bread pudding”,<br>“breakfast burrito”,<br>“bruschetta”,<br>“caesar salad”,<br>“cannoli”,<br>“caprese salad”,<br>“carrot cake”,<br>“ceviche”,<br>“cheesecake”,<br>“cheese plate”,<br>“chicken curry”,<br>“chicken quesadilla”,<br>“chicken wings”,<br>“chocolate cake”,<br>“chocolate mousse”,<br>“churros”,<br>“clam chowder”,<br>“club sandwich”,<br>“crab cakes”,<br>“creme brulee”,<br>“croque madame”,<br>“cup cakes”,<br>“deviled eggs”,<br>“donuts”,<br>“dumplings”,<br>“edamame”,<br>“eggs benedict”,<br>“escargots”,<br>“falafel”,<br>“filet mignon”,<br>“fish and chips”,<br>“foie gras”,<br>“french fries”,<br>“french onion soup”,<br>“french toast”,<br>“fried calamari”,<br>“fried rice”,<br>“frozen yogurt”,<br>“garlic bread”,<br>“gnocchi”,<br>“greek salad”,<br>“grilled cheese sandwich”,<br>“grilled salmon”,<br>“guacamole”,<br>“gyoza”,<br>“hamburger”,<br>“hot and sour soup”,<br>“hot dog”,<br>“huevos rancheros”,<br>“hummus”,<br>“ice cream”,<br>“lasagna”,<br>“lobster bisque”,<br>“lobster roll sandwich”,<br>“macaroni and cheese”,<br>“macarons”,<br>“miso soup”,<br>“mussels”,<br>“nachos”,<br>“omelette”,<br>“onion rings”,<br>“oysters”,<br>“pad thai”,<br>“paella”,<br>“pancakes”,<br>“panna cotta”,<br>“peking duck”,<br>“pho”,<br>“pizza”,<br>“pork chop”,<br>“poutine”,<br>“prime rib”,<br>“pulled pork sandwich”,<br>“ramen”,<br>“ravioli”,<br>“red velvet cake”,<br>“risotto”,<br>“samosa”,<br>“sashimi”,<br>“scallops”,<br>“seaweed salad”,<br>“shrimp and grits”,<br>“spaghetti bolognese”,<br>“spaghetti carbonara”,<br>“spring rolls”,<br>“steak”,<br>“strawberry shortcake”,<br>“sushi”,<br>“tacos”,<br>“takoyaki”,<br>“tiramisu”,<br>“tuna tartare”,<br>“waffles” |
| Cuisine | “japanese”,<br>“indian”,<br>“american”,<br>“greek”,<br>“spanish”,<br>“mexican”,<br>“italian”,<br>“vietnamese”,<br>“canadian”,<br>“korean”,<br>“chinese”,<br>“middle eastern”,<br>“french”,<br>“thai”,<br>“general” |
| Course | “appetizer”, “main course”, “side dish”, “dessert”, “breakfast” |
| Diet | “omnivore”, “vegan”, “vegetarian”, “gluten free” |

### B.2 Details on Hard Grouping Criteria Annotation

**Table 6: Annotated criteria for the six benchmarks. The basic criteria are annotated on per-image level for each benchmark, while the hard criteria (those not in the basic criteria) are further exhaustively annotated by human annotators for further evaluating the performance of the rule proposer in SMC task.**
| COCO-4c | Food-4c | Action-3c |  |  |  |
| --- | --- | --- | --- | --- | --- |
| Basic criteria | Hard criteria | Basic criteria | Hard criteria | Basic criteria | Hard criteria |
| Total: 4 | Total: 17 | Total: 4 | Total: 11 | Total: 3 | Total: 11 |
| Activity | Activity | Food Type | Food Type | Action | Action |
| Location | Location | Cuisine | Cuisine | Mood | Mood |
| Mood | Mood | Course | Course | Location | Location |
| Time of Day | Time of Day | Diet | Diet |  | Clothing Style |
|  | Interaction |  | Tableware Type |  | Number of People Present |
|  | Number of People Present |  | Presentation Style |  | Age or Age Composition |
|  | Group Dynamics |  | Color Palette |  | Race or Race Composition |
|  | Clothing Style |  | Setting/Theme |  | Occasion or Event Type |
|  | Occasion or Event Type |  | Primary Taste |  | Group Dynamics |
|  | Photo Style |  | Primary Ingredient |  | Lighting Condition |
|  | Type of Animal Present |  | Cooking Method |  | Gender or Gender Composition |
|  | Weather |  |  |  |  |
|  | Type of Primary Object |  |  |  |  |
|  | Continent |  |  |  |  |
|  | Age or Age Composition |  |  |  |  |
|  | Race or Race Composition |  |  |  |  |
|  | Gender or Gender Composition |  |  |  |  |
| Clevr-4c | Card-2c | Fruit-2c |  |  |  |
| Basic criteria | Hard criteria | Basic criteria | Hard criteria | Basic criteria | Hard criteria |
| Total: 4 | Total: 7 | Total: 2 | Total: 4 | Total: 2 | Total: 8 |
| Color | Color | Rank | Rank | Species | Species |
| Texture | Texture | Suit | Suit | Color | Color |
| Shape | Shape |  | Color |  | Size |
| Count | Count |  | Illustration Style |  | Seasonality |
|  | Spatial Positioning |  |  |  | Primary Taste |
|  | Count of Surface |  |  |  | Texture |
|  | Complexity of Geometry |  |  |  | Ripeness |
|  |  |  |  |  | Fruit Quantity and Arrangement |

In Tab. 6, we present the additional annotated Hard grouping criteria ground truth alongside the Basic criteria for each benchmark.

While we have established more rigorous and challenging benchmarks such as COCO-4c and Food-4c, which feature up to four distinct grouping criteria, these annotated criteria sets do not encompass all potential grouping criteria within the image collections. This is particularly true for more complex and realistic datasets like COCO-4c, Food-4c, and Action-3c. As a result, the performance differences between different criteria proposers on these basic criteria, as shown in Fig. 4, tend to be close to each other, limiting our understanding of each proposer’s ability to generate comprehensive grouping criteria.

To address this limitation, we employed human annotators to further identify and propose grouping criteria across the six benchmarks, resulting in a more extensive ground-truth set for each benchmark. This provides a better basis for evaluating the comprehensiveness of the different proposers. We refer to this set of larger annotation criteria as the Hard criteria, in contrast to the Basic criteria, which involve per-image annotations. Note that for the Hard criteria, per-image label annotation is not provided due to the high cost of annotation. The procedure for obtaining the Hard grouping criteria is as follows:

(1) Criteria Discovery: We divided each dataset into batches of 100 images, displaying each batch in a 10$\times$10 grid. Five human annotators were assigned to each batch and instructed to identify as many valid grouping criteria as possible. The proposed criteria from each annotator were then combined to form a comprehensive set of grouping criteria for the dataset.

(2) Criteria Merging: After collecting the annotated criteria from all five annotators, we aggregated the criteria and manually cleaned the set by merging semantically similar criteria (e.g.,, Location and Place) and discarding binary grouping criteria, as the inclusion of binary criteria can result in an unmanageable number of grouping criteria for complex datasets.

By following this process, we developed a more comprehensive grouping criteria set as the Hard ground-truth for each benchmark, as shown in Tab. 6. This resulted in sets containing 8 criteria for Fruit-2c, 4 criteria for card, 11 criteria for Action-3c, 7 criteria for Clevr-4c, 17 criteria for COCO-4c, and 11 criteria for Food-4c. These expanded ground-truth sets enable us to more effectively evaluate the capabilities of various criteria discovery methods, providing a clearer understanding of different criteria proposers.

## Appendix C Further Implementation Details

In this section, we provide detailed descriptions of the exact prompts used in our framework, along with additional implementation details for the proposed Criteria Proposer in App. C.1 and the Semantic Grouper in App. C.2.

### C.1 Prompts and Implementation Details of Criteria Proposer

Image-based Proposer:

**Table 7: Prompts for the MLLM in the image-based proposer for criteria proposing.**
| Prompt purpose | Prompt |
| --- | --- |
| System Prompt | You are a helpful AI assistant |
| Input Explanation | This image contains 64 individual images arranged in 8 columns and 8 rows. |
| Goal Explanation | I am a machine learning researcher trying to identify all the possible clustering criteria or rules that could be used to group these images so I can better understand my data. |
| Task Instruction | Your job is to carefully analyze the entire set of the 64 images, and identify five distinct clustering criteria or rules that could be used to cluster or group these images. Please consider different characteristics. |
| Output Instruction | Please write a list of the 5 identified clustering criteria or rules (separated by bullet points “*”). |
| Task Reinforcement | Again, I want to identify all the possible clustering criteria or rules that could be used to group these images. List the 5 distinct clustering criteria or rules that you identified from the 64 images. Answer with a list (separated by bullet points “*”).<br>Your response: |
|  |  |

In Tab. 7, we present the exact prompt used in the image-based proposer for querying the MLLM LLaVA-NeXT-Interleave-7B (Li et al., ). Given a target image set, we first randomly shuffle the images and divide them into disjoint subsets, each containing 64 images. Each subset is then stitched into an $8\times 8$ image grid, treated as a single image, and fed into the MLLM. For each subset, the MLLM is prompted to propose 5 distinct grouping criteria for organizing the images within that subset, using the prompt shown in Tab. 7. After iterating through all subsets, we take the union of the criteria proposed for each subset as the discovered criteria for the target image set. Finally, we deduplicate the discovered criteria and accumulate them into the criteria pool.

Tag-based Proposer:

**Table 8: Prompts for the LLM used in the tag-based proposer for criteria proposing. We embed the exact image captions by replacing the placeholders "{TAGS}" in the prompt.**
| Prompt purpose | Prompt |
| --- | --- |
| System Prompt | You are a helpful assistant. |
| Input Explanation | The following are the tagging results of a set of images in the format of “Image ID: tag 1, tag 2, …, tag 10”. These assigned tags reflect the visible semantic content of each image: |
| Tag Embedding | Image 1: "{TAGS}"<br>Image 2: "{TAGS}"<br>…<br>Image N: "{TAGS}" |
| Goal Explanation | I am a machine learning researcher trying to figure out the potential clustering or grouping criteria that exist in these images. So I can better understand my data and group them into different clusters based on different criteria. |
| Task Instruction | Please analyze these images by using their assigned tags. Come up with an array of distinct clustering criteria that exist in this set of images. |
| Output Instruction | Please write a list of clustering criteria (separated by bullet points “*”). |
| Task Reinforcement | Again, I want to figure out what are the potential clustering or grouping criteria that I can use to group these images into different clusters.<br>List an array of clustering or grouping criteria that often exist in this set of images based on the tagging results. Answer with a list (separated by bullet points “*”).<br>Your response: |
|  |  |

In Tab. 8, we present the exact prompt used in the tag-based proposer for querying the LLM Llama-3.1-8B (Meta, ). For a given target image set, we first utilize an open-vocabulary tagger, CLIP ViT-L/14 (Radford et al., ), to assign 10 related natural language tags to each image. These tags are selected from the WordNet (Miller, ) vocabulary, which contains 118k English synsets, and represent the semantic content of the images. We employ the standard prompt “A photo of {concept}” provided by CLIP for image tagging. Next, we embed the assigned tags into the prompt shown in Tab. 8 to carry the semantics of the entire image set and query the LLM to propose grouping criteria. The criteria proposed by the LLM are then added to the criteria pool. Note that in this case, we embed the tags for the entire dataset into a single prompt for criteria proposal, without reaching the LLM context length limits (e.g.,, 128k for Llama-3.1-8B) for the datasets used in our experiments. However, for larger datasets, it may be necessary to split the dataset into subsets, prompt the LLM for each subset, and use the union of the proposed criteria as the final output.

