MIMOSA: Multimodal Concept-based representations

4. Hyperparameter Specification

5. Training and Freezing Components

• Trainable Components: All components, including encoders, decoders, concept embedding layer, and task predictor, are trainable. For the CUB dataset, Stable Diffusion is fine-tuned on concept embeddings.
• Frozen Components: Only for MNIST+ and cdSprites+, we use the text encoder frozen as on these datasets, the extracted representation of the last attention layer is already sufficiently rich.

6. Reproducibility of Experiments

Experiments were conducted three times with different seeds. Results represent averages with standard deviations to reflect variability. Long training ensured the convergence of the decoder models, producing consistent results.

7. Equation 1 Problems

Thank you for highlighting the typos in Equation 1. These will be corrected as follows:

• $\oplus$ represents the pooling operator (sum in our case).
• $\phi$ denotes the concept embedding layer, which generates both concept predictions $\hat{c}$ and concept embeddings.

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Thank you again for your detailed feedback. We believe that these updates will strengthen our paper and enhance its clarity, and we look forward to addressing any further questions you may have.

Dear Reviewer arW7,

Thank you for your valuable feedback.

To address the concerns raised, we would like to start by emphasizing our contributions:

1. Multimodal interpretable by-design concept-based model
   MIMOSA is an interpretable by-design concept-based model, as it allows for the interpretation of its predictions through concept prediction. Specifically, users can identify which concepts contributed to the final task prediction by inspecting the concept predictions. This approach aligns with the principles of interpretable by-design concept-based models such as Concept Bottleneck Models (CBMs) introduced by Koh et al. (2020) and Concept Embedding Models (CEMs) introduced by Espinosa Zarlenga et al. (2022). These models explicitly use intermediate concepts to influence task predictions, providing built-in interpretability without relying on post-hoc explanations.

   Unlike traditional concept-based models, which typically focus on a single input modality, MIMOSA supports multiple modalities, incorporating both textual and visual inputs, bridging an important gap in current concept-based explainability approaches.

2. Novel interpretability through concept prototype visualization
   We also provide another form of interpretability via concept prototypes. Current concept-based models are unable to visualize the concepts learned. Instead, MIMOSA allows for visualization of the concepts the model relies on to make the final prediction by projecting the concepts.

3. Shared concept embedding representation
   A previous attempt to create a multimodal CBM was proposed in SHARCS by Dominici et al. (2023). However, SHARCS is limited in its employment since it uses a separate concept representation. On the contrary, MIMOSA employs a shared embedding space for concepts derived from both modalities. This allows a unique concept representation that is valid across modalities, more interveneable, and allows a complete concept prototype visualization in both modalities.

4. SOTA performance among interpretable methods with single concept representation
   While MIMOSA’s primary focus is interpretability, it achieves state-of-the-art accuracy among CBMs with single concept representation, with only a minimal gap compared to the SHARCS and end-to-end (E2E) models (that does not rely on concepts). Additional analyses, such as the impact of interventions on task predictions and qualitative visualizations of concept prototypes, further demonstrate its capability.

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Responses to Specific Concerns

1. Presentation Problems

Thank you for pointing out the presentation errors. They will all be addressed in the revised version.

2. Detailed Model Architecture

We appreciate your suggestion to provide further details about the model structure. Below is a breakdown of the MIMOSA architecture:

• Encoders:

  • Image Encoder: Utilizes a pre-trained ResNet50 backbone.
  • Text Encoder: Initialized with a pre-trained language model (BERT base for MNIST+ and cdSprites+ datasets, BERT large for CUB).

• Concept Embedding Layer:

  • Based on the implementation from Espinosa Zarlenga et al. (2022) (CEMs).
  • Trained from scratch using binary cross-entropy loss for concept predictions.

