Semantic segmentation in hyperbolic space enables compact modeling of hierarchical structure while providing inherent uncertainty quantification. Prior approaches predominantly rely on the Poincaré ball model, which suffers from numerical instability, optimization, and computational challenges. We propose a novel, tractable, architecture-agnostic semantic segmentation framework (pixel-wise and mask classification) in the hyperbolic Lorentz model. We employ text embeddings with semantic and visual cues to guide hierarchical pixel-level representations in Lorentz space. This enables stable and efficient optimization without requiring a Riemannian optimizer, and easily integrates with existing Euclidean architectures. Beyond segmentation, our approach yields free uncertainty estimation, confidence map, boundary delineation, hierarchical and text-based retrieval, and zero-shot performance, reaching generalized flatter minima. We introduce a novel uncertainty and confidence indicator in Lorentz cone embeddings. Further, we provide analytical and empirical insights into Lorentz optimization via gradient analysis. Extensive experiments on ADE20K, COCO-Stuff-164k, Pascal-VOC, and Cityscapes, utilizing state-of-the-art per-pixel classification models (DeepLabV3 and SegFormer) and mask classification models (mask2former and maskformer), validate the effectiveness and generality of our approach. Our results demonstrate the potential of hyperbolic Lorentz embeddings for robust and uncertainty-aware semantic segmentation. Code is available at https://github.com/mxahan/Lorentz_semantic_segmentation.
Open-vocabulary semantic segmentation requires adapting image-level vision-language models such as CLIP to dense pixel-level prediction, which is challenging due to the mismatch between hierarchical structure and semantic alignment in the embedding space. While recent works leverage hyperbolic geometry to model hierarchical relationships, they align embeddings across hierarchical levels but overlook semantic misalignment among embeddings within the same level. In this work, we propose HyRo, a hyperbolic fine-tuning framework that decouples hierarchical and semantic alignment in the Poincaré ball model. HyRo aligns hierarchical levels by adjusting the hyperbolic radius and refines semantic relationships through angular alignment using an orthogonal transformation that theoretically preserves the hyperbolic radius. Experiments on standard open-vocabulary semantic segmentation benchmarks demonstrate that HyRo achieves state-of-the-art performance over prior methods.
While Vision-Language Models (VLMs) have achieved remarkable performance, their Euclidean embeddings remain limited in capturing hierarchical relationships such as part-to-whole or parent-child structures, and often face challenges in multi-object compositional scenarios. Hyperbolic VLMs mitigate this issue by better preserving hierarchical structures and modeling part-whole relations (i.e., whole scene and its part images) through entailment. However, existing approaches do not model that each part has a different level of semantic representativeness to the whole. We propose UNcertainty-guided Compositional Hyperbolic Alignment (UNCHA) for enhancing hyperbolic VLMs. UNCHA models part-to-whole semantic representativeness with hyperbolic uncertainty, by assigning lower uncertainty to more representative parts and higher uncertainty to less representative ones for the whole scene. This representativeness is then incorporated into the contrastive objective with uncertainty-guided weights. Finally, the uncertainty is further calibrated with an entailment loss regularized by entropy-based term. With the proposed losses, UNCHA learns hyperbolic embeddings with more accurate part-whole ordering, capturing the underlying compositional structure in an image and improving its understanding of complex multi-object scenes. UNCHA achieves state-of-the-art performance on zero-shot classification, retrieval, and multi-label classification benchmarks. Our code and models are available at: https://github.com/jeeit17/UNCHA.git.
CLIP, a foundational vision-language model, has emerged as a powerful tool for open-vocabulary semantic segmentation. While freezing CLIP's text encoder is known to preserve its generalization capability, recent studies show that fine-tuning both CLIP's text and image encoders jointly significantly enhances segmentation performance, especially for classes from open sets. In this work, we explain this phenomenon from the perspective of hierarchy alignment, since during fine-tuning, the hierarchical level of image embeddings shifts from image-level to pixel-level. We achieve this by leveraging hyperbolic space, which naturally encodes hierarchical structures. Our key observation is that, during fine-tuning, the hyperbolic radius of CLIP's text embeddings decreases, facilitating better alignment with the pixel-level granularity of visual data. Building on this, we propose HyperCLIP++, a novel and parameter-efficient adaptation strategy. HyperCLIP++ directly adjusts the hyperbolic radius of CLIP's embeddings via scaling transformations to achieve a hierarchy alignment to the target task, i.e., segmentation. To ensure this hierarchy alignment is effected consistently across both modalities and preserves their cross-modal alignment during training, HyperCLIP++ integrates a Dual Cross-Relation Communication (DCRC) module that synchronizes these adjustments between the vision and text pathways. Our experiments show that HyperCLIP++ achieves state-of-the-art performance across three benchmarks while fine-tuning only approximately 5% of CLIP's total parameters. More importantly, we observe that after adjustment, CLIP's text embeddings exhibit a relatively fixed hyperbolic radius across datasets, suggesting that the hierarchical level required for this segmentation task might be quantified using the hyperbolic radius.