Caption-based Proposer:

**Table 9: Prompts for the MLLM in the caption-based proposer for generating detailed descriptions of the images.**
| Prompt purpose | Prompt |
| --- | --- |
| System Prompt | You are a helpful AI assistant |
| Task Instruction | Describe the following image in detail. |
|  |  |

**Table 10: Prompts for the LLM used in the caption-based proposer for criteria proposing. We embed the exact image captions by replacing the placeholders "{CAPTION}" in the prompt.**
| Prompt purpose | Prompt |
| --- | --- |
| System Prompt | You are a helpful assistant. |
| Input Explanation | The following are the result of captioning a set of images: |
| Caption Embedding | Image 1: "{CAPTION}"<br>Image 2: "{CAPTION}"<br>…<br>Image N: "{CAPTION}" |
| Goal Explanation | I am a machine learning researcher trying to figure out the potential clustering or grouping criteria that exist in these images. So I can better understand my data and group them into different clusters based on different criteria. |
| Task Instruction | Come up with ten distinct clustering criteria that exist in this set of images. |
| Output Instruction | Please write a list of clustering criteria (separated by bullet points “*”). |
| Task Reinforcement | Again I want to figure out what are the potential clustering/grouping criteria that I can use to group these images into different clusters. List ten clustering or grouping criteria that often exist in this set of images based on the captioning results. Answer with a list (separated by bullet points “*”).<br>Your response: |
|  |  |

We present the prompt used in the caption-based proposer for the MLLM LLaVA-NeXT-7B (Liu et al., ) in Tab. 9, and the prompt for the LLM Llama-3.1-8B (Meta, ) in Tab. 10. Specifically, we first use the MLLM with a general prompt to generate detailed descriptions for each image in the target dataset, effectively translating the visual information into natural language. The generated captions are then randomly shuffled and split into disjoint subsets, each containing 400 captions. Next, we embed the captions from each subset into the prompt shown in Tab. 10 and use it to query the LLM to propose grouping criteria for the images represented by the captions. After iterating through all subsets, we take the union of the proposed criteria across subsets as the discovered criteria for the target image set. Finally, we deduplicate these criteria and add them to the criteria pool. Due to the context window limitations of LLMs, embedding all captions into a single prompt is infeasible. To address this, we limit each subset to 400 captions, which results in approximately 115k tokens per subset. This strategy allows us to remain within the context length limits of modern LLMs (e.g.,, 128k tokens for both Llama-3.1 and GPT-4o) while maximizing the number of samples per query to effectively propose clustering criteria.

Criteria Pool Refinement:

**Table 11: Prompts for the LLM used in Proposed Criteria Refinement step We embed the exact initially discovered criteria by replacing the placeholders "{CRITERION}" in the prompt.**
| Prompt purpose | Prompt |
| --- | --- |
| System Prompt | You are a helpful assistant. |
| Input Explanation | I am a machine learning researcher working with a set of images. I aim to cluster this set of images based on the various clustering criteria present within them. Below is a preliminary list of clustering criteria that I’ve discovered to group these images: |
| Criteria Embedding: | * Criterion 1: "{CRITERION}"<br>* Criterion 2: "{CRITERION}"<br>…<br>* Criterion L: "{CRITERION}" |
| Goal Explanation | My goal is to refine this list by merging similar criteria and rephrasing them using more precise and informative terms. This will help create a set of distinct, optimized clustering criteria. |
| Task Instruction | Your task is to first review and understand the initial list of clustering criteria provided. Then, assist me in refining this list by:<br>* Merging similar criteria.<br>* Expressing each criterion more clearly and informatively. |
| Output Instruction | Please respond with the cleaned and optimized list of clustering criteria, formatted as bullet points (using “*”).<br>Your response: |
|  |  |

In Tab. 11, we present the exact prompt used for criteria pool refinement when querying the LLM Llama-3.1-8B (Meta, ). Since the accumulated criteria pool $\widetilde{\mathcal{R}}$ may contain highly similar or noisy clustering criteria, we embed the criteria from the pool into the prompt shown in Tab. 11 and ask the LLM to merge similar criteria and rephrase their names to enhance clarity. This process yields a refined set of grouping criteria, which is then passed to the next stage for image grouping.

### C.2 Prompts and Implementation Details of Semantic Grouper

Image-based Grouper:

**Table 12: Prompts for the LLM used in the image-based grouper for automatic criterion-specific VQA question generation. We embed the exact discovered criterion by replacing the placeholder "{CRITERION}" in the prompt.**
| Prompt purpose | Prompt |
| --- | --- |
| System Prompt | You are a helpful assistant. |
| Goal Explanation | Hello! I am a machine learning researcher focusing on image categorization based on the aspect of "{CRITERION}" depicted in images. |
| Task Instruction | Therefore, I need your assistance in designing a prompt for the Visual Question Answering (VQA) model to help it identify the "{CRITERION}" category in a given image at three different granularity. Please help me design and generate this prompt using the following template: "Question: [Generated VQA Prompt Question] Answer (reply with an abstract, a common, and a specific category name, respectively):". The generated prompt should be simple and straightforward. |
| Output Instruction | Please respond with only the generated prompt using the following format “* Answer *”.<br>Your response: |
|  |  |

In Tab. 12, we present the prompt used to query the LLM Llama-3.1-8B (Meta, ) for automatically generating criterion-specific VQA questions for the image-based grouper. The objective at this stage is to condition the VQA model BLIP-2 Flan-T5${}_{\text{XXL}}$ (Li et al., ) to label each image across three different semantic granularity levels based on a specific criterion. To guide the VQA model effectively, a criterion-specific question is required.

Rather than manually creating these questions, we embed the target criterion into the prompt shown in Tab. 12 and query the LLM to automatically generate high-quality, criterion-specific questions. These questions are then used to direct the VQA model, enabling it to accurately label each image according to the visual content relevant to the target criterion.

Tag-based Grouper:

**Table 13: Prompts for the LLM used in the tag-based grouper for generating middle-grained criterion-specific tags. We embed the exact discovered criterion by replacing the placeholder "{CRITERION}" in the prompt.**
| Prompt purpose | Prompt |
| --- | --- |
| System Prompt | You are a helpful assistant. |
| Goal Explanation | Hello! I am a machine learning researcher focusing on image categorization of a certain aspect. I’m interested in generating a list of tags specifically for categorizing the types of "{CRITERION}" depicted in images. |
| Task Instruction | Please provide a list of potential "{CRITERION}" category names. Please generate diverse category names. Do not include too general or specific category names such as “Sports”. |
| Output Instruction | Please respond with the list of category names. Each category should be formatted as follows: “* Category Name”.<br>Your response: |
|  |  |

**Table 14: Prompts for the LLM used in the tag-based grouper for generating coarse-grained criterion-specific tags. We embed the exact discovered criterion and middle-grained category by replacing the placeholder "{CRITERION}" and "{MIDDLE-GRAINED CATEGORY NAME}" in the prompt, respectively.**
| Prompt purpose | Prompt |
| --- | --- |
| System Prompt | You are a helpful assistant. |
| Task Instruction | Generate a list of three more abstract or general "{CRITERION}" super-categories that the following "{CRITERION}" category belongs to and output the list separated by “&” (without numbers): "{MIDDLE-GRAINED CATEGORY NAME}" |
| Output Instruction | Your response: |
|  |  |

**Table 15: Prompts for the LLM used in the tag-based grouper for generating fine-grained criterion-specific tags. We embed the exact discovered criterion and middle-grained category by replacing the placeholder "{CRITERION}" and "{MIDDLE-GRAINED CATEGORY NAME}" in the prompt, respectively.**
| Prompt purpose | Prompt |
| --- | --- |
| System Prompt | You are a helpful assistant. |
| Task Instruction | Generate a list of ten more detailed or specific "{CRITERION}" sub-categories of the following "{CRITERION}" category and output the list separated by “&” (without numbers): "{MIDDLE-GRAINED CATEGORY NAME}" |
| Output Instruction | Your response: |
|  |  |

We present the prompts used in the tag-based grouper for querying the LLM Llama-3.1-8B. The prompt for generating criterion-specific tags is shown in Tab. 13, while the prompts for generating coarse-grained and fine-grained tags are shown in Tab. 14 and Tab. 15, respectively.

In the tag-based grouper, we begin by embedding the target criterion into the prompt from Tab. 13 to generate criterion-specific tags at a middle granularity. To enhance the diversity and coverage of the tags, we query the LLM 10 times and take the union of the generated tags after deduplication as candidates. Following the SHiNe framework (Liu et al., ), for each middle-grained tag, we further embed it into the prompts from Tab. 14 and Tab. 15 to generate 3 super-categories (coarse-grained) and 10 sub-categories (fine-grained) for each tag.

After generating coarse and fine-grained categories for all middle-grained tags, we take the union of the super-categories as the coarse-grained tag candidates and the union of the sub-categories as the fine-grained tag candidates. Lastly, we use the open-vocabulary tagger CLIP ViT-L/14 to assign the most relevant tags to each image based on cosine similarity, using candidates from each granularity level. After tagging all the images, we group those sharing the same tag into clusters, yielding the clustering result. Note that we do not utilize lexical databases such as WordNet (Miller, ) or ConceptNet (Speer et al., ) for tag generation, as they do not support free-form input and may not capture certain discovered criteria.