• Decoders:

  • For MNIST+/cdSprites+:
    • Image decoders are convolutional neural networks trained from scratch. Losses tested include Mean Squared Error (MSE), L1 distance, and Structural Similarity Index (SSIM).
    • Text decoders compute cross-entropy loss over predicted captions.
  • For CUB:
    • Image decoder employs a pre-trained Stable Diffusion v1-4 model. Unlike conventional usage, where the model is prompted with text for inference, we fine-tune the decoder using the concept embeddings generated by MIMOSA. These embeddings act as a representation of concepts in a latent space. This fine-tuning allows Stable Diffusion to visualize the concepts directly, even without textual prompts. The fine-tuning process uses SSIM as the primary loss to ensure alignment between visualized concepts and the input data.

These details will be included in the revised paper.

3. Training Objectives

MIMOSA uses the following objectives:

• Concept Prediction Loss: Binary Cross Entropy Loss for supervised concept predictions.
• Task Loss: Cross-Entropy loss for the final classification task.
• Reconstruction Loss: Modality-specific losses (e.g., MSE and SSIM for images, Cross-Entropy for text) ensure the alignment of shared concept embeddings with input modalities.

The overall training objective combines these losses:

$\text{L} = \lambda_\text{task} L_\text{task} + \lambda_\text{concept} L_\text{concept} + \lambda_\text{dec} L_\text{dec}$

Dear Reviewer pUyV,

Thank you for your valuable feedback.

Below, we provide responses to the specific concerns raised:

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1. Detailed Model Architecture

We appreciate your suggestion to provide further details about the model structure. Below is a breakdown of the MIMOSA architecture:

• Encoders:

  • Image Encoder: Utilizes a pre-trained ResNet50 backbone.
  • Text Encoder: Initialized with a pre-trained language model (BERT base for MNIST+ and cdSprites+ datasets, BERT large for CUB).

• Concept Embedding Layer:

  • Based on the implementation from Espinosa Zarlenga et al. (2022) (CEMs).
  • Trained from scratch using binary cross-entropy loss for concept predictions.

• Task predictor f: A feedforward neural network with two linear layers separated by a LeakyReLU activation and Dropout for regularization. It maps concept embeddings to task predictions and is trained using cross-entropy loss.

• Decoders:

  • For MNIST+/cdSprites+:
    • Image decoders are convolutional neural networks trained from scratch. Losses tested include Mean Squared Error (MSE), L1 distance, and Structural Similarity Index (SSIM).
    • Text decoders compute cross-entropy loss over predicted captions.
  • For CUB:
    • Image decoder employs a pre-trained Stable Diffusion v1-4 model. Unlike conventional usage, where the model is prompted with text for inference, we fine-tune the decoder using the concept embeddings generated by MIMOSA. These embeddings act as a representation of concepts in a latent space. This fine-tuning allows Stable Diffusion to visualize the concepts directly, even without textual prompts. The fine-tuning process uses SSIM as the primary loss to ensure alignment between visualized concepts and the input data.

These details will be included in the revised paper.

2. Training Objectives

MIMOSA uses the following objectives:

• Concept Prediction Loss: Binary Cross Entropy Loss for supervised concept predictions.
• Task Loss: Cross-Entropy loss for the final classification task.
• Reconstruction Loss: Modality-specific losses (e.g., MSE and SSIM for images, Cross-Entropy for text) ensure the alignment of shared concept embeddings with input modalities.

The overall training objective combines these losses:

$\text{L} = \lambda_\text{task} L_\text{task} + \lambda_\text{concept} L_\text{concept} + \lambda_\text{dec} L_\text{dec}$

3. Figure 1 Alignment

Thank you for noting the ambiguity in Figure 1 regarding the location of the network $\psi$. We will update the figure with the correct notation to match the expression in the manuscript.

4. Positioning with Recent Literature

We appreciate your recommendations on relevant recent works, including LaBO, BotCL, and ResCBM.

• The suggested works leverage Vision-Language Models (VLMs), such as CLIP, by passing images to the visual encoder and directly using textual concepts (in text format) as input to the language encoder. These models ensure alignment between the visual and textual concepts to form a concept bottleneck layer, which is then used for the final classification task.
• MIMOSA’s distinct approach:
  • MIMOSA’s text encoder operates on input texts that contain information not only related to the concepts but also to the task (see Figure 1, for instance; the task can be inferred by looking at both the image and textual inputs).
  • The concepts here are predicted through a shared representation of both input modalities in a supervised manner through the concept embedding layer.

