Hyperbolic Representation Learning

Follow this topic Ask about this topic

Momentum

17 papers in the last four weeks, up 467% on the four weeks before. 0.2% of all new papers.

Jul 13Week of Sep 28

Latest papers 60

Jul 10, 2026cs.CV

HiHR: Hierarchical Hyperbolic Representation for Aerial-Ground Person Re-Identification

Aerial-Ground Person Re-IDentification (AG-ReID) aims to retrieve the same person across heterogeneous aerial and ground camera platforms. Although great progress has been made, existing methods remain suboptimal due to the direct feature alignment across views, overlooking view-specific cues. To address this issue, we propose a novel Hierarchical Hyperbolic Representation (HiHR) framework for AG-ReID. More specifically, we first extract multi-granularity features based on pre-trained visual-text encoders. Then, we propose a Text-guided Multi-granularity Fusion (TMF) to fuse multi-granularity features and enhance the representation ability of identity features. Furthermore, we introduce the Hierarchical Hyperbolic Learning (HHL) to construct a hierarchical feature structure in a hyperbolic space. This hierarchy includes a coarse level that ensures identity separability and cross-view consistency, and a fine level that preserves view-specific discriminative cues. As a result, our proposed framework can effectively aggregate view-invariant and view-specific discriminative features for AG-ReID. Extensive experiments on four AG-ReID benchmarks demonstrate the effectiveness of our framework. The source code is available at https://github.com/YangQiWei3/HiHR.

Qiwei Yang, Pingping Zhang

Dalian University of Technology, Dalian, China

Hierarchical Representation Learning Hyperbolic Representation Learning Person Re-Identification

Jul 8, 2026cs.CV

Navigating Hierarchy: Hyperbolic Learning on Brain Graphs for Disorder Diagnosis

Functional brain networks exhibit a hierarchical organization across ROI, community, and whole-brain levels, supporting local processing, inter-community coordination, and global integration. Recent studies have demonstrated that brain community-aware modeling is beneficial for both diagnosis and biomarker identification of brain networks. However, existing brain graph modeling methods often struggle to model ROI-community interactions, thereby failing to fully exploit the hierarchy across ROI, community, and whole-brain network levels. To address this issue, inspired by deep hyperbolic learning in modeling hierarchical structures, we propose a novel framework, termed Hyperbolic Learning on Brain Graphs (HLBG), for brain network analysis. The core idea of HLBG is to exploit the inherent hierarchical geometry of hyperbolic space to model the hierarchical relationships among ROIs, functional communities, and the whole-brain network, thereby learning hierarchy-aware and highly discriminative representations for brain network data. Specifically, HLBG first projects representations from ROIs, communities, and the whole-brain network into Lorentzian hyperbolic space. Then, the multi-level hierarchy is imposed via two geometric entailment constraints. In addition, we introduce a new Graph-aware Mamba (GaMamba) model, which incorporates topology-derived structural prompts into Mamba to capture long-range dependencies while preserving graph topological information. Experiments on ABIDE-I and REST-MDD demonstrate that HLBG outperforms state-of-the-art methods and identifies disorder-relevant functional biomarkers.

Yapeng Li, Bo Jiang, Ziyan Zhang +2

School of Computer Science and Technology, Anhui University, 111 Jiulong Road, Hefei, 230601, China

Medical Diagnosis Hierarchical Representation Learning Neuroimaging Hyperbolic Representation Learning Brain Network Analysis

Jul 6, 2026cs.CV

Is the Geometry Doing the Work? An Operating-Point Audit of Hierarchy in Hyperbolic Vision-Language Models

Whether a hyperbolic representation model uses its geometry cannot be inferred from curvature alone: what matters is the dimensionless operating point

\sqrt{c}ρ

and whether the radial and cone mechanisms are operational there. We develop necessary-condition diagnostics and audit three published hyperbolic vision-language families -- MERU, HyCoCLIP, and PHyCLIP -- across released checkpoints and matched interventions. All converged checkpoints remain near-Euclidean (

H(u)\approx1

; none reaches

\sqrt{c}ρ>1

), and releasing the curvature floor changes

c

and norms without leaving this regime or substantially degrading downstream performance. Entailment cones are inactive or saturated, and graded traversal fails under controlled readouts, including the models' native distance metrics. External parent-child ordering shows no shuffle-controlled pair-specific radial signal at quantified sensitivity; the only surviving pair-specific signal, a statistically detectable but small residual on the GRIT box-to-full-caption relation, remains non-operative under the evaluated readouts. Taxonomy correlations show no detectable norm contribution beyond cosine, and coarse-retrieval gains co-vary with box/compositional supervision without establishing an active radial mechanism. Gradient diagnostics expose a low-curvature, wide-cone shortcut in the entailment objective. A closed-form aperture identity places the saturation edge at

\sqrt{c}ρ\le2K

: with the floor released, all trained relation-level parent means lie at or below this edge, leaving the parent cones fully or nearly saturated. Entailment-off runs pass the edge and continue contracting. The shortcut is the dominant accelerator of collapse, not its sole cause. These audited formulations do not show an operative radial/cone mechanism under our diagnostics. We distill the audit into a five-number geometry report for hierarchy claims.