Caption-based Grouper:

**Table 16: Prompts for the MLLM used in the caption-based grouper for generating criterion-specific captions. We embed the exact discovered criterion by replacing the placeholder "{CRITERION}" in the prompt.**
| Prompt purpose | Prompt |
| --- | --- |
| System Prompt | You are a helpful AI assistant. |
| Task Instruction | Analyze the image focusing specifically on the "{CRITERION}". Provide a detailed description of the "{CRITERION}" depicted in the image. Highlight key elements and interactions relevant to the "{CRITERION}" that enhance the understanding of the scene. |
| Output Instruction | Your response: |
|  |  |

**Table 17: Prompts for the LLM used in the caption-based grouper at the Initial Naming step for initially assigning a criterion-based category name to the image based on its criterion-specific caption. We embed the exact discovered criterion and the corresponding criterion-specific caption by replacing the placeholder "{CRITERION}" and "{CRITERION-SPECIFIC CAPTION}" in the prompt, respectively.**
| Prompt purpose | Prompt |
| --- | --- |
| System Prompt | You are a helpful assistant. |
| Input Explanation | The following is the description about the "{CRITERION}" of an image: |
| Caption Embedding | "{CRITERION-SPECIFIC CAPTION}" |
| Goal Explanation | I am a machine learning researcher trying to assign a label to this image based on what is the "{CRITERION}" depicted in this image. |
| Task Instruction | Understand the provided description carefully and assign a label to this image based on what is the "{CRITERION}" depicted in this image. |
| Output Instruction | Please respond in the following format within five words: "*Answer*". Do not talk about the description and do not respond long sentences. The answer should be within five words. |
| Task Reinforcement | Again, your job is to understand the description and assign a label to this image based on what is the "{CRITERION}" shown in this image.<br>Your response: |
|  |  |

**Table 18: Prompts for the LLM used in the caption-based grouper at the Multi-granularity Cluster Generation step for refining the initially assigned names to a structured three granularity levels. We embed the exact discovered criterion and the initially assigned name categories by replacing the placeholder "{CRITERION}" and "{MIDDLE-GRAINED CATEGORY NAME}" in the prompt, respectively.**
| Prompt purpose | Prompt |
| --- | --- |
| System Prompt | You are a helpful assistant. |
| Input Explanation | The following is an initial list of "{CRITERION}" categories. These categories might not be at the same semantic granularity level. For example, category 1 could be “cutting vegetables”, while category 2 is simply “cutting”. In this case, category 1 is more specific than category 2. |
| Category Embedding | * "{MIDDLE-GRAINED CATEGORY NAME}"<br>* "{MIDDLE-GRAINED CATEGORY NAME}"<br>…<br>* "{MIDDLE-GRAINED CATEGORY NAME}" |
| Task Instruction | These categories might not be at the same semantic granularity level. For example, category 1 could be “cutting vegetables”, while category 2 is simply “cutting”. In this case, category 1 is more specific than category 2.<br>Your job is to generate a three-level class hierarchy (class taxonomy, where the first level contains more abstract or general coarse-grained classes, the third level contains more specific fine-grained classes, and the second level contains intermediate mid-grained classes) of "{CRITERION}" based on the provided list of "{CRITERION}" categories. Follow these steps to generate the hierarchy. |
| Sub-task Instruction | Follow these steps to generate the hierarchy:<br>Step 1 - Understand the provided initial list of "{CRITERION}" categories. The following three-level class hierarchy generation steps are all based on the provided initial list.<br>Step 2 - Generate a list of abstract or general "{CRITERION}" categories as the first level of the class hierarchy, covering all the concepts present in the initial list.<br>Step 3 - Generate a list of middle-grained "{CRITERION}" categories as the second level of the class hierarchy, in which the middle-grained categories are the subcategories of the categories in the first level. The categories in the second-level are more specific than the first level but should still cover and reflect all the concepts present in the initial list.<br>Step 4 - Generate a list of more specific fine-grained "{CRITERION}" categories as the third level of the class hierarchy, in which the categories should reflect more specific "{CRITERION}" concepts that you can infer from the initial list. The categories in the third-level are subcategories of the second-level.<br>Step 5 - Output the generated three-level class hierarchy as a JSON object where the keys are the level numbers and the values are a flat list of generated categories at each level, structured like:<br>{<br>“level 1": [“categories”],<br>“level 2": [“categories”],<br>“level 3": [“categories”]<br>} |
| Output Instruction | Please only output the JSON object in your response and simply use a flat list to store the generated categories at each level.<br>Your response: |
|  |  |

**Table 19: Prompts for the LLM used in the caption-based grouper at the Final Assignment step. We embed the exact discovered criterion and the refined category names from each granularity level, by replacing the placeholder "{CRITERION}" and "{CANDIDATE CATEGORY NAME}" in the prompt, respectively.**
| Prompt purpose | Prompt |
| --- | --- |
| System Prompt | You are a helpful assistant. |
| Input Explanation | The following is a detailed description about the "{CRITERION}" of an image. |
| Caption Embedding | "{CRITERION-SPECIFIC CAPTION}" |
| Task Instruction | Based on the content and details provided in the description, classify the image into one of the specified "{CRITERION}" categories listed below: |
| Candidate Category<br>Embedding | "{CRITERION}" categories:<br>* "{CANDIDATE CATEGORY NAME}"<br>* "{CANDIDATE CATEGORY NAME}"<br>…<br>* "{CANDIDATE CATEGORY NAME}" |
| Output Instruction | Ensure that your classification adheres to the details mentioned in the image description. Respond with the classification result in the following format: “*category name*”.<br>Your response: |
|  |  |

We first present the MLLM prompt used for LLaVA-NeXT-7B (Liu et al., ) to generate criterion-specific captions in Tab. 16. Following this, we present the LLM Llama-3.1-8B prompts used in the caption-based grouper for the Initial Naming step in Tab. 17, the Multi-granularity Cluster Refinement step in Tab. 18, and the Final Assignment step in Tab. 19.

Specifically, we begin by generating criterion-specific captions for each image using LLaVA-NeXT-7B with the prompt shown in Tab. 16. For each image, we then embed its criterion-specific caption and the relevant criterion into the LLM prompt shown in Tab. 17, querying the LLM to assign an initial name based on the target criterion. Once the initial names for all images in the dataset are obtained, we embed these names along with the target criterion into the prompt in Tab. 18 to query the LLM for cluster name refinement across three semantic granularity levels: coarse, middle, and fine.

Finally, for each image, we embed the target criterion, its criterion-specific caption, and cluster candidates from each granularity level into the prompt shown in Tab. 19, and use this to query the LLM for final cluster assignment at each granularity level.

## Appendix D Further Implementation Details of the Compared Methods

In this section, we provide the implementation details of the compared methods, IC$\mid$TC (Kwon et al., ) and MMaP (Yao et al., ).

Implementation details of IC$\mid$TC (Kwon et al., ):
In the original implementation of IC$\mid$TC, LLaVA-1.5 (Liu et al., ) was used as the MLLM, and GPT-4-2023-03-15-preview (OpenAI, ) as the LLM. However, since the GPT-4-2023-03-15-preview API has been deprecated, we re-implemented IC$\mid$TC using the state-of-the-art MLLM LLaVA-NeXT-7B (Liu et al., ) and the latest version of GPT-turbo-2024-04-09 as the LLM, while strictly adhering to the original IC$\mid$TC prompt design in our experiments to ensure a fair comparison.

Implementation details of MMaP (Yao et al., ):
We closely followed the training configuration outlined in the original MMaP paper. Specifically, GPT-turbo-2024-04-09 was used as the LLM to generate reference words for each dataset. We then prompt-tuned CLIP-ViT/B32 using Adam with a momentum of 0.9, training the model for 1,000 epochs for each criterion across all datasets. Hyperparameters were optimized according to the loss score of MMaP, with the learning rate searched in {0.1, 0.05, 0.01, 0.005, 0.001, 0.0005}, weight decay in {0.0005, 0.0001, 0.00005, 0.00001, 0}, $\alpha$ and $\beta$ in {0.0, 0.1, 0.2, …, 1.0}, and $\lambda$ fixed at 1 for all experiments. After training, KMeans, with the ground-truth number of clusters, was applied for each criterion and dataset to perform clustering.

## Appendix E Supplementary Results of the Quantitative Experiments

In this section, we present additional numerical experiment results to supplement the figures in the main paper. In Sec. E.1, we provide supplementary results for the evaluation of the Criteria Proposer in our framework. In Sec. E.2, we present additional results for the evaluation of the Semantic Grouper across various criteria on the six tested benchmarks. Furthermore, we include expanded results comparing our framework to prior criteria-conditioned clustering methods. Lastly, we present detailed results from the ablation study of the multi-granularity refinement component in Sec. E.4.

### E.1 Supplementary Results for Criteria Proposer Evaluation

We provide detailed numerical results corresponding to Fig. 4(a) in Tab. 20 and Fig. 4(c) in Tab. 21 for the six tested benchmarks.

Although captions generated by the MLLM may exhibit some information loss (e.g.,, ignoring small objects or attributes) (He et al., ) and hallucinations (e.g.,, introducing objects not present in the images) Liu et al. (), these issues generally occur at the object or fine-grained attribute level. However, when reasoning about grouping criteria for SMC task, the focus is on identifying general thematic elements shared across the image set. As a result, these minor inconsistencies in the captions do not hinder the LLM in our framework from effectively reasoning about grouping criteria, helping the Caption-based Proposer to achieve the best performance among all the studied design choices.

**Table 20: Comparison of True Positive Rate (TPR) (%) for criteria proposers across the six SMC benchmarks. TPR performance is reported for both Basic and Hard ground-truth criteria. The best performance is highlighted in bold.**
|  | COCO-4c | Food-4c | Action-3c | Clevr-4c | Card-2c | Fruit-2c | Average |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
|  | Basic | Hard | Basic | Hard | Basic | Hard | Basic | Hard | Basic | Hard | Basic | Hard | Basic | Hard |
| Image-based | 100.0 | 52.9 | 25.0 | 36.4 | 66.7 | 54.6 | 50.0 | 28.6 | 50.0 | 25.0 | 50.0 | 20.0 | 56.9 | 36.2 |
| Tag-based | 50.0 | 35.3 | 100.0 | 72.7 | 66.7 | 36.4 | 75.0 | 42.9 | 50.0 | 50.0 | 50.0 | 20.0 | 65.3 | 42.9 |
| Caption-based | 100.0 | 64.7 | 100.0 | 81.8 | 100.0 | 72.7 | 100.0 | 71.4 | 100.0 | 100.0 | 100.0 | 60.0 | 100.0 | 75.1 |

**Table 21: Study of the impact of data scale on criteria discovery. The Caption-based Proposer is used for criteria discovery, and TPR performance (%) is reported on the Hard ground-truth criteria sets across the six SMC benchmarks for different data scales. The best performance is highlighted in bold.**
| Data scales | COCO-4c | Food-4c | Action-3c | Clevr-4c | Card-2c | Fruit-2c | Average |
| --- | --- | --- | --- | --- | --- | --- | --- |
| 100% | 64.7 | 81.8 | 72.7 | 71.4 | 100.0 | 60.0 | 75.1 |
| 80% | 47.1 | 72.7 | 54.6 | 71.4 | 75.0 | 30.0 | 58.5 |
| 60% | 52.9 | 63.6 | 54.6 | 71.4 | 100.0 | 50.0 | 65.4 |
| 40% | 41.2 | 45.5 | 45.5 | 85.7 | 100.0 | 40.0 | 59.6 |
| 20% | 35.3 | 45.5 | 36.4 | 42.9 | 100.0 | 40.0 | 50.0 |
| 1 img | 23.5 | 36.4 | 27.3 | 57.1 | 75.0 | 50.0 | 44.9 |