This distinction allows MIMOSA to address use cases, such as medical imaging with broader text annotations or audio-video classification, where other models are limited.

We will clarify this distinction and highlight the novelty of integrating multiple modalities in a concept-based framework in the revised manuscript.

5. Limited Dataset Scope

We acknowledge the importance of diverse dataset evaluation and are working to expand the experiments.

• We would like to kindly mention that the CUB dataset has already been included in our experiments.
• Also, the CelebA, CheXpert, and AWA2 datasets are not suitable for the proposed methodology as they only provide input images and lack additional modalities such as text. We found a variant of CelebA that provides textual captions and might be suitable for expanding the experimental campaign.

6. Text data source clarification:

To improve transparency, we will provide detailed descriptions of the text data source and preprocessing steps in the Appendix:

1. MNIST+:

   • Each image pair is assigned a caption randomly generated by varying a range of templates.
   • These templates are created through multiple variations of digit descriptions and concatenation of descriptive sentences.
   • Specifically, we defined 10 unique descriptions for each digit (example for 5: “the number of fingers on one hand”) and 10 concatenations of descriptive sentences (example of a sentence: “the first digit is [description1] and the second [description2]”), potentially creating a different sentence for each image (a couple of digits) available in the dataset.

2. cdSprites+: Textual descriptions are directly included in the original dataset alongside predefined attributes serving as concepts.

3. CUB: We started from the extended dataset version incorporating 10 descriptive captions paired with the bird images ¹ .

• During the dataset preparation, each caption's quality was revised (check for unknown words or duplicates) to ensure that only accurate captions accompanied each image.
• Then, the alignment with the original dataset² containing the concepts was performed to ensure that each image was paired with its corresponding caption and associated concepts.
• This process resulted in an enhanced version of the CUB dataset, with carefully aligned images, corresponding concepts, and captions.

We are planning to release these datasets.

7. Expanded model comparisons

MIMOSA’s primary objective is to compare it against state-of-the-art unimodal concept-based interpretable by-design models (CBM, CEM).

• Comparison with CBM and CEM:
  • CBM and CEM models were evaluated in their standard visual-only setting and with text-only setting following two recent contributions (Tan et al., 2024; De Santis et al., 2024), and we evaluated their performance as baselines.
• Comparison with E2E:
  • We compared MIMOSA against an end-to-end (E2E) model that does not have a concept layer and so does not rely on concept predictions to do the final task. We did this comparison to highlight the value of interpretability.
• Comparison with SHARCS:
  • This comparison is proposed since SHARCS employs multimodal inputs and relies on concept-based interpretability. However, this has separate concept representations for modalities, unlike MIMOSA’s shared concept space.

Methods like LaBO and Post-hoc CBM were not included, as they use concepts themselves as textual input rather than broader textual inputs such as captions of the images. Our focus with MIMOSA is on leveraging textual descriptions and visual data to generate shared, interpretable concept representations rather than directly inputting predefined concepts. This distinction aligns with our goal of developing a unified framework for multimodal interpretability.

We will highlight this choice in the revised manuscript.

8. Negative Intervention Experiment

We appreciate this insightful suggestion. To present a more comprehensive evaluation of MIMOSA, we are incorporating negative intervention experiments. This addition will provide further insights into MIMOSA’s robustness and behavior under varied intervention scenarios.

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Thank you again for your detailed feedback. We believe that these updates will strengthen our paper and enhance its clarity, and we look forward to addressing any further questions you may have.

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Footnotes

1. https://www.kaggle.com/datasets/coolerextreme/cub-200-2011 ↩

2. https://www.vision.caltech.edu/datasets/cub_200_2011/ ↩

5. Concept accuracy in Table 2

Concept Accuracy refers to the proportion of correctly predicted concepts in a model's output compared to the ground truth. It measures how well the model can identify or predict the high-level, interpretable features (concepts) associated with the input data.