Jaeyoung Kim, Eunseok Kim, Dongsuk Jang

MADI

VLM Evaluation Vision-Language Models Hierarchical Representation Learning Hyperbolic Representation Learning

Jul 1, 2026cs.LG

Group-Equivariant Poincaré Convolutional Networks

While recent advancements like the Poincaré ResNet have demonstrated the potential of learning visual representations directly in hyperbolic space, their optimisation remains hampered by the computationally intensive nature of Riemannian gradients and the strict boundaries of the manifold. Furthermore, standard hyperbolic networks treat spatial transformations of the same object as distinct hierarchical concepts, leading to redundant parameter usage and vanishing signals. We propose Equivariant Poincaré ResNets, combining hyperbolic geometry with discrete symmetry groups (

C_4

and

D_4

). We identify critical roadblocks in applying Euclidean equivariance to hyperbolic space and propose geometrically safe tensor reshaping, left-regular permutations for hyperbolic group convolutions, and joint-orientation Poincaré Midpoint Batch normalisation. Empirically, embedding equivariance drastically reduces the optimisation space, accelerating convergence while accelerating convergence while respecting the boundary constraints of the Poincaré ball and preserving spatial-group equivariance.

Aiden Durrant, Rahul Baburajan, Georgios Leontidis

School of Computing Sciences, University of East Anglia, NR4 7TJ, Norwich, UK · Department of Physics and Technology, UiT The Arctic University of Norway, NO-9037, Tromsø, Norway

Equivariant Neural Networks Hyperbolic Representation Learning

Jul 1, 2026cs.CV

HyFL-CLIP: Hyperbolic Fine-Tuning of CLIP for Robust Long-Context Understanding

CLIP (Contrastive Language-Image Pre-training) has become a de facto paradigm for image-text alignment, but it struggles with long-context descriptions (>77 tokens) due to absolute positional encoding and pretraining on short captions. In long contexts, sentences are often reordered, summarized, or partially omitted. Although prior works extend CLIP with longer positional encodings, they often suffer from degraded image-text alignment under such text perturbations. We attribute this limitation to the Euclidean contrastive objective, which enforces strict one-to-one matching and lacks explicit mechanisms for modeling hierarchical relationships between global context and its constituent elements. To address this issue, we propose HyFL-CLIP, a hyperbolic fine-tuning framework that distills the well-established text-image alignment learned in Euclidean CLIP into hyperbolic space via cross-manifold similarity distillation, leveraging its geometry to capture hierarchical and entailment relations. Our method models hierarchical semantics by linking summarized token-wise features, long-context descriptions, constituent short textual components, and images, capturing part-whole relationships via hyperbolic entailment with Einstein midpoint aggregation. Experiments on diverse benchmarks, including long-context cross-modal retrieval, cross-modal retrieval with caption perturbations, intra-modality retrieval, and short-text cross-modal retrieval, show that HyFL-CLIP achieves more robust long-context understanding. In particular, it yields up to 19.5% improvement in long-text cross-modal retrieval under textual perturbations over the best prior method. We also show HyFL-CLIP can be seamlessly integrated into other model frameworks by applying it to Stable Diffusion XL (SDXL).

Ji Ha Jang, Hayeon Kim, Chulwon Lee +2

1Dept. of Electrical and Computer Engineering, 2IPAI, 3INMC & AIIS, Seoul National University, Republic of Korea

VLM Robustness Vision-Language Models Vision-Language Retrieval Vision-Language Alignment Hyperbolic Representation Learning Long-Context VLMs

Jun 30, 2026cs.CV

HyperVLP: Enhancing Hierarchical Surgical Video-Language Pre-training in Hyperbolic Space

Surgical vision-language foundation models typically adopt educational materials, such as surgical lecture videos, to transfer surgical knowledge encoded in language into visual representations. These knowledge are multi-dimensional and hierarchical: fine-grained action cues appear in narration, mid-level key steps are summarized in subsection headings, and global procedural context, such as patient history and surgical strategy, is described in abstract texts. Prior work largely collapses these heterogeneous signals into a single flat embedding space, implicitly assuming independence across hierarchy levels. However, this is suboptimal because it ignores cross-level semantic containment, e.g., actions belong to steps, steps compose phases, weakens long-range dependency modeling. To this end, we propose a hyperbolic surgical video-language pre-training framework that explicitly preserves the hierarchical structure by mitigating structural false negatives induced by procedural context and enforcing semantic consistency between parent phases and their constituent child steps. Extensive experiments on multiple surgical benchmarks show consistent gains in zero- and few-shot phase recognition across procedures and institutions.

Yaojun Hu, Kun Yuan, Nassir Navab +3

Zhejiang University, Hangzhou, China · University of Strasbourg, CNRS, INSERM, ICube, UMR7357, Strasbourg, France · IHU Strasbourg, Strasbourg, France +1

Hierarchical Representation Learning Surgical Video Understanding Medical VLMs Vision-Language Alignment Hyperbolic Representation Learning

Jun 28, 2026cs.CV

Rank-Aware Hyperbolic Alignment for Vision-Language Dataset Distillation

Vision-language dataset distillation (VLDD) compresses a large image-text paired dataset into a small set of synthetic pairs that can efficiently train contrastive vision-language models under strict data and compute budgets. Most existing methods match expert trajectories or cross-modal statistics, yet still enforce full-dimensional alignment in a Euclidean embedding space. This is often overly restrictive due to rank-deficient image--text correlation, with shared semantics concentrated in a low-dimensional range and remaining variation spread across a weakly correlated residual subspace. LoRS relaxes alignment at the similarity level by low-rank factorization, but does not explicitly control dominant alignment capacity and structure in the representation space. We thus propose a rank-aware hyperbolic alignment (RAHA) that combines hierarchical geometry with explicit alignment-capacity control. RAHA lifts multimodal representations to hyperbolic space and optimizes distilled pairs with asymmetric objectives that enforce geodesic alignment in the shared range while regularizing the residual subspace to preserve modality-private diversity and improve transfer robustness. Experiments on benchmarks show that RAHA demonstrates competitive cross-modal retrieval and improved transfer indicators under fixed budgets.