### E.2 Supplementary Results for Semantic Grouper Evaluation

In this section, we present the expanded numerical results comparing different semantic groupers to supplement the summary in Fig. 5. Specifically, we provide detailed results for the evaluation of the six tested datasets as follows:

- •
COCO-4c (Fig. 5(a)) in Tab. 22
- •
Card-2c (Fig. 5(b)) in Tab. 23
- •
Action-3c (Fig. 5(c)) in Tab. 24
- •
Food-4c (Fig. 5(d)) in Tab. 25
- •
Fruit-2c (Fig. 5(e)) in Tab. 26
- •
Clevr-4c (Fig. 5(f)) in Tab. 27

**Table 22: Comparison of Semantic Groupers on COCO-4c. We report Clustering Accuracy (CAcc), Semantic Accuracy (SAcc), and their Harmonic Mean (HM) in percentages (%). These results are plotted in Fig. 5(a).**
| Methods | Activity | Location | Mood | Time of Day |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| CAcc | SAcc | HM | CAcc | SAcc | HM | CAcc | SAcc | HM | CAcc | SAcc | HM |  |
| CLIP Zero-shot | 62.6 | 73.5 | 67.6 | 34.3 | 51.5 | 41.1 | 22.4 | 43.3 | 29.5 | 40.6 | 74.1 | 52.4 |
| KMeans CLIP | 34.4 | - | - | 32.7 | - | - | 18.9 | - | - | 38.6 | - | - |
| KMeans DINOv1 | 34.8 | - | - | 37.5 | - | - | 17.9 | - | - | 36.5 | - | - |
| KMeans DINOv2 | 38.2 | - | - | 37.9 | - | - | 22.5 | - | - | 43.8 | - | - |
| Img-based BLIP-2 | 48.7 | 64.1 | 55.3 | 39.6 | 48.0 | 43.4 | 30.2 | 37.5 | 33.4 | 40.7 | 60.3 | 48.6 |
| Img-based LLaVA | 46.5 | 61.8 | 53.1 | 34.0 | 46.3 | 39.2 | 28.0 | 24.7 | 26.3 | 39.4 | 51.7 | 44.7 |
| Tag-based | 43.2 | 51.5 | 47.0 | 28.6 | 46.6 | 35.5 | 13.0 | 25.6 | 17.2 | 19.3 | 48.8 | 27.7 |
| Caption-based | 44.1 | 48.9 | 46.4 | 55.2 | 55.6 | 55.4 | 38.1 | 32.6 | 35.2 | 67.6 | 56.7 | 61.7 |

**Table 23: Comparison of Semantic Groupers on Card-2c. We report Clustering Accuracy (CAcc), Semantic Accuracy (SAcc), and their Harmonic Mean (HM) in percentages (%). These results are plotted in Fig. 5(b).**
| Methods | Suit | Rank |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- |
| CAcc | SAcc | HM | CAcc | SAcc | HM |  |
| CLIP Zero-shot | 47.9 | 69.5 | 56.7 | 35.0 | 64.2 | 45.3 |
| KMeans CLIP | 45.0 | - | - | 28.6 | - | - |
| KMeans DINOv1 | 38.5 | - | - | 20.7 | - | - |
| KMeans DINOv2 | 36.7 | - | - | 22.3 | - | - |
| Img-based BLIP-2 | 66.7 | 77.7 | 71.8 | 47.5 | 54.4 | 50.7 |
| Img-based LLaVA | 36.8 | 65.8 | 47.2 | 24.6 | 49.8 | 32.9 |
| Tag-based | 39.2 | 32.9 | 35.8 | 22.3 | 39.1 | 28.4 |
| Caption-based | 54.5 | 73.6 | 62.6 | 92.1 | 95.1 | 93.6 |

**Table 24: Comparison of Semantic Groupers on Action-3c. We report Clustering Accuracy (CAcc), Semantic Accuracy (SAcc), and their Harmonic Mean (HM) in percentages (%). These results are plotted in Fig. 5(c).**
| Methods | Action | Location | Mood |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| CAcc | SAcc | HM | CAcc | SAcc | HM | CAcc | SAcc | HM |  |
| CLIP Zero-shot | 97.1 | 99.2 | 98.1 | 66.7 | 67.1 | 66.9 | 75.5 | 80.7 | 78.0 |
| KMeans CLIP | 62.3 | - | - | 58.3 | - | - |  | - | - |
| KMeans DINOv1 | 49.3 | - | - | 61.4 | - | - |  | - | - |
| KMeans DINOv2 | 75.7 | - | - | 67.6 | - | - |  | - | - |
| Img-based BLIP-2 | 79.7 | 80.9 | 80.3 | 43.3 | 42.4 | 42.8 | 43.1 | 43.8 | 43.4 |
| Img-based LLaVA | 70.1 | 60.5 | 65.0 | 45.8 | 42.8 | 44.2 | 32.0 | 38.0 | 34.7 |
| Tag-based | 70.2 | 55.0 | 61.6 | 36.8 | 48.1 | 41.7 | 50.7 | 47.6 | 49.1 |
| Caption-based | 82.8 | 82.8 | 82.8 | 69.8 | 55.2 | 61.6 | 52.3 | 50.2 | 51.2 |

**Table 25: Comparison of Semantic Groupers on Food-4c. We report Clustering Accuracy (CAcc), Semantic Accuracy (SAcc), and their Harmonic Mean (HM) in percentages (%). These results are plotted in Fig. 5(d).**
| Methods | Food Type | Cuisine | Course | Diet |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| CAcc | SAcc | HM | CAcc | SAcc | HM | CAcc | SAcc | HM | CAcc | SAcc | HM |  |
| CLIP Zero-shot | 90.6 | 94.6 | 92.6 | 54.9 | 81.4 | 65.6 | 63.5 | 84.7 | 72.6 | 47.6 | 59.9 | 53.0 |
| KMeans CLIP | 66.1 | - | - | 29.8 | - | - | 49.5 | - | - | 36.9 | - | - |
| KMeans DINOv1 | 33.6 | - | - | 15.3 | - | - | 38.1 | - | - | 41.4 | - | - |
| KMeans DINOv2 | 72.7 | - | - | 22.5 | - | - | 47.6 | - | - | 43.4 | - | - |
| Img-based BLIP-2 | 54.2 | 71.4 | 61.6 | 54.8 | 73.3 | 62.7 | 42.3 | 71.0 | 53.0 | 34.2 | 53.8 | 41.9 |
| Img-based LLaVA | 42.2 | 64.0 | 50.9 | 33.7 | 57.6 | 42.6 | 46.9 | 73.1 | 57.1 | 27.0 | 40.5 | 32.4 |
| Tag-based | 45.0 | 63.3 | 52.6 | 48.8 | 42.1 | 45.2 | 42.7 | 70.1 | 53.1 | 25.2 | 34.1 | 29.0 |
| Caption-based | 34.6 | 54.2 | 42.2 | 47.0 | 65.9 | 54.9 | 69.1 | 85.7 | 76.5 | 41.5 | 54.0 | 46.9 |

**Table 26: Comparison of Semantic Groupers on Fruit-2c. We report Clustering Accuracy (CAcc), Semantic Accuracy (SAcc), and their Harmonic Mean (HM) in percentages (%). These results are plotted in Fig. 5(e).**
| Methods | Species | Color |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- |
| CAcc | SAcc | HM | CAcc | SAcc | HM |  |
| CLIP Zero-shot | 84.0 | 93.1 | 88.3 | 54.8 | 83.5 | 66.1 |
| KMeans CLIP | 67.1 | - | - | 39.6 | - | - |
| KMeans DINOv1 | 53.8 | - | - | 36.0 | - | - |
| KMeans DINOv2 | 71.2 | - | - | 36.7 | - | - |
| Img-based BLIP-2 | 70.7 | 68.3 | 69.5 | 40.9 | 70.6 | 51.8 |
| Img-based LLaVA | 63.9 | 67.8 | 65.8 | 51.0 | 83.2 | 63.2 |
| Tag-based | 64.0 | 67.1 | 65.5 | 54.1 | 44.1 | 48.6 |
| Caption-based | 76.9 | 70.7 | 73.7 | 53.3 | 51.5 | 52.4 |

**Table 27: Comparison of Semantic Groupers on Clevr-4c. We report Clustering Accuracy (CAcc), Semantic Accuracy (SAcc), and their Harmonic Mean (HM) in percentages (%). These results are plotted in Fig. 5(f).**
| Methods | Color | Texture | Count | Shape |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| CAcc | SAcc | HM | CAcc | SAcc | HM | CAcc | SAcc | HM | CAcc | SAcc | HM |  |
| CLIP Zero-shot | 77.7 | 94.0 | 85.1 | 34.1 | 41.9 | 37.6 | 43.7 | 81.5 | 56.9 | 71.1 | 72.7 | 71.9 |
| KMeans CLIP | 48.8 | - | - | 61.4 | - | - | 44.2 | - | - | 56.1 | - | - |
| KMeans DINOv1 | 53.0 | - | - | 58.4 | - | - | 47.5 | - | - | 67.0 | - | - |
| KMeans DINOv2 | 44.1 | - | - | 46.9 | - | - | 52.5 | - | - | 87.0 | - | - |
| Img-based BLIP-2 | 69.3 | 76.5 | 72.7 | 57.8 | 34.4 | 43.1 | 25.7 | 55.9 | 35.2 | 69.1 | 62.6 | 65.7 |
| Img-based LLaVA | 56.5 | 63.5 | 59.8 | 51.9 | 26.9 | 35.4 | 53.7 | 39.4 | 45.4 | 64.3 | 71.3 | 67.6 |
| Tag-based | 66.6 | 55.3 | 60.4 | 57.2 | 40.2 | 47.3 | 47.4 | 8.3 | 14.1 | 62.7 | 36.5 | 46.2 |
| Caption-based | 70.3 | 63.4 | 66.7 | 65.3 | 42.1 | 51.2 | 65.7 | 73.3 | 69.3 | 58.4 | 38.5 | 46.4 |

### E.3 Supplementary Results for Comparison Criteria-Conditioned Clustering Methods

We provide expanded results in Tab. 28 for each criterion and benchmark, detailing the comparison of criteria-conditioned clustering methods presented in Tab. 2 in the main paper.

