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Codebook-Guided Cross-Modal Knowledge Distillation for Structurally Heterogeneous Features
Dae Ung Jo, Jongin Lim, YoungJoon Yoo, Daeho Um
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 89%
Last extracted: 10/2/2026, 8:39:06 AM
Summary
The paper proposes a Codebook-Guided Cross-Modal Knowledge Distillation (CMKD) framework to address the challenge of transferring knowledge between structurally heterogeneous features (e.g., 2D visual grids vs. 1D audio sequences). Unlike existing methods that assume structural alignment, this approach uses a vector-quantized codebook to abstract teacher features into discrete, concept-level anchors. These codes are selected based on task relevance and student compatibility, allowing the student model to learn from teacher knowledge without requiring direct unit-level feature alignment. The method is validated across audio-visual, image-text, and RGB-depth scenarios for classification and semantic segmentation tasks.
Entities (8)
Relation Signals (7)
Codebook-Guided Cross-Modal Knowledge Distillation → uses → Vector-Quantized Codebook
confidence 95% · we propose a cross-modal distillation framework that enables effective knowledge transfer across structurally heterogeneous feature spaces via a vector-quantized codebook.
Vector-Quantized Codebook → abstracts → Teacher Features
confidence 92% · teacher features are abstracted into a set of vector-form codes regardless of their original feature structure
Codebook-Guided Cross-Modal Knowledge Distillation → solves → Structurally Heterogeneous Features
confidence 90% · To address this challenge, we propose a cross-modal distillation framework... for structurally heterogeneous features
Code Selection → guidedby → Task Relevance
confidence 88% · Code selection is guided by both task relevance and student compatibility
Code Selection → guidedby → Student Compatibility
confidence 88% · Code selection is guided by both task relevance and student compatibility
Codebook-Guided Cross-Modal Knowledge Distillation → appliedto → Audio-Visual Distillation
confidence 85% · We validate the proposed method across diverse cross-modal distillation settings, including audio-visual
Codebook-Guided Cross-Modal Knowledge Distillation → appliedto → Semantic Segmentation
confidence 85% · demonstrate the effectiveness of the proposed framework on classification and semantic segmentation tasks.
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Abstract
Abstract:Cross-modal knowledge distillation transfers knowledge from a teacher modality to a student modality. Existing feature-level alignment methods typically assume that teacher and student features reside in structurally alignable representation spaces. However, this assumption does not hold when cross-modal features are structurally heterogeneous and lack clear unit-level correspondence, such as 2D spatial visual grids and 1D temporal audio sequences, thereby limiting the applicability of feature-level alignment. To address this challenge, we propose a cross-modal distillation framework that enables effective knowledge transfer across structurally heterogeneous feature spaces via a vector-quantized codebook. Specifically, teacher features are abstracted into a set of vector-form codes regardless of their original feature structure, and the selected codes serve as concept-level anchors for student learning. Code selection is guided by both task relevance and student compatibility, allowing the student to receive transferable teacher knowledge without requiring direct unit-level feature alignment. Experimental results across diverse cross-modal distillation scenarios demonstrate the effectiveness of the proposed framework on classification and semantic segmentation tasks.
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- Source: https://arxiv.org/abs/2609.37243v2
- Canonical: https://arxiv.org/abs/2609.37243v2
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Codebook-Guided Cross-Modal Knowledge Distillation for Structurally Heterogeneous Features Dae Ung Jo Affiliation: Kyungpook National University Email: daeung.jo@knu.ac.kr Jongin Lim Affiliation: AX/PI Center, Samsung Electronics Email: jonny.lim@samsung.com YoungJoon Yoo* Affiliation: Chung-Ang University, SNUAILAB Email: yjyoo3312@cau.ac.kr Daeho Um* Affiliation: University of Seoul Email: daehoum@uos.ac.kr Abstract Cross-modal knowledge distillation transfers knowledge from a teacher modality to a student modality. Existing feature-level alignment methods typically assume that teacher and student features reside in structurally alignable representation spaces. However, this assumption does not hold when cross-modal features are structurally heterogeneous and lack clear unit-level correspondence, such as 2D spatial visual grids and 1D temporal audio sequences, thereby limiting the applicability of feature-level alignment. To address this challenge, we propose a cross-modal distillation framework that enables effective knowledge transfer across structurally heterogeneous feature spaces via a vector-quantized codebook. Specifically, teacher features are abstracted into a set of vector-form codes regardless of their original feature structure, and the selected codes serve as concept-level anchors for student learning. Code selection is guided by both task relevance and student compatibility, allowing the student to receive transferable teacher knowledge without requiring direct unit-level feature alignment. Experimental results across diverse cross-modal distillation scenarios demonstrate the effectiveness of the proposed framework on classification and semantic segmentation tasks. †footnotetext: *Corresponding authors. 1 Introduction Cross-modal knowledge distillation (CMKD) aims to improve a student model operating on a target modality by transferring knowledge from an auxiliary teacher modality available during training Gupta et al. (2016). This setting is practically important when an informative modality can provide rich supervision during training, while the deployed model must rely on a single modality at inference time due to sensing constraints, deployment cost, privacy concerns, or missing data Hoffman et al. (2016); Vapnik and Vashist (2009). Unlike single-modality distillation Hinton et al. (2015), CMKD transfers knowledge between models built on different modalities, whose inputs, representations, and inductive biases can differ. To address this modality gap Jo et al. (2025); Xue et al. (2023), early approaches Huo et al. (2024) focused on selectively distilling task-relevant information that is beneficial to the student modality, primarily at the prediction level. More recent methods Jang et al. (2023); Liu et al. (2026) have extended this line of work by incorporating not only prediction-level signals but also feature-level cues, such as structural or modality-consistent representations. While promising, existing approaches inherently assume structural compatibility between teacher and student representations, which enables alignment via projection or shared embedding spaces. However, such an assumption does not hold in general cross-modal settings, where representation structures can differ fundamentally. For example, visual features are organized as spatial grids, whereas audio and text features are organized as sequences. As illustrated in Fig. 1, the same semantic cue can appear as a spatial pattern in one modality and as a sequential pattern in another. Directly matching feature units across such heterogeneous structures can impose misleading correspondences. In this paper, we address cross-modal knowledge distillation between intermediate representations with distinct structural organizations. Our key idea is to avoid direct alignment between raw teacher and student feature units, and instead represent teacher-side intermediate knowledge as a discrete set of transferable anchors. Specifically, we learn a vector-quantized teacher codebook over intermediate representations, where the codes serve as anchors that capture recurring task-related patterns in the teacher feature space. Since not all teacher-side codes are equally useful for the student, we estimate the importance of each code by jointly considering its task relevance and its compatibility with the student modality. The selected codes are then used to guide student-side representation learning, allowing the student to exploit fine-grained teacher-side intermediate cues without requiring explicit correspondence between heterogeneous feature units. We validate the proposed method across diverse cross-modal distillation settings, including audio-visual, image-text, and RGB-depth scenarios. Our experiments cover both classification and segmentation tasks, and compare the proposed framework with prediction-level distillation, feature-level distillation, and modality-gap-aware CMKD baselines. The results demonstrate that the proposed framework can effectively leverage intermediate teacher knowledge even when teacher and student features have structurally different organizations. Our contributions are summarized as follows: • We address cross-modal knowledge distillation between intermediate representations with distinct structural organizations, where direct feature alignment is unreliable due to the absence of clear unit-level correspondence between teacher and student features. • We propose a codebook-guided CMKD framework that learns discrete anchors from teacher intermediate representations, selects transferable teacher-side codes, and uses them to guide student learning without requiring direct feature-unit alignment. • We validate the proposed framework across diverse cross-modal benchmarks and tasks, including classification and segmentation, demonstrating its effectiveness over prediction-level, feature-level, and modality-gap-aware distillation baselines. 