Jongoh Jeong, Sun-Kyung Lee, Kuk-Jin Yoon

Korea Advanced Institute of Science and Technology (KAIST), Republic of Korea · Electronics and Telecommunications Research Institute (ETRI), Republic of Korea

Dataset Distillation Vision-Language Alignment Multimodal Contrastive Learning Hyperbolic Representation Learning

Jun 24, 2026quant-ph

Two-dimensional Hyperbolic RNN Neural Quantum State

In the first part of this work, we construct the first type of two-dimensional (2D) hyperbolic neural quantum state (NQS) in the form of the Lorentz 2DRNN (Recurrent Neural Network) and benchmark its performance against the Euclidean 2DRNN in the paradigmatic

N\times N

2D Transverse Field Ising Model (2DTFIM) setting with different lattice sizes up to

N=12

and at different transverse magnetic field strengths. We find that hyperbolic Lorentz 2DRNN NQS definitively outperform Euclidean 2DRNN NQS when the system is at the phase transition point when the physics can be described by a conformal field theory (CFT), which is known to be dual to an Anti-de-Sitter (AdS) space whose spatial geometry is hyperbolic. In the second part of this work, we benchmark the performances of the recently introduced one-dimensional (1D) hyperbolic NQS including Poincaré RNN/GRU and Lorentz RNN/GRU against their Euclidean NQS versions in

N\times N

2DTFIM, which has to be converted to a one-dimensional setting to allow for the use of 1D NQS. The findings in this case extend our previous results that 1D hyperbolic NQS definitively outperform 1D Euclidean NQS, thanks to the combined effects of the hierarchical structure comprising the first and

N^{th}

neighbor interactions present in the 1D system arising from the 2D lattice and the CFT physics at the critical point. While more studies with larger system sizes are required, our work serves as a proof-of-concept for the utility, effectiveness as well as the superior performances of one- and two-dimensional hyperbolic NQS ansatzes compared to the existing Euclidean NQS in many-body quantum physics systems, especially when these systems exhibit structural hierarchy or when they are at criticality, or a combination of both.

H. L. Dao

Neural Quantum States Recurrent Neural Networks Quantum Many-Body Physics Hyperbolic Representation Learning

Jun 23, 2026cs.LG

Hyperbolic Manifold Constrained Tabular Neural Network

Tabular prediction is central to a wide range of real-world applications. Tabular data typically contain heterogeneous features as well as rich and complex relational information that can imply a latent structural manifold. Hyperbolic geometry can help capture complex structural relations in data. However, most existing tabular prediction models are constructed and optimized in Euclidean space. How to incorporate hyperbolic geometry into supervised tabular learning remains underexplored. We propose \textbf{HTNN}, a supervised hyperbolic manifold constrained tabular neural network for tabular prediction. HTNN consists of a hyperbolic feature-value representation layer for heterogeneous categorical and numerical features, followed by a conventional MLP predictor. HTNN employs a \emph{geometry-aware training} and \emph{geometry-free inference} optimization framework. The \emph{geometry-aware training} allows hyperbolic geometry to shape the latent representation learning of heterogeneous feature values. After training, the latent hyperbolic representations can be converted into ordinary Euclidean space for efficient \emph{geometry-free inference}. We conducted extensive experiments on the TALENT benchmark. HTNN ranks first among 36 methods on 200 classification datasets and third among 34 methods on 100 regression datasets. Experimental results show that the proposed hyperbolic manifold constrained tabular neural network is effective.

Tian Li, Huizhi Liang, Lucy Robinson +1

Newcastle University Newcastle upon Tyne, UK

Tabular Classification Tabular Representation Learning Tabular Prediction Hyperbolic Representation Learning

Jun 18, 2026cs.CV

HypOProto: Hyperbolic Ordinal Prototypes for Left Ventricular Filling Pressure Classification

Echocardiography (echo) is a widely used imaging modality for assessing cardiac function, with Left Ventricular Filling Pressure (LVFP) serving as a critical physiological marker for conditions such as heart failure. Standard LVFP classification into normal \emph{vs} elevated categories relies on the Doppler-derived

E/e'

ratio, which is operator-dependent and often unavailable in resource-limited settings, motivating methods that infer LVFP directly from B-mode echo. Existing deep learning approaches achieve high performance but remain largely black-box, limiting clinical interpretability. We propose HypOProto, a hyperbolic, ordinal prototype-based framework for interpretable LVFP classification using a frozen, explainable foundation model backbone. HypOProto arranges prototypes along the physiological

E/e'

scale, placing borderline cases near the hyperboloid root where small angular differences separate similar cases, while normal and elevated cases occupy outward positions reflecting increasing diagnostic certainty. This hyperbolic geometry encodes clinically meaningful ordinal relationships and improves interpretability. We also introduce a novel Hyperbolic Prototype Angular Separation (HyperPAS) loss, enforcing inter-class prototype separation in hyperbolic space. HypOProto achieves SOTA performance while maintaining transparency, and highlights clinically relevant regions in visualizations. This work represents the first prototype-based framework for LVFP classification in echo. Our code can be found at https://github.com/DeepRCL/HypOProto.