**Table 28: Comparison with criteria-conditioned clustering methods on the six SMC benchmarks. We report Clustering Accuracy (CAcc) and Semantic Accuracy (SAcc)as percentages (%). Average (Avg.) CAcc and SAcc across different criteria on each dataset is also provided. For reference, we include the pseudo upper-bound (UB) performance of CLIP ViT-L/14 in zero-shot transfer, using ground-truth criteria and class names. Note that both IC$\mid$TC and MMaP utilize ground-truth criteria and the number of clusters for clustering. These expanded results correspond to Tab. 2.**
| Benchmark | Criterion | UB | IC$\mid$TC | MMaP | Ours |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| CAcc | SAcc | CAcc | SAcc | CAcc | SAcc | CAcc | SAcc |  |  |
| COCO-4c | Activity | 62.6 | 73.5 | 51.3 | 53.2 | 33.8 | - | 44.1 | 48.9 |
| Location | 34.3 | 51.5 | 58.5 | 54.0 | 35.3 | - | 55.2 | 55.6 |  |
| Mood | 22.4 | 43.3 | 23.2 | 40.4 | 20.9 | - | 38.1 | 32.6 |  |
| Time of Day | 40.6 | 74.1 | 62.8 | 65.2 | 45.7 | - | 67.6 | 56.7 |  |
| $Avg.$ | 40.1 | 60.6 | 48.9 | 53.2 | 33.9 | - | 51.2 | 48.4 |  |
| Food-4c | Food Type | 90.6 | 94.6 | 36.0 | 52.6 | 48.9 | - | 34.6 | 54.2 |
| Cuisine | 54.9 | 81.4 | 46.8 | 42.4 | 31.7 | - | 47.0 | 65.9 |  |
| Course | 63.5 | 84.7 | 70.5 | 89.5 | 48.6 | - | 69.1 | 85.7 |  |
| Diet | 47.6 | 59.9 | 48.5 | 62.1 | 45.9 | - | 41.5 | 54.0 |  |
| $Avg.$ | 64.1 | 80.2 | 50.5 | 61.7 | 43.8 | - | 48.1 | 64.9 |  |
| Clevr-4c | Color | 77.7 | 94.0 | 51.2 | 43.2 | 75.3 | - | 70.3 | 63.4 |
| Texture | 34.1 | 41.9 | 64.9 | 26.4 | 56.5 | - | 65.3 | 42.1 |  |
| Count | 43.7 | 81.5 | 46.9 | 39.0 | 53.9 | - | 65.7 | 73.3 |  |
| Shape | 71.1 | 72.7 | 70.0 | 38.7 | 65.5 | - | 58.4 | 38.5 |  |
| $Avg.$ | 56.7 | 72.5 | 58.3 | 36.8 | 62.8 | - | 64.9 | 54.3 |  |
| Action-3c | Action | 97.1 | 99.2 | 86.4 | 58.7 | 51.3 | - | 82.8 | 76.3 |
| Location | 66.7 | 67.1 | 82.0 | 52.9 | 59.4 | - | 69.8 | 55.2 |  |
| Mood | 75.5 | 80.7 | 60.8 | 57.4 | 71.0 | - | 52.3 | 50.2 |  |
| $Avg.$ | 79.8 | 82.3 | 76.4 | 56.3 | 60.6 | - | 68.3 | 60.6 |  |
| Card-2c | Suit | 47.9 | 69.5 | 54.9 | 65.6 | 41.3 | - | 54.5 | 73.6 |
| Rank | 35.0 | 64.2 | 94.6 | 96.8 | 32.6 | - | 92.1 | 95.1 |  |
| $Avg.$ | 41.4 | 66.9 | 74.8 | 81.2 | 36.9 | - | 73.3 | 84.3 |  |
| Fruit-2c | Species | 84.0 | 93.1 | 69.3 | 66.9 | 58.8 | - | 76.9 | 70.7 |
| Color | 54.8 | 83.5 | 57.2 | 43.3 | 43.3 | - | 53.3 | 51.5 |  |
| $Avg.$ | 69.4 | 88.3 | 63.3 | 55.1 | 51.0 | - | 65.1 | 61.1 |  |

### E.4 Supplementary Results for Studying the Necessity of Multi-granularity Cluster Generation.

We present expanded results in Tab. 29 for the ablation study on multi-granularity refinement, providing a detailed breakdown of the summary shown in Fig. 6 in the main paper.

**Table 29: Ablation study of multi-granularity refinement on the six SMC benchmarks. We compare three ways of constructing cluster names: Initial Names (IN), Flat Refinement (FR), Multi-granularity Refinement (MR). We report Clustering Accuracy (CAcc) and Semantic Accuracy (SAcc)as percentages (%). Average (Avg.) CAcc and SAcc across different criteria on each dataset is also provided. These expanded results correspond to the plotting shown in Fig. 6.**
| Benchmark | Criterion | IN | FR | MR |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- |
| CAcc | SAcc | CAcc | SAcc | CAcc | SAcc |  |  |
| COCO-4c | Activity | 14.1 | 48.5 | 34.5 | 40.5 | 44.1 | 48.9 |
| Location | 30.0 | 51.9 | 41.4 | 56.0 | 55.2 | 55.6 |  |
| Mood | 6.6 | 34.7 | 21.9 | 32.1 | 38.1 | 32.6 |  |
| Time of Day | 24.4 | 50.5 | 28.2 | 54.4 | 67.6 | 56.7 |  |
| $Avg.$ | 18.8 | 46.4 | 31.5 | 45.8 | 51.2 | 48.4 |  |
| Food-4c | Food Type | 33.9 | 52.4 | 35.5 | 54.3 | 34.6 | 54.2 |
| Cuisine | 30.6 | 39.7 | 27.6 | 36.5 | 47.0 | 65.9 |  |
| Course | 52.9 | 81.1 | 62.8 | 83.0 | 69.1 | 85.7 |  |
| Diet | 14.0 | 46.6 | 36.8 | 58.2 | 41.5 | 54.0 |  |
| $Avg.$ | 32.9 | 55.0 | 40.7 | 58.0 | 48.1 | 64.9 |  |
| Clevr-4c | Color | 56.5 | 49.7 | 60.9 | 53.0 | 70.3 | 63.4 |
| Texture | 56.5 | 26.0 | 60.9 | 33.0 | 65.3 | 42.1 |  |
| Count | 56.5 | 39.6 | 56.5 | 40.8 | 65.7 | 73.3 |  |
| Shape | 47.8 | 33.6 | 47.8 | 41.8 | 58.4 | 38.5 |  |
| $Avg.$ | 54.3 | 37.2 | 56.5 | 42.2 | 64.9 | 54.3 |  |
| Action-3c | Action | 72.2 | 63.6 | 90.5 | 63.0 | 82.8 | 76.3 |
| Location | 46.0 | 50.4 | 65.9 | 59.3 | 69.8 | 55.2 |  |
| Mood | 20.6 | 41.9 | 46.0 | 51.0 | 52.3 | 50.2 |  |
| $Avg.$ | 46.3 | 52.0 | 67.5 | 57.8 | 68.3 | 60.6 |  |
| Card-2c | Suit | 40.9 | 50.1 | 45.7 | 45.7 | 54.5 | 73.6 |
| Rank | 43.0 | 55.1 | 47.7 | 54.6 | 92.1 | 95.1 |  |
| $Avg.$ | 42.0 | 52.6 | 46.7 | 50.2 | 73.3 | 84.3 |  |
| Fruit-2c | Species | 59.2 | 68.6 | 64.1 | 67.0 | 76.9 | 70.7 |
| Color | 41.8 | 56.7 | 44.7 | 42.3 | 53.3 | 51.5 |  |
| $Avg.$ | 50.5 | 62.7 | 54.4 | 54.7 | 65.1 | 61.1 |  |

## Appendix F Further Studies of the Proposed Framework

In this section, we provide additional studies on our proposed framework, using the main configuration (Caption-based Proposer and Caption-based Grouper) for the analysis. In Sec. F.1, we conduct control experiments to examine the system sensitivity of our framework to different multimodal large language models (MLLMs) and large language models (LLMs). In Sec. F.2, we demonstrate how incorporating advanced prompting strategies can further enhance the framework’s performance on fine-grained criteria.

### F.1 Further System Sensitivity Analysis of Various MLLMs and LLMs

Figure: Figure 10: Sensitivity analysis of different MLLMs and LLMs on the six SMC benchmarks. Top (a): We fix the LLM to Llama-3.1-8B and study the impact of different MLLMs. Bottom (b): We fix the MLLM to LLaVA-NeXT-7B and study the impact of different LLMs. The average clustering accuracy(%) across different criteria is reported on the left, while the average semantic accuracy(%) is reported on the right.
Refer to caption: x12.png

In Fig. 10, we perform a system-level sensitivity analysis using our default system configuration (caption-based proposer and caption-based grouper) to examine the impact of different MLLMs and LLMs on the system performance. Since all variants successfully propose the basic criteria in each benchmark, we report the average clustering accuracy (CAcc) and semantic accuracy (SAcc) across various criteria for comparative analysis.

Specifically, in Fig. 10(a), we first fix the LLM in our system to Llama-3.1-8B (Meta, ) and assess the influence of various MLLMs: GPT-4V (OpenAI, ), BLIP-3-4B (Xue et al., ), and LLaVA-NeXT-7B (Liu et al., ). Next, in Fig. 10(b), we set the MLLM to LLaVA-NeXT-7B and evaluate different LLMs: GPT-4-turbo (OpenAI, ), GPT-4o (OpenAI, ), Llama-3-8B (Meta, ), and Llama-3.1-8B.

Findings in Fig. 10(a) indicate a direct correlation between the size of the MLLM and the ability of our system to uncover substructures, highlighting the significant role of MLLMs in translating visual information into natural language. On the other hand, this scalability demonstrates that our system can enhance performance with more robust MLLMs, thanks to its training-free design, which ensures compatibility with any MLLM. Despite this, we use LLaVA-NeXT-7B as our default MLLM due to its reproducibility, being open-source and unaffected by API changes, and its capacity for local deployment, which upholds privacy by not exposing sensitive image data to external entities.

As for the LLMs, as depicted in Fig. 10(b), despite GPT-4-turbo showing marginally superior performance, the open-source Llama-3.1-8B achieves similar results across benchmarks, making it our default LLM. Notably, except for the Card-2c dataset, system performance remains largely consistent regardless of the power of the LLM. This consistency suggests that the reasoning task for SMC, given the capabilities of modern LLMs to tackle complex problems (Street et al., ), is relatively straightforward.

### F.2 Further Study on Fine-grained Image Collections

Image collections may include fine-grained grouping criteria, such as Bird species in bird photography. Fine-grained criteria pose unique challenges for substructure discovery due to small inter-class differences and large intra-class variations (Zhang et al., ; Vedaldi et al., ; He & Peng, ). This requires the model to detect subtle visual distinctions to accurately infer cluster names and guide the grouping process. The straightforward captioning process in our current framework may not fully capture these subtle visual nuances. However, the modular design of our framework allows for seamless integration of advanced cross-modal chain-of-thought (CoT) prompting strategies to address this issue.