2 Related Work 2.1 Cross-modal Knowledge Distillation Knowledge distillation (KD) transfers supervision from a teacher model to a student model. A common form of KD encourages the student to mimic the teacher’s predictions by matching output distributions or logits Hinton et al. (2015). Beyond such prediction-level transfer, many studies have explored richer supervision in the representation space. MLLD Jin et al. (2023) improves distillation through multi-level prediction alignment, FitNets Romero et al. (2015) transfers intermediate hint features, RKD Park et al. (2019) distills relational structure among samples, CRD Tian et al. (2019) uses contrastive learning to preserve representation-level knowledge, and OFA Hao et al. (2023) enables distillation across heterogeneous architectures by projecting intermediate features into an aligned logits-like space. More recently, cross-modal knowledge distillation (CMKD) has attracted increasing attention in settings where an auxiliary modality is available during training but not at test time. Compared with conventional KD, CMKD is more challenging because teacher and student are built on different modalities and thus encode both shared semantics and modality-specific factors. In this setting, recent studies have emphasized that effective transfer should account for the modality gap between teacher and student, rather than indiscriminately enforcing the student to imitate all teacher signals Xue et al. (2023); Jo et al. (2025). C2KD explicitly addresses the modality gap through customized distillation strategies for modality imbalance and soft-label misalignment Huo et al. (2024). STXD reduces cross-modal discrepancy through structural and temporal distillation Jang et al. (2023), while FDD disentangles feature components in the frequency domain so that modality-consistent information can be transferred more strongly Liu et al. (2026). Despite these advances, most CMKD methods implicitly assume that teacher and student representations lie in structurally comparable spaces, enabling alignment via projection or shared embeddings. However, this assumption becomes less straightforward when modalities exhibit substantially different structures. Consequently, cross-modal distillation across structurally heterogeneous representations remains a challenging problem. In this work, we address this problem with a codebook-based distillation framework that abstracts teacher representations into discrete anchors for student learning. 2.2 Codebook Learning and Vector Quantization Vector quantization (VQ) maps continuous representations to a finite set of learned codewords by assigning each feature to its nearest code. This discrete abstraction was popularized by VQ-VAE, which learns a codebook with codebook and commitment objectives Van Den Oord et al. (2017), and has since been extended through hierarchical quantization and high-resolution visual representation learning Esser et al. (2021); Razavi et al. (2019). By replacing continuous features with reusable codewords, VQ provides a compact representation space that can capture recurring patterns in intermediate features. Beyond compression and reconstruction, recent studies have explored codebooks as semantic interfaces for multimodal representation learning. Language-guided codebook learning aligns visual codes with textual semantics Liang et al. (2024), while unified codebook learning has been explored for multimodal large language models Zheng et al. (2024). Conceptual codebooks further connect visual representations with conceptual language prompts Zhang et al. (2024), and recent work on multimodal unified representations refines discrete code spaces for cross-modal generalization Huang et al. (2025). These studies suggest that learned codebooks can organize continuous feature-level information into compact and semantically meaningful discrete units. However, these studies do not specifically address cross-modal knowledge distillation between structurally heterogeneous intermediate features, where teacher and student feature units lack direct correspondence. In contrast, our work uses a teacher-side VQ codebook as a distillation interface, abstracting teacher representations into discrete concept anchors and selecting transferable codes based on task relevance and student compatibility. This enables feature-level teacher knowledge to guide the student without imposing explicit unit-to-unit alignment across heterogeneous modalities. Figure 1: Overview of the proposed framework. We learn a teacher-side vector-quantized codebook (Sec. 3.3), select task-relevant and student-compatible codes (Sec. 3.4), and use the selected codes for student-side distillation (Sec. 3.5). The framework enables feature-level CMKD without requiring explicit unit-level correspondence between structurally different teacher and student representations. 3 Proposed Method 3.1 Notations and Problem Statement We consider a cross-modal knowledge distillation setting with paired teacher-modality (t) and student-modality (s) inputs and corresponding targets, (t)=i(t)i=1N,(s)=i(s)i=1N,=ii=1N,X^(t)=\x_i^(t)\_i=1^N, ^(s)=\x_i^(s)\_i=1^N, =\y_i\_i=1^N, (1) where N denotes the number of training samples. The same subscript i indicates that i(t)x_i^(t), i(s)x_i^(s), and iy_i correspond to the same sample (i.e., the i-th sample). For each modality m∈t,sm∈\t,s\, let i(m)=f(m)(i(m),θ(m))∈ℝL(m)×D(m),i(m)=g(m)(i(m),ϕ(m)),z_i^(m)=f^(m)(x_i^(m);θ^(m)) ^L^(m)× D^(m), _i^(m)=g^(m)(z_i^(m);φ^(m)), (2) where f(m)f^(m) and g(m)g^(m) denote the modality-specific encoder and task head, respectively. Here, i(m)z_i^(m) represents the modality-specific feature representation, and i(m)p_i^(m) denotes the corresponding task prediction (e.g., class probabilities in classification). D(m)D^(m) is the feature dimension and L(m)L^(m) is the number of modality-specific structured feature units. Because the teacher and student are built on different modalities, their intermediate features may have different structural organizations and sizes. For example, in a 2D visual feature map of image data, L(m)L^(m) may denote the number of spatial locations (i.e., width × height), whereas in a 1D sequential feature of audio data, L(m)L^(m) may denote the number of temporal positions. Given paired cross-modal training data and a pretrained teacher model θ∗(t),ϕ∗(t)\θ^*(t),φ^*(t)\, our goal is to learn the student model θ(s),ϕ(s)\θ^(s),φ^(s)\ by transferring useful knowledge from the teacher modality to improve task performance of the student model. 3.2 Overall Framework The proposed CMKD framework for heterogeneously structured features is illustrated in Fig. 1. The proposed framework consists of three stages: teacher-side codebook learning, code-wise importance estimation, and selective codebook-based distillation. First, we introduce a teacher-side codebook branch and learn a vector-quantized codebook that captures task-related patterns in the teacher feature space. (Sec. 3.3) Second, we estimate the importance of each code by jointly considering task relevance and student compatibility. (Sec. 3.4) Third, we select high-importance codes and use them as a codebook for student-side quantization, enabling feature-level distillation without explicit unit-level correspondence between teacher and student representations. We further perform prediction-level alignment between the student and the teacher-side codebook-branch prediction during student training. (Sec. 3.5) 3.3 Stage-1: Teacher-Side Codebook Learning In this stage, we freeze the pretrained teacher model with parameters θ∗(t),ϕ∗(t)\θ^*(t),φ^*(t)\. For each teacher-modality input i(t)x_i^(t), we extract the intermediate feature i(t)z_i^(t) using the fixed teacher encoder: i(t)=f(t)(i(t),θ∗(t)).z_i^(t)=f^(t)(x_i^(t);θ^*(t)). (3) To obtain a discrete abstraction of i(t)z_i^(t), we introduce a learnable codebook ∈ℝB×DC ^B× D with two projection layers, Πin(t) _in^(t) and Πout(t) _out^(t), which project the feature into the code space and reconstruct it back to the original feature space, respectively. The reconstructed feature is then fed into a teacher-side codebook-branch prediction head gcp(t)(⋅,ϕcp(t))g_cp^(t)(·; _cp^(t)), which follows the architecture of the original teacher task head but has separate learnable parameters. The overall forward process is given by i(t)=VQ(Πin(t)(i(t)),),i(t)=gcp(t)(Πout(t)(i(t)),ϕcp(t)),e_i^(t)=VQ ( _in^(t)(z_i^(t));C ), _i^(t)=g_cp^(t) ( _out^(t)(e_i^(t)); _cp^(t) ), (4) where vector quantization (VQ) assigns each projected token to its nearest codeword in C, thereby converting the continuous teacher feature into a discrete code-based representation Van Den Oord et al. (2017). Here, i(t)e_i^(t) denotes the quantized representation, and i(t)q_i^(t) denotes the prediction from the codebook branch. To train the teacher-side codebook branch, we optimize the task loss together with the standard vector-quantization objective, consisting of the codebook loss and the commitment loss Van Den Oord et al. (2017): ℒS1code=∑i=1N(ℒtask(i(t),i)+‖sg[Πin(t)(i(t))]−i(t)‖22+βcom‖Πin(t)(i(t))−sg[i(t)]‖22),L_S1^code= _i=1^N (L_task(q_i^(t),y_i)+ \! [ _in^(t)(z_i^(t)) ]-e_i^(t) _2^2+ _com _in^(t)(z_i^(t))-sg\! [e_i^(t) ] _2^2 ), (5) where sg[⋅]sg[·] denotes the stop-gradient operator, βcom _com is the commitment loss weight and ℒtaskL_task denotes the task-specific loss (e.g., cross-entropy for classification). For effective student distillation, the learned teacher codebook should preserve task-relevant information while remaining compatible with the student modality. We therefore jointly train the teacher-side codebook branch together with the student model. Specifically, let i(s)p_i^(s) denote the prediction from the original student task head. We introduce a codebook-induced prediction matching term that aligns i(t)q_i^(t) with i(s)p_i^(s). The overall objective is given by ℒS1=ℒS1code+∑i=1N(ℒtask(i(s),i)+‖i(t)−i(s)‖22).L_S1=L_S1^code+ _i=1^N (L_task(p_i^(s),y_i)+ _i^(t)-p_i^(s) _2^2 ). (6) 3.4 Stage-2: Code-wise Importance Estimation Although Eq. 6 encourages the teacher-side codebook to learn codes that are compatible with the student modality, not all codes are equally beneficial for transfer. We therefore estimate the importance of each code and select a subset of high-importance codes for subsequent distillation. To estimate code importance, we use the teacher-side codebook branch learned in Stage-1 and evaluate how its prediction changes when each code is removed. For each code k, we form a leave-one-code-out codebook −kC_-k by removing it from C and compute the corresponding teacher-side codebook-branch prediction: ¯i(t)=VQ(Πin(t)(i(t)),−k),¯i(t)=gcp(t)(Πout(t)(¯i(t)),ϕcp(t)). e_i^(t)=VQ ( _in^(t)(z_i^(t));C_-k ), q_i^(t)=g_cp^(t) ( _out^(t)( e_i^(t)); _cp^(t) ). (7) We then estimate the importance of the excluded code from two perspectives: task relevance and student compatibility, ukrel=i[ℒtask(¯i(t),i)−ℒtask(i(t),i)],ukcomp=i[‖¯i(t)−i(s)‖22−‖i(t)−i(s)‖22],u_k^rel=E_i\! [L_task( q_i^(t),y_i)-L_task(q_i^(t),y_i) ],u_k^comp=E_i\! [ q_i^(t)-p_i^(s) _2^2- _i^(t)-p_i^(s) _2^2 ], (8) where i(t)q_i^(t) is the teacher-side codebook branch prediction obtained with the full codebook C. The relevance score ukrelu_k^rel measures how much removing the k-th code degrades the teacher-side task prediction. A larger value indicates that the code is more important for preserving task-relevant information. The compatibility score ukcompu_k^comp measures how much removing the code increases the discrepancy between the teacher-side codebook-branch prediction and the student prediction. A larger value indicates that the code provides guidance that is more compatible with the student modality. After normalizing the two scores, we compute the final code importance by uk=ukrel+ukcomp.u_k=\,u_k^rel+\,u_k^comp. (9) The resulting scores are used to rank teacher codes and select a subset for the next distillation stage. 