Align2Concept: Language Guided Interpretable Image Recognition by Visual Prototype and Textual Concept Alignment

Venue: acmmm_org_ACMMM_2024_Conference
Published: 2024-04-01 16:35:33

Abstract: Most works of interpretable neural networks strive for learning the semantics concepts merely from single modal information such as images. However, humans usually learn semantic concepts from multiple modalities and the semantics is encoded by the brain from fused multi-modal information. 
Inspired by cognitive science and vision-language learning, we propose a Prototype-Concept Alignment Network (ProCoNet) for learning visual prototypes under the guidance of textual concepts. In the ProCoNet, we have designed a visual encoder to decompose the input image into regional features of prototypes, while also developing a prompt generation strategy that incorporates in-context learning to prompt large language models to generate textual concepts. To align visual prototypes with textual concepts, we leverage the multimodal space provided by the pre-trained CLIP as a bridge. Specifically, the regional features from the vision space and the cropped regions of prototypes encoded by CLIP reside on different but semantically highly correlated manifolds, i.e. follow a multi-manifold distribution.  We transform the multi-manifold distribution alignment problem into optimizing the projection matrix by Cayley transform on the Stiefel manifold. Through the learned projection matrix, visual prototypes can be projected into the multimodal space to align with semantically similar textual concept features encoded by CLIP. We conducted two case studies on the CUB-200-2011 and Oxford Flower dataset. Our experiments show that the ProCoNet provides higher accuracy and better interpretability compared to the single-modality interpretable model. Furthermore, ProCoNet offers a level of interpretability not previously available in other interpretable methods.