We demonstrate this by enhancing our Caption-based Grouper with FineR (Liu et al., ), a cross-modal CoT prompt method specifically designed for fine-grained visual recognition. When the proposer identifies fine-grained criteria, such as Bird species, the framework switches to a FineR-enhanced captioning strategy that provides more detailed attribute descriptions, such as “Wing color: Blue-grey,” to enrich the captions and capture per-attribute visual characteristics to better support the subsequent substructure uncovering process.

**Table 30: Study of substructure discovery for fine-grained criteria. We report clustering accuracy (CAcc) and semantic accuracy (SAcc) as percentages (%). The pseudo upper-bound (UB) performance is obtained using CLIP (Radford et al., ) ViT-L/14 in a zero-shot transfer setting with the ground-truth class names. †: We compare with FineR (Liu et al., ) without its post-class name refinement step to ensure a fair comparison.**
|  | CUB200 | Car196 |  |  |
| --- | --- | --- | --- | --- |
|  | CAcc | SAcc | CAcc | SAcc |
| UB | 57.4 | 80.5 | 63.1 | 66.3 |
| FineR† | 44.8 | 64.5 | 33.8 | 52.9 |
| Ours | 30.1 | 56.7 | 21.3 | 35.9 |
| Ours + FineR | 45.1 | 68.9 | 31.1 | 47.3 |

We evaluate this on two image collections containing fine-grained criteria: CUB200 (Wah et al., ) and Stanford Cars196 (Khosla et al., ). Our framework successfully discovers the fine-grained criteria Bird species for CUB200 and Car model for Cars196. As shown in Tab. 30, when uncovering fine-grained substructures, integrating the FineR prompting strategy significantly improves performance by up to +15.0% CAcc and +12.2% SAcc, achieving results comparable to FineR itself. This demonstrates the flexibility of our system, allowing future adaptations to specific application needs, such as fine-grained image collections.

## Appendix G Further Qualitative Results

In this section, we visualize the grouping results predicted by the best configuration of our proposed framework (Caption-based Proposer and Caption-based Grouper). Specifically, we present example clustering results across different criteria for COCO-4c in Fig. 11, Food-4c in Fig. 12, Action-3c in Fig. 13, Clevr-4c in Fig. 14, and Card-2c in Fig. 15. Additionally, we showcase example clustering results at different predicted granularity levels for COCO-4c in Fig. 16.

Figure: Figure 11: Example predicted clusters of COCO-4c.
Refer to caption: x13.png

Figure: Figure 12: Example predicted clusters of Food-4c.
Refer to caption: x14.png

Figure: Figure 13: Example predicted clusters of Action-3c.
Refer to caption: x15.png

Figure: Figure 14: Example predicted clusters of Clevr-4c.
Refer to caption: x16.png

Figure: Figure 15: Example predicted clusters of Card-2c.
Refer to caption: x17.png

Figure: Figure 16: Example predicted clusters of COCO-4c at different granularities.
Refer to caption: x18.png

## Appendix H Further Failure Case Analysis

Figure: Figure 17: Failure case analysis. We show wrongly predicted images with their ground-truth label for four clusters.
Refer to caption: x19.png

In Fig. 17, we present several failure cases from the best configuration of our proposed framework (Caption-based Proposer and Caption-based Grouper). As observed, our method frequently mis-assigns “Surfing” to the “Kayaking” cluster under the Activity criterion. Upon examining the intermediate criterion captions generated by the MLLM, we found that this error is largely due to the MLLM incorrectly describing a “Surfboard” as a “Kayak”. This highlights the importance of the MLLM’s ability to accurately describe images, as it is critical for the performance of our system. Potential improvements could include majority voting or model ensembling using different MLLM models.

Another issue arises in crowded scenes. When multiple people are present in an image, the model consistently assigns the Mood label “Communal” to the images. We speculate that this occurs because, in the presence of multiple people, the model struggles to accurately determine the mood of one key individual.

Finally, we observed that our method sometimes fails to distinguish subtle, fine-grained differences between images, leading to incorrect labels. For example, as shown in Fig. 17, “Edamame” or “Pho” are typical dishes from China, Vietnam, and Japan, but they may be presented differently depending on the cuisine. The “Edamame” shown in Fig. 17 is presented in a traditional Japanese style, yet our model incorrectly predicted it as Chinese cuisine. This oversight of fine-grained details could be improved by employing a more advanced prompting strategy (Liu et al., ).

## Appendix I Further Details on Application Study

In this section, we present additional implementation details, evaluation results, and findings for the application study discussed in Sec. 5 of the main paper. Specifically, Sec. I.1 offers further evaluation results and implementation details on using our predicted distribution to train a debiased model with GroupDRO (Sagawa et al., ). Sec. I.2 outlines the implementation of the user study that assesses the alignment between predicted biases and human judgments, along with comprehensive findings for all studied occupations and identified criteria. Finally, Sec. I.3 provides additional insights from the analysis of social media image popularity.

### I.1 Further Details on Discovering and Mitigating Dataset Bias

In this section, we provide additional evaluation results and implementation details for the application study presented in Sec. 5 of the main paper.

Additional Evaluation:
To further evaluate the prediction quality of our method for hair color and gender, we used the ground-truth labels from the CelebA dataset (Liu et al., ) to assess the classification accuracy of them. Our method achieved an impressive classification accuracy of 99.1% for gender and 87.4% for hair color on the 162,770 training images, demonstrating its effectiveness for uncovering gender and hair color substructures within the training set.

In addition, we quantified the spurious correlation between hair color and gender using the metric proposed by Yang et al. (). Specifically, given the correlated gender attribute distribution $A$ and the target hair color distribution $Y$, we computed the normalized mutual information between $A$ and $Y$ to quantify the spurious correlation as:

$$ $I(A;Y)=\frac{2I(A;Y)}{H(A)+H(Y)}$ (1) $$

where $H(A)$ and $H(Y)$ represent the normalized entropy of the gender and hair color distributions, respectively. A value of $H(A)$ or $H(Y)$ equal to 1 indicates a uniform distribution (i.e., no class imbalance). We then used the ground-truth distribution from the dataset’s labels and our predicted distribution to estimate the spurious correlation intensity using the score from Eq. 1. For gender and hair color, our method’s predictions yielded a score of $I_{Pred}=0.10$, which is nearly identical to the ground-truth score of $I_{GT}=0.11$. This demonstrates that our method effectively identifies and confirms the bias directly from the training set.

Implementation Details of Training GroupDRO:
To conduct debiased training using GroupDRO (Sagawa et al., ), we first used our predicted distribution to define four distinct training groups, rather than relying on the ground-truth distribution. We closely followed the training protocol outlined in B2T (Kim et al., ) and GroupDRO (Sagawa et al., ). Specifically, we fine-tuned a ResNet-50 (He et al., ) model pre-trained on ImageNet (Deng et al., ), using the training split of the CelebA dataset (Liu et al., ). The training was performed using the SGD optimizer (Ruder, ) with a momentum of 0.9, a batch size of 64, and a learning rate of $1\times 10^{-5}$. We applied a weight decay of 0.1 and set the group adjustment parameter to zero. The model was trained over 50 epochs. For evaluation, we reported both the average and worst-group test accuracies, selecting the model from the epoch that achieves the highest worst-group accuracy on the validation set. The final evaluation and comparison results are provided in Fig. 7.

### I.2 Further Details on Discovering Novel Bias in Text-to-Image Diffusion Models

Figure: Figure 18: Bias quantification results and human evaluation for each occupation and criterion across the two studied T2I models, DALL·E3 and SDXL. The bias intensity score is reported.
Refer to caption: x20.png

Image Generation for the Subject Occupation:
Following prior studies (Bianchi et al., ; Bolukbasi et al., ), we selected nine occupations for our study: three stereotypically biased towards females (Nurse, Cleaning staff, Call center employee), three biased towards males (CEO, Firefighter, Basketball player), and three considered gender-neutral (Teacher, Computer user, Marketing coordinator). We used two state-of-the-art T2I diffusion model, DALL·E3 (Betker et al., ) and Stable Diffusion (SDXL) (Podell et al., ) to generate 100 images for each occupation for our study. This resulted in a total of 1,800 images. For each occupation, we provide some examples of images generated by DALL·E3 in Fig. 20, while provide some examples of images generated by SDXL in Fig. 21. We only used the simple prompt “A portrait photo of a $<$OCCUPATION$>$” for image generation for all occupations and did not include any potential biases in the prompt.

Bias Discovery and Quantification:
We applied our method to 1,800 generated images and automatically identified 10 grouping criteria (bias dimensions) along with their predicted distributions for each occupation image set. For this study, we utilized the mid-granularity output of our system. To evaluate the biases, we first identified the dominant cluster for each criterion—the cluster containing the largest number of images—as the bias direction. We then calculated the normalized entropy of the distribution for each criterion of the occupation’s images to determine the bias intensity score, following the method proposed by D’Incà et al. ():

$$ $\mathcal{H}_{bias}^{l}=1+\frac{\sum_{c^{l}\in\mathcal{C}^{l}}\log(p(c^{l}| \mathcal{C}^{l},\mathcal{D}_{\text{Occupation}}))}{\log(|\mathcal{C}^{l}|)}$ (2) $$

where $\mathcal{D}_{\text{Occupation}}$ represents the generated images for each occupation, $\mathcal{C}^{l}$ denotes the clusters discovered under the $l$-th criterion, and $p(c^{l}|\mathcal{C}^{l})$ is the probability of each cluster under the current distribution. The resulting score is bounded between $\mathcal{H}_{bias}^{l}\in[0,1]$, where 0 indicates no bias towards a specific cluster (concept) under the evaluated criterion, and 1 indicates that the images are completely biased towards a particular cluster (concept) (e.g.,, “Grey” hair color) within the current bias dimension (e.g., Hair color). We used the score defined in Eq. 2 to quantify the biases for each occupation across the 10 discovered grouping criteria. We report the bias intensity score for each occupation and each model across the 10 discovered grouping criteria in Fig. 18.

Human Evaluation Study Details:
To assess the alignment between our method’s predictions and human judgments on bias detection, we conducted a user study to gather human evaluation results for the generated images. As shown in the questionnaire example in Fig. 22, participants were presented with images generated by DALL-E3 and SDXL for each occupation and were asked to identify the bias direction (dominant class) for each of the 10 discovered criteria and rate the bias intensity on a scale from 0 to 10. We collected responses from 54 anonymous participants, resulting in 6 human evaluations for each occupation and each criterion.

The Absolute Mean Error (AME) between the bias intensity scores predicted by our system and those rated by humans (scaled to 0 to 1) was 0.1396. Additionally, our system’s predicted bias directions aligned with human evaluations 72.3% of the time, with most discrepancies occurring in the criteria of “Age group,” “Skin tone,” and “Accessories worn.” These findings indicate a strong correlation between our system’s predictions and human judgments, validating the effectiveness of our approach. Detailed user study results are provided in Sec. I.2. We believe the discrepancies in certain criteria may be due to the influence of personal subjective cognition on respondents’ answers. In Fig. 18, we present the human evaluation results, averaged across all participants for each model, occupation, and criterion, with the human ratings scaled from 0 to 1.