Victoria Wu, Nima Hashemi, Hooman Vaseli +3

Department of Electrical and Computer Engineering, The University of British Columbia, Vancouver, BC, Canada · Vancouver General Hospital, Vancouver, BC, Canada

Prototype-Based Classification Echocardiography Ordinal Regression Explainable Medical Image Analysis Hyperbolic Representation Learning

Jun 4, 2026cs.CV

HyperVis: Continuous Latent Visual Relational Graphs on the Lorentz Hyperboloid for Compositional Reasoning

Vision-Language Models (VLMs) struggle with compositional reasoning that requires understanding inter-object relationships. A natural remedy is to inject explicit scene graph triplets

\langle s, p, o \rangle

from an off-the-shelf scene graph generator (SGG), but we show this backfires: discrete text labels collide with the continuous visual modality, degrading GQA accuracy from 60.38% to 58.86%. We propose \textbf{HyperVis}, which bypasses the SGG semantic bottleneck entirely. From

N

class-agnostic region proposals, we compute a dense

O(N^2)

visual relation tensor via spatially-biased cross-attention, project it onto a Lorentz hyperboloid, and enforce hierarchy through spatial physics, namely IoA-driven entailment cones and exterior-angle repulsion. We discover that HyperVis contributes in two complementary ways: (1) as a \emph{training-time regularizer}, the hyperbolic relational losses shape LoRA representations that improve generative VQA (GQA 61.03% vs.\ 57.21% for LoRA fine-tuning without relational losses, recovering and surpassing the baseline); and (2) as an \emph{inference-time relational encoder}, hyperbolic prefix tokens boost discriminative compositional scoring (SugarCrepe 79.94%,

+

6.25pp over baseline). The learned curvature stabilises at

κ{=}4.0

, an order of magnitude above prior hyperbolic VLMs where

κ

typically collapses toward zero, indicating that continuous visual features genuinely require the exponential volume of strongly curved space. A controlled Euclidean ablation confirms this decomposition: the relational pipeline regularises LoRA comparably in flat space (GQA 60.81%), but the compositionality gain is specifically hyperbolic (SugarCrepe

+

4.58pp over Euclidean), with entailment loss

{\sim}6{\times}

higher in Euclidean training. Codes are available at TBA.

Moshiur Farazi, Sameera Ramasinghe, Mahbub Ahmed Turza +1

Data Science and AI, University of Doha for Science and Technology, Qatar · Pluralis Research, Australia · Department of Electrical and Computer Engineering, North South University, Bangladesh

Visual Reasoning VLM Reasoning Visually Grounded Reasoning Relational Deep Learning Compositional Representation Learning Hyperbolic Representation Learning

Jun 2, 2026cs.CV

SkelHCC: A Hyperbolic CLIP-Driven Cache Adaptation Framework for Skeleton-based One-Shot Action Recognition

Skeleton-based action recognition aims to understand human behaviors from body joint sequences and is especially challenging in the one-shot setting, where only a single labeled exemplar is available for each novel action. A key challenge is learning representations that capture the hierarchical and compositional structure of human motion while aligning effectively with high-level action semantics under extreme data scarcity. Existing approaches, largely based on Euclidean embeddings and low-level motion cues, struggle to model the tree-like organization of skeleton data, limiting cross-modal alignment and generalization to unseen action categories. We propose SkelHCC, a unified skeleton hyperbolic CLIP-driven cache adaptation framework for one-shot skeleton-based action recognition. SkelHCC introduces an Explicitly Hierarchical Hyperbolic CLIP (EH-HCLIP) module that embeds skeleton sequences and action language into a shared hyperbolic space. By leveraging the negative curvature and exponential volume growth of hyperbolic geometry, EH-HCLIP naturally encodes the joint-part-body hierarchy of human anatomy and yields structurally consistent cross-modal representations. To support efficient one-shot adaptation, SkelHCC further integrates a training-free LLM-guided Multi-granularity Voting Cache (LMV-Cache) for context-aware inference. Experiments on NTU RGB+D 60, NTU RGB+D 120, and PKU-MMD demonstrate that SkelHCC consistently outperforms state-of-the-art methods.

Yanan Liu, Anqi Zhu, Jingmin Zhu +6

Yunnan University, Kunming, China · Monash University · Lancaster University +1

Skeleton-Based Action Recognition Cross-Modal Representation Learning Hierarchical Representation Learning Few-Shot Learning Hyperbolic Representation Learning

May 28, 2026cs.SI

SAHG: Sector-Anisotropic Hyperbolic Graph Model for Social Bot Detection

LLM-driven social bots can generate fluent, human-like text, reducing the discriminative advantage of content-based detection alone. However, coordinated campaigns still leave relational patterns -- interactions, behavioral similarity, shared neighborhoods, community positions, and coordinated activity -- that graph-based methods can exploit. Existing graph detectors face two challenges when exploiting such evidence. First, Euclidean GNNs distort hierarchical and scale-free social graphs; while hyperbolic geometry addresses this volume-growth mismatch, fixed-curvature models still assign uniform geometric resolution to structural directions with different densities and separation needs. Second, relational evidence is not always reliable: sophisticated bots forge heterophilic connections with genuine users, causing neighborhood aggregation to mix bot and human signals and dilute account-level evidence. We propose SAHG (Sector-Anisotropic Hyperbolic Graph), addressing both challenges. SAHG learns a direction-dependent curvature field

γ(u)

that adapts geometric resolution across structural directions, and uses sector prototypes to convert angular concentration and alignment into classifier-readable features. To prevent contaminated aggregation from overwhelming account-level evidence, SAHG encodes per-account features and graph-neighborhood representations in two independent SAH channels, fusing them only at the classifier. Experiments on Fox8-23, BotSim-24, and MGTAB show that SAHG achieves the highest accuracy and F1 on all three benchmarks, outperforming feature-based, graph-based, LLM-based, and isotropic hyperbolic baselines. Ablation and geometric analyses confirm the effectiveness of the anisotropic geometry and dual-channel design.