Main paper: 
 introduction: 
 Deep learning has demonstrated remarkable performance and has been extensively utilized in various fields, such as image recognition [15, 17] and object detection [11, 36] . However, despite its impressive performance, deep neural networks are still perceived as a black-box model that lacks interpretability. This limitation restricts their application in high-stakes areas such as finance, selfdriving, and disease diagnosis. Therefore, interpretability is crucial in these critical domains, and it is essential to understand precisely how the model makes decisions. Interpretability of neural networks has recently gained significant attention, and self-explaining convolutional neural networks (CNNs) based on prototype learning [4, 8, 30, 50] have emerged as a major research direction for interpretable computer vision. Rosch [37, 38] , the main representative of prototype theory in cognitive science, confirmed through a series of psychological experiments that semantic concepts consist of two factors: the prototype or best instance, and the degree of category membership, which depends on the resemblance to the prototype. Inspired by the prototype theory, the prototypical part network (ProtoPNet [4] ) and its extension works [30, 50] first learn the set of prototypes (semantic concepts) from the images in the training set as shown in Figure 1 a) and then make predictions by comparing the similarity between the prototypes and the parts of images. The explanation generated by this method is "the bird is an European Goldfinch because parts of the image resemble the prototype parts of the European Goldfinch". Visual prototype-based interpretable models can be seen as a type of introspection explanation system, which explains how the model determines its final outpute.g., "it is an European Goldfinch because Prototype No.7 has high activation... ").Additionally, there is a justification explanation system that generates descriptive sentences detailing how visual evidence is compatible with the system's output (e.g., "it is an European Goldfinch because it has a yellow wing... "). For example, Hendricks et al. proposed [16] focusing on generating sentence-level explanations for object-level images, while Yang et al. proposed [52] focusing on generating phrase-level explanations for object-level images. However, most introspective explanation systems still focus on learning semantic concepts from a single modality (such as images), while current justification explanation systems lack the part-level visual evidence attribution.Abundant psychological evidence suggests that humans learn more semantic information by combining language and its meaning in the physical world [12, 33] . In our work, we propose a novel interpretable framework called Prototype-Concept Alignment Network (ProCoNet), which serves as both an introspective explanation system and a justification explanation system. The Prototype-Concept Alignment Network aligns visual part-level prototypes with textual concepts as illustrated in Figure 1 b ). Through this network, we can not only determine that this bird is identified because a prototype has high activation but also explain what human-interpretable textual concept corresponds to this highly activated region. Specifically, ProCoNet consists of three spaces: a vision space for extracting prototype region representations, a human-interpretable textual concept space, and a multimodal space for aligning visual prototypes with textual concepts. Firstly, to generate textual concepts that can match visual prototypes, our approach leverages in-context learning and prompt generation strategies with large language models (LLMs). By using pre-annotated textual concepts as contextual clues, our method enables the LLM to directly produce relevant and concise concept descriptions. Then, we employ a prototypical part network [4] to extract regional representations of prototypes in the vision space.A major challenge is that aligning fine-grained visual prototypes with textual descriptions of concepts is difficult without explicit supervisory signals. To address this issue, we utilize the multimodal space of the pre-trained vision and language model CLIP [34] as an intermediary bridge, employing manifold alignment to learn mapping from the vision space to the multimodal space. Figure 2 illustrates the basic idea of manifold alignment, which aims to construct relationships between different datasets and project data points to a common subspace while preserving local geometry structures. Specifically, the regional features of the prototypes and the features of the region images encoded by the CLIP image encoder reside on different but semantically highly correlated manifolds, i.e., a multi-manifold distribution. To align the both features, we adopt the manifold alignment method by learning a projection matrix that project them into a common subspace. In this subspace, we enforce both features that share similar semantic meanings to be close, i.e. feature matching, while preserving their neighborhood relationships in the original feature spaces, i.e. local geometry preserving. We convert the manifold alignment problem into an optimization problem with orthogonality constraints on the projection matrix, taking into account the criteria of feature matching and geometry preserving. We then transform the optimization problem with Cayley transform and update the the projection matrix using a curvilinear search on the Stiefel manifold. Through the feature transformation of the projection matrix, visual prototypes and text concepts encoded by CLIP text can be aligned within the same space.We have conducted extensive experiments on two case studies, bird species identification and flower species identification, to evaluate the performance of our model in terms of both interpretability and accuracy. To measure interpretability, we compared the output region of semantic concepts with annotated object parts, which provides a quantifiable metric that was previously missing from ProtoPNet-based methods. Furthermore, we designed a baseline model that learns concepts directly from features without manifold alignment to demonstrate the effectiveness of our proposed framework. Our model outperformed classical interpretable models in both accuracy and interpretability. The contributions of our work are summarized as follows:𝒳 𝒳 ! Common Subspace 𝑥 ! " 𝑥 # " 𝑑 !# " 𝑧 ! " 𝑧 # " ≈ ≈ 𝑑 !# " 𝑥! 𝑥 # 𝑑!# 𝑧! 𝑧# 𝑑 !#• A new framework of interpretable image recognition guided by language is first proposed that can learn semantics concepts from both visual and linguistic modality. To my knowledge, this is the first interpretable framework that is both an introspective explainable system and a justification explainable system. • To obtain textual concepts related to visual prototypes, we developed an innovative prompt generation strategy that integrates in-context learning, prompting large language models to directly produce text concepts that are visually recognizable without the need for post-processing. This significantly simplifies the concept extraction process and enhances the relevance and clarity of the generated descriptions. • We design a manifold alignment method to optimize the projection matrices on the Stiefel manifold by the Cayley transform, which transforms the features of multi-manifold distributions into a common subspace. Besides, an alternating optimization algorithm is proposed to optimize objectives of manifold alignment and concept learning. • We apply quantitative metrics of interpretability for the ProtoPNet-based methods. Extensive experiments have demonstrated that reasonable utilization of natural language guidance can improve the accuracy and interpretability of the self-explaining model. 
related work: 