3.5 Stage-3: Selective Codebook-Based Distillation In the final stage, we select the top-K codes according to the importance scores obtained in Stage-2 and construct the selected teacher codebooks selC_sel, which is used as teacher-derived anchors for student-side quantization. Specifically, we build a student codebook branch with learnable projection layers Πin(s) _in^(s) and Πout(s) _out^(s), along with a student-side codebook-branch prediction head gcp(s)(⋅,ϕcp(s))g_cp^(s)(·; _cp^(s)). Through this branch, student features are quantized using the selected teacher codebook, allowing teacher-side intermediate knowledge to guide student learning without direct feature-unit alignment. Given the student intermediate feature i(s)z_i^(s), the student-side codebook-branch produces i(s)=VQ(Πin(s)(i(s)),sel),i(s)=gcp(s)(Πout(s)(i(s)),ϕcp(s)),e_i^(s)=VQ ( _in^(s)(z_i^(s));C_sel ), _i^(s)=g_cp^(s) ( _out^(s)(e_i^(s)); _cp^(s) ), (10) where selC_sel is fixed during this stage. Since the codebook is no longer updated, the codebook branch is trained only with the task loss and the commitment loss: ℒS3code=ℒtask(i(s),i)+βcom‖Πin(s)(i(s))−sg[i(s)]‖22.L_S3^code=L_task(q_i^(s),y_i)+ _com _in^(s)(z_i^(s))-sg\! [e_i^(s) ] _2^2. (11) The teacher-side codebook branch learned in Stage-1 produces a codebook-induced prediction that reflects quantized teacher knowledge. To fully leverage the learned teacher codebook, we use its induced prediction to guide the student task prediction, allowing the codebook to jointly shape student-side quantization and final prediction learning. Specifically, we introduce a codebook-induced prediction matching term between i(t)q_i^(t) and i(s)p_i^(s), leading to the Stage-3 objective: ℒS3=ℒtask(i(s),i)+λdist(ℒS3code+‖i(t)−i(s)‖22),L_S3=L_task(p_i^(s),y_i)+ _dist (L_S3^code+ _i^(t)-p_i^(s) _2^2 ), (12) where λdist _dist controls the contribution of the distillation terms. Through this stage, the student is trained with the original task objective and two codebook-based distillation signals, which guide both student intermediate representations and task predictions using the learned teacher codebook, without requiring direct alignment between structurally heterogeneous features. Algorithm 1 in Appendix C provides the pseudo-code of the proposed method. Table 1: Classification results. A, V, T, and I denote audio, video, text, and image modalities, respectively, and each arrow indicates the teacher-to-student distillation direction. We report accuracy averaged over five independent runs, with the best result in each column shown in bold. Method RAVDESS VGG-Sound CrisisMMD M-IMDB A → V V → A A → V V → A T → I I → T T → I I → T w/o KD 0.9208 0.6826 0.5031 0.6058 0.5403 0.5500 0.6645 0.7294 General distillation baselines KLD 0.9118 0.6972 0.5153 0.6176 0.5377 0.5578 0.6732 0.7310 MLLD 0.9292 0.6889 0.5135 0.6122 0.5357 0.5562 0.6699 0.7320 FitNets 0.9062 0.7146 0.4916 0.5962 0.5281 0.5507 0.6759 0.7296 RKD 0.9236 0.7014 0.5066 0.6085 0.5432 0.5569 0.6668 0.7317 CRD 0.9299 0.7007 0.5063 0.6110 0.5377 0.5560 0.6685 0.7299 OFA 0.9215 0.6562 0.5100 0.6129 0.5362 0.5565 0.6715 0.7339 Modality-gap-aware CMKD baselines MGDFR 0.9313 0.7264 0.5225 0.6186 0.5440 0.5584 0.6725 0.7382 C2KD 0.9306 0.7021 0.5123 0.6154 0.5410 0.5520 0.6670 0.7372 STXD 0.9035 0.7250 0.5067 0.6093 0.5421 0.5485 0.6761 0.7265 FDD 0.9153 0.7055 0.5028 0.6063 0.5382 0.5547 0.6670 0.7323 Ours 0.9431 0.7486 0.5299 0.6229 0.5433 0.5592 0.6768 0.7434 4 Experiments We validate the proposed method on five multimodal benchmarks spanning classification and semantic segmentation tasks in CMKD settings. Implementation details are provided in the Appendix A. 4.1 Classification Experiments Datasets. We use four multimodal classification benchmarks. RAVDESS Livingstone and Russo (2018) contains paired speech audio and facial video recordings for eight-class emotion recognition. VGG-Sound Chen et al. (2020) is a video–audio event classification dataset, where we use the curated 141-class subset following Li et al. (2025). CrisisMMD-v2.0 Alam et al. (2018); Ofli et al. (2020) consists of disaster-related image–text social media posts for eight-class humanitarian category classification. M-IMDB Arevalo et al. (2017) contains paired movie posters and plot descriptions for movie genre classification. For all datasets, we use a 6:2:2 train/validation/test split and report test accuracy from the best validation checkpoint, averaged over five runs. Baselines. We compare our method with general distillation methods including KLD Hinton et al. (2015) and MLLD Jin et al. (2023), FitNets Romero et al. (2015), RKD Park et al. (2019), CRD Tian et al. (2019), and OFA Hao et al. (2023); and modality-gap-aware CMKD methods, including MGDFR Xue et al. (2023), C2KD Huo et al. (2024), STXD Jang et al. (2023), and FDD Liu et al. (2026). For feature-alignment baselines, which are not directly applicable to structurally heterogeneous features, we use pooled representations and add projection layers when feature dimensions differ. Implementation. Image and video inputs are represented as 2D spatial feature using ResNet- and ViT-based feature extractors Dosovitskiy et al. (2020); He et al. (2016). Audio inputs are represented as 1D temporal feature sequences using Wav2Vec2- and VGGish-style feature extractors Baevski et al. (2020); Hershey et al. (2017). Text inputs are represented as token-level sequence features using transformer-based feature extractors including BERTweet and FLAVA Nguyen et al. (2020); Singh et al. (2022). We select the top 50% of teacher codes according to the proposed importance score. Results. Tab. 1 summarizes the classification results. Our method achieves the best performance in seven out of eight settings and the second-best result on CrisisMMD T → I. It also improves over the student trained without distillation in all transfer directions, showing that the proposed framework provides useful supervision across both audio-visual and text-image scenarios. Modality-gap-aware CMKD baselines are generally competitive, which supports the importance of accounting for cross-modal discrepancy. Nevertheless, our method obtains stronger results in most settings, suggesting that useful teacher-side cues can be extracted from structurally heterogeneous intermediate features and transferred through a codebook-level interface. Table 2: Semantic segmentation results on NYU-Depth. Left: quantitative comparison for two distillation scenarios, where the first modality denotes the teacher and the second denotes the student. Right: class-wise recall comparison of RGB-only, depth-only, and our RGB → Depth student models. Method Depth → RGB RGB → Depth OA ↑ CA ↑ mIoU ↑ OA ↑ CA ↑ mIoU ↑ w/o KD 0.5582 0.2748 0.1850 0.5269 0.2100 0.1366 MLLD 0.5599 0.2792 0.1911 0.5250 0.2118 0.1399 CRD 0.5592 0.2677 0.1806 0.5261 0.2111 0.1385 OFA 0.5607 0.2881 0.1982 0.5242 0.2123 0.1409 MGDFR 0.5601 0.2737 0.1878 0.5213 0.2162 0.1442 C2KD 0.5587 0.2771 0.1878 0.5214 0.2093 0.1396 STXD 0.5616 0.2786 0.1925 0.5231 0.2164 0.1425 FDD 0.5608 0.2744 0.1855 0.5252 0.2122 0.1403 Ours 0.5632 0.2909 0.2003 0.5218 0.2184 0.1456 4.2 Semantic Segmentation Experiments Dataset. We evaluate semantic segmentation on NYU-Depth V2 Silberman et al. (2012), an indoor RGB-D benchmark with aligned RGB-depth image pairs and pixel-wise annotations for 40 classes. Following Li et al. (2025), we report Overall Accuracy (OA), Class-averaged Accuracy (CA), and mean Intersection-over-Union (mIoU), which measure pixel-level accuracy, average class-wise recall, and average region overlap, respectively. We use a 6:2:2 train/validation/test split and report results averaged over five runs. Baselines. We use representative baselines from the classification experiments. Since RGB and depth inputs are spatially aligned, dense correspondence between teacher and student feature maps is available. Thus, feature-level baselines are applied directly to corresponding intermediate feature maps when applicable, with projection layers added only to match channel dimensions. Implementation. We use a ResNet-34 He et al. (2016) based feature extractor for both RGB and depth modalities, and apply our method to the resulting 14×1414× 14 grid features. The codebook contains 1024 codes, from which the top 12.5% are selected based on the estimated importance scores. Results. Tab. 2 reports the semantic segmentation results. The left part provides quantitative comparisons, and the right part shows class-wise recall for selected categories in the RGB→ setting. Our method achieves the best performance on most metrics, with the only exception being OA in RGB→ , where the w/o KD baseline remains slightly higher. Since OA is weighted by pixel frequency, recall drops in high-occupancy categories can noticeably affect the overall score (Appendix B.5). The decrease on floor in the class-wise recall comparison provides one representative example. Meanwhile, our method improves CA and mIoU, with recall gains on categories such as door, picture, and other_structure, where depth-only features