Hanning Lu, Yingguang Yang, Jinwei Su +8

University of Leeds · University of Science and Technology of China · 3South China Normal University +6

Social Media Analysis Graph Neural Networks Hyperbolic Representation Learning

May 27, 2026cs.LG

Temporal Hyperbolic Graph Representation Learning for Scale-Free Internet Routing and Delay Prediction

Predicting Internet round-trip time (RTT) is critical for routing optimization, quality-of-service (QoS) provisioning, and traffic engineering, yet remains challenging due to long-term temporal dependencies, evolving routing dynamics, and heavy-tailed latency distributions. While Temporal Graph Neural Networks (TGNNs) can model evolving network topologies, most existing approaches operate in Euclidean space, which poorly captures the hierarchical and scale-free structure of Internet routing graphs. Hyperbolic geometry provides a more suitable representation space. We propose HERMIT (Hyperbolic Edge-aware RTT Modeling via Integrated Topology), a hybrid framework combining a hyperbolic manifold-preserving temporal GNN with a Random Forest regressor for joint link prediction and RTT prediction. Built on HMPTGN, HERMIT introduces RTT-aware edge features and a learnable edge encoder to improve modeling of evolving link states and routing behavior. The resulting hyperbolic node representations are combined with historical RTT statistics for robust latency prediction. We evaluate HERMIT on a large-scale real Internet dataset spanning 2015-2024. HERMIT consistently outperforms a strong Random Forest baseline using only historical RTT statistics, achieving a 6% RMSE improvement while reducing large errors on heavy-tailed samples. It also surpasses prior hyperbolic TGNN models, including HMPTGN and HTGN, in link prediction performance. These results demonstrate that combining hyperbolic temporal graph learning with tree-based regression provides a scalable solution for RTT prediction in real-world Internet topologies.

Yi-Ling Kuo, Hao-Yu Tien, Shih-Yu Tsai

Department of Information Management and Finance, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan

Temporal GNNs Temporal Link Prediction Hyperbolic Representation Learning

May 12, 2026cs.CV

H2G: Hierarchy-Aware Hyperbolic Grouping for 3D Scenes

Hierarchical 3D grouping aims to recover scene groups across multiple granularities, from fine object parts to complete objects, without relying on semantic labels or a fixed vocabulary. The main challenge is to transform 2D foundation-model cues into coherent hierarchy supervision and embed that hierarchy in a 3D representation. We propose H2G, a hyperbolic affinity field for hierarchical 3D grouping. Our method derives semantically organized tree supervision by interpreting foundation-model affinities through Dasgupta's objective for similarity-based hierarchical clustering. This supervision is distilled into a single Lorentz hyperbolic feature field, whose geometry is well suited for tree-like branching structures. A hierarchy-aware objective aligns the field with fine-level assignments, coarse object structure, compact feature clusters, and LCA (Lowest Common Ancestor) ordering. This formulation represents multiple grouping levels in one feature space, enabling semantic hierarchical grouping grounded in 2D foundation-model knowledge.

ByungHa Ko, Youngmin Lee, Dong Hwan Kim

Department of Computer Science and Engineering, Korea University · Intelligence and Interaction Research Center, Korea Institute of Science and Technology

Clustering Hierarchical Representation Learning 3D Representation Learning Hyperbolic Representation Learning

May 11, 2026cs.CV

HYPERPOSE: Hyperbolic Kinematic Phase-Space Attention for 3D Human Pose Estimation

We introduce HYPERPOSE, a novel 3D human pose estimation framework that performs spatio-temporal reasoning entirely within the Lorentz model of hyperbolic space

\mathbb{H}^d

to natively preserve the hierarchical tree topology of the human skeleton. Current state-of-the-art pose estimators aim to capture complex joint dynamics by relying on transformers and graph convolutional networks. Since these architectures operate exclusively in Euclidean space which fundamentally mismatches the inherent tree structure of the human body, these methods inevitably suffer from exponential volume distortion and struggle to maintain structural coherence. To this end, we depart from flat spaces and aim to improve geometric fidelity with Hyperbolic Kinematic Phase-Space Attention (HKPSA), natively embedding complex joint relationships without distortion, alongside a multi-scale windowed hyperbolic attention mechanism that efficiently models temporal dynamics in

O(TW)

complexity. Furthermore, to overcome the well-known instability of training non-Euclidean manifolds, HYPERPOSE introduces a novel Riemannian loss suite and an uncertainty-weighted curriculum, enforcing physical geodesic constraints like bone length and velocity consistency. Extensive evaluations on the Human3.6M and MPI-INF-3DHP datasets demonstrate that HYPERPOSE achieves state-of-the-art structural and temporal coherence, significantly reducing both volume distortion and velocity error, while establishing new state-of-the-art benchmarks in overall positional accuracy.

Vinduja Thekkath, Ashish Musale, Ajay Waghumbare +1

3D Human Pose Estimation Attention Mechanisms Hyperbolic Representation Learning

May 10, 2026cs.CV

HyNeuralMap: Hyperbolic Mapping of Visual Semantics to Neural Hierarchies

Understanding the intricate mappings between visual stimuli and neural responses is a fundamental challenge in cognitive neuroscience. While current approaches predominantly align images and functional magnetic resonance imaging (fMRI) responses in Euclidean space, this geometry often struggles to preserve fine-grained semantic relationships and latent hierarchical structures across visual and neural modalities. To overcome this, we propose HyNeuralMap, a framework that employ hyperbolic Lorentz model to map visual semantics into a shared, cross-subject neural hierarchy. By leveraging the negative curvature of hyperbolic space as an inductive bias, the proposed framework better captures hierarchical semantic organization and cross-subject neural similarities. Specifically, visual and neural embeddings are jointly optimized through hyperbolic geometric alignment, where geodesic distances preserve semantic proximity and hierarchical relationships more effectively than Euclidean embeddings. Experiments demonstrate that HyNeuralMap consistently outperforms state-of-the-art Euclidean baselines in both multi-label semantic prediction and cross-modal retrieval tasks. This confirms hyperbolic geometry's superiority for cross-modal semantic alignment and hierarchical modeling, providing a new avenue for vision-neural representation learning.