The evaluation of concept accuracy in Table 2 measures the model’s ability to predict predefined concepts based on concept ground-truth annotations correctly. Notice that the concept prediction does not entail the decoders, whose purpose is only to provide a visual representation of the concepts and whose annotations are represented by the same input modalities.

We will clarify this in the revised paper.

6. Text-only benchmark in Table 1

• The text-only benchmark was included to evaluate the independent contribution of the textual modality. This analysis highlights the role of textual data in concept-based multimodal learning. We will make this point clearer in the revised manuscript.

• CBM and CEM were natively designed for image data. However, we followed the architectural modifications and text processing methods described in two recent contributions (Tan et al., 2024; De Santis et al., 2024), and we evaluated their performance as baselines also with textual inputs. We did this as an ablation study to verify which of the two modalities alone performed better.

We will further clarification on these experimental setups to avoid confusion.

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Thank you again for your detailed feedback. We believe that these updates will strengthen our paper and enhance its clarity, and we look forward to addressing any further questions you may have.

Dear Reviewer YUpA,

Thank you for your valuable feedback.

Below, we provide responses to the specific concerns raised:

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1. Multimodal Interpretability and Purpose of MIMOSA

The primary goal of MIMOSA is to create a multimodal model based on explainable concepts, aiming to strike a balance between interpretability and accuracy. While achieving state-of-the-art predictive performance is valuable, it is not the central focus of this work. MIMOSA offers a novel approach by extending concept-based models to the multimodal domain, seamlessly integrating both textual and visual explanations into a unified framework. This design prioritizes understanding and transparency, recognizing that interpretability might sometimes influence accuracy.

MIMOSA is inherently interpretable by design, allowing users to trace task predictions back to the contributing concepts. This approach builds on the principles of Concept Bottleneck Models (CBMs) and Concept Embedding Models (CEMs), where intermediate concepts are explicitly used to influence predictions, ensuring interpretability without reliance on post-hoc explanations. The core purpose of MIMOSA is to enhance interpretability in multimodal settings through its concept-based model while maintaining competitive accuracy.

We will clarify this in the revised manuscript.

2. Concept Interventions:

Concept Interventions are applied at the concept level, following the approach proposed by Koh et al. (2020), where no modifications are made to the input features, as altering them may not be interpretable for domain experts.

These interventions are reported in terms of task accuracy improvements, as they directly influence predictions. The accuracy increases with intervention because the model benefits from progressively more accurate concept corrections, which improve prediction performance. This behavior simulates an expert interacting with the model—acting as an oracle—by correcting predictions and testing if the model can recover the correct task prediction.

Additionally, MIMOSA introduces a unique perspective by visualizing the effects of concept interventions at the decoder output, thanks to its concept visualization with decoders. We also plan to supplement this work with experiments involving negative interventions on both image and text inputs, as suggested by Reviewer pUyV.

3. Ablation Experiments

Ablation studies are indeed very important in understanding the contribution of each part of a model. While we agree that further studies could have been conducted, we already presented two ablation studies in the paper. We tested different multimodal concept representations for our model depending on the concept layer adopted (CBM-Linear, CBM-MLP, and CEM).

We also compared MIMOSA with different unimodal versions of CBM-Linear, CBM-MLP, and MIMOSA, both for image and textual data.

This experimental analysis aimed to assess whether the improved quality of MIMOSA stems from leveraging one specific modality or from integrating text as an additional mode.

The results demonstrated that the inclusion of textual data, while alone it is not sufficient for competitive performance, contributes to the model’s overall performance. In the revised manuscript, we will expand on these findings and include further ablation studies on other components, such as the pooling mechanism, to provide a more comprehensive analysis of the factors influencing MIMOSA’s performance and interpretability.

4. Clarification on textual descriptions in CUB

To implement the CUB dataset with captions and concepts we: -Started from the extended dataset version incorporating 10 descriptive captions paired with the bird images ¹ .

