Hierarchical Representation Learning

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18 papers in the last four weeks, up 260% on the four weeks before. 0.2% of all new papers.

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Latest papers 154

Oct 5, 2026cs.LG

Hyperbolic Graph Representation Learning: Embed in One Metric, Optimize with Another

Hierarchical graphs embed in hyperbolic space with lower distortion than in Euclidean space owing to its negative curvature. However, their gradient-based learning is hampered at large radii, where the Poincaré ball and the Lorentz hyperboloid models fail numerically. Polar coordinates avoid this problem, but the hyperbolic metric scales the angular step by the hyperbolic sine of the radius, freezing angular motion. We observe that this factor is a choice, silently fixed by existing implementations: the Euclidean tangent parametrization, for instance, uses the radius itself. We show that other choices are not only possible but preferable. They are endpoints of a one-parameter family of optimization preconditioners with curvatures from

-1

to

0

, while the embedding remains at curvature

-1

. We show that since the Euclidean preconditioner rearranges a layout but refines it poorly, while an intermediate one refines far better once a layout is in place, combining them in two stages reduces the loss on real-world trees by 46-74% over the best single curvature.

Federico Larroca, Paola Bermolen, Marcelo Fiori +1

Facultad de Ingenier´ıa Universidad de la Rep´ublica Uruguay

Riemannian Optimization Hierarchical Representation Learning Graph Embedding Hyperbolic Representation Learning

Oct 5, 2026cs.LG

HiER-BLS: A Hierarchy-Guided and Error-Correcting Robust Incremental Broad Learning System

Broad Learning System (BLS) supports analytical training and incremental expansion, but its growth needs guidance on which inputs new blocks should learn from. Weight errors pose a further challenge by displacing learned outputs across class boundaries. We propose HiER-BLS to couple hierarchy-guided representation growth with error-correcting learning. Successive blocks focus on inputs selected by feature importance and correlation while preserving earlier representations. The evolving branch guides encoded learners through subspace size and sample confidence, so its learning experience informs both their feature views and supervision. For finite broad readouts, we show how codeword correlations transform fitted class scores. Prediction preservation depends on the distance from the actual output to the nearest decoding boundary relative to the model's sensitivity to weight errors. Experiments on five image and five tabular datasets demonstrate improved classification performance over representative BLS variants. Component studies show that hierarchy guidance benefits the encoded branch even when the guiding branch has lower standalone accuracy, with further gains from combining their scores. Longer codes continue to improve accuracy under stronger Gaussian weight errors after clean accuracy has largely saturated.

Gongli Zhang, C. L. Philip Chen, Zhulin Liu

Guangdong Provincial Key Laboratory of Computational AI Models and Cognitive Intelligence, the School of Computer Science and Engineering, South China University of Technology, Guangzhou 510006, China, also with the Pazhou Lab, Guangzhou 510335, China, and also with the Engineering Research Center of the Ministry of Education on Health Intelligent Perception and Paralleled Digital-Human, Guangzhou 510641, China

Hierarchical Representation Learning Neural Network Robustness Incremental Learning

Sep 29, 2026cs.CV

HIGS: Hierarchical Implicit Grids for Joint Geometric and Semantic Scene Understanding

Neural implicit representations have had a significant impact on scene reconstruction by enabling robots to build continuous, differentiable, and high-fidelity 3D maps. Most existing works focus on geometric reconstruction and lack semantic information for high-level spatial understanding and task planning. Also, as the scale and complexity of the environment increase, neural representations face the challenge of maintaining computational efficiency in back-end optimization. To resolve these two challenges, we introduce a hierarchical neural field that leverages multiresolution submaps to achieve an efficient and scalable implicit representation, and a unified query and decoding mechanism to support both geometric and semantic features. More specifically, the learnable map features can be converted to the output with the query and decoding process for both training and inference. For large-scale representation, we decompose a scene into overlapping submaps and do hierarchical optimization within each local submap, thus enabling scalable computation. To further improve efficiency, we design feature encoders that predict initial hierarchical grid features to substantially reduce the time needed to optimize the submap features from scratch. To correct estimation drift among submaps, we align and fuse them entirely within the implicit feature space, leading to substantial acceleration by avoiding the need to decode the final output. Building upon this efficient hierarchical representation, we embed both geometric features and vision-language latent features into the map, and demonstrate it on both Signed Distance Field (SDF) construction and open-vocabulary object grounding. Our approach significantly improves computation and memory efficiency, maintains high estimation accuracy, and endows the robot with spatial awareness on large-scale real-world benchmarks.