may provide less discriminative cues but can benefit from guidance provided by the RGB teacher. These results suggest that the proposed method can transfer useful teacher-side information for class-level segmentation quality. Figure 2: Codebook analysis on RAVDESS. (a) Example frames from the dataset. (b,c) Spatial usage maps of top-ranked and bottom-ranked codes according to the proposed importance score. Table 3: Ablation study on Stage-3 loss components. “Code” denotes the student-side codebook-branch objective. “Pred-Match” denotes the codebook-induced prediction matching term. Code Pred RAVDESS VGG-Sound CrisisMMD M-IMDB Match A → V V → A A → V V → A T → I I → T T → I I → T - - 0.9208 0.6826 0.5031 0.6058 0.5403 0.5500 0.6645 0.7294 ✓ - 0.9202 0.7333 0.5067 0.6098 0.5387 0.5534 0.6716 0.7363 - ✓ 0.9285 0.7479 0.5294 0.6204 0.5367 0.5529 0.6770 0.7421 ✓ ✓ 0.9431 0.7486 0.5299 0.6229 0.5433 0.5592 0.6768 0.7434 Table 4: Ablation on the prediction matching target in Stage-3 Loss. Pred-Match Target RAVDESS VGG-Sound CrisisMMD M-IMDB A → V V → A A → V V → A T → I I → T T → I I → T Original branch ((t))(p^(t)) 0.8903 0.6201 0.5173 0.6171 0.5425 0.5539 0.6654 0.7351 Codebook branch ((t))(q^(t)) 0.9431 0.7486 0.5299 0.6229 0.5433 0.5592 0.6768 0.7434 4.3 Analysis Do High-Importance Codes Capture Informative Patterns? We further analyze the learned codebook on RAVDESS, where the actor faces are well aligned across videos, making the spatial usage patterns of codes easier to interpret. We consider the visual-teacher setting and visualize where each code is assigned over the spatial feature grid across the dataset. Fig. 2 shows the usage maps of the top-10 and bottom-10 codes according to the importance score. Since RAVDESS requires emotion recognition from acted facial and vocal expressions, task-relevant visual concepts are expected to be concentrated around centered regions, especially the face and mouth. Consistent with this intuition, high-score codes are mainly activated around the central regions, suggesting that they capture visual concepts that are informative to the task and likely useful for cross-modal transfer. In contrast, low-score codes tend to show more scattered or peripheral usage patterns, indicating that they are less consistently associated with meaningful regions. Effect of Distillation Loss Components. Tab. 3 analyzes the contribution of the two main Stage-3 loss components in Eq. 12. “Code” denotes the student-side codebook-branch objective in Eq. (11), which constrains student features through the selected teacher codebook and provides representation-level guidance. “Pred-Match” denotes the codebook-induced prediction matching term in Eq. (12), which guides the student task prediction using the teacher prediction derived from quantized representations. While each component improves several transfer directions, combining them yields the strongest overall performance, suggesting complementary effects between representation guidance and codebook-induced prediction guidance. Tab. 4 further examines the target used for prediction matching by comparing the original teacher prediction (t)p^(t) with the codebook-induced teacher prediction (t)q^(t). Matching (t)q^(t) outperforms matching (t)p^(t) across all evaluated datasets and transfer directions, indicating that the gain from “Pred-Match” does not come from generic output-level supervision alone, but from using a guidance signal shaped by the learned teacher codebook. Effect of Code Selection. Fig. 3 analyzes the effect of the selected code ratio by varying the percentage of teacher codes used for student-side quantization from 25% to 100%, where the dashed line denotes the w/o KD baseline. The proposed method remains above the w/o KD baseline in most cases, indicating that its benefit is not limited to a single carefully tuned ratio. The best ratio varies across settings, suggesting that the amount of useful teacher-side code information can depend on the dataset and transfer direction. In the main classification experiments in Sec. 4.1, we use a fixed ratio of 50% for all settings to maintain a simple and consistent evaluation protocol (Appendix B.4). Tab. 5 further analyzes the effect of different code selection criteria under the fixed 50% selection ratio used in Sec. 4.1. Compared with random selection, score-based criteria generally improve performance, indicating that the learned scores provide useful signals for selecting teacher codes. When codes are selected based only on task relevance or only on student compatibility score, the two criteria show different strengths across scenarios. Using their combined score achieves the best or competitive performance in most cases, suggesting that jointly considering task relevance and student compatibility provides a more balanced criterion for identifying useful teacher codes. Table 5: Ablation study on code selection criteria. Selection Criteria RAVDESS VGG-Sound CrisisMMD M-IMDB A → V V → A A → V V → A T → I I → T T → I I → T Random 0.9292 0.7396 0.5252 0.6211 0.5353 0.5536 0.6718 0.7353 Task relevance only 0.9396 0.7361 0.5276 0.6233 0.5435 0.5558 0.6727 0.7351 Student compatibility only 0.9375 0.7417 0.5275 0.6222 0.5437 0.5565 0.6722 0.7346 Combination (Ours) 0.9431 0.7486 0.5299 0.6229 0.5433 0.5592 0.6768 0.7434 Figure 3: Selected code ratio ablation. We vary the percentage of selected teacher codes used for student-side quantization from 25% to 100%. The dashed line denotes the w/o KD baseline. 5 Conclusion We presented a codebook-guided framework for cross-modal knowledge distillation between structurally heterogeneous features. Instead of directly aligning teacher and student feature units, our method abstracts teacher representations into a vector-quantized codebook and selects task-relevant and student-compatible codes for student learning. The selected codes are then fully leveraged through student-side codebook quantization and codebook-induced prediction matching. This design allows the student to exploit fine-grained teacher-side information without requiring explicit unit-level correspondence between heterogeneous feature structures, such as spatial grids and temporal sequences. Across diverse cross-modal classification and semantic segmentation settings, our method achieves strong performance compared with general and modality-gap-aware distillation baselines. Further analyses support the proposed framework design and suggest that codebook-guided distillation is a practical strategy for transferring knowledge across structurally heterogeneous features. Future work. In the current framework, code selection relies on a fixed ratio and an offline importance estimation stage. The fixed ratio may not capture the varying amount of useful teacher-side information across cross-modal scenarios, while offline scoring can increase the cost for larger codebooks (Appendix B.3). Future work will explore adaptive and efficient strategies for selecting appropriate code subsets according to the distillation scenario. Acknowledgments This research was supported by Kyungpook National University Research Fund, 2025. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (RS-2026-25495369). 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Appendix A Implementation Details A.1 Computational Resources All experiments were conducted on a single workstation equipped with an AMD Ryzen 9 9900X CPU, an NVIDIA RTX PRO 6000 Blackwell Workstation Edition GPU with 96GB memory, and 64GB RAM. Unless otherwise specified, each training run was performed on a single GPU. Table 6: Implementation details for each dataset. Dataset Epochs Learning rate Weight decay Batch size #Code Code Dim. βcom _com λdist _dist RAVDESS 100 1×10−31× 10^-3 1×10−41× 10^-4 64 512 128 0.25 1×10−21× 10^-2 VGG-Sound 100 1×10−31× 10^-3 1×10−41× 10^-4 128 512 128 0.25 1×10−21× 10^-2 CrisisMMD 100 1×10−31× 10^-3 1×10−41× 10^-4 64 256 128 0.25 1×10−21× 10^-2 M-IMDB 100 1×10−31× 10^-3 1×10−41× 10^-4 64 512 64 0.25 1×10−21× 10^-2 NYU-Depth V2 100 1×10−41× 10^-4 1×10−41× 10^-4 6 1024 256 0.25 1×10−21× 10^-2 A.2 General Training Details Table 6 summarizes the training settings used in our experiments. Unless otherwise specified, we train each model using AdamW with β=(0.9,0.999)β=(0.9,0.999). For a fair comparison, additional training stages required by FitNets Romero et al. (2015), MGDFR Xue et al. (2023), and our method are also trained for 100 epochs. These correspond to the hint regression stage of FitNets, the co-training stage of MGDFR, and Stage-1 of our method, respectively. A.3 Implementation Details for Distillation For our method, codebook sizes (#Code), dimension of each code (Code Dim.), commitment coefficient βcom _com and distillation loss coefficient λdist _dist are summarized in Table 6. We use a linear projector to map the intermediate features into the code space before vector quantization. Quantization is performed by assigning each projected feature to its nearest code according to the squared Euclidean distance. During Stage-1, we additionally include a small entropy-based code usage regularization term to stabilize codebook learning. Before Stage-3, we re-initialize the student parameters and train the final student from scratch using the selected teacher codebook. For feature-alignment baselines, we use pooled features for feature-level distillation when the teacher and student intermediate features have different structural forms, and add a projection layer if necessary. When dense correspondence between teacher and student features is available, as in NYU-Depth V2, we apply feature-level distillation directly to the corresponding intermediate features without pooling. A.4 RAVDESS Dataset Specification. We use the Ryerson Audio-Visual Database of Emotional Speech and Song (RAVDESS) for audio-visual emotion classification Livingstone and Russo (2018). In our experiments, we use the speech subset and construct paired speech-audio and speech-video samples. The task is formulated as an 8-way emotion classification problem with the following emotion categories: neutral, calm, happy, sad, angry, fearful, disgust, and surprised. Each paired audio-video sample shares the same emotion label. The resulting dataset contains 1,440 paired samples, which are split into training, validation, and test sets with a ratio of 60%/20%/20%. Preprocessing. For audio data, we convert each waveform to mono when necessary, resample it to 16 kHz, and normalize its duration to 3.6 seconds. Longer clips are center-cropped, while shorter clips are symmetrically zero-padded. The resulting waveform is passed through a pretrained Wav2Vec2-Base model Baevski et al. (2020), and the final hidden representations are used as the audio feature sequence. The extracted audio features are arranged as D×T=768×179D× T=768× 179, where D denotes the feature dimension and T denotes the temporal length. For video data, we uniformly sample 10 frames from each video. Each frame is center-cropped, resized to 224×224224× 224, and normalized using ImageNet statistics Deng et al. (2009). We then feed each frame into an ImageNet-pretrained ResNet-18 He et al. (2016) and use the layer-3 feature map as the frame-level visual representation. The frame-level features are averaged over the sampled frames to obtain a single spatial feature map for each video. The extracted visual features have size D×H×W=256×14×14D× H× W=256× 14× 14, where D denotes the channel (feature) dimension and H×WH× W denotes the spatial resolution. Model. We use lightweight classifiers on top of the pre-extracted audio and video features. The audio classifier receives Wav2Vec2 features and applies two 1D convolutional blocks. The resulting encoder output, with shape B×256×TB× 256× T, is used as the audio intermediate feature, where B denotes batch size. It is average-pooled over the temporal dimension and passed through a linear layer with ReLU activation and an 8-way classifier. The video classifier receives ResNet-18 layer-3 features and applies two 2D convolutional blocks. The resulting encoder output, with shape B×256×H×WB× 256× H× W, is used as the video intermediate feature, where B denotes batch size. It is average-pooled over the spatial dimensions and passed through a linear layer with ReLU activation and an 8-way classifier. In both classifiers, each convolutional block consists of convolution, batch normalization, and ReLU activation, and the hidden dimension before the final classifier is set to 64. A.5 VGG-Sound Dataset Specification. VGG-Sound Chen et al. (2020) is a large-scale audio-visual event classification dataset consisting of short audio-video clips collected from YouTube videos. Following Zhou et al. (2022); Li et al. (2025), we use a subset of 48,755 paired samples covering 141 real-world event classes. Each paired audio-video sample shares the same event label, and the task is formulated as 141-way event classification. We split the dataset into training, validation, and test sets with a ratio of 60%/20%/20%. Preprocessing. Following the preprocessing protocol of Zhou et al. (2022), the visual features are extracted using VGG19 Simonyan and Zisserman (2014) and the audio features are extracted using VGGish Hershey et al. (2017). Each audio feature is represented as a temporal sequence of size T×D=10×128T× D=10× 128, where T denotes the temporal length and D denotes the feature dimension. For visual features, the original pre-extracted representation contains frame-level spatial features. We average the visual features over the temporal dimension and use the resulting spatial feature map of size H×W×D=7×7×512H× W× D=7× 7× 512, where H×WH× W denotes the spatial resolution and D denotes the channel dimension. Model. We use lightweight modality-specific classifiers on top of the pre-extracted features. The audio classifier applies two 1D convolutional blocks to obtain the audio intermediate feature of shape B×128×TB× 128× T, where B denotes batch size. This intermediate feature is further processed by an additional 1D convolutional stage, average-pooled over time, and passed through a linear layer with ReLU activation and a 141-way classifier. The video classifier applies a 1×11× 1 convolutional reduction layer to obtain the video intermediate feature of shape B×128×H×WB× 128× H× W. The intermediate feature is further processed by a 2D convolutional block, average-pooled over the spatial dimensions, and passed through a linear layer with ReLU activation and a classifier. In both classifiers, convolutional blocks consist of convolution, batch normalization, and ReLU activation. We set the hidden dimension before the final classifier to 128. A.6 CrisisMMD Dataset Specification. We use CrisisMMD-V2 Ofli et al. (2020), an updated version of the CrisisMMD multimodal disaster dataset Alam et al. (2018), for image-text tweet classification in humanitarian crisis settings. The dataset contains 16,058 paired image-text samples, and the task is formulated as 8-way humanitarian category classification. The categories are not_humanitarian, affected_individuals, infrastructure_and_utility_damage, injured_or_dead_people, missing_or_found_people, rescue_volunteering_or_donation_effort, vehicle_damage, and other_relevant_information. Each paired image-text sample shares the same label. We split the dataset into training, validation, and test sets with a ratio of 60%/20%/20%. Preprocessing. For image data, we resize each image to 224×224224× 224 and normalize it using ImageNet statistics Deng et al. (2009). The processed image is passed through an ImageNet-pretrained ResNet-34 He et al. (2016), and we use the layer-3 feature map as the image representation. The extracted image features have size D×H×W=256×14×14D× H× W=256× 14× 14, where D denotes the channel dimension and H×WH× W denotes the spatial resolution. For text data, we use BERTweet Nguyen et al. (2020) to extract token-level representations from the tweet text. Each tweet is tokenized with a maximum length of 128, and the last hidden states of BERTweet are used as the text feature sequence. The extracted text features have size Ti×D=Ti×768T_i× D=T_i× 768, where TiT_i denotes the valid token length of the i-th tweet and D denotes the feature dimension. Model. We use lightweight modality-specific classifiers on top of the pre-extracted image and text features. The image classifier applies two 2D convolutional blocks. The resulting encoder output, with shape B×128×H×WB× 128× H× W, is used as the image intermediate feature, where B denotes batch size. It is average-pooled over the spatial dimensions and passed through a linear layer with ReLU activation and an 8-way classifier. The text classifier applies two 1D convolutional blocks. The resulting encoder output, with shape B×128×TB× 128× T, is used as the text intermediate feature, where T denotes the token sequence length. For text pooling, we average only over valid token positions using the token lengths. The pooled representation is then passed through a linear layer with ReLU activation and an 8-way classifier. In both classifiers, each convolutional block consists of convolution, batch normalization, and ReLU activation, with hidden dimensions set to 64. A.7 M-IMDB Dataset Specification. We use M-IMDB Arevalo et al. (2017) for image-text movie genre classification. Although the original dataset is a 23-class multi-label genre classification benchmark, we construct a single-label subset for our experiments. Several distillation methods in our comparison are formulated for single-label classification using softmax-normalized logits, and extending them to the multi-label setting would require redesigning their original distillation formulations. We therefore adopt a controlled single-label setting so that the comparison primarily reflects differences among the CMKD methods rather than differences in their multi-label extensions. Specifically, we first remove four extremely rare genres, News, Adult, Talk-Show, and Reality-TV, from the genre labels of each sample, and discard samples that have no remaining genre label. We then retain only samples with exactly one remaining genre label. Finally, we remove genres with fewer than 50 single-label samples, together with their samples. The resulting dataset contains 5,778 paired poster-text samples from 8 classes: Action, Comedy, Documentary, Drama, Horror, Sci-Fi, Thriller, and Western, and the number of samples per class is reported in Table 7. Each paired poster-text sample shares the same label. Because this filtering substantially changes both the size and the class distribution of the original benchmark, we do not use the official split. Instead, for each seed, we construct a stratified 60%/20%/20% split for training, validation, and testing, which is shared across all compared methods. Accordingly, the M-IMDB results should be interpreted as a customized single-label proxy for controlled CMKD comparison, and they are not directly comparable with results reported under the standard multi-label protocol. Table 7: Number of samples per class in the single-label M-IMDB dataset. Class # Samples Drama 2,681 Comedy 1,337 Documentary 918 Horror 417 Western 173 Thriller 143 Sci-Fi 56 Action 53 Total 5,778 Preprocessing. For image and text preprocessing, we use FLAVA Singh et al. (2022) to extract modality-specific hidden representations from movie posters and plot descriptions. For image data, each poster is processed by the FLAVA image encoder, whose output consists of a CLS token and 14×1414× 14 patch tokens. To reduce the sequence length, we average-pool the patch tokens over non-overlapping 2×22× 2 regions while preserving the CLS token. This yields image features of size L×D=50×768L× D=50× 768, where L=1+7×7L=1+7× 7 denotes the resulting token length and D denotes the feature dimension. For text data, we use the movie plot as the text input. If the plot is unavailable, we use the movie title as a fallback. The text is tokenized with a maximum length of 128 and passed through the FLAVA text encoder. We preserve the CLS token and adaptively average-pool the remaining token representations to obtain a fixed-length text sequence. This yields text features of size L×D=64×768L× D=64× 768, where L denotes the pooled token length and D denotes the feature dimension. Model. We use lightweight sequence classifiers on top of the pre-extracted FLAVA image and text features. For both modalities, each token feature is passed through a linear projection, layer normalization, and GELU activation to obtain the intermediate feature for distillation. The intermediate feature has shape B×50×64B× 50× 64 for image data and B×64×64B× 64× 64 for text data. We use attention pooling to obtain the pooled representation, with the text attention mask used to ignore padded positions. The pooled representation is passed through layer normalization, a linear layer with GELU activation, and a final 8-way classifier. Hidden dimensions are set to 64. A.8 NYU-Depth V2 Dataset Specification. We use NYU-Depth V2 Silberman et al. (2012) for RGB-depth semantic segmentation for indoor scenes. The dataset contains 1,449 paired RGB-depth samples captured from indoor scenes, with pixel-wise label maps of size 480×640480× 640. The semantic categories include common indoor structures and objects, such as wall, floor, ceiling, bed, chair, table, door, and window. We use 41 label indices, consisting of 40 semantic classes and one void class, and exclude the void class from evaluation. We split the dataset into training, validation, and test sets with a ratio of 60%/20%/20%. Preprocessing. For RGB data, we first apply min-max normalization to each image, resize it to 224×224224× 224, and normalize it using ImageNet statistics Deng et al. (2009). The processed RGB image is passed through an ImageNet-pretrained ResNet-34 He et al. (2016), and we use the layer-3 feature map as the RGB representation. For depth data, we apply min-max normalization to each depth map and replicate the single-channel depth input into three channels. We then apply the same 224×224224× 224 resizing and ImageNet normalization, and pass the result through the same ResNet-34 layer-3 feature extractor. The extracted RGB and depth features have size D×H×W=256×14×14D× H× W=256× 14× 14, where D denotes the channel dimension and H×WH× W denotes the spatial resolution. The semantic label maps are kept at their original spatial resolution of 480×640480× 640 and are used as pixel-wise supervision for segmentation. Model. We use lightweight segmentation heads on top of the pre-extracted RGB and depth features. The RGB and depth branches share the same architecture and differ only in the input modality. Each branch applies two 2D convolutional blocks to the ResNet-34 layer-3 feature map. The resulting encoder output, with shape B×256×14×14B× 256× 14× 14, is used as the intermediate feature for distillation, where B denotes batch size. For segmentation prediction, the intermediate feature is passed through an upsampling decoder. The decoder progressively upsamples the feature map and produces dense semantic logits with spatial size 480×640480× 640. The output dimension is 41, corresponding to 40 semantic classes and one void class. The model is trained with pixel-wise cross-entropy loss, where the void label is ignored. For NYU-Depth V2, where RGB and depth features are spatially aligned, we apply each feature-alignment baseline to the corresponding dense intermediate feature maps whenever possible, rather than pooling the features. Appendix B Additional Experimental Results B.1 Results with Standard Deviations Tables 8 and 9 report the classification and semantic segmentation results from the main paper with standard deviations over five independent runs. The mean values are identical to those reported in the corresponding main result tables, while the standard deviations provide additional information about variability across random seeds. Tables 10, 11, and 12 further report the ablation results in Tables 3, 4, and 5 with standard deviations under the same protocol. Table 8: Classification results. A, V, T, and I denote audio, video, text, and image modalities, respectively, and each arrow indicates the teacher-to-student distillation direction. We report mean accuracy ± standard deviation over five independent runs, with the best mean result in each column shown in bold. Method RAVDESS VGG-Sound A → V V → A A → V V → A w/o KD 0.9208± 0.0164 0.6826± 0.0189 0.5031± 0.0035 0.6058± 0.0086 KLD 0.9118± 0.0156 0.6972± 0.0674 0.5153± 0.0067 0.6176± 0.0090 MLLD 0.9292± 0.0140 0.6889± 0.0461 0.5135± 0.0056 0.6122± 0.0047 FitNets 0.9062± 0.0188 0.7146± 0.0385 0.4916± 0.0105 0.5962± 0.0128 RKD 0.9236± 0.0132 0.7014± 0.0269 0.5066± 0.0068 0.6085± 0.0018 CRD 0.9299± 0.0199 0.7007± 0.0246 0.5063± 0.0032 0.6110± 0.0075 OFA 0.9215± 0.0183 0.6562± 0.0577 0.5100± 0.0093 0.6129± 0.0050 MGDFR 0.9313± 0.0206 0.7264± 0.0090 0.5225± 0.0034 0.6186± 0.0084 C2KD 0.9306± 0.0139 0.7021± 0.0314 0.5123± 0.0049 0.6154± 0.0045 STXD 0.9035± 0.0093 0.7250± 0.0165 0.5067± 0.0048 0.6093± 0.0033 FDD 0.9153± 0.0090 0.7055± 0.0158 0.5028± 0.0078 0.6063± 0.0093 Ours 0.9431± 0.0097 0.7486± 0.0231 0.5299± 0.0017 0.6229± 0.0059 Method CrisisMMD M-IMDB T → I I → T T → I I → T w/o KD 0.5403± 0.0085 0.5500± 0.0050 0.6645± 0.0092 0.7294± 0.0159 KLD 0.5377± 0.0063 0.5578± 0.0049 0.6732± 0.0103 0.7310± 0.0079 MLLD 0.5357± 0.0062 0.5562± 0.0059 0.6699± 0.0113 0.7320± 0.0096 FitNets 0.5281± 0.0202 0.5507± 0.0091 0.6759± 0.0101 0.7296± 0.0114 RKD 0.5432± 0.0058 0.5569± 0.0061 0.6668± 0.0117 0.7317± 0.0109 CRD 0.5377± 0.0110 0.5560± 0.0114 0.6685± 0.0109 0.7299± 0.0077 OFA 0.5362± 0.0080 0.5565± 0.0032 0.6715± 0.0150 0.7339± 0.0105 MGDFR 0.5440± 0.0103 0.5584± 0.0026 0.6725± 0.0105 0.7382± 0.0135 C2KD 0.5410± 0.0052 0.5520± 0.0082 0.6670± 0.0041 0.7372± 0.0101 STXD 0.5421± 0.0069 0.5485± 0.0083 0.6761± 0.0116 0.7265± 0.0168 FDD 0.5382± 0.0088 0.5547± 0.0067 0.6670± 0.0108 0.7323± 0.0105 Ours 0.5433± 0.0062 0.5592± 0.0071 0.6768± 0.0055 0.7434± 0.0139 Table 9: Semantic segmentation results on NYU-Depth. Quantitative comparison for two distillation scenarios, where the first modality denotes the teacher and the second denotes the student. Results are reported as mean ± standard deviation over five independent runs. Method Depth → RGB RGB → Depth OA ↑ CA ↑ mIoU ↑ OA ↑ CA ↑ mIoU ↑ w/o KD 0.5582± 0.0112 0.2748± 0.0218 0.1850± 0.0154 0.5269± 0.0070 0.2100± 0.0155 0.1366± 0.0110 MLLD 0.5599± 0.0122 0.2792± 0.0226 0.1911± 0.0169 0.5250± 0.0063 0.2118± 0.0150 0.1399± 0.0152 CRD 0.5592± 0.0101 0.2677± 0.0158 0.1806± 0.0108 0.5261± 0.0061 0.2111± 0.0125 0.1385± 0.0107 OFA 0.5607± 0.0119 0.2881± 0.0146 0.1982± 0.0107 0.5242± 0.0085 0.2123± 0.0125 0.1409± 0.0123 MGDFR 0.5601± 0.0123 0.2737± 0.0196 0.1878± 0.0165 0.5213± 0.0099 0.2162± 0.0097 0.1442± 0.0083 C2KD 0.5587± 0.0089 0.2771± 0.0090 0.1878± 0.0052 0.5214± 0.0062 0.2093± 0.0092 0.1396± 0.0074 STXD 0.5616± 0.0108 0.2786± 0.0220 0.1925± 0.0171 0.5231± 0.0102 0.2164± 0.0125 0.1425± 0.0124 FDD 0.5608± 0.0114 0.2744± 0.0279 0.1855± 0.0234 0.5252± 0.0063 0.2122± 0.0146 0.1403± 0.0153 Ours 0.5632± 0.0103 0.2909± 0.0260 0.2003± 0.0194 0.5218± 0.0078 0.2184± 0.0154 0.1456± 0.0105 Table 10: Ablation study on Stage-3 loss components with standard deviations. “Code” denotes the student-side codebook-branch objective. “Pred-Match” denotes the codebook-induced prediction matching term. Results are reported as mean ± standard deviation over five independent runs. Code Pred-Match RAVDESS VGG-Sound A → V V → A A → V V → A - - 0.9208± 0.0164 0.6826± 0.0189 0.5031± 0.0035 0.6058± 0.0086 ✓ - 0.9202± 0.0260 0.7333± 0.0397 0.5067± 0.0029 0.6098± 0.0033 - ✓ 0.9285± 0.0234 0.7479± 0.0175 0.5294± 0.0013 0.6204± 0.0056 ✓ ✓ 0.9431± 0.0097 0.7486± 0.0231 0.5299± 0.0017 0.6229± 0.0059 Code Pred-Match CrisisMMD M-IMDB T → I I → T T → I I → T - - 0.5403± 0.0085 0.5500± 0.0050 0.6645± 0.0092 0.7294± 0.0159 ✓ - 0.5387± 0.0129 0.5534± 0.0037 0.6716± 0.0037 0.7363± 0.0065 - ✓ 0.5367± 0.0100 0.5529± 0.0018 0.6770± 0.0054 0.7421± 0.0136 ✓ ✓ 0.5433± 0.0062 0.5592± 0.0071 0.6768± 0.0055 0.7434± 0.0139 Table 11: Ablation on the prediction matching target in Stage-3 loss with standard deviations. Results are reported as mean ± standard deviation over five independent runs. Pred-Match Target RAVDESS VGG-Sound A → V V → A A → V V → A Original branch ((t))(p^(t)) 0.8903± 0.0140 0.6201± 0.0788 0.5173± 0.0024 0.6171± 0.0079 Codebook branch ((t))(q^(t)) 0.9431± 0.0097 0.7486± 0.0231 0.5299± 0.0017 0.6229± 0.0059 Pred-Match Target CrisisMMD M-IMDB T → I I → T T → I I → T Original branch ((t))(p^(t)) 0.5425± 0.0081 0.5539± 0.0046 0.6654± 0.0158 0.7351± 0.0139 Codebook branch ((t))(q^(t)) 0.5433± 0.0062 0.5592± 0.0071 0.6768± 0.0055 0.7434± 0.0139 Table 12: Ablation study on code selection criteria with standard deviations. Results are reported as mean ± standard deviation over five independent runs. Selection Criteria RAVDESS VGG-Sound A → V V → A A → V V → A Random 0.9292± 0.0134 0.7396± 0.0214 0.5252± 0.0049 0.6211± 0.0051 Task relevance only 0.9396± 0.0063 0.7361± 0.0134 0.5276± 0.0055 0.6233± 0.0063 Student compatibility only 0.9375± 0.0078 0.7417± 0.0124 0.5275± 0.0077 0.6222± 0.0052 Combination (Ours) 0.9431± 0.0097 0.7486± 0.0231 0.5299± 0.0017 0.6229± 0.0059 Selection Criteria CrisisMMD M-IMDB T → I I → T T → I I → T Random 0.5353± 0.0076 0.5536± 0.0043 0.6718± 0.0135 0.7353± 0.0116 Task relevance only 0.5435± 0.0047 0.5558± 0.0072 0.6727± 0.0139 0.7351± 0.0104 Student compatibility only 0.5437± 0.0052 0.5565± 0.0058 0.6722± 0.0138 0.7346± 0.0103 Combination (Ours) 0.5433± 0.0062 0.5592± 0.0071 0.6768± 0.0055 0.7434± 0.0139 B.2 Statistical Significance Analysis Following the protocol of MST-Distill Li et al. (2025), the data split and the teacher checkpoint vary across seeds in our main experiments. Within each seed, all methods share the same data split and teacher checkpoint, ensuring a fair comparison under identical experimental conditions. While this protocol evaluates performance across diverse CMKD settings, the reported standard deviations include variability arising from the data split and the teacher model in addition to that arising from the distillation method itself. Controlled Significance Test. To isolate the effect of the distillation method, we conduct controlled experiments in which the data split and the teacher checkpoint are fixed and only the remaining training randomness is varied over ten runs. We compare our method with the strongest competing method in Table 1 using a two-sided paired t-test. As shown in Table 13, our method achieves statistically significant improvements (p<0.05p<0.05) in five of the eight transfer directions. Two additional settings, CrisisMMD I→ and M-IMDB T→ , show near-threshold evidence with p-values close to 0.05. In CrisisMMD T→ , MGDFR achieves a slightly higher mean, but the evidence for a reliable difference is limited, indicating that our method remains competitive in this setting. Average Rank Analysis. We further evaluate whether the performance gains remain consistent across variations in the data split under the original varying-split protocol. For each seed, we rank all methods evaluated with the same data split and teacher checkpoint, and then average the ranks over five seeds. As shown in Table 14, our method achieves the best average rank in seven of the eight transfer directions and the second-best average rank in CrisisMMD T→ . This indicates that the proposed method remains consistently competitive across changes in both the data split and the teacher checkpoint, rather than benefiting from only a few favorable runs. Significance of Loss Components. Under the same controlled setting, we examine whether the contribution of the “Code” term can be explained by run-to-run noise. As shown in Table 15, adding the “Code” term to “Pred-Match” improves the mean performance in all eight transfer directions. The improvement is statistically significant in four settings, with suggestive trends in two additional settings. “Pred-Match” is expected to produce a larger individual gain because it provides supervision more directly related to the task output, whereas the “Code” term regularizes the intermediate representation. Note that the target of “Pred-Match” is the codebook-induced teacher prediction (t)q^(t) rather than the original teacher prediction (t)p^(t). Both terms are therefore derived from the learned teacher codebook and provide complementary supervision at the representation and prediction levels. Significance of Code Selection Criterion. We further evaluate whether the proposed code selection criterion provides a reliable advantage over random code selection. As shown in Table 16, the combined criterion improves the mean performance in all eight transfer directions and achieves statistically significant improvements in seven of them. The remaining M-IMDB I→ setting also shows a positive trend (p=0.0659p=0.0659). This indicates that the proposed criterion identifies codes that are systematically more useful for cross-modal distillation than random selection. Table 13: Controlled significance tests against the runner-up methods for the classification results. The data split and the teacher checkpoint are fixed, and results are reported as mean ± standard deviation over ten runs. p-values are computed using a two-sided paired t-test. The runner-up is STXD for M-IMDB T→ and MGDFR for all other settings. Method RAVDESS VGG-Sound A → V V → A A → V V → A Runner-up 0.9271± 0.0080 0.7351± 0.0144 0.5219± 0.0046 0.6126± 0.0043 Ours 0.9420± 0.0071 0.7556± 0.0120 0.5273± 0.0041 0.6158± 0.0029 p-value 0.001 0.007 0.028 0.007 Method CrisisMMD M-IMDB T → I I → T T → I I → T Runner-up 0.5486± 0.0062 0.5550± 0.0034 0.6680± 0.0048 0.7443± 0.0057 Ours 0.5448± 0.0084 0.5581± 0.0019 0.6724± 0.0037 0.7482± 0.0051 p-value 0.105 0.060 0.055 0.046 Table 14: Average rank of classification methods across five runs with varying data splits and teacher checkpoints. Lower values indicate better performance, and the best average rank in each column is shown in bold. Method RAVDESS VGG-Sound CrisisMMD M-IMDB A → V V → A A → V V → A T → I I → T T → I I → T KLD 7.4 6.4 4.6 3.8 7.4 5.4 4.0 7.0 MLLD 4.8 7.2 4.4 5.8 8.6 5.0 5.8 6.4 FitNets 7.8 5.8 10.8 10.8 7.4 7.8 4.4 7.4 RKD 5.4 7.0 8.0 8.2 4.4 4.6 7.6 6.6 CRD 4.6 7.4 7.8 7.8 6.2 4.8 5.8 7.0 OFA 5.8 8.8 5.6 5.0 7.2 5.2 6.0 5.6 MGDFR 4.0 4.0 2.0 2.8 3.4 3.8 5.8 3.6 C2KD 4.4 6.6 4.8 4.2 5.2 7.6 8.0 3.6 STXD 10.2 3.8 7.8 7.8 5.0 9.8 4.6 8.8 FDD 7.0 5.8 9.0 8.0 6.4 7.2 8.4 6.4 Ours 2.4 2.0 1.0 1.4 3.8 3.4 4.0 2.0 Table 15: Controlled significance tests for the contribution of the “Code” term. The data split and the teacher checkpoint are fixed, and results are reported as mean ± standard deviation over ten runs. p-values are computed using a two-sided paired t-test. Code Pred-Match RAVDESS VGG-Sound A → V V → A A → V V → A - ✓ 0.9274± 0.0110 0.7469± 0.0060 0.5246± 0.0031 0.6129± 0.0031 ✓ ✓ 0.9420± 0.0071 0.7556± 0.0120 0.5273± 0.0041 0.6158± 0.0029 p-value 0.0031 0.0885 0.1215 0.0504 Code Pred-Match CrisisMMD M-IMDB T → I I → T T → I I → T - ✓ 0.5377± 0.0057 0.5518± 0.0081 0.6690± 0.0045 0.7448± 0.0028 ✓ ✓ 0.5448± 0.0084 0.5581± 0.0019 0.6724± 0.0037 0.7482± 0.0051 p-value 0.0223 0.0348 0.0116 0.1302 Table 16: Controlled significance tests for the code selection criterion. The data split and the teacher checkpoint are fixed, and results are reported as mean ± standard deviation over ten runs. p-values are computed using a two-sided paired t-test. Selection Criteria RAVDESS VGG-Sound A → V V → A A → V V → A Random 0.9316± 0.0100 0.7423± 0.0073 0.5242± 0.0029 0.6125± 0.0023 Combination (Ours) 0.9420± 0.0071 0.7556± 0.0120 0.5273± 0.0041 0.6158± 0.0029 p-value 0.0333 0.0205 0.0309 0.0287 Selection Criteria CrisisMMD M-IMDB T → I I → T T → I I → T Random 0.5339± 0.0074 0.5527± 0.0061 0.6668± 0.0043 0.7443± 0.0024 Combination (Ours) 0.5448± 0.0084 0.5581± 0.0019 0.6724± 0.0037 0.7482± 0.0051 p-value 0.0105 0.0147 0.0034 0.0659 B.3 Computational Cost Analysis We analyze the training cost of the proposed method on VGG-Sound in terms of end-to-end wall-clock training time, peak GPU memory usage, and floating-point operations (FLOPs). For FLOPs, we exclude the teacher and student backbone forward passes, which are largely shared across methods, and report only the additional scoring or alignment operations introduced by each method. As shown in Table 17, our method requires the longest wall-clock training time because of its three-stage training procedure. Other multi-stage or computationally intensive methods, such as CRD, FitNets, and MGDFR, also require substantially longer training time than the student trained without distillation. However, the peak memory usage and alignment-related FLOPs of our method are not consistently higher than those of the compared methods. For instance, our method requires less peak memory and fewer alignment-related FLOPs than MGDFR. The leave-one-code-out scoring in Stage-2 accounts for only 7.9% and 7.7% of the total training time for V→ and A→ , respectively, indicating that it is not the dominant computational cost under the default configuration. Effect of Codebook Size. Table 18 reports the stage-wise training time and accuracy under different codebook sizes B. The runtime of Stage-2 increases approximately linearly with B, whereas the runtimes of Stage-1 and Stage-3 remain nearly constant. Performance is generally robust to B, and an intermediate codebook size (B=512B=512, our default) provides the best trade-off between accuracy and computational cost. We also observe that code utilization decreases for oversized codebooks. With B=2048B=2048, more than 30% of the codes frequently remain unused, and B=1024B=1024 yields approximately 10-15% unused codes, whereas B≤512B≤ 512 generally maintains 99-100% code utilization. This suggests that excessively large codebooks increase the scoring cost while introducing redundant or underutilized codes without consistent performance gains. The code utilization measured in Stage-1 can therefore serve as a practical diagnostic for identifying unnecessarily large codebooks. Nevertheless, since the cost of Stage-2 scales linearly with B, it may become a bottleneck for substantially larger codebooks, and more efficient importance estimation remains a direction for future work. Inference Cost. All additional components, including the teacher, the codebook, the projection layers, and the codebook branches, as well as the Stage-2 scoring procedure, are used only during training. At inference time, they are entirely removed, and only the original student encoder and task head are retained. Therefore, the proposed method introduces no additional parameters, memory, or computation at inference compared with the student trained without distillation, and the teacher modality is not required at deployment. Table 17: Training computational costs on VGG-Sound. Time and Mem denote the end-to-end wall-clock training time (s) and peak GPU memory usage (MB), respectively. TFLOPs are measured only for the method-specific scoring and alignment operations, excluding the teacher and student forward passes that are largely shared across methods. ↪ Stage-2 denotes the cost of the leave-one-code-out scoring in our method. Method V → A A → V Time Mem TFLOPs Time Mem TFLOPs w/o KD 82.69 25.40 – 168.44 77.25 – KLD 172.95 76.29 0.62 176.04 80.34 0.62 MSE 171.78 76.35 0.62 165.68 80.40 0.62 CRD 325.45 88.22 0.63 324.03 94.71 0.63 FitNets 338.17 78.26 1.24 339.19 83.05 1.24 MGDFR 327.07 178.07 76.81 316.99 177.95 784.21 Ours 458.85 122.86 31.56 452.29 103.65 148.21 ↪ Stage-2 36.24 95.69 31.56 34.87 93.18 148.21 Table 18: Stage-wise training time (s) and accuracy under different codebook sizes B on VGG-Sound. Accuracy is averaged over five independent runs. Our default setting is B=512B=512. B V → A A → V Stage-1 Stage-2 Stage-3 Acc. Stage-1 Stage-2 Stage-3 Acc. 128 231.53 10.48 182.34 0.6202 224.55 10.56 179.26 0.5270 256 228.37 18.54 190.97 0.6213 225.65 18.65 193.02 0.5272 512 226.81 36.24 195.80 0.6229 225.70 34.87 191.72 0.5299 1024 226.90 79.93 191.29 0.6201 224.92 68.62 190.45 0.5283 2048 228.29 184.83 202.42 0.6205 221.61 131.78 199.46 0.5262 B.4 Discussion on the Code Retention Ratio The proposed method retains a fixed ratio of teacher codes for student-side quantization, which is set to 50% for all classification experiments and 12.5% for all segmentation experiments. These values were coarsely chosen from a small set of candidate values and then fixed across all settings of each task to avoid extensive scenario-specific tuning. They should therefore be regarded as practical default operating points rather than individually optimized settings. Fig. 3 shows that the best ratio varies across datasets and transfer directions, indicating that the appropriate amount of retained teacher-side information depends on the distillation scenario. A smaller ratio may discard useful teacher-side information, whereas a larger ratio may include codes that are less relevant to the task or less compatible with the student modality. Nevertheless, performance remains relatively stable over a broad range of ratios