 Our work is related to interpretability in image recognition and manifold alignment. In this section, we will give a brief overview of related works.Interpretability in Image Recognition. Previous methods of interpreting deep neural networks can be broadly classified into two types, one devoted to visualizing the underlying patterns of the black-box model, and the other focusing on modeling clear semantic representations. There are a lot of visualization methods to compute the relevance score at each pixel-level location of the image, including the saliency-based methods [7, 26, 54, 57] , perturbation-based forward propagation methods [9, 10] , and backpropagation-based methods [2, 28, [42] [43] [44] [45] 55] . But the collection of pixels cannot build the connection with semantics concepts of humans and lack of illustrating knowledge hidden behind all activations. Therefore, some methods aim to learn semantics concepts to construct a selfexplaining model during the training process, such as [5, 24, 56] focus on learning interpretable filters by restricting each filter response to a specific concept. For grasping the concepts, some researchers try to represent the semantics patterns as the prototype vectors [4, 8, 22, 29, 30, 50] . [4] proposed a prototypical part network (ProtoPNet) to learn the prototypes and can generate a part-level attention map as an explanation by calculating the distance between an input image and learned prototypes. Further, the ProtoPNet has been extended many times [8, 22, 29, 50] and different methods have added different properties to the prototypes. [50] designed a plug-in transparent embedding space, which is spanned by disentangled basis concepts on the Grassmann manifold. Nauta et al. proposed a Neural Prototype Tree that combines prototype learning with decision trees and can explain a prediction by outlining a decision path. However, the above methods only learn semantic concepts from visual modality and lack other modal information to guide concept learning. In contrast, our model is the first framework to learn the visual prototypes guided by textural concepts and a manifold alignment method is proposed to align the multi-modal manifold distribution. In this way, the concepts can capture richer semantic information and provide better interpretability.Another class of explainable methods involves constructing Concept Bottleneck Models (CBMs) [39] to establish relationships between images and human-understandable attributes. Specifically, these models introduce a bottleneck layer composed of humanunderstandable attributes between the input and prediction, and predictions are then made by linearly combining these attributes. However, CBMs often require costly attribute annotations. To address this issue, Post-hoc Concept Bottleneck Models (PCBMs) [53] have been proposed, which utilize information from static knowledge bases. Additionally, LaBo [52] has suggested using GPT-3 [3] to first extract sentences containing attribute information about categories, followed by manually annotating some sample pairs to finetune a T5 model [35] to segment sentences into smaller attribute descriptions. Ultimately, an optimizable submodule is trained to filter out the most relevant concept sets. However, the recent paper [27] have conducted a thorough analysis of CBMs using post hoc interpretability methods, revealing that CBMs may not effectively correspond to semantically meaningful representations in input space, thereby questioning their current utility and their ability to achieve their intended goals of interpretability, predictability, and intervenability. In our work, we have designed a prompt generation strategy that allows GPT to produce textual concepts focused on prototype descriptions. This approach reduces the dependency on costly attribute information and eliminates the need for complex post-processing. Additionally, because ProCoNet possesses introspective capabilities, it avoids the traditional bottleneck layer issue of failing to generate expected visual explanations.Manifold Alignment. Manifold alignment has been widely used in many fields of machine learning and data mining. The main objective of manifold alignment is to align the sets of data from different manifold distributions by matching the corresponding instances of different manifold distributions and preserving the local geometry of each manifold. Depending on whether the correspondence information is available or not, manifold alignment can be classified into semi-supervised manifold alignment [13, 25, 49] and unsupervised manifold alignment [6, 20, 32, 48] . Generally, the manifold alignment problem is transformed into an optimization problem that finds the projection matrices from the original spaces to a common subspace, and the projection matrices are solved in closed form by eigenvalue decomposition like Canonical Correlation Analysis (CCA) [14] . Different from existing methods, we develop the optimization algorithm of the projection matrices based on the Cayley transform for preserving the orthogonality constraints, which can obtain the global optimal solution [51] . Our model doesn't require the region images of prototypes for guidance during inference, whereas the traditional CCA method requires guidance from corresponding features in multimodal space during testing. 
method: 
 In this section, we will introduce our proposed framework named Prototyp-Concept Alignment Network (ProCoNet) for image classification in Section 3.1, and the overall architecture is shown in Figure 3 . For constructing textual concept space, we crafted a strategy that employs in-context learning techniques for generating prompts, which are then fed into the large language model GPT-3 [3] . This approach generates a diverse set of textual concepts for each category, which are amenable to visual recognition (Section 3.2), and then we employ a pretrained vision-language model, CLIP [34] to encode these textual concepts to multimodal space. Additionally, we propose a manifold alignment method that utilizes the CLIP visual embeddings of cropped regions consistent with visual prototypes to project visual prototype representations into a multimodal space, while preserving the local geometry of the vision space (Section 3.3). In the multimodal space, the projected visual prototype embeddings and textual concept embeddings can compute their mutual similarity and derive scores for each concept. We combine the scores of different concepts through learning a class-concept weight matrix, applying linear weighting, to ultimately obtain the predicted logits in the final classification. Finally, Section 3.4 introduces the implementation details of the two-step alternating optimization process in ProCoNet.Figure 3 illustrates the framework of our ProCoNet. Given the image set {𝐼 𝑣 } 𝑁 1 with labels {𝑦} 𝑁 1 and the textual concept {𝐼 𝑙 } 𝑁 𝑏 1 , the objective of the ProCoNet is to learn part-level visual prototype B, the projection matrix P which projects visual features into the multimodal space, and a decision function ŷ = 𝜓 (I 𝑣 , I 𝑙 ; B, P, 𝜃 ), where 𝜃 is the paramerters of 𝜓 . Specifically, we can decompose the function into four parts, region feature extraction of visual prototypes, region feature projection by manifold alignment, textural conceptual space construction, and visual prototypes and textual concepts alignment.Region Feature Extraction of Visual Prototypes. In the vision space, we first pre-trained a standard ProtoPNet [4] on the image dataset to learn visual part-level prototypes. Specifically, we denote the input image as I 𝑣 and its features extracted by the vision , where 𝜙 𝑤,ℎ (X 𝑣 ) denotes the operation of taking the (𝑤, ℎ)-th location in the visual feature map. If the patch 𝜙 (X 𝑣 ) is closer to the prototype 𝑏 𝑚 , the function will produce a higher similarity score. Given an input image, an activation map Q 𝑐 𝑚 with shape 𝑊 × 𝐻 of the 𝑚-prototype in class 𝑐 can be calculated by computing the similarity between each prototype and the features. The activation map can be up-sampled to the input image to illustrate how strongly the prototype 𝑏 𝑐 𝑚 is activated in the image and the score of the prototype can be obtained by performing a global max pooling on the similarity map. Finally, the output logits can be generated by multiplying the similarity score by the weights of the fully connected layer. Then, a softmax function is applied to calculate the probability that the current image belongs to all categories, with the highest probability corresponding to the category ȳ predicted by the ProtoPNet network. For a pre-trained ProtoP-Net, an image can re-represent its high-level features on different prototypes, while displaying prototype activation regions on the original image. Furthermore, it can make classification decisions based on the similarity with different prototypes.⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋮ ⋮ ⋮ 𝑏!,! 𝑏!,# 𝑏!,$ 𝑏#,! 𝑏#,# 𝑏#,$ 𝑏%,!𝑏%,# 𝑏%,$ 𝑟! " 𝑟# " 𝑟$ " ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ Prototype-Concept Similarity Matrix " 𝑟 & ' ( ! ⋯ ⋯ ⋯ ⋯ ⋯ 𝑏!,! 𝑏!,# 𝑏!,$ 𝑏#,! 𝑏#,# 𝑏#,$ 𝑏%,!𝑏%,# 𝑏%,$ ⋮ ⋮ ⋮ ⋮ ⋮ Concept Scores ⋯ ⋯ Predicted Logits × Concept-Class Weight Matrix Dot Product Softmax SUM 𝑾 *' ∈ ℝ (×,! 𝑾 -∈ ℝ !×,! 𝑾 '' ∈ ℝ ,!×. ℝ % ⋯ 𝒛 * ∈ ℝ "×) 𝒁 ! ∈ ℝ "×+ 𝒁 , ∈ ℝ "×-! 𝑸 ' ∈ ℝ ).