Hanwen Cao, Wenqiang Wu, Kuang-Ting Tu +5

University of California San Diego, La Jolla, CA, USA · Southern University of Science and Technology, Shenzhen, Guangzhou, China · Norwegian University of Science and Technology, Trondheim, Norway +2

Implicit Neural Representations Hierarchical Representation Learning 3D Scene Representation 3D Scene Understanding 3D Visual Grounding

Sep 29, 2026cs.CV

Minkowski Attractor Networks: Closed-Form Hyperbolic Flows for Visual Representations

Geometric representation learning predominantly scaffolds representations onto flat Euclidean subspaces or compact product tori (

\mathbb{T}^K

). However, flat manifolds possess vanishing curvature and polynomial volume growth, inherently suffering from metric distortion when embedding multi-scale, tree-like visual hierarchies. While hyperbolic spaces (

\mathbb{H}^m

) circumvent this via constant negative curvature (

K<0

) and exponential volume expansion, prior hyperbolic deep architectures are hindered by computationally cumbersome Riemannian optimization, non-linear gyrovector calculus, and floating-point instabilities. In this work, we introduce \textbf{Minkowski Attractor Networks (MAN)}, an operator-splitting-inspired framework that embeds representations within pseudo-Riemannian Minkowski spacetime (

\mathbb{R}^{1,m}

). By framing hyperbolic manifolds as quadric level sets, MAN resolves hyperbolic geometry by combining linear Lorentz group transport with non-linear cone lifting and closed-form radial rescaling, evaluating in a single forward pass without numerical ODE solvers or iterative retractions. We establish \textbf{MAN-2D} (

\mathbb{R}^{1,1} \to \mathbb{H}^1

) as our primary, high-throughput visual backbone, which maximizes channel factorization granularity into

D/2

independent two-dimensional Minkowski blocks. We further formulate \textbf{MAN-4D} (

\mathbb{R}^{1,3} \to \mathbb{H}^3

) as a spacetime extension, leveraging a commuting Cartan-subalgebra parameterization of

\mathrm{SO}^+(1,3)

to evaluate 4D Lorentz isometries via two commuting 2D planar maps without matrix-exponential overhead.

Zhongping Ji

Visual Representation Learning Hierarchical Representation Learning Geometric Representation Learning Hyperbolic Representation Learning

Sep 25, 2026cs.LG

Learning Hierarchical Causal Representations of the Effects of Forcings on Temperature in Climate Models

Machine learning (ML) emulators provide a fast and cost-effective method to simulate climate change scenarios after being trained on Earth System Models projections. However, the black-box nature of those data-driven approaches limit the usability and trustworthiness of their outputs and in particular their use as causal attribution tools. Here, we develop a hierarchical causal representation learning framework applied to sea surface temperature fields from a state-of-the-art global climate model. As a key advance over previous work, our framework explicitly models both atmospheric dynamical interactions arising from internal climate variability and forced responses due to changes in atmospheric greenhouse gas and aerosol concentrations. When trained on future climate change scenarios, our method accurately predicts the long-term global mean and regional temperature evolution and shows physically realistic responses to perturbations in greenhouse gas and aerosol concentrations when evaluated on unseen scenarios. Our results underline the potential of causal representation learning frameworks for advancing climate model emulation.

Shan Zhao, Ilija Trajkovic, Julia Kaltenborn +4

Technical University of Munich Munich, Germany · Karlsruhe Institute of Technology Karlsruhe, Germany · McGill University & Mila Montreal, Canada +1

Surrogate Modeling Causal Representation Learning Hierarchical Representation Learning Climate Modeling

Sep 22, 2026cs.CV

A Hierarchy-Aware Video-Language Model Evaluation and Hyperbolic Baseline for Surgery