• During the dataset preparation, each caption's quality was revised (check for unknown words or duplicates) to ensure that only accurate captions accompanied each image.
• Then, the alignment with the original dataset² containing the concepts was performed to ensure that each image was paired with its corresponding caption and associated concepts.
• This process resulted in an enhanced version of the CUB dataset, with carefully aligned images, corresponding concepts, and captions.

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Footnotes

1. https://www.kaggle.com/datasets/coolerextreme/cub-200-2011 ↩

2. https://www.vision.caltech.edu/datasets/cub_200_2011/ ↩

Dear Reviewer nZCv,

Thank you for your valuable feedback.

Below, we provide responses to the specific concerns raised:

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1. Innovations and Distinctions from CEM

MIMOSA introduces several innovations specific to the multimodal setting.

• Unlike CEM, MIMOSA aggregates information from multiple modality-dependent encoders to form a shared concept embedding layer, integrating cross-modal information.
• Additionally, MIMOSA enables the visualization of concept prototypes. Unlike standard decoders, MIMOSA’s decoders initiate the reconstruction process directly from the shared concept representation space rather than from the modality-specific encodings of the input data.
• Furthermore, to the best of our knowledge, MIMOSA is the first supervised concept-based model to employ decoders. Decoders are typically used in unsupervised concept-based models to learn disentangled concept representations. Instead, we propose using them on top of a supervised concept representation to visualize it.

We will clarify these distinctions more explicitly in the revised manuscript.

2. Performance on MNIST+ and cdSprites+

The improvements of MIMOSA on MNIST+ and cdSprites+ are indeed modest. However, the goal of MIMOSA is not solely to enhance performance but to increase interpretability through concept-based explanations across multiple modalities. For example, on cdSprites+, MIMOSA can identify and explain factors like "object shape", "color," and "position" that influence predictions.

3. Ablation studies

Ablation studies are indeed very important in understanding the contribution of each part of a model. While we agree that further studies could have been conducted, we already presented two ablation studies in the paper. We tested different multimodal concept representations for our model depending on the concept layer adopted (CBM-Linear, CBM-MLP, and CEM).

We also compared MIMOSA with different unimodal versions of CBM-Linear, CBM-MLP, and MIMOSA, both for image and textual data.

This experimental analysis aimed to assess whether the improved quality of MIMOSA stems from leveraging one specific modality or from integrating text as an additional mode.

The results demonstrated that the inclusion of textual data, while alone it is not sufficient for competitive performance, contributes to the model’s overall performance. In the revised manuscript, we will expand on these findings and include further ablation studies on other components, such as the pooling mechanism, to provide a more comprehensive analysis of the factors influencing MIMOSA’s performance and interoperability.

4. Definition of Concepts in MNIST+

In MIMOSA, the input consists of images, their textual descriptions, and associated concepts. In the case of MNIST+, the digits themselves serve as the concepts, while the descriptions are processed by the textual encoder. As an example, we can look at Figure 4 - Original. In this example, the concepts are 4 and 3, while the textual description is the one reported below.

We will clarify this setup in the manuscript to make the distinction between concepts and descriptions more explicit.

5. Comparisons with CBM and CEM

In the revised manuscript, we will clarify that the comparisons between MIMOSA, CBM, and CEM are intended to establish a baseline for concept-based interpretability rather than to conduct a direct, one-to-one performance evaluation.

While CBM and CEM were originally designed for image data, we adapted them to handle textual inputs by following the architectural modifications and text processing methods outlined in recent works (Tan et al., 2024; De Santis et al., 2024). We evaluated these modified versions as baselines to assess the performance of each model when applied to textual data. This ablation study was conducted to investigate the performance of the models with individual modalities (image vs. text) and to determine which modality, when used alone, led to better performance.

6. Pooling Operator choice and Ablation studies:

Thank you for the suggestion. In our ablation studies, we are adding additional pooling strategies (e.g., max pooling, concatenation) to analyze their effect on performance and will include this analysis in the revised draft.