$×%For the predicted class ȳ in the trained prototype network, we can encode each region with high activation for each prototype on the feature maps based on the activation maps Q ȳ = {Q ȳ 𝑚 } 𝑀 𝑚=1 and prototypes B ȳ . The region features are achieved through non-linear feature encoding [18, 21, 23] as follows:EQUATIONwhere 𝑞 𝑚 𝑤,ℎ = 𝜙 𝑤,ℎ (Q ȳ 𝑚 ) represents the activation value of each coordinate on the activation map and 𝑥 𝑤,ℎ = 𝜙 𝑤,ℎ (X 𝑣 ) denotes the (𝑤, ℎ)-th location in the feature maps. Therefore, we obtained the region features R 𝑣 = {𝑟 𝑚 } 𝑀 𝑚=1 ∈ R 𝐷 ×𝑀 of pixels assigned to the prototypes, which can represent the features of the corresponding prototype for predicted class ȳ on the image.Region Feature Projection by Manifold Alignment. To better project the region features of the visual space to the multimodal space for aligning with future and textual concepts, we first offline crop and resize the regions corresponding to the prototypes in trained ProtoPNet on the image. Then, we input them into the pretrained vision language model CLIP's image encoder 𝑓 𝐼 (•) to obtain representations of the corresponding regions in the multimodal space. We denote the clip's image embedding of cropped part-level region asZ 𝑠 = {𝑧 𝑠 𝑚 } 𝑀 𝑚=1 ∈ R 𝐷 ×𝑀 with 𝑧 𝑠 𝑚 = crop(I 𝑣 , 𝑟 𝑚 ).Therefore, the region features R 𝑣 from the vision space and the cropped region features Z 𝑠 encoded by CLIP from the multimodal space respectively represent the features of the same image region in different spaces. Without any processing, the two sets of features would be different but semantically highly correlated manifold distributions. Our goal is to learn a projection P 𝑣 ∈ R 𝐷 ×𝐷 to transfer the vision region features to a common subspace with the cropped region features encoded by CLIP in multimodal space such that the two distributions can be aligned semantically. The transformed features of vision region features R 𝑣 is denoted as Z 𝑣 = P ⊤ 𝑣 R 𝑣 in the multimodal space, which can serve as the representation of visual prototypes in the multimodal space. The specific method of learning this projection matrix P 𝑣 will be detailed in Section 3.3.Textual Conceptual Space Construction. To construct a textual concept space recognizable by visual prototypes, our model designs a prompt generation method based on in-context learning to prompt the large language model, GPT-3 [3] , to generate a set of 𝐾 textual concepts describing visual information for each category. In our model, we collected a total of 𝑁 𝑏 textual concepts 𝑙 𝑐,𝑘 from the GPT-3. These textual concepts are encoded by the text encoder 𝑓 𝐿 (•) of CLIP, ultimately forming a concept representation 𝑍 𝑙 ∈ R 𝐷 ×𝑁 𝑏 . The specific method for generating prompts will be described in Section 3.2.Visual Prototypes and Textual Concepts Alignment. Given the projection Z 𝑣 of visual region features in multimodal space and the textual concept representation Z 𝑙 , we first calculate the cosine similarity between both to construct a prototype-concept similarity matrix W 𝑝𝑐 ∈ R 𝑀 ×𝑁 𝑏 . The value at each position (𝑚 1 , 𝑛 𝑏 ) in the matrix is calculated byW (𝑚 1 ,𝑛 𝑏 ) 𝑝𝑐 = z 𝑣 𝑚 ⊤ z 𝑙 𝑛 𝑏 /(||z 𝑣 𝑚 || 2 • ||z 𝑙 𝑛 𝑏 || 2 )and each element represents the score of different visual prototypes of the image on textual concepts. Then we sum over the dimensions of the prototypes to obtain a score vector 𝑊 𝑠 ∈ R 1×𝑁 𝑏 , reflecting the total score of all prototypes in each concept. To establish a mapping from concept scores to final predictions, we learn a linear function for predicting categories, where the weights of the linear layer are denoted as 𝜔 𝑐𝑐 ∈ R 𝑁 𝑏 ×𝐶 , encoding the correlation between concepts and categories. Furthermore, due to the inherent category prior information in textual concepts, we initialize the conceptcategory matrix 𝜔 𝑐𝑐 using linguistic priors. If the textual concept 𝑙 𝑐,𝑘 is within category 𝑐, we initialize the elements in the weight matrix related to category 𝑐 and concept 𝑙 𝑐,𝑘 as 1, otherwise as -0.5. Finally, the prediction based on concepts can be formalized by ŷ = argmax(𝜎 (𝑊 𝑠 • 𝜔 𝑐𝑐 )), where 𝜎 (•) is the softmax activation function.Main Objective Function. The main objective of our model is to learn visual prototypes that can align with textual concepts. To learn part-level visual prototypes, the patches of feature maps in the vision space are clustered on at least one semantically similar prototypes of the ground truth category and separated from prototypes of the other category. Therefore, the introduced clustering and separation losses are formalized in [4] as:EQUATION)where 𝑁 is the number of training set and 𝑦 𝑖 is the label of instance 𝑖. The optimization problem combined with the cross-entropy loss (CrsEnt) to penalize the misclassification of ŷ can be formed as follows:EQUATIONwhere 𝜆 1 and 𝜆 2 is the hyper-parameter. A semantically meaningful concept space will be constructed under the constraints of these terms. Through the above optimization, visual prototypes can be discovered in the vision space.Step 1: 20 seed texts with manually annotated concept The textual concept space generated by the large language model (LLM). We have designed a prompt generation method that combines in-context learning, and the generated textual concepts can be recognized by visual prototypes.Previous work Labo [52] utilized simple prompts, such as "describe what the [CLASS NAME] looks like", to prompt GPT-3 to generate related sentences, then split the sentences into shorter concepts using a T-5 model [35] fine-tuned on a small set of annotated sentenceconcept pairs, and finally used a submodular optimization to filter out concept sets. LaBo pioneered the use of large language models to collect concept descriptions. However, the method involves cumbersome steps, requiring post-processing of sentences generated by large models with multiple models. Furthermore, even after multiple rounds of preprocessing, the concept set filtered by LaBo still contains many concepts that are mixed and cannot be visually recognized, such as "This bird's song is particularly melodious", "This bird's habitat is in the United States", "Longevity, with some individuals living over 50 years" and etc.To address the aforementioned issues, we have designed a prompt generation strategy that incorporates in-context learning to prompt large language models, which enables the direct generation of textual concepts by the LLM without any post-processing, as illustrated in Figure 4 . Specifically, we first annotate 20 text concepts for each category as seed texts for in-context learning, and then randomly select 8-12 from the text pool as guiding in context information during prompt generation. Next, we designed instructions specifically for prompting large language models to generate textual descriptions for visual prototypes. The instructions include the task name, the role the large language model needs to play, considerations for completing the task, task criteria, as well as examples of suitable and unsuitable phrases. Due to space limitations, detailed instructions will be presented in the appendix. The concatenated prompt is composed of instructions designed by us, in-context instances randomly sampled from the text pool, and the category names that need to be expanded. This merged prompt is inputted into the large language model, ultimately resulting in 20 text descriptions focusing on describing potential visual prototypes for the given category.The objective of the classical manifold alignment algorithm is to learn a projection that maps features from different spaces to a common subspace simultaneously matching the corresponding instances and preserving the local geometry of each manifold. Matching the corresponding instance implies that instances with comparable semantic meanings from distinct manifolds will be projected onto neighboring regions following transformation, while preserving the local geometry implies that the relationship of the neighborhood of the instances in each manifold will remain consistent after transformation. Therefore, solving the alignment problem without correspondence needs to find two unknown variables, i.e.the correspondence, and the projection matrix. In our work, we aim to learn a projection matrix through manifold alignment to better map the vision space to the multimodal space while preserving the geometric relationships among the original region features in vision space.Constructing the Correspondence. In our model, there is a clear one-to-one correspondence between the region feature 𝑟 𝑚 of the visual space and the cropped regions 𝑧 𝑠 𝑚 encoded by CLIP corresponding to the visual prototypes. Therefore, we can leverage this property to construct the corresponding matrix as follows:EQUATIONwhere𝑊 (𝑚 1 ,𝑚 2 ) 𝑣𝑠 ∈ R 𝑀 ×𝑀 is the element of the correspondence matrix W 𝑣𝑠 . If 𝑚 1 -th visual region feature is corresponding with 𝑚 2 -th cropped regions encoded by CLIP, 𝑊 (𝑚 1 ,𝑚 2 ) 𝑣𝑠 is set to 1 or vice versa.Objective Function of Manifold Alignment. In our work, the manifold alignment is used to make visual region features and cropped CLIP-encoded region features with similar semantics close after projected to the common subspace. To achieve the above goals, the objective function can be defined as follows: minEQUATION)where 𝑀 is the number of corresponding pairs, i.e. the number of element 𝑊 (𝑖,𝑗 ) 𝑣𝑙 equals 1 in correspondence matrix W 𝑣𝑙 . 