Complete Results and Additional Findings:
In Fig. 18, we present the detailed bias detection results for each model, occupation, and criterion, alongside human evaluation scores for reference. A particularly interesting phenomenon emerges: While DALL·E3 significantly outperforms SDXL on the well-known bias dimensions (e.g.,, Gender, Race, Age, and Skin tone), both DALL·E3 and SDXL exhibit moderate to strong biases along the novel bias dimensions (e.g.,, Hair color, Mood, Attire, and Accessories).

We speculate that DALL·E3’s superior performance in mitigating well-known biases may be attributed to its “guardrails” (OpenAI, ), designed as part of its industrial deployment to avoid amplifying social biases via its easily accessible APIs. However, these guardrails do not prevent it from exhibiting biases along the novel dimensions discovered by our method, as these dimensions remain understudied. This observation highlights the importance of studying novel biases that could potentially exist in widely used T2I generative models to prevent further bias amplification.

### I.3 Further Details on Analyzing Social Media Image Popularity

Figure: Figure 19: Complete analysis of social media photo popularity on the SPID dataset. We display the viral and major popular clusters, along with the popularity distribution of data points within these clusters across all ten discovered criteria (in Grey).
Refer to caption: x21.png

With the rise of image-centric content on social media platforms like Instagram, Flickr, and TikTok, understanding what makes an image popular has become crucial for applications such as marketing, content curation, and recommendation systems. Traditional research often approaches image popularity as a regression problem (Ortis et al., ; Cheng et al., ), utilizing metadata like hashtags, titles, or follower counts. However, the specific semantic visual elements that contribute to an image’s popularity remain largely unexplored. In this study, we applied our proposed method to automatically categorize social media images based on semantic visual elements across different dimensions (criteria). By analyzing these interpretable results alongside image popularity metrics (e.g.,, number of views), we gained insights into the factors contributing to virality and identified common visual traits among popular images. These insights can provide valuable guidance for content creators and advertisers, enhancing productivity and informing strategic decision-making.

To expand on the discussion in Sec. 5 of the main paper, we present the complete findings across all ten discovered criteria in Fig. 19. Notably, we consistently observed a sharp semantic contrast between the visual elements in viral images and those in the majority of popular images across all ten criteria. For instance, there is a contrast between Urban sophisticated and Modern minimalist under Interior Design, Rustic architecture and Modern architecture under Architecture Style, and Event venues versus Urban residential areas under Location.

This recurring observation reinforces the idea that viral content tends to capture more attention, likely because it features novel, surprising, or striking visual elements. Humans are inherently attracted to stimuli that deviate from the norm (Priester et al., ; Bruni et al., ; Palmer & Gore, ). On the other hand, widely popular yet “neutral” content is shared more often due to its familiarity and broad appeal, though it is less likely to provoke the strong emotional responses that fuel virality. We believe the insights generated by our method could offer valuable guidance to social media platform practitioners, helping them tailor their content more effectively to target audiences and gain a deeper understanding of social media image trends from various perspectives.

Figure: Figure 20: Samples of DALL·E3 generated images. For each occupation, the simple prompt “A portrait photo of a $<$OCCUPATION$>$”, that does not reference any potential bias dimensions such as gender, race or hair color, is fed to DALL·E3 to generate 100 images. We present a random sample of 30 generated images.
Refer to caption: x22.png

Figure: Figure 21: Samples of SDXL generated images. For each occupation, the simple prompt “A portrait photo of a $<$OCCUPATION$>$”, that does not reference any potential bias dimensions such as gender, race or hair color, is fed to SDXL to generate 100 images. We present a random sample of 30 generated images.
Refer to caption: x23.png

Figure: Figure 22: Example of the questionnaire for human evaluation study.
Refer to caption: x24.png

## Appendix J In-depth Discussion of Related Settings

Distinction from Multiple Clustering:
Multiple clustering involves finding diverse clusterings from the same dataset in either a semi-supervised (Bae & Bailey, ; Ren et al., ) or unsupervised (Caruana et al., ; Mautz et al., ; Yao et al., ) manner. However, multiple clustering methods require users to specify the number of clusterings and clusters (or rely on ground-truth annotations for evaluation) (Yu et al., ). In other words, $L$ (the number of clusterings) and $K_{l}$ (the number of clusters within each clustering) are assumed as prior knowledge in multiple clustering settings. This strong assumption creates a chicken-or-egg dilemma and is often impractical in real-world applications: Users want to employ multiple clustering methods to understand their data, but how can they predefine the number of valid clusterings and clusters without already having a deep understanding of the entire dataset? Although some strategies exist to determine the number of clusters, most of these methods (Monti et al., ; Zhang et al., ; Liu et al., ) only work for single clustering. In contrast, SMC requires the model to automatically discover both the number of clusterings and the clusters within them.

Additionally, while multiple clustering methods can reveal diverse sample division patterns and underlying data structures, they do not provide interpretations of the results—specifically, what rules the output clustering follows and the semantic meaning of the clusters. As a result, users often need to manually investigate the clustering outcomes. In stark contrast, SMC methods provide interpretability by describing both the clustering rules and the semantic meanings of the clusters in natural language. This not only offers a more comprehensive understanding of the data but also allows users to combine different clusterings to gain deeper insights into the data distribution.

Although recent work such as IC$\mid$TC Kwon et al. () and MMaP (Yao et al., ) allows users to specify clustering criteria and propose text-conditioned clustering based on user-defined criteria and cluster numbers, these approaches do not resolve the dilemma of traditional multiple clustering. They still require users to have prior knowledge of large image collections, which is impractical in many real-world scenarios. In contrast, our method automatically discovers clustering criteria, expressed in natural language, from unstructured image collections and provides interpretable results, allowing users to freely explore their data.

Distinction from Multi-label Zero-shot Classification:
SMC differs from multi-label zero-shot classification in that the latter (Lee et al., ; Huang et al., ; Ali & Khan, ; Gupta et al., ) requires predefined sets of classes under different rules, with the goal being to assign each image to multiple classes from these sets. In contrast, SMC requires discovering the class names (or cluster semantics). In fact, multi-label zero-shot classification can be viewed as a specific instance of SMC when the user explicitly and precisely defines all the clusters and their semantic meanings under different clustering rules.

## Peer Reviews

confidence: 3
contribution: 2
initial_rating: 3
presentation: 2
questions: (Q1) In Section 3.1, "Caption-based Proposer": For each subset of captions, the proposed method prompts a LLM to elicit a set of partitioning criteria.  How consistent are the sets of partitioning criteria elicited from different subsets of captions?  Would a LLM generate criteria using different English words which are semantically the same?  How does the proposed method accumulate the subsets of captions and consolidate partitioning criteria that are semantically similar?

(Q2) In Section 3.2, "Caption-based Grouper": How diverse are the initial set of class names that are generated and assigned to the images?  How diverse are the output of the "multi-granularity cluster refinement"?  By the way, can we show some experimental data (perhaps in the "Experiments" section) about the number of images in the data sets and the number of distinct groups at each granularity level?

(Q3) In Section 4, "Evaluation metrics for Criteria Discovery": In the formula of TPR, how does it compute the intersection of the set of generated criteria (the set R) and the ground-truth criteria (the set Y)?  How does a "criterion token" in the set R match with a "criterion token" in the ground-truth set Y?  Do the criteria tokens in the set R and the set Y come from a small superset of common tokens?  

(Q4) In Section 4, "Evaluation metrics for substructure uncovering": Can we formulate the evaluation method of "Semantic Consistency" in a math formula?  For example, it will be helpful to show the math formula of the Semantic Accuracy (SAcc) metric.

(Q5) Figure 4:  Can we have some descriptions about how to read the figures in Figure 4?  

(Q6) Figure 5:  Can we have some descriptions about how to read the figures in Figure 5?  

(Q7) In Section 4.2, Table 2, "Comparison with criterion-conditioned clustering methods": How does the computation of CAcc(%) and SAcc(%) done, if the TeDeSC method generates more groupings than the ground-truth groupings?  Does having more groupings than the ground-truth groupings boost the value of CAcc(%) and SAcc(%)?
soundness: 1
strengths: (S1) Besides the main proposed approach "TeDeSC", the paper also describes other interesting approaches of using LLMs to build the "criteria proposer" and the "semantic grouper".  The descriptions of those other approaches set a nice context to highlight and differentiate the main features of the proposed "TeDeSC" approach.

(S2) The three applications described in Section 5 are quite motivating.  Those applications illustrate how an approach for "semantic multiple clustering" (such as the proposed "TeDeSC" method) can be used in discovering spurious correlations and human bias in data, and in data understanding.  However, I feel that the paper should focus more on describing the details of the TeDeSC method, rather than using two pages to describe the three applications.

(S3) The new benchmark data sets produced in this work may be interesting for future work.
summary: The paper proposes a LLM-based method (the "TeDeSC" method) to address a proposed variant of the "semantic multiple clustering" problem, where both the clustering criteria and the groupings within each criterion are not known a priori and have to be generated with respect to the given data set.  

Given a set of images, the proposed TeDeSC (Text Driven Semantic Multiple Clustering) method leverages the ability of LLMs and MLLMs to generate the clustering criteria for the images and the groupings in each criterion.  For generating the clustering criteria, multi-modal LLMs (MLLMs) are used first to generate a caption for each image, and then the generated captions are fed to LLMs to generate a set of criteria that are relevant to the given images.  For generating the groupings within a criterion C, each image is first fed to a MLLM to generate a caption, conditioned on the criterion C; then, the captions of all of the images will go through a three-step process using LLMs to assign to each image a triplet of group labels, at three levels of semantic granularity.

Along the development of the proposed method, previously existent benchmark data sets are expanded with richer ground-truth clustering criteria and groupings.  The expanded ground-truth clustering criteria and groupings provide better coverage over the many valid grouping options in collections of images with high scene complexity.
weaknesses: (W1) The paper puts too much content in the appendix.  Much of that content should be in the main text to make the paper self-contained.  For example, the paper can be more readable if it has more descriptions on the proposed approach, on the evaluation metrics and methodology, etc.

(W2) More descriptions are needed about the proposed methods.

(W3) More descriptions are needed about the evaluation metrics and methodology.

(W4) The figures are too small (for example, Figures 4, 5, and 6).   

(W5) The definition of the proposed variant of the "semantic multiple clustering" problem seems to be not fully defined.  The definition doesn't specify the objective that the generated clusters should achieve (e.g., optimal with respect to some notions, etc.).

---

confidence: 4
contribution: 2
initial_rating: 5
presentation: 4
questions: In addition to the weakness, there is one more question as below.

1. If we choose different LLMs, how they will influence the performance of the proposed framework?
soundness: 3
strengths: 1. The paper is well-organized and clearly written, with figures that effectively illustrate the motivation and methodology. 