Surgical procedures follow a phase-to-step hierarchy, yet the video-language models used to recognize them are evaluated with flat per-level metrics that ignore cross-level coherence and error structure. In this paper we make two contributions to address this problem, (i) we introduce SurgHiBench, the first hierarchy-aware evaluation suite for surgical video understanding, with three tasks measuring recognition, consistency, and severity across granularity levels. We evaluate a general-purpose CLIP model, a Euclidean surgical model, and, as second contribution: (ii) HyperSurg, a new hyperbolic model that enforces phase-step containment via entailment cones, across four (existing) datasets spanning three procedure types. The suite reveals that two models with the same accuracy can produce predictions of very different error severity, ranging from sibling confusions within the correct phase to unrelated cross-phase predictions. Hyperbolic geometry shifts predictions toward the correct procedural neighborhood, and these gains scale with the tree-likeness of each dataset's annotation hierarchy, providing a principled indicator when hierarchy-aware geometry helps.

Ana Manzano Rodríguez, Pascal Mettes, Marlies P. Schijven +1

Data Science Center HAVA-Lab, University of Amsterdam · Video & Image Sense Lab, Informatics Institute, University of Amsterdam · Amsterdam UMC Location University of Amsterdam, Surgery +2

Video-Language Model Evaluation Hierarchical Representation Learning Surgical Video Understanding Hyperbolic Representation Learning Temporal Video Understanding

Sep 22, 2026cs.LG

Geometry-Aware Hyperbolic Residual Quantization

Residual Vector Quantization turns continuous representations into discrete, multi-level token sequences. Yet most methods operate in Euclidean space, despite the coarse-to-fine structure of the resulting codes and the latent hierarchies present in many data domains. Hyperbolic geometry offers a natural alternative for hierarchical representations, but naive hyperbolic extensions introduce geometric inconsistencies: non-associative hyperbolic addition prevents consistent residual aggregation, while standard straight-through gradient estimation ignores the geometry of the latent space. We propose a geometry-aware hyperbolic residual quantization that addresses these issues in both the forward and backward passes. In the forward pass, Hyperbolic Residual Aggregation restores the telescoping behavior of residual quantization on the Poincare ball. In the backward pass, a discounted Hyperbolic Straight-Through Estimator routes the reconstruction gradient through the quantizer as a single geometric block, avoiding unstable recursive gradient transport across residual stages. Evaluations on hierarchical prediction, recommendation, image tokenization, and neural audio coding tasks show that our method improves the stability and structural organization of hyperbolic residual codes over naive hyperbolic baselines. At the same time, we observe a clear structure-compression trade-off: Euclidean residual quantization remains preferable for pure compression, while geometry-aware hyperbolic quantization is most useful for hierarchically organized discrete latent spaces.

Alessio Colombo, Melika Ayoughi

Universiteit van Amsterdam, Amsterdam, Netherlands

Residual VQ Hierarchical Representation Learning Hyperbolic Representation Learning

Sep 22, 2026cs.AI

Canonical locks that encode part-whole hierarchies

One of the challenges in representational learning is how to encode part-whole hierarchies in a neural net. Prior works rely on flattening tree-like structures into string-like sequences and training a sequence-to-sequence model via autoregression. While such a representation works for parse-trees in NLP, it is not entirely clear how to make it work for images. Thus, we propose a geometric primitive called canonical locks. The key idea is that parts/wholes can be modelled as higher-dimensional vectors (

d \geq 4

), and information can be encoded in their relative phase differences. Inductively, the net consists of positionally-bound bottom-up and top-down neural fields, which drive each other to achieve a state of thermal equilibrium. Additionally, we show the existence of a few symmetrical configurations in the net. The computational iterations taken to break these symmetries depend on the angle between parts/wholes arranged on a disk (or more precisely a ring) in higher dimensions. It also appears to have connections to the psychological phenomenon of mental rotation.

Rajat Modi, Yogesh Singh Rawat

Department of Computer Science, University of Central Florida, United States.