𝑧 𝑣 𝑚 1 presents the projection of 𝑟 𝑚 1 in multimodal space . If 𝑟 𝑚 1 and 𝑧 𝑠 𝑚 2 correspond to each other in original space, the distance between 𝑧 𝑣 𝑚 1 and 𝑧 𝑠 𝑚 2 will be penalized in projected space. In the common subspace unrolled by the manifolds, the nearest neighbor relationships of each manifold are expected to be protected, i.e. the local geometry should not be destroyed. In many manifold learning algorithms [6, 47] , the local geometry is characterized by computing the local adjacency weight matrix, i.e. the similarity between instances in the manifold. According to the previous work [1, 41] , the image and sentence structure are encoded by the similarities of the visual features with different locations and language features with different words. In our work, for preserving the local geometry, the orthogonal constraints are added on the projection matrix P 𝑣 , i.e. P ⊤ 𝑣 P 𝑣 = 𝐼 . Under the constraint of projection matrix orthogonality, the local geometry can be preserved and the proof is as follows:EQUATIONThe original structure of visual features will be preserved with the orthogonal constraint in the projected common subspace.For matching the semantically similar features among manifolds and protecting the local geometry of each manifold, we can combine the objective function Equation 5with the orthogonal constraint. Firstly, we convert the Equation 5 to the following form: minEQUATIONwhereU 𝑣𝑠 = W 𝑣𝑠 /𝑀, D 𝑣 ∈ R 𝑀 ×𝑀 is a diagonal matrix with the element D 𝑣 (𝑚 1 , 𝑚 1 ) = 𝑀 𝑚 2 =1 U 𝑣𝑠 (𝑚 1 , 𝑚 2 ). The similar with D 𝑠 ∈ R 𝑀 ×𝑀 is a diagonal matrix with the element D 𝑠 (𝑚 2 , 𝑚 2 ) = 𝑀 𝑚 1 =1 U 𝑣𝑠 (𝑚 1 , 𝑚 2 )and tr(•) is the trace. However, considering the orthogonal constraint of projection matrices, the first and second terms are irrelevant to P 𝑣 . The final manifold alignment problem can be transformed into solving the following optimization problem with constraints: minEQUATIONSolving the above optimal solution is difficult directly since the orthogonal constraints can lead to many local optimal solutions. The traditional approach utilizes Singular Value Decomposition (SVD) to solve the above equations, such as Canonical Correlation Analysis (CCA) [14] . However, this method relies on local batch data, requiring corresponding cropped region features from the multimodal space for each projection computation. Therefore, we propose a new solution to the aforementioned orthogonal problem, i.e. Equation (8) , which can search for the global optimal solution across all data and does not require CLIP-encoded regional features during test inference. Specifically, we solve the optimization problem based on the Cayley transform and optimize the projection matrices on the Stiefel manifold in our work. In the Stiefel manifold, the feasible set P = {P ∈ R 𝐶 ×𝐶 : P ⊤ P = 𝐼 } and projection matrix P 𝑣 is updated by a curvilinear search [51] in the feasible set through the Cayley transform:EQUATIONwhere 𝑡 is the present step, 𝑡 + 1 is the next step, A = G(P (𝑡 ) ) -P (𝑡 ) G ⊤ is a skew-symmetric matrix obtained by Cayley transform, G is the gradient of the objective function and 𝜂 is the learning rate. We can derive the closed-form solution for the gradient of the objective function as follows:EQUATIONThe stochastic gradient of a mini-batch is calculated to replace G in each step and momentum is applied to accelerate and stabilize the stochastic gradient. Through manifold alignment, we can obtain a projection matrix to project region features from the visual space onto the cropped region features in the multimodal space derived from the same visual prototype. These features share similar semantics, and the projection results will tightly lie on the aligned manifold in the multimodal space. Our model implementation consists of three stages. In the first stage, we pretrain a ProtoPNet and encode the images cropped from prototypes using the CLIP image encoder. In the second stage, we use a large language model to construct a set of textual concepts and encode them using the CLIP text encoder. In the third stage, we train our ProCoNet model to optimize the two optimization problems described in the previous sections. The first optimization problem is to learn the projection matrices P 𝑣 to align cross-modal manifold and the second optimization problem is the main objective to learn visual prototypes. We optimize the framework by alternating optimization that two objectives are optimized in turns. Algorithm Update P 𝑣 by Eq. 9 
experiments: 
 In the experiments, two case studies are conducted to evaluate our modal with other interpretable models in terms of accuracy and interpretability. The first case study is the bird species identification with 200 bird species on the CUB-200-2011 datasets [46] , which is popular on the prototype-based concept learning [4, 30, 50] . The second case study is the flower species identification with 102 flower species on the Oxford Flowers datasets [31] . We adopt different CNN architectures as encoders in the vision space and verify the generality of our model for different visual encoders.Evaluation Metric: We evaluate our model in terms of accuracy and interpretability for fine-grained image recognition. For accuracy, we compare the predicted label with the ground truth category to calculate the top-1 accuracy as considered in the previous interpretable image recognition tasks. However, interpretability has not been quantified in the previous ProtoNet and the extension methods. Inspired by the previous part discovery for fine-grained recognition [18] , we designed different quantitative metrics of interpretability schemes for datasets with different annotations. In the CUB-200-2011 dataset, there are 15 part landmarks for each image and we measure the object part localization error by comparing the response region of the learned semantic concept with the annotated part landmarks. The part localization error has been adopted by [18, 19] . For the datasets without part annotations such as Flower-102, we adopt the protocol of Pointing Game [55] , which is a popular method to quantify interpretability in visualization methods [40, 55] , and calculate the object localization error using the annotated segmentation. The detailed metrics are described in the supplement. Localization Results (Interpretability). The part localization error is evaluated on various CNN vision encoders and we compare the results to ProtoPNet at the bottom of Table 1 . Our model greatly reduces the localization error of ProtoPNet (0.93% on average). The results provide quantifiable evidence of the interpretability of our model.Reasoning Process. Figure 5 illustrates the reasoning process of our model. Through concept visualization, we observe that our model learns the typical features of the Green Jay, such as the distinctive blue head, green wings, and black throat, solely from label supervision. For a given test image, activation maps are generated by computing the distances between various regions of the image and the prototypes. Additionally, similarity maps are obtained by calculating the similarity scores between regions and textual concepts. Finally, these similarity scores are weighted by concept weights and contribute to the final classification. Compared to the traditional ProtoPNet reasoning process, our model not only highlights regions with high prototype activations but also understands the corresponding textual concepts of visual prototypes, thus providing better interpretability. Ablation Study. We conducted an ablation study on the CUB dataset to evaluate the components of the manifold alignment. We designed two variants: one without aligning the region images and another using L1 loss to optimize the projection matrix without enforcing orthogonality constraints. We compared these variants using VGG-19 as the visual encoder. As shown in Table 2 , omitting the alignment of cropped region images leads to a decrease in model accuracy and interpretability. Additionally, compared to optimizing the projection matrix with L1 loss, manifold alignment optimization of the projection matrix improves both model accuracy(+0.8%) and interpretability(+0.4%). Recognition Results (Accuracy). Our results on recognition are summarized at the top of Table 3 . Since flowers do not have obvious object parts, they are more judged based on shapes and colors, thus, the ProtoPNet-based method, which is good at learning object parts, is not as good as the baseline model. Our model can improve accuracy by 0.6%-2.3% for ProtoPNet.Localization Results (Interpretability). Further, the Pointing game results are reported at the bottom of Table 3 . Our model achieves a lower localization error compared to ProtoPNet. To a certain extent, our models can capture more foreground concepts.Evidence for this flower being a Pink Primrose: Reasoning Process. Figure 6 shows the reasoning process to identify a flower. The model can accurately learn bright purple petals and white pistil in the center. Since flowers lack sufficient object parts and there are few images in the training set, there is some redundancy in concepts. 
conclusion: 
 In this paper, we introduce ProCoNet, a novel framework for interpretable image recognition that uniquely integrates semantic concepts from both visual and linguistic modalities. This first-of-itskind system combines introspective and justification explainability, offering a new form of interpretability. Through our innovative prompt generation strategy, we have simplified the process of extracting text concepts and enhanced the clarity of descriptions. Additionally, we have introduced a manifold alignment method optimized via the Cayley transform on the Stiefel manifold, which, together with an alternating optimization algorithm, ensures robust alignment and concept learning. Extensive testing with interpretability metrics has demonstrated that incorporating text concept guidance significantly enhances the model's accuracy and interpretability, setting a new standard for interpretable AI systems in image recognition. 
 