Zihan Ma, Tian Xia, Kexin Wang +3

School of Electronic Information (School of Artificial Intelligence), the Xi’an Key Laboratory of Radiomics and Intelligent Perception, Northwest University, Xi’an 710127, China

Neural Representation Geometry Cross-Modal Alignment Hyperbolic Representation Learning

May 9, 2026cs.CV

Semantic Alignment in Hyperbolic Space for Open-Vocabulary 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.

Hoang M. Truong, Hai Nguyen-Truong, Dang Huynh

Fulbright University Vietnam

VLM Adaptation Hierarchical Representation Learning Open-Vocabulary Semantic Segmentation Vision-Language Alignment Hyperbolic Representation Learning

May 9, 2026cs.CV

Curvature-Aware Captioning:Leveraging Geodesic Attention for 3D Scene Understanding

Accurate 3D scene description is fundamental to robotic navigation and augmented reality, yet current dense captioning methods face significant limitations in processing sparse point cloud data. % Existing approaches that apply Euclidean embedding spaces struggle to simultaneously preserve fine-grained local geometric details and model exponentially growing global semantic hierarchies, leading to either inaccurate localization or disjointed, shallow scene descriptions. % In this work, we propose a novel \textbf{\textsc{Curvature-Aware Captioning}} framework, integrating novel non-Euclidean geodesic attention mechanisms, to resolve the localization-contextualization conflict. % Specifically, self-attention within Oblique space enforces dimensional homogeneity while establishing long-range dependencies. Bidirectional geodesic cross-attention within Lorentz space models hierarchical semantic relationships across scene instances, enabling simultaneous precision in object localization and coherence in scene descriptions. % Theoretical analysis confirms that the curvature complementarity between the Oblique manifold and Lorentz hyperboloid resolves the Euclidean-hyperbolic conflict, ensuring feature stability via isotropic optimization while preserving inherent hierarchical relationships. Extensive experiments on ScanRefer and Nr3D benchmarks demonstrate state-of-the-art performance, with significant gains in both localization accuracy and descriptive richness.

Ziyao He, Yingjie Liu, ZhangYangRui +3

East China Normal University

Attention Mechanisms Hyperbolic Representation Learning 3D Scene Understanding 3D VLMs 3D Visual Grounding

May 7, 2026cs.LG

Hyperbolic Concept Bottleneck Models

Concept Bottleneck Models (CBMs) have become a popular approach to enable interpretability in neural networks by constraining classifier inputs to a set of human-understandable concepts. While effective, current models embed concepts in flat Euclidean space, treating them as independent, orthogonal dimensions. Concepts, however, are highly structured and organized in semantic hierarchies. To resolve this mismatch, we propose Hyperbolic Concept Bottleneck Models (HypCBM), a post-hoc framework that grounds the bottleneck in this structure by reformulating concept activation as asymmetric geometric containment in hyperbolic space. Rather than treating entailment cones as a pre-training penalty, we show they encode a natural test-time activation signal: the margin of inclusion within a concept's entailment cone yields sparse, hierarchy-aware activations without any additional supervision or learned modules. We further introduce an adaptive scaling law for hierarchically faithful interventions, propagating user corrections coherently through the concept tree. Empirically, HypCBM rivals post-hoc Euclidean models trained on 20

\times

more data in sparse regimes required for human interpretability, with stronger hierarchical consistency and improved robustness to input corruptions.

Daniel Uyterlinde, Swasti Shreya Mishra, Pascal Mettes

Informatics Institute, University of Amsterdam, The Netherlands

Concept Bottleneck Models Hierarchical Representation Learning Neural Network Interpretability Hyperbolic Representation Learning

May 6, 2026cs.CV

Geometry-Aware State Space Model: A New Paradigm for Whole-Slide Image Representation

Accurate analysis of histopathological images is critical for disease diagnosis and treatment planning. Whole-slide images (WSIs), which digitize tissue specimens at gigapixel resolution, are fundamental to this process but require aggregating thousands of patches for slide-level predictions. Multiple Instance Learning (MIL) tackles this challenge with a two-stage paradigm, decoupling tile-level embedding and slide-level prediction. However, most existing methods implicitly embed patch representations in homogeneous Euclidean spaces, overlooking the hierarchical organization and regional heterogeneity of pathological tissues. This limits current models' ability to capture global tissue architecture and fine-grained cellular morphology. To address this limitation, we introduce a hybrid hyperbolic-Euclidean representation that embeds WSI features in dual geometric spaces, enabling complementary modeling of hierarchical tissue structures and local morphological details. Building on this formulation, we develop BatMIL, a WSI classification framework that leverages both geometric spaces. To model long-range dependencies among thousands of patches, we employ a structured state space sequence model (S4) backbone that encodes patch sequences with linear computational complexity. Furthermore, to account for regional heterogeneity, we introduce a chunk-level mixture-of-experts (MoE) module that groups patches into regions and dynamically routes them to specialized subnetworks, improving representational capacity while reducing redundant computation. Extensive experiments on seven WSI datasets spanning six cancer types demonstrate that BatMIL consistently outperforms state-of-the-art MIL approaches in slide-level classification tasks. These results indicate that geometry-aware representation learning offers a promising direction for next-generation computational pathology.