Visual Representation Learning Hierarchical Representation Learning Geometric Representation Learning Compositional Representation Learning

Sep 21, 2026cs.CV

MIND the Gap: A Geographic Implicit Neural Representation with Adjustable Spatial Scale

Geographic measurements are often sparse, leaving large areas without labels for the quantities we want to map. Geographic implicit neural representations (INRs) address this by learning smooth, general-purpose embeddings that can be queried at any coordinate. Downstream models combine these embeddings with sparse labels to predict target values at unsampled locations without satellite imagery at inference. However, generalization to distant regions remains largely unexplored, despite its importance for remote sensing applications. We introduce Matryoshka Implicit Neural Distillation (MIND), which distills embeddings from specialist pretrained geospatial models into a single generalist coordinate embedding with adjustable spatial granularity. MIND uses nested supervision at several embedding dimensions, which define a series of contiguous chunks. In our experiments, early chunks capture coarser geographic variation, while later chunks add more fine-grained details. A downstream predictor can retain only leading chunks or be fitted with our Chunked Penalty to downweight later chunks while keeping the full embedding, without retraining the INR. To measure MIND and compare to existing approaches around the world, we introduce CoordBench, a large-scale INR evaluation suite of

52

datasets and

78

targets that aims to test both local interpolation and prediction in held-out regions at various spatial scales. MIND and its Chunked Penalty variant achieve the highest aggregate regression and classification scores among tested INRs, and the highest scores overall under regional holdout, setting a new state-of-the-art for geographic INRs.

Isaac Corley, Arjun Rao, Esther Rolf +7

Taylor Geospatial · University of British Columbia · Vector Institute +7

Geospatial Representation Learning Hierarchical Representation Learning Spatial Generalization Knowledge Distillation

Sep 21, 2026cs.CV

Hierarchical Prompt Learning for Hyperbolic Vision-Language Models

Hyperbolic vision-language models (VLMs) represent image and text features in a geometry naturally suited to hierarchy, but their adaptation to downstream tasks has largely relied on fixed prompts. Existing prompt learning methods, meanwhile, treat class labels as a flat set and do not exploit available taxonomic structure. We address this gap with a hierarchical prompt learning plug-in for frozen hyperbolic VLMs. Given a fixed offline parent-class hierarchy, it augments a class prompt learner with a separate parent prompt learner, parent-level supervision, hyperbolic entailment regularization, and parent-feedback logit fusion. We instantiate the method with CoOp, CoCoOp and MaPLe, yielding HyPLO, CoHyPLO and MaHyPLO. Across the standard 11-dataset benchmark, all variants improve base-to-new generalization and cross-dataset transfer, and remain comparable to their prompt learning baselines under domain shift. Six hierarchical metrics and embedding analyses show that the method produces more taxonomically consistent predictions and induces a hierarchy-consistent organization of parent, class, and image embeddings in hyperbolic space. Its gains are largest when novel classes must be placed within a fixed taxonomy, and smallest for fine-grained confusions among sibling classes or shifts affecting only the image distribution.

Andro Erdelez, Pascal Mettes, Behzad Bozorgtabar

Aarhus University · University of Amsterdam

Vision-Language Models Prompt Learning VLM Adaptation Hierarchical Representation Learning Image Classification

Sep 21, 2026cs.CV

The Visual Target Matters: Learning across the Visual Hierarchy for Brain-to-Image Retrieval

Brain-to-image retrieval seeks to identify the visual stimulus that elicited a non-invasive neural response. Candidate images are typically represented by pretrained vision models, whose internal representations vary in abstraction across depth. Existing methods usually train the neural encoder to recover a fixed final-layer visual target. Under this formulation, the visual hierarchy is reduced to a single prescribed endpoint, preventing representations at other depths from directly shaping the visual target. This limitation motivates learning how information across visual depths should contribute to the retrieval target. To this end, we introduce NeuroGlyph, which learns a trial-independent visual target from multiple depths of a frozen visual backbone. NeuroGlyph decomposes the target into factor-specific subspaces. Each subspace learns an image-conditioned allocation over visual depth. The resulting subspaces are fused into a single embedding for retrieval. Across THINGS-EEG and THINGS-MEG, NeuroGlyph outperforms final-layer supervision in all controlled comparisons. It also surpasses the post hoc best fixed-layer oracle in three of four comparisons. Parameter-matched ablations support both factorized target construction and image-conditioned depth allocation. Under comparable 200-way retrieval protocols, NeuroGlyph achieves the strongest system-level performance in six of eight reported metrics. These results support learning retrieval targets across the visual hierarchy rather than prescribing one visual depth.

Ye Wang, Haokun Ren, Hong Yu +4

School of Artificial Intelligence, Chongqing University of Posts and Telