HIDISC: A Hyperbolic Framework for Domain Generalization with Generalized Category Discovery

Reviewer Concern: Why does the hyperbolic adaptation of DGCD-Net lead to decreased overall performance compared to the original DG²CD-Net?

Rebuttal:
We appreciate the reviewer’s observation. While hyperbolic geometry is beneficial for semantic modeling, a naive substitution of the embedding space is insufficient. Below, we explain the performance drop in Hyp-DG²CD-Net relative to the original DG²CD-Net:

• (1) Task Vector Arithmetic Mismatch: DG²CD-Net performs episodic training and aggregates task vectors via Euclidean averaging. In hyperbolic space, arithmetic operations (e.g., vector addition) do not preserve associativity or commutativity, leading to distortion when such operations are naively retained. The adapted Hyp-DG²CD-Net preserves these Euclidean components, which conflict with the curved geometry.

• (2) Episodic Prototype Drift: Synthetic novel classes introduced episodically may cause representation drift. In hyperbolic space, repeated feature injection without curvature-aware constraints can result in embeddings accumulating near the boundary, degrading class separability and inducing overconfidence.

• (3) Lack of Geometry-Aware Losses: Hyp-DG²CD-Net reuses the original DG²CD-Net's loss functions, which were not designed to operate on hyperbolic manifolds. In contrast, HIDISC leverages curvature-aligned supervision via Busemann loss, geodesic-aware contrastive regularization, and adaptive outlier repulsion. The absence of these elements in Hyp-DG²CD-Net limits its effectiveness.

• (4) Empirical Evidence: As shown in Table 1, Hyp-DG²CD-Net performs worse than both DG²CD-Net and our proposed HIDISC across all benchmarks. This highlights the importance of full-stack geometric alignment—not merely embedding substitution—for successful adaptation to hyperbolic space.

We will clarify this in the final version and emphasize that hyperbolic adaptation must be end-to-end, not just at the representation level.

Reviewer Concern: In Sup. Tab. 7, why does more known classes (50–15 vs. 40–25) drop Old accuracy by ~1%?

This drop arises from two interacting effects:

• Boundary crowding: Adding more “Old” classes packs additional prototypes near the Poincaré boundary, slightly increasing overlap and confusion among old categories. However, this boundary density actually benefits discovery of “New” classes—by pushing unfamiliar samples more decisively toward the interior—resulting in the observed tradeoff (Old ↓, New ↑).

• Per-class sample dilution: Under a fixed data budget, increasing the number of known classes means fewer samples per class. This mildly raises per-class variance, which may contribute to the slight drop in Old accuracy.

We will clarify these effects in the Supplement Sec 6.4.

Reviewer Concern: Wall-clock cost of GPT-based generation.

The image synthesis process (via InstructPix2Pix + GPT-guided prompts) is performed once offline and does not affect model training or inference. On our setup using an NVIDIA A100 GPU, image generation averaged 1-2 seconds per image.

To support reproducibility and reduce compute barriers, we commit to publicly releasing the entire set of synthetic images—so future work can reuse our domain expansions without needing to regenerate them.

Reviewer Concern: If source domains ↑ and target domains ↓, does HiDISC still hold its lead?

Response:
Yes, HiDISC remains robust and effective even as the number of target domains decreases. Because our training paradigm is source-only and domain-agnostic, HiDISC inherently generalizes well to shifts in the source-to-target distribution. To thoroughly validate this, we conduct a controlled ablation study where we systematically vary the number of source and target domains while keeping the total image budget fixed. For each setting, the remaining domains are treated as target domains, and we report the average performance over all possible target domain combinations.

The results, shown in the table below, demonstrate that HiDISC consistently holds or exceeds the performance of the baseline DG$^2$CD-Net across all scenarios. We will include a detailed comparison and additional analysis in the Supplementary material.

Addressing the weaknesses mentioned by the reviewer:

We thank the reviewer for highlighting these points

W-1 We thank the reviewer and respectfully clarify that HiDISC is not a minor extension of prior hyperbolic methods, but introduces key innovations tailored to the unique challenges of Domain Generalized Generalized Category Discovery (DG-GCD)—a setting unaddressed by HypCD or HyProMeta.

Novel Task Scope: HiDISC is the first hyperbolic method for DG-GCD, which simultaneously addresses open-set recognition, domain generalization, and label shift without access to target domains. In contrast, prior works handle only subsets of these challenges in isolation.

Architectural Contributions: HiDISC introduces (i) Tangent CutMix, a geometry-aware augmentation strategy in hyperbolic space, (ii) a hybrid contrastive loss that fuses angular and geodesic similarities, (iii) penalized Busemann regularization to prevent radial saturation and overconfidence, and (iv) an adaptive outlier repulsion loss that pushes pseudo-novel samples away from known prototypes.

Empirical Strength: HiDISC significantly outperforms both Euclidean and prior hyperbolic baselines. For instance, HPDR achieves 15.05% overall accuracy, while HiDISC achieves 56.78% on the same benchmark—demonstrating its superior generalization under the DG-GCD setting.

We will revise the manuscript to emphasize these distinctions more clearly and cite all relevant prior works.

W-2 We conducted a comprehensive ablation over all key knobs—curvature c, slope ϕ, radius before mapping, contrastive weight α_d, and loss‐term weights (λ₁, λ₂, λ₃) on the OfficeHome dataset—and found that only the penalized‑Busemann slope and mapping radius materially affect results, with robust defaults (ϕ = 0.75, radius = 1.5) generalizing across benchmarks. For the remaining loss weights, setting (λ₁, λ₂, λ₃) = (0.60, 0.25, 0.15) balances our alignment, contrastive, and outlier terms and yields 56.78% overall accuracy (59.23% old, 53.21% new). Swapping to (0.15, 0.60, 0.25) or (0.25, 0.15, 0.60) only reduces overall accuracy to 52.12% and 51.37%, respectively—drops of ~4–5 points—demonstrating that our defaults achieve near‑optimal performance without exhaustive tuning.

W-3 GPT-4o is used exclusively to generate text prompts, while the InstructPix2Pix diffusion model synthesizes images—mirroring the DG$^2$CD-Net (CVPR ’25) baseline and original DG-GCD setup. This separation ensures augmentations leverage InstructPix2Pix’s strengths rather than GPT’s priors.

Though GPT-guided diffusion relies on pretrained generative priors and doesn’t sample uniformly over the domain space, uniform coverage is neither well-defined nor necessary for effective DG-GCD generalization. Our justification:

• Task-Aware Domain Coverage: Let $\mathcal{D} \subset \mathcal{X}$ be the latent domain manifold. Uniform sampling $P(x) \sim \mathcal{U}(\mathcal{D})$ is intractable in high-dimensional spaces. Instead, we use a conditional distribution $P_G(x|t)$ from prompts $t$ semantically aligned with domain shifts, producing diverse, task-relevant perturbations that increase domain discrepancy (Eq. 1).

• Empirical Diminishing Returns: Fig. 3 (right) shows that adding more synthetic domains yields diminishing returns. The generative loss $\mathcal{L}_{\text{gen}}$ satisfies

  $$\frac{\partial^2 \mathcal{L}_{\text{gen}}}{\partial N^2} > 0 \quad \text{for } N > 2,$$

  indicating potential overfitting and validating our selective augmentation strategy.

• Hyperbolic Geometry Benefits: Key gains arise from hyperbolic learning. Without synthetic domains, HiDISC attains 56.07% on OfficeHome, outperforming Euclidean and augmented baselines. As per Sec. 3.4,

  $$\Delta_{\mathbb{H}} \leq \Delta_{\mathbb{E}},$$

  implying fewer samples suffice under hyperbolic curvature.

In sum, our GPT-guided augmentation introduces diverse yet semantically structured domain shifts, and combined with a geometry-aware learning framework, achieves strong generalization without uniform domain sampling. We will expand this in the revised paper.

We thank the reviewer for highlighting these points

Reviewer Concern: Does Tangent CutMix truly preserve hyperbolic consistency? Linear interpolation in the tangent space (Eq. (2)) might not guarantee valid hyperbolic embeddings after reprojection. Were there cases where synthetic samples violated geometric constraints?

Rebuttal:
We appreciate the reviewer’s insightful concern regarding the geometric validity of Tangent CutMix under the Poincaré ball model of hyperbolic space. We clarify below with precise mathematical justification.

Let $\mathbb{D}^d_c = { z \in \mathbb{R}^d : |z| < 1/\sqrt{c} }$ denote the $d$-dimensional Poincaré ball with curvature $-c$. Given two hyperbolic embeddings $z_i, z_j \in \mathbb{D}^d_c$, we first map them to the tangent space at the origin $T_0 \mathbb{D}^d_c \cong \mathbb{R}^d$ using the logarithmic map (see Sec. 3.3.3):

This results in $v_i, v_j \in \mathbb{R}^d$, ensuring they lie in a flat Euclidean space where linear interpolation is valid.

Tangent CutMix proceeds by linearly interpolating these vectors:

We then project the mixed vector back to the hyperbolic manifold via the exponential map:

Since $\tanh(x) < 1$ for all $x > 0$, it follows that $\|z_{\text{mix}}\| < 1/\sqrt{c}$, and thus $z_{\text{mix}} \in \mathbb{D}^d_c$. Therefore, Tangent CutMix guarantees that the interpolated sample remains a valid hyperbolic embedding.

In addition to geometric correctness, we also regularize the embeddings using the penalized Busemann loss (Eq. (4)), which includes a term $\log(1 - \|z\|^2)$ that discourages embeddings from drifting too close to the boundary, thereby maintaining numerical stability and preventing degeneracy.

Empirically, we observed no violation of hyperbolic constraints throughout training. Moreover, substituting Tangent CutMix with Euclidean CutMix led to a significant performance drop (-3.96% on Office-Home; Table 4), further confirming that preserving hyperbolic consistency is essential for effective generalization.

We hope this mathematical clarification addresses the reviewer’s concern. We will incorporate this discussion into the final version to improve clarity.

Reviewer Concern: The claim that hyperbolic geometry’s “exponential capacity” reduces the need for augmentation (Sec. 3.3.1) is not intuitive. Is there theoretical or empirical support for this?

Rebuttal:
We thank the reviewer for raising this important question. The statement is supported both by geometric theory and by ablation studies provided in the paper.

• (1) Theoretical Justification:
  In hyperbolic space with curvature $-c$, the volume of a ball grows exponentially with radius, i.e., $V_{\text{Hyp}}(r) \sim \exp(\sqrt{c}r)$, unlike the polynomial growth $V_{\text{Euc}}(r) \sim r^d$ in Euclidean space. This exponential growth yields greater representational capacity for semantic separation, requiring fewer samples to cover the space with minimal distortion. As a result, even sparse or low-coverage augmentations are sufficient to populate the embedding space for robust generalization.

• (2) Empirical Evidence:
  As shown in Table 4, training without any synthetic domains still achieves 56.07% accuracy on Office-Home—surpassing several Euclidean and hyperbolic baselines that use 6–9 augmentations. Adding only 1–2 GPT-guided augmentations leads to further gains (56.78%), while additional domains degrade novel-class performance due to overfitting (see Fig. 3, right). This empirically supports that hyperbolic embeddings generalize better with fewer but diverse augmentations.

• (3) Generalization Bound (Sec. 3.4):
  Equation (9) presents a Rademacher-based generalization bound in hyperbolic space, where the hyperbolic discrepancy term $\Delta_{\mathbb{H}}(S', T)$ is provably tighter than its Euclidean counterpart $\Delta_{\mathbb{E}}(S', T)$ under identical augmentation budgets. This supports the theoretical claim that fewer augmentations are needed to approximate the target domain’s support in hyperbolic geometry.

We will revise the final paper to explicitly highlight this geometric intuition and cite formal results from hyperbolic geometry and volume theory.

Reviewer’s concern: The dataset for Table 5 is unspecified.
Response:
Thank you for pointing this out. We will revise both the caption and the corresponding reference in the main text to explicitly state that Table 5 reports results on the OfficeHome dataset. While this is consistent with Tables 3 and 4, we agree that it should be clearly indicated to avoid ambiguity and ensure clarity for the reader.

Reviewer Concern: Why choose the Poincaré ball over alternatives like the Lorentz model? Prior work (e.g., Hyperbolic ViTs) suggests Lorentz may offer better stability—was this considered?

Rebuttal:
Thank you for the insightful question. We chose the Poincaré ball model over the Lorentz model based on its compatibility with our core design elements, both mathematically and empirically.

• Tangent CutMix and Closed-Form Mappings:
  Our Tangent CutMix strategy (Sec. 3.3.3) relies on linear interpolation in the tangent space and exponential/logarithmic maps. The Poincaré model offers closed-form, numerically stable expressions for these operations. In contrast, the Lorentz model requires projection onto the hyperboloid and normalization constraints, increasing implementation complexity.

• Conformal Geometry for Contrastive Learning:
  The Poincaré ball is conformal (angle-preserving), which makes cosine similarity in the tangent space well-defined and compatible with the angular term in our hybrid contrastive loss (Eq. 6). This is crucial for combining local angular coherence and global geodesic structure.

• Empirical Stability:
  While we did an experiment with a Lorentzian version early on, we encountered unstable gradients and poorer convergence when optimizing Busemann-aligned or contrastive losses. The optimization constraints (e.g., maintaining Minkowski norm) in Lorentz space were harder to manage under our regularization and sampling framework.

• Visualization and Interpretability:
  The Poincaré disk allows intuitive and bounded 2D visualization (e.g., Fig. 4), which is preferable for cluster analysis and qualitative evaluations in DG-GCD.

While Lorentz models (e.g., Hyperbolic ViTs) have benefits in certain contexts, the Poincaré ball aligned better with our goals of closed-form interpolation, angular reasoning, and geometric interpretability. We will include this justification and relevant citations in the final version.

Below, we present a comparison between the Lorentz model and the Poincaré ball using the OfficeHome dataset:

As evident from the table, the Poincaré ball outperforms the Lorentz model across all splits in our DG-GCD setting.

Addressing the weaknesses mentioned by the reviewer:

W1 As noted in Line 327 of the main paper, we acknowledge the potential risks of using diffusion-based augmentations, particularly for safety-critical applications, and plan to explore mitigation strategies in future work.

W2 We appreciate the concern about hyperparameter complexity. In fact, we conducted a comprehensive ablation over all key knobs—curvature c, slope ϕ, radius before mapping, contrastive weight α_d, and loss‐term weights (λ₁, λ₂, λ₃) on the OfficeHome dataset —and found that only the penalized‑Busemann slope and mapping radius materially affect results, with robust defaults (ϕ = 0.75, radius = 1.5) generalizing across benchmarks. For the remaining loss weights, setting (λ₁, λ₂, λ₃) = (0.60, 0.25, 0.15) balances our alignment, contrastive, and outlier terms and yields 56.78% overall accuracy (59.23% old, 53.21% new). Swapping to (0.15, 0.60, 0.25) or (0.25, 0.15, 0.60) only reduces overall accuracy to 52.12% and 51.37%, respectively—drops of ~4–5 points—demonstrating that our defaults achieve near‑optimal performance without exhaustive tuning.

Ablation Study: Overconfidence Regularizers

To rigorously evaluate the effectiveness of our proposed Penalized Busemann Loss (Eq. 4), we perform a controlled ablation comparing it against three widely used overconfidence mitigation strategies. Each variant substitutes only the penalty term in the Busemann component of the HiDISC loss while keeping all other elements identical. This isolates the contribution of the regularizer in controlling overconfident or radially saturated embeddings in hyperbolic space.

Alternative Regularizers Considered

• Penalized Busemann Loss (HiDISC)

  $$\mathcal{L}_{\mathrm{Buse}} = \log\Bigl(\tfrac{\|z - p\|^2}{1 - c\|z\|^2 + \epsilon}\Bigr) + \phi\log\bigl(1 - \|z\|^2\bigr).$$

  This term penalizes radial overconfidence while maintaining geometric consistency in the Poincaré ball.

• Entropy Regularization

  We replace the penalty term in Eqn. 4 with the following term:
  $\mathcal{L}_{\mathrm{Ent}} = -\sum_i p_i \log p_i$, where $p = \mathrm{softmax}(-d(z, (p_k)))$.

  Encourages high‐entropy (uncertain) predictions.

• Confidence Penalty (KL to Uniform)

where $$p = \mathrm{softmax}(-d)$.$

Penalizes confident deviation from a uniform prior.

Logit Margin Penalty

Loss is : $\mathcal{L}_{\mathrm{Margin}} = \max(0, S)$,

where $S = s_{\mathrm{y}} - s_{\mathrm{2nd}} - \delta$ , $s = -d(z, (p_k))$ and $\delta = 0.5$.

Enforces separation between the top‐1 and runner‐up logits.

Experimental Protocol

All settings were kept constant across variants:

• Backbone: ViT‑DINO with learned hyperbolic curvature
• Head: identical projection layers, no auxiliary classifier
• Training: same optimizer, learning rate, batch size, epochs
• Loss weights: $\{0.60,\,0.25,\,0.15\}$ for (regularizer, contrastive, outlier)
• Logits: negative hyperbolic distances to prototypes

Results and Discussion

As shown, our Penalized Busemann Loss yields the best trade‑off, especially on novel‐class discovery, while KL and margin penalties tend to over‐penalize valid novel assignments and entropy struggles under domain shift.

Geometric Motivation & Theoretical Properties

1. Busemann‐based Penalty Aligns with Hyperbolic Geometry.
   The Busemann function

   $$B_p(z) = \log\\frac{\|z - p\|^2}{1 - c\|z\|^2}$$

   measures signed distance to the horosphere at prototype $p$. Penalizing $B_p(z)$

   • aligns with true geodesic bisectors,
   • adapts to curvature $c$ via the denominator,
   • yields uniform radial repulsion without directional bias.

2. Theoretical Properties.

   • Isometry‐invariance: horosphere distances are invariant under hyperbolic isometries.
   • Convexity in Busemann coordinates: reparametrizing $u = B_p(z)$ makes the penalty convex, aiding optimization.

• Unified geometric form:

Unlike Euclidean entropy or margin penalties, our loss is intrinsically hyperbolic, principled by geometry, and thus more effective at controlling overconfidence in Poincaré embeddings.

We thank the reviewer for their thoughtful and constructive feedback. Below we address all concerns point-by-point, with supporting theoretical and empirical justifications.

1. Reproducibility and Missing Code

Concern: No code provided; concerns about reproducibility.

Response:
As noted in the footnote of Page 1 (main paper), we will release the full codebase upon paper acceptance. Implementation details are already provided in:

• Main Paper Sec. 4: Training, datasets, optimization details.
• Supplement Sec. 8.2: Hyperparameters, data splits, batch sizes.
• Supplement (Pseudocode): Full pipeline breakdown.

The released repository will include config files, fixed seeds, scripts to regenerate tables/figures, and domain generation prompts. If permitted, we are willing to share an anonymized code link with the AC during review.

2. Fairness of Comparison with DG²CD-Net

Concern: DG²CD-Net is not public; how can comparisons be fair?

Response:
We received DG²CD-Net code directly from its authors for academic benchmarking (acknowledged below Table 1 (main paper)). All experiments follow:

• Identical datasets, splits, and evaluation protocols.
• Matched environment and seeds.
• Hyperparameters and loss settings from the original config.

Supplement Sec. 8.1 details our setup for reproducing DG²CD-Net and its hyperbolic variant.

3. Novelty vs. Prior Hyperbolic Works [A–G]

Concern: HiDISC appears to combine existing methods—what's new?

Response:
We appreciate the reviewer’s feedback and clarify the novelty of HiDISC in relation to prior hyperbolic contrastive learning and prototype anchoring works:

• [A] Ge et al. (CVPR 2023) focus on hierarchical scene-object representation with hyperbolic contrastive learning, while HiDISC targets Domain Generalization with Generalized Category Discovery (DG-GCD), jointly handling domain shifts and novel category discovery without target data.

• [B] Yue et al. (WACV 2024) provide theoretical insights on hyperbolic metric learning and hard negative mining. In contrast, HiDISC integrates these into a prototype anchoring framework with penalized Busemann loss and adaptive outlier repulsion for open-set domain generalization.

• [C] Liu et al. (IEEE TAFFC) apply hyperbolic contrastive learning to EEG data, differing fundamentally from our visual DG-GCD setting involving unseen domains and categories.

• [D] Sun & Ma (ECML 2024) and [E] Rongali et al. (CIKM 2024) address recommendation systems with model-level augmentations, whereas HiDISC introduces geometry-aware synthetic domain augmentation and Tangent CutMix tailored for visual DG-GCD.

• [F] Choi et al. (IEEE TIP 2024) explore hierarchical self-supervised hashing, while HiDISC offers a supervised framework explicitly addressing domain and category shifts via unified loss and prototype anchoring.

• [G] Hu et al. (CVPR 2024) focus on generalizable face anti-spoofing with hierarchical prototypes. HiDISC instead targets open-world visual recognition with simultaneous domain and category generalization, incorporating Tangent CutMix for pseudo-novel sample synthesis.