 Appendix:  


Decision: This is a borderline submission with mixed reviews. There were some concerns related to the lack of clarity, which has been addressed well in the author's rebuttal. Reviewer rEwH's concerns remain, but the AC believes these concerns are too challenging to address in a single paper. Considering the idea is well-motivated and experimental results are promising, the final decision is a borderline acceptance.

Reviews: review: paper_summary: paper_summary: This paper proposes an approach, ProCoNet to learn semantic concepts based on Prototype theory via both linguistic and visual modalities, implementing for interpretable image recognition. Specifically, it follows a two-stream model in which a manifold alignment method is utilised among the language feature manifold and visual feature manifold by learning the projection matrices through Cayley transform on the Stiefel manifold. The author further verifies the validity of the model by testing on the CUB-200-2011 and Oxford Flowers datasets.
strength_weakness: strength_weakness: - The problem of concern in this paper has a practical background and is reasonably motivated. It has research value.
- The structure of the paper is clear, the logic is smooth, and the proposed method is clearly demonstrated.
- The idea of semantically meaningful concepts to be interpretable is promising.
- Given the empirical experiments, the proposed ProCoNet shows performance improvements over the baseline model in terms of both accuracy and interpretability.
limitations: limitations: - The analysis of manifold algorithms is somewhat weak, as learning semantic concepts is straightforward from both text and image features in the original space. Also, authors should provide hyperparameter details (optimiser, learning rate for both text and visual encoder, coefficients, etc.) for reproducibility.