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Thank you again for your detailed feedback. We believe that these updates will strengthen our paper and enhance its clarity, and we look forward to addressing any further questions you may have.

Dear Reviewer R7PW,

Thank you for your valuable feedback.

Below, we provide responses to the specific concerns raised:

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1. Clarity in initial sections

Thank you for pointing out the issues on clarity. We will include the following clarifications:

• Clarification on concept embeddings: Concept embeddings are fundamental components in concept-based models like MIMOSA, serving as vector representations of predefined, human-understandable concepts. These embeddings encapsulate the semantic and relational information of each concept, enabling the model to effectively interpret and reason about the input data across multiple modalities.
• The discussion on multimodal representations will be streamlined to remove redundancy and focus on aspects directly relevant to our contributions, improving the flow and reducing confusion.

2. Training Details

Thank you for pointing out the need for further details on the model structure. MIMOSA uses the following objectives:

• Concept Prediction Loss: Binary Cross Entropy Loss for supervised concept predictions.
• Task Loss: Cross-Entropy loss for the final classification task.
• Reconstruction Loss: Modality-specific losses (e.g., MSE and SSIM for images, Cross-Entropy for text) ensure the alignment of shared concept embeddings with input modalities.

The overall training objective combines these losses:

$\text{L} = \lambda_\text{task} L_\text{task} + \lambda_\text{concept} L_\text{concept} + \lambda_\text{dec} L_\text{dec}$

3. Detailed Explanation of Concept Prediction and its Significance

Concept prediction in MIMOSA involves assigning scores to predefined concepts based on the shared embedding space. These scores reflect the presence of concepts in the input data. This approach aligns with the principles of interpretable-by-design models, such as Concept Bottleneck Models (CBMs) (Koh et al., 2020) and Concept Embedding Models (CEMs) (Espinosa Zarlenga et al., 2022), where intermediate concepts are explicitly used to guide predictions.

The significance of concept prediction lies in its ability to offer interpretable insights into the model's reasoning process, providing built-in interpretability and ensuring that the reasoning process is transparent and accessible without relying on post-hoc explanation methods. Concepts are designed to represent human-understandable units of information, allowing users to gain a deeper understanding of the factors influencing a model’s decision.

Moreover, concept prediction enables interactive exploration through concept interventions. Users can modify the predicted concept scores to observe how changes in concepts affect the final task prediction.

4. Training Objectives for the Decoder and Bias Mitigation

The decoders are trained to reconstruct the input data (images and text) from the shared concept embedding using reconstruction loss (e.g., Mean Squared Error or SSIM for images and Cross-Entropy for text).

We did not specifically focus on bias mitigation in this work, as our primary objective was to achieve accurate reconstructions and robust concept-based interpretability. However, our model might help in the detection of these biases by means of concept visualizations.

Indeed, while standard CBMs only allow us to check the concept predictions, our model also enables visualization of the concept representations, which can highlight the presence of biases. As an example of bias that we found, on the MNIST+ dataset, on input digits particularly thin, the model was more prone to predict them as 1 or 7, while instead, they were 8 or 9.

We will better describe this in the paper, acknowledging the importance of identifying and addressing potential biases.

5. Generalization Capability of Concept-Based Models and Improvement through Concept Embeddings

The architecture of Concept Bottleneck Models (CBMs) relies on a concept layer where each concept is represented by a single neuron. While this design facilitates interpretability, it imposes a bottleneck on the model's representation capacity, often limiting its generalization performance, as highlighted in prior research [Koh et al., 2020].

In contrast, Concept Embedding Models (CEMs) [Espinosa Zarlenga M. et al., 2022] leverage richer concept representations by using vectorial embeddings, which provide more expressive and flexible representations of concepts.

MIMOSA builds upon CEM by integrating not just richer concept embeddings but also multimodal information from both visual and textual modalities. This multimodal approach enhances the model's generalization capabilities while maintaining its interpretability.

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Thank you again for your detailed feedback. We believe that these updates will strengthen our paper and enhance its clarity, and we look forward to addressing any further questions you may have.