Key innovations of HiDISC include a unified hyperbolic framework for DG-GCD, penalized Busemann prototype anchoring that reserves space for unknown categories, curvature-aware tangent space augmentation for pseudo-novel samples, and lightweight synthetic domain augmentation via GPT-guided style transfer.

4. Citation and Comparison with Hu et al. (CVPR 2024)

Concern: Hu et al. also uses hyperbolic prototypes—why not cited/compared?

Response:
We thank the reviewer and will cite Hu et al. (CVPR 2024) in the revised version. Hu et al. (CVPR 2024) address domain generalization for face anti-spoofing—a binary classification task—by leveraging hyperbolic prototypes to enhance robustness across visual domains. While their work employs hyperbolic embeddings for domain robustness, it does not address the open-set or generalized category discovery (GCD) setting. In contrast, our work targets the DG-GCD task, which is fundamentally more challenging and general: it requires discovering novel categories in an unseen domain at test time without access to any unlabeled target data during training.

To further ground this distinction empirically, we re-implemented the embedding learning component of Hu et al. within our DG-GCD framework. As shown in the table below, their method (denoted HPDR) performs significantly worse than our approach (HiDISC) on the Office-Home benchmark.

Explanation of performance gap:

• Closed‑set binary vs. open‑set multi‑class discovery. HPDR is trained to separate two classes (live vs. spoof) using hyperbolic prototypes, with no mechanism to create or refine prototypes for unseen classes in an unseen domain.

• Lack of clustering/discovery losses. HPDR optimizes a closed‑set classification loss and distribution‑refinement regularizer but does not encourage cluster‑friendly embeddings for novel classes. Simply clustering HPDR’s embeddings yields near‑random groupings among new classes, explaining the low “New” accuracy.

• Domain shift without adaptation. HPDR generalizes across source spoof examples but never sees or models target‑domain distributions of new categories. In contrast, HiDISC integrates domain‑generalization regularizers with discovery losses to align source and unseen‑domain distributions while structuring novel‑class geometry.

5. Experimental Analysis Requests

Concern: Please compare HiDISC vs. HiDISC-Euc, show t-SNEs, analyze prototypes, and clarify Fig/Table.

Response:

We appreciate these suggestions and will include the following in the revision:

• Euclidean vs. Hyperbolic (HiDISC-Euc vs. HiDISC):
  We already evaluated Euclidean analogues of our modules (Supp. Sec. 6.2, Table 8). We will move the core comparison into the main text, e.g.:

• t-SNE visualizations:
  We have generated side-by-side t-SNE plots comparing embedding spaces from HiDISC-Euc and HiDISC, which show qualitatively improved cluster separation under hyperbolic geometry. While we cannot include these visualizations here due to conference policy, they will be included in the revised Supplementary Material (Sec. 6.2) and final paper upon acceptance.

• Prototype count analysis:
  We ablated the number of prototypes per class $($P \in {1, 2, 4}$)$ on Office-Home. Results:

Performance peaks at $P=1$, suggesting one discriminative prototype per class suffices in hyperbolic space. Larger values sometimes hurt generalization, possibly due to overfitting or redundancy. This will be discussed in the Supplement.

• Clarification:
  "Vanilla" in Table 3 = no proposed losses, Euclidean ViT.
  Fig. 4 distortion arises from UMAP projection; radial tree-like hierarchy is preserved in native Poincaré space but appears flattened due to 2D projection.

6. Theoretical Justification

In Supplement Table 11, we compare generalization gap $\Delta$:

• PACS: +73% gain with hyperbolic head
• Office-Home: +215%
• DomainNet: +243%

We also show (Sec. 3.4 main paper, Sec. 6 Supplement) that for hierarchical data:

where $N$ = number of classes, $K$ = prototypes, $d$ = latent dimension. This favors hyperbolic models under category expansion, typical in DG-GCD.

Conclusion

We appreciate the reviewer's detailed feedback. Our revised paper will include:

• Detailed comparisons to [A–G] and Hu et al.
• Euclidean ablations, t-SNEs, prototype analysis.
• Clarifications on visualization and tables.

We believe these additions establish the novelty, rigor, and broad relevance of our work. We respectfully request the reviewer to reconsider and support acceptance.