- Also, how ProtoNet is different from a multi-manifold scenario? I would have liked to see some instances of images and concepts/texts that are close to each other.

- The authors should justify and provide explanations on how the value of manifold alignment, in particular, ProCoNet as compared to other approaches such as MCD [4] and Prototypical relevance propagation [5].

- The baseline comparisons [2,3] and experiments can be strengthened with some benchmarked datasets [1] which employ manifold learning, this could well reason with the shown model performance.

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1. Zhao, L., Zheng, K., Zheng, Y., Zhao, D., & Zhou, J. (2023, July). RLEG: vision-language representation learning with diffusion-based embedding generation. In International Conference on Machine Learning

2. Mugnai, D., Pernici, F., Turchini, F., & Del Bimbo, A. (2022). Fine-grained adversarial semi-supervised learning. ACM Transactions on Multimedia Computing, Communications, and Applications (TOMM)

3. Korsch, D., Bodesheim, P., & Denzler, J. (2021, September). End-to-end learning of fisher vector encodings for part features in fine-grained recognition. In DAGM German Conference on Pattern Recognition

4. Vielhaben, J., Bluecher, S., & Strodthoff, N. (2023). Multi-dimensional concept discovery (MCD): A unifying framework with completeness guarantees. Transactions on Machine Learning Research.