Enhui Chai, Sicheng Chen, Tianyi Zhang +4

PuzzleLogic Pte Ltd, Singapore 229594, Singapore · Nhu Department of Electrical Engineering and Computer Science, University of California, Irvine · Department of Electrical & Computer Engineering, National University of Singapore

Histopathology Image Classification Multiple Instance Learning Whole-Slide Image Analysis Hyperbolic Representation Learning

May 4, 2026cs.CV

Hyp2Former: Hierarchy-Aware Hyperbolic Embeddings for Open-Set Panoptic Segmentation

Recognizing unknown objects is crucial for safety-critical applications such as autonomous driving and robotics. Open-Set Panoptic Segmentation (OPS) aims to segment known thing and stuff classes while identifying valid unknown objects as separate instances. Prior OPS approaches largely treat known categories as a flat label set, ignoring the semantic hierarchy that provides valuable structural priors for distinguishing unknown objects from in-distribution classes. In this work, we propose Hyp2Former, an end-to-end framework for OPS that does not require explicit modeling of unknowns during training, and instead learns hierarchical semantic similarities continuously in hyperbolic space. By explicitly encoding hierarchical relationships among known categories, the model learns a structured embedding space that captures multiple levels of semantic abstraction. As a result, unknown objects that cannot be confidently classified as known categories still remain in close proximity to higher-level concepts (e.g., an unknown animal remains closer to "animal" or "object" than to unrelated concepts such as "electronics" or "stuff") and can therefore be reliably detected, even if their fine-grained category was not represented during training. Empirical evaluations across multiple public datasets such as MS COCO, Cityscapes, and Lost&Found demonstrate that Hyp2Former outperforms existing methods on OPS, achieving the best balance between unknown object discovery and in-distribution robustness.

Yao Lu, Rohit Mohan, Florian Drews +2

Department of Computer Science, University of Freiburg, Germany · Bosch Research, Robert Bosch GmbH, Germany

Image Segmentation Panoptic Segmentation Hierarchical Representation Learning Open-Set Recognition Hyperbolic Representation Learning

Apr 30, 2026cs.LG

A Unified Framework of Hyperbolic Graph Representation Learning Methods

Hyperbolic geometry has emerged as an effective latent space for representing complex networks, owing to its ability to capture hierarchical organization and heterogeneous connectivity patterns using low-dimensional embeddings. As a result, numerous hyperbolic graph representation learning methods have been proposed in recent years. However, their practical adoption and systematic comparison remain challenging, as implementations are fragmented and shared tools for reproducible and fair evaluation are lacking. In this work, we introduce a unified open-source framework for hyperbolic graph representation learning that integrates several widely used embedding methods under a common optimization interface. The novel framework enables consistent training, visualization, and evaluation of hyperbolic embeddings, and interfaces seamlessly with standard network analysis tools. Leveraging this unified setup, we conduct an experimental study of hyperbolic embedding methods on real-world networks, focusing on two canonical downstream tasks: link prediction and node classification. Beyond predictive accuracy, the study offers practical insights into the strengths and limitations of existing approaches, thereby facilitating informed method selection and fostering reproducible research in hyperbolic graph representation learning.

Sofía Pérez Casulo, Marcelo Fiori, Bernardo Marenco +1

Facultad de Ingenier´ıa, Universidad de la Rep´ublica, Uruguay · Centro Interdisciplinario en Ciencia de Datos y Aprendizaje Autom´atico (CICADA), Universidad de la Rep´ublica, Uruguay

Graph Representation Learning Graph Embedding Hyperbolic Representation Learning

Apr 26, 2026cs.CV

HAC: Parameter-Efficient Hyperbolic Adaptation of CLIP for Zero-Shot VQA

Recent advances in representation learning have shown that hyperbolic geometry can offer a more expressive alternative to the Euclidean embeddings used in CLIP models, capturing hierarchical structures and leading to better-organized representations. However, current hyperbolic CLIP variants are trained entirely from scratch, which is computationally expensive and resource-intensive. In this work, we propose HAC (Hyperbolic Adaptation of CLIP), a parameter-efficient framework that enables pretrained CLIP models to transition into hyperbolic space via lightweight fine-tuning. We apply HAC to Visual Question Answering (VQA), where models must interpret visual elements and align them with textual queries. Notably, HAC's training is performed on a dataset with no overlap with any VQA benchmark, resulting in a strict zero-shot evaluation paradigm that underscores HAC's task-agnostic adaptability. We evaluate HAC across a diverse suite of VQA benchmarks spanning General, Reasoning, and OCR categories. Both HAC-S (small) and HAC-B (medium) consistently surpass Euclidean baselines and prior hyperbolic approaches, with HAC-B delivering up to a +1.9 point average improvement over CLIP-B on reasoning-intensive tasks. Our code is available at https://github.com/fdibiton/HAC

Francesco Dibitonto, Cigdem Beyan, Vittorio Murino

Department of Computer Science, University of Verona, Verona, Italy · EVS - Embedded Vision Systems Srl, Verona, Italy · AI for Good (AIGO), Istituto Italiano di Tecnologia, Genova, Italy

Visual Question Answering Zero-Shot Learning VLM Adaptation Hyperbolic Representation Learning Parameter-Efficient Fine-Tuning

Apr 22, 2026cs.AI

HypEHR: Hyperbolic Modeling of Electronic Health Records for Efficient Question Answering

Electronic health record (EHR) question answering is often handled by LLM-based pipelines that are costly to deploy and do not explicitly leverage the hierarchical structure of clinical data. Motivated by evidence that medical ontologies and patient trajectories exhibit hyperbolic geometry, we propose HypEHR, a compact Lorentzian model that embeds codes, visits, and questions in hyperbolic space and answers queries via geometry-consistent cross-attention with type-specific pointer heads. HypEHR is pretrained with next-visit diagnosis prediction and hierarchy-aware regularization to align representations with the ICD ontology. On two MIMIC-IV-based EHR-QA benchmarks, HypEHR approaches LLM-based methods while using far fewer parameters. Our code is publicly available at https://github.com/yuyuliu11037/HypEHR.