and generally exceeds the w/o KD baseline. This indicates that the effectiveness of the proposed method does not depend on a single carefully tuned ratio. Although the fixed ratio provides consistent improvements, it does not adapt to the varying amount of transferable information across cross-modal scenarios. Adaptive code retention, which automatically determines the number of retained codes for each scenario, is therefore a promising direction for future work. B.5 Class-wise Analysis on NYU-Depth V2 As shown in Table 2, the OA of our method in the RGB→ setting is slightly lower than that of the student trained without distillation (0.5218 vs. 0.5269). To examine whether this decrease reflects negative transfer, we analyze the class-wise recall difference between our method and the student trained without distillation. Table 19 reports the five classes with the largest recall increases and decreases. The analysis shows that the decrease in OA is strongly influenced by class imbalance rather than by a general degradation across classes. The recall of wall decreases by 0.0274, and since this class occupies 25.6% of all pixels, this change substantially affects the pixel-weighted OA. In contrast, several less frequent classes, including other_furniture, mirror, television, desk, and curtain, show much larger recall improvements of 0.13-0.18, although their contributions to OA are limited by their low pixel frequencies. Accordingly, CA, which assigns equal importance to each class, improves from 0.2100 to 0.2184 despite the slight decrease in OA, and mIoU also improves from 0.1366 to 0.1456. These results indicate that the proposed method improves class-balanced performance, and that the OA decrease reflects a class-specific trade-off rather than systematic negative transfer across classes. The gains on several less frequent classes are also consistent with the benefit of complementary semantic cues provided by the RGB teacher. Table 19: Class-wise recall analysis on NYU-Depth V2 in the RGB→ setting. Freq. denotes the percentage of pixels belonging to each class, and Δ denotes the recall difference between our method and the student trained without distillation. Top-5 increased classes Top-5 decreased classes Class Freq. Δ Class Freq. Δ other_furniture 2.7% +0.1807 person 0.3% −-0.1298 mirror 1.2% +0.1519 counter 1.7% −-0.0478 television 0.7% +0.1324 bookshelf 2.1% −-0.0398 desk 0.8% +0.1315 clothes 0.8% −-0.0294 curtain 1.8% +0.1311 wall 25.6% −-0.0274 B.6 Hard and Soft Code Assignment We use a discrete codebook because it provides an explicit and structure-independent concept interface between heterogeneous teacher and student features. Mapping each feature unit to a finite set of codes allows us to evaluate the contribution of individual concepts, rank them, and retain only the transferable subset. Such code-level selection is less directly defined when each feature is represented by an unrestricted continuous mixture of anchors. To examine whether hard assignment to the selected codes is necessary during transfer, we replace the nearest-code assignment in Stage-3 with a soft assignment over the same learned and selected codes. Specifically, each student unit is represented by a similarity-weighted combination of the selected codes rather than by its single nearest code. As shown in Table 20, the two variants achieve comparable performance, with hard assignment yielding slightly higher mean accuracy in both transfer directions. This result shows that the selected codes remain effective under soft assignment, while hard assignment is already sufficient in the current setting. B.7 Code Reuse Across Student Units The proposed method does not enforce an exclusive one-to-one correspondence between student units and teacher codes. Multiple student units can be assigned to the same code, allowing a concept to be represented across several temporal or spatial locations. To quantify this behavior, we measure the proportion of activated codes that are assigned to more than one student unit over the VGG-Sound test set. We observe that 94.48% and 97.47% of the activated codes are reused by multiple student units for A→ and V→ , respectively. This indicates that code usage is predominantly many-units-to-one-code rather than one-unit-to-one-code. Although code assignment is performed independently for each student unit, the quantized student units retain their temporal or spatial organization and are subsequently processed jointly by the codebook-branch head. The head can therefore exploit the positions, repetition patterns, and overall arrangement of the assigned codes, which allows concepts distributed across multiple student units to be captured. However, the current assignment does not explicitly model such distributed concepts before quantization. Extending the framework to model concepts spanning multiple student units more explicitly is an interesting direction for future work. Table 20: Comparison of hard and soft code assignment in Stage-3 on VGG-Sound. Results are reported as mean ± standard deviation over five independent runs. Assignment A → V V → A Hard 0.5299± 0.0017 0.6229± 0.0059 Soft 0.5254± 0.0024 0.6208± 0.0082 B.8 Qualitative Analysis of Learned Codes Figs. 4(a) and 4(b) provide qualitative examples of the learned codes on CrisisMMD and M-IMDB, respectively. We consider image-teacher distillation settings and visualize selected image-teacher codes together with high-weight tokens from the distilled text student. For each selected code, we show its associated image regions and the corresponding token weights from the text student. In the CrisisMMD example, the sample belongs to the infrastructure_and_utility_damage class. The selected image-teacher codes are associated with regions around damaged door or gate structures. On the text side, the distilled student assigns relatively high weights to related textual contexts, including tokens such as damage, doors, gates, and DOOR. In the M-IMDB example, the sample belongs to the Drama class. The selected codes attend to visually salient regions in the movie poster, while the text student places relatively high weights on narrative phrases related to dramatic content, such as tragedy, methods, prepared the groundwork, downfall, and English throne. These examples suggest that the learned codes can be associated with semantically related visual and textual cues, providing qualitative support for code-based cross-modal transfer. (a) CrisisMMD (b) M-IMDB Figure 4: Qualitative analysis of learned codes. For each selected image-teacher code, the pair shows its associated image region and corresponding high-weight tokens from the distilled text student. Appendix C Pseudo Algorithm of The Proposed Framework Algorithm 1 Codebook-Guided Cross-Modal Knowledge Distillation 1: Paired data (i(t),i(s),i)i=1N\(x_i^(t),x_i^(s),y_i)\_i=1^N, pretrained teacher f(t)(⋅,θ∗(t)),g(t)(⋅,ϕ∗(t))\f^(t)(·;θ^*(t)),g^(t)(·;φ^*(t))\, student f(s)(⋅,θ(s)),g(s)(⋅,ϕ(s))\f^(s)(·;θ^(s)),g^(s)(·;φ^(s))\, codebook size B, number of selected codes K, code dimension D. 2: Trained student parameter θ(s),ϕ(s)θ^(s),φ^(s) 3: Stage-1: Teacher-side codebook learning 4: Freeze the pretrained teacher parameters θ∗(t),ϕ∗(t)θ^*(t),φ^*(t). 5: Initialize codebook ∈ℝB×DC ^B× D, projections Πin(t),Πout(t) _ in^(t), _ out^(t), and codebook branch head gcp(t)(⋅,ϕcp(t))g_ cp^(t)(·; _ cp^(t)). 6: for each training iteration do 7: for i=1i=1 to N do 8: Extract teacher features i(t)=f(t)(i(t),θ∗(t))z_i^(t)=f^(t)(x_i^(t);θ^*(t)). 9: Quantize teacher features with C and compute codebook-induced prediction i(t)q_i^(t). 10: Compute student prediction i(s)p_i^(s). 11: end for 12: Compute loss according to Eq. 6. 13: Update ,Πin(t),Πout(t),ϕcp(t),θ(s),ϕ(s)C, _ in^(t), _ out^(t), _ cp^(t),θ^(s),φ^(s). 14: end for 15: Stage-2: Code-wise importance estimation 16: for each code k∈1,…,Bk∈\1,…,B\ do 17: Remove the k-th code to construct −kC_-k. 18: Compute leave-one-code-out teacher prediction ¯i(t) q_i^(t). 19: Compute full codebook teacher prediction i(t)q_i^(t). 20: Compute student prediction i(s)p_i^(s). 21: Estimate task relevance ukrelu_k rel and student compatibility ukcompu_k comp according to Eq. 8. 22: Compute final importance score uk=ukrel+ukcompu_k=u_k rel+u_k comp. 23: end for 24: Select the top-K codes according to ukk=1B\u_k\_k=1^B and form selC_ sel. 25: Stage-3: Selective codebook-based distillation 26: Initialize student-side projections Πin(s),Πout(s) _ in^(s), _ out^(s) and student-side codebook branch head gcp(s)(⋅,ϕcp(s))g_ cp^(s)(·; _ cp^(s)). 27: Re-initialize student model parameters θ(s),ϕ(s)θ^(s),φ^(s). 28: Fix the selected teacher codebook selC_ sel. 29: for each training iteration do 30: for i=1i=1 to N do 31: Extract student features i(s)=f(s)(i(s),θ(s))z_i^(s)=f^(s)(x_i^(s);θ^(s)). 32: Quantize student features with selC_ sel and compute student-side codebook-induced prediction i(s)q_i^(s). 33: Compute teacher-side codebook-induced prediction i(t)q_i^(t). 34: Compute student task prediction i(s)p_i^(s). 35: end for 36: Compute loss according to Eq. 12. 37: Update the student model parameters θ(s),ϕ(s)θ^(s),φ^(s). 38: end for 39: return Trained student parameter θ(s),ϕ(s),Πin(s),Πout(s),ϕcp(s)θ^(s),φ^(s), _ in^(s), _ out^(s), _ cp^(s). Algorithm 1 provides the pseudo-code of the proposed framework. The procedure consists of three stages, corresponding to the method description in Sec. 3: teacher-side codebook learning, code-wise importance estimation, and selective codebook-based distillation. Although the pseudo-code is written at the dataset level for clarity, all optimization steps are implemented with mini-batch training. Appendix D Broader Impact This work studies a general cross-modal knowledge distillation framework and is not tied to a specific deployment scenario. A potential positive impact is that the method may improve efficient model learning by transferring useful knowledge from auxiliary modalities to compact or single-modality students. However, as with other distillation methods, the student may inherit biases, spurious correlations, or undesirable behavior from the teacher model and training data. Therefore, deployment in sensitive applications should require careful evaluation of fairness, privacy, and robustness under the target use case.