2. The experimental setup is thorough, with well-designed evaluation criteria and informative visual representations. 

3. The proposed method is technically sound. Using LLM and multi-modal learning can improve the performance of many AI-related tasks.
summary: The paper proposed a new way to organize image collections by leveraging LLM-assisted semantic multiple clustering. The proposed framework, TeDeSC, uses LLMs to convert images into texts and build a criteria proposer and a semantic grouper to discover potential semantic clusters describing a dataset. The TeDeSC provides us with a way to uncover the semantic structures and underlying biases of a dataset. Empirical studies on real-world datasets and AI-generated images validated its effectiveness.
weaknesses: 1.  The proposed method leverages multiple LLMs to generate criteria and semantic labels, with each LLM component requiring dedicated prompt engineering. This introduces numerous design choices that may impact the system’s overall performance. To enhance the framework, it would be helpful if the authors provided quantitative metrics, such as a clearly defined loss function, to clarify the objectives behind the design choices and to better evaluate the approach's effectiveness.

2. ​​​​There is a growing trend to apply large language models (LLMs) to enhance various AI-related tasks. While this paper is innovative from an application perspective, it would benefit from a deeper discussion of its scientific contributions. 

3. The overall design is primarily empirical. It could be strengthened by incorporating more theoretical analysis on the integration of its components. For example, a discussion on why using LLMs can improve image clustering, compared to previous studies, would provide valuable insights.

4. Biases in benchmark datasets have garnered considerable attention in recent years. For instance, [1] investigated geographic biases within the COCO dataset (used as a benchmark in this paper), and [2] explored spurious correlations between attributes like "Blond" and "Female" in the CelebA dataset. In response, developers of LLM products such as GPT and DALL-E have curated their training datasets and models to mitigate such spurious correlations. While the proposed method benefits from these mitigated biases by incorporating pre-trained LLMs into its pipeline, its contribution may be less impactful than suggested in Section 5, especially when compared to baseline methods trained from scratch on biased datasets.

[1] https://arxiv.org/pdf/1906.02659
[2] https://arxiv.org/pdf/2007.10075

---

confidence: 4
contribution: 3
initial_rating: 6
presentation: 2
questions: Same as in weaknesses
soundness: 3
strengths: The proposed method implements many approaches to discover the clustering criteria and compared the results.  For each proposer approach, a grouper approach is implemented which combines the similar criteria and assigns a name to it.
The results are analysed against the hard ground truth (annotated by human oracle)
The proposed method is applied on different applications achieved good results.
summary: The paper presents semantic multiple clustering of images based on text generated through LLMs or MLLMs through prompting. The proposed method is unsupervised and produces multiple clusterings based on the criteria given in natural language without specifying number of clusters. The method automatically discovers multiple criteria for clustering and produces clustering at multiple granularities.  The paper also introduces two new benchmarks COCO-4c and Food-4c sourced from Food-101 and COCO-val with each having four clustering criteria. TeDeSC is applied to a variety of applications, including discovering biases in real-world datasets and text-to-image generative models, and analyzing the popularity of social media images.
weaknesses: The entire method is based on use of LLMs or MLLMs through prompting. What is the effect of hallucination and biases present in these models? 

The comparison with existing models is limited. Only two methods IC/TC and MMaP are considered.

In image-based proposer, an image grid (8x8) is constructed and passed to a MLLM for criteria generation. What is the significance of such a grid? The grid would have different type of images and will confuse the MLLM.

Criteria pool refinement process takes the model generated text and work on it. It may lead to hallucination. How would you justify it? 

Typos
Page 1 last line …remove the
Table 28 – Highlighted values for Action-3c … both CACC

---

confidence: 3
contribution: 2
initial_rating: 5
presentation: 3
questions: First, I find the concept of multi-granularity clustering in your Semantic Grouper quite interesting. Still, I'm a bit unclear on how you determine the different granularity levels (coarse, middle, fine). Could you provide more details on this process? An illustrative example showing how these levels impact the clustering results would be beneficial.

Second, given that TeDeSC heavily relies on large language models (LLMs) and multimodal LLMs (MLLMs), I'm concerned about potential biases in these models affecting your clustering outcomes—especially in sensitive applications like bias detection. How have you addressed or mitigated these biases within your framework to ensure fair and unbiased results?

Third, in your evaluation of criteria discovery, you use True Positive Rate (TPR) but don't seem to account for false positives. Could you explain the reasoning behind this choice? How might false positives impact your system's performance, and do you think incorporating metrics that consider false positives would provide a more comprehensive assessment?

Finally, in the application section on bias discovery in text-to-image generative models, you mention a user study but provide limited details. Could you elaborate on the study design? Information such as the number of participants, their demographics, the questions they were asked, and the statistical methods used for analysis would enhance the credibility of your findings and help readers better understand the significance of your results.
soundness: 2
strengths: This paper tackles the challenge of organizing unstructured image collections without prior knowledge by introducing a new task called Semantic Multiple Clustering (SMC). This significant contribution fills a clear gap in the existing literature. The authors present a TeDeSC framework, which cleverly leverages large language models (LLMs) and multimodal LLMs (MLLMs) to automatically discover clustering criteria by turning visual data into text. This approach is innovative and showcases originality in methodology.

They conduct thorough experiments and introduce two new challenging datasets, COCO-4c and Food-4c, which better reflect real-world complexity. By comparing various design choices using appropriate metrics like True Positive Rate (TPR), Semantic Accuracy (SAcc), and Clustering Accuracy (CAcc), they provide a comprehensive evaluation of their method.

The paper is well-written, with a clear problem statement and a structured presentation. The effective use of figures and tables enhances understanding. Practical applications—such as uncovering biases in text-to-image generative models and analyzing social media image popularity—underscore the work's significance across different domains.
summary: The paper addresses the challenge of organizing large, unstructured image collections by introducing the task of Semantic Multiple Clustering (SMC). SMC aims to automatically group images into semantically meaningful clusters based on multiple, unknown criteria without requiring prior human input or predefined categories. To tackle this problem, the authors propose TeDeSC (Text Driven Semantic Multiple Clustering). This framework leverages large language models (LLMs) and multimodal LLMs (MLLMs) to discover clustering criteria and organize images accordingly. By translating visual data into textual form, TeDeSC enables the identification of hidden patterns within image collections. The authors evaluate their method on two new benchmarks they contribute—COCO-4c and Food-4c—and demonstrate its applicability in tasks such as discovering biases in text-to-image generative models and analyzing social media image popularity.
weaknesses: 1. The explanation of the multi-granularity clustering in the Semantic Grouper isn't detailed enough, making it challenging to understand and reproduce the method thoroughly. Additionally, the paper doesn't discuss the computational costs or how well TeDeSC scales with large datasets, which is essential given that LLMs and MLLMs can be quite resource-intensive.

2. The paper doesn't sufficiently explore the potential limitations of TeDeSC, such as the risk of introducing biases from LLMs and MLLMs into the clustering results. It would benefit from a deeper discussion on these biases, how to mitigate them, and the ethical implications—especially in sensitive areas like bias detection. Also, there's no discussion on how TeDeSC might be applied to other unstructured data types beyond images.

3. Using True Positive Rate (TPR) to evaluate criteria discovery without considering false positives might not give the complete picture. Including additional metrics or discussing how false positives could impact the results would provide a more comprehensive assessment. Moreover, the comparative analysis could be strengthened by adding more baseline methods or conducting ablation studies to isolate the contributions of each component within TeDeSC.

4. The user study on bias discovery in text-to-image generative models doesn't offer enough methodological detail. Providing more information about how the study was designed, who the participants were, what questions were asked, and the statistical methods used would enhance the credibility of the findings and help readers better assess the conclusions.

---

confidence: 2
contribution: 4
initial_rating: 6
presentation: 3
questions: Please refer to the Weakness.

In sum, I think this paper is an interesting paper. I would like to raise my score after further discussions.
soundness: 4
strengths: 1.	This work introduces a new task, i.e., Semantic Multiple Clustering (SMC), which is interesting and important for real-world applications.

2.	The framework can automatically discover both the criteria and the corresponding clusters from a image set from various granularities, which reduces the cost of manual annotation.

3.	The experimental part is quite comprehensive and presented with a rich and diverse manner.
summary: This paper introduces the semantic multiple clustering task and proposes a two-stage framework named TeDeSC, which consists of Criteria Proposer and Semantic Grouper. This framework utilizes text as a proxy to automatically discovers grouping criteria in natural language from large image collections and uncovers interpretable data substructures. Extensive experiments conducted on 6 benchmarks and various real-world applications demonstrate its utility to reveal valuable insights.
weaknesses: 1.	The framework proposed by the authors relies heavily on a variety of pre-trained LLMs and MLLMs, it is important to discuss the costs of time and resource required.

2.	The “ill-posed nature” in the Introduction needs further explanations. In addition, there is a lack of clear explanation of the meaning of the values in Figure 4 (b).

Meta-review: I have read all the materials of this paper including the manuscript, appendix, comments, and response. Based on collected information from all reviewers and my personal judgment, I can make the recommendation on this paper, reject. No objection from reviewers who participated in the internal discussion was raised against the reject recommendation.

**Research Question**

This paper considers the multiple clustering problem with the extra LLM model.

**Challenge Analysis**

The motivation of this paper is unclear. After communicating with the authors, the authors aim to tackle how to accurately translate visual content from images into text that LLMs can effectively reason with. In the revised version, two specific challenges are outlined: 1) the current VLM cannot effectively identify valid clustering criteria, and 2) no prior knowledge of user-preferred clustering granularity is provided. 

**Philosophy**

I did not find any philosophy in this paper to tackle the above challenges.

**Solution**

Instead, the authors directly provided their solutions. The technical part is engineering-like without too much rationality (One reviewer points out that the overall design is primarily empirical.). For example, it is unclear why the proposed method can find the valid clustering criteria. In the introduction, the authors aim to find “all” and “valid” criteria. I do not know if finding “all” valid criteria is possible; moreover, the authors need to define what is a valid criterion. I am also confused about criteria refinement. 

**Experiments**

1.	What is the ground truth? It is a single criterion or multiple criteria.
2.	The evaluation metrics mainly rely on the LLM’s prior; thus, the evaluation is self-biased. It is suggested to employ downstream tasks for evaluation. In general, I did not see a solid evaluation process, especially on multiple clustering. 
3.	The authors aim to answer which criteria proposer or semantic groups is the best. Again, this is a self-defined question. Why these questions are meaningful or interesting? 
4.	I do not think the experimental results can well support the targeted challenges.

**Presentation**

The presentation needs to be further improved (Several reviewers have similar concerns). In the first version, I did not find a clear motivation. For the technical part, a roadmap or overview might be helpful. Moreover, the logic can be enhanced as well.

I understand the authors put tremendous effort into this paper. However, the current version is far below the bar of a top machine learning conference.

Decision: Reject