Yuyu Liu, Sarang Rajendra Patil, Mengjia Xu +1

Department of Computer Science, Stony Brook University · Department of Data Science, New Jersey Institute of Technology · Department of Biomedical Informatics, Stony Brook University

Healthcare Hierarchical Representation Learning Clinical QA Medical QA Electronic Health Records Hyperbolic Representation Learning

Apr 19, 2026cs.CV

HSG: Hyperbolic Scene Graph

Scene graph representations enable structured visual understanding by modeling objects and their relationships, and have been widely used for multiview and 3D scene reasoning. Existing methods such as MSG learn scene graph embeddings in Euclidean space using contrastive learning and attention based association. However, Euclidean geometry does not explicitly capture hierarchical entailment relationships between places and objects, limiting the structural consistency of learned representations. To address this, we propose Hyperbolic Scene Graph (HSG), which learns scene graph embeddings in hyperbolic space where hierarchical relationships are naturally encoded through geometric distance. Our results show that HSG improves hierarchical structure quality while maintaining strong retrieval performance. The largest gains are observed in graph level metrics: HSG achieves a PP IoU of 33.17 and the highest Graph IoU of 33.51, outperforming the best AoMSG variant (25.37) by 8.14, highlighting the effectiveness of hyperbolic representation learning for scene graph modeling. Code: https://github.com/AIGeeksGroup/HSG.

Liyang Wang, Zeyu Zhang, Hao Tang

School of Computer Science, Peking University

Graph Representation Learning Hierarchical Representation Learning Graph-Based Retrieval 3D Scene Representation Hyperbolic Representation Learning

Apr 19, 2026cs.CL

Modeling Multi-Dimensional Cognitive States in Large Language Models under Cognitive Crowding

Modeling human cognitive states is essential for advanced artificial intelligence. Existing Large Language Models (LLMs) mainly address isolated tasks such as emotion analysis or stance detection, and fail to capture interactions among cognitive dimensions defined in psychology, including emotion, thinking style, stance, and intention. To bridge this gap, we construct CognitiveBench, the first benchmark with unified annotations across the above four dimensions. Experiments on CognitiveBench show that although LLMs perform well on single dimension tasks, their performance drops sharply in joint multi-dimensional modeling. Using Gromov

δ

-hyperbolicity analysis, we find that CognitiveBench exhibits a strong hierarchical structure. We attribute the performance bottleneck to ``Cognitive Crowding'', where hierarchical cognitive states require exponential representational space, while the Euclidean space of LLMs grows only polynomially, causing representation overlap and degraded performance. To address this mismatch, we propose HyCoLLM, which models cognitive states in hyperbolic space and aligns LLM representations via Hyperbolic Guided Alignment Tuning. Results show that HyCoLLM substantially improves multi-dimensional cognitive understanding, allowing 8B parameter model to outperform strong baselines, including GPT-4o.

Lin Zhong, Siyu Zhu, Zizhen Yuan +5

Harbin Institute of Technology, Shenzhen, China · City University of Macau, Macao SAR, China · Peng Cheng Laboratory, Shenzhen, China

LLM Alignment Cognitive Modeling Hyperbolic Representation Learning

Apr 18, 2026cs.LG

Hyperbolic Enhanced Representation Learning for Incomplete Multi-view Clustering

Incomplete Multi-View Clustering (IMVC) faces the challenge of learning discriminative representations from fragmentary observations while maintaining robustness against missing views. However, prevalent Euclidean-based methods suffer from a geometric mismatch when modeling real-world data with intrinsic hierarchies, leading to semantic blurring where representations drift towards spatially proximal but semantically distinct neighbors. To bridge this gap, we propose HERL, a Hyperbolic Enhanced Representation Learning framework for IMVC. Operating within the Poincaré ball, HERL constructs a structure-aware latent space to enhance representation learning. Specifically, we design a dual-constraint hyperbolic contrastive mechanism optimizing: an angular-based loss to preserve semantic identity via directional alignment, and a distance-based loss to enforce hierarchical compactness. Furthermore, a hyperbolic prototype head is introduced to rectify global structural drift by aligning cross-view hierarchy-aware prototype distributions. Consequently, HERL disentangles fine-grained semantic correlations to sharpen cluster boundaries and imposes geometric constraints to rectify the data recovery process. Extensive experimental results demonstrate that HERL consistently outperforms state-of-the-art approaches.

Tianyi Chen, Haobo Wang, Kai Tang +5

School of Software Technology, Zhejiang University, Zhejiang 310027, China · College of Computer Science and Technology, Zhejiang University, Zhejiang 310027, China · Beijing Key Laboratory of Traffic Data Analysis and Mining, Beijing Jiaotong University, Beijing 100044, China +2

Contrastive Learning Hierarchical Representation Learning Multi-View Learning Multi-View Clustering Hyperbolic Representation Learning

Apr 18, 2026cs.CV

Lorentz Framework for Semantic Segmentation

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.

Zahid Hasan, Masud Ahmed, Nirmalya Roy

Department of Information Systems, University of Maryland, Baltimore County

Segmentation Uncertainty Estimation Semantic Segmentation Hyperbolic Representation Learning

Mar 23, 2026cs.CV

Uncertainty-guided Compositional Alignment with Part-to-Whole Semantic Representativeness in Hyperbolic Vision-Language Models

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.

Hayeon Kim, Ji Ha Jang, Junghun James Kim +1

Dept. of Electrical and Computer Engineering, Seoul National University, Republic of Korea · INMC & IPAI, Seoul National University, Republic of Korea

Vision-Language Models Hierarchical Representation Learning Vision-Language Alignment Hyperbolic Representation Learning