5. Gautam, S., Höhne, M. M. C., Hansen, S., Jenssen, R., & Kampffmeyer, M. (2023). This looks more like that: Enhancing self-explaining models by prototypical relevance propagation. Pattern Recognition.
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paper_summary: paper_summary: The paper introduces ProCoNet, Prototype-Concept Alignment Network, a novel method for enhancing interpretability and accuracy in image recognition by aligning visual prototypes with textual concepts. ProCoNet uses a visual encoder to extract regional image features and a large language model to generate relevant textual concepts. These are aligned using the pre-trained vision-language model CLIP through a manifold alignment method optimized with the Cayley transform on the Stiefel manifold.

Methodology involves decomposing images into visual prototypes, generating textual concepts using prompt strategies, and aligning these modalities in a common subspace. This alignment preserves the local geometry of the original features, ensuring semantic consistency.

Experiments on the CUB-200-2011 and Oxford Flowers-102 datasets show that ProCoNet achieves higher accuracy and better interpretability compared to single-modality models like ProtoPNet. The results demonstrate improved part localization and reduced localization errors.
strength_weakness: strength_weakness: The theoretical foundation of ProCoNet is robust, utilizing distribution matching for aligning visual and textual modalities. The optimization of the projection matrix using the Cayley transform on the Stiefel manifold is mathematically sound, ensuring that the local geometry of the feature space is preserved. This rigorous approach guarantees the technical correctness and reliability of the model.

The paper introduces a groundbreaking approach by integrating multi-modal information for image recognition. ProCoNet aligns visual prototypes with textual concepts, a novel method that enhances both interpretability and accuracy. This approach mimics human cognitive processes, making the model more intuitive and effective in understanding and explaining its decisions.
limitations: limitations: The related work section of the paper is currently kind of lengthy and lacks a focus on the most relevant and recent studies. This makes it difficult for readers to quickly grasp the essential background and context. Additionally, the literature review omits important recent works on multi-modal interpretability, which are crucial for the core contributions of this paper. Also, the connection between related works and the proposed method is not always explicit, which can obscure the significance of ProCoNet's innovations.

In the experimental section, several limitations need to be addressed to improve the clarity and comprehensiveness of the presented research. The paper lacks detailed explanations of key hyperparameters such as mini-batch size, training steps, and initial learning rate, which are essential for replicating the experiments. Additionally, the evaluation metrics are not clearly defined within the context of the study's objectives, making it challenging to understand their significance. The comparative analysis and specific process descriptions are also insufficiently detailed, limiting the understanding of how ProCoNet outperforms existing models.
paper_summary: paper_summary: The paper "Align2Concept: Language Guided Interpretable Image Recognition by Visual Prototype and Textual Concept Alignment" introduces a novel approach to interpretable image recognition by proposing the Prototype-Concept Alignment Network (ProCoNet). This model uniquely integrates visual prototypes and textual concepts using the pre-trained CLIP model to align visual features from images with corresponding textual descriptions. The framework aims to enhance both the interpretability and accuracy of image recognition models by leveraging linguistic information alongside visual data.
strength_weakness: strength_weakness: The primary strengths of this paper lie in its innovative approach and robust technical methodology. The introduction of ProCoNet represents a significant advancement in the field of interpretable AI, combining insights from cognitive science with cutting-edge vision-language models. The use of manifold alignment to project visual features into a multimodal space, aligning them with textual concepts, is a technically sound and well-justified approach. Furthermore, the optimization of the projection matrix using the Cayley transform on the Stiefel manifold is a noteworthy technical contribution. The paper is also commendable for its comprehensive evaluation, using the CUB-200-2011 and Oxford Flower datasets to demonstrate that ProCoNet achieves higher accuracy and better interpretability compared to existing single-modality models. The clarity of the presentation, with well-structured explanations and illustrative diagrams, aids in understanding the proposed framework. Additionally, the potential applications of this method in high-stakes domains, such as medical diagnosis and autonomous driving, where interpretability is crucial, underscore its practical relevance.
limitations: limitations: However, the paper does have several limitations. One major concern is the complexity of the proposed framework, which involves multiple stages of training and optimization. This complexity might hinder the reproducibility and practical implementation of the model. The effectiveness of ProCoNet is demonstrated on specific datasets, and it remains to be seen how well the model performs on more diverse datasets with different characteristics. The process of generating textual concepts relies heavily on large language models (LLMs), which may introduce biases inherent in these models, potentially affecting the performance and interpretability of the system. While the paper introduces new metrics for interpretability, it does not extensively compare them with existing metrics, which would have provided stronger validation of the proposed approach. Additionally, the scalability of the ProCoNet framework is not thoroughly discussed, raising concerns about its application to larger datasets or real-time scenarios. Finally, the paper focuses primarily on academic benchmarks without addressing real-world deployment challenges such as computational costs, inference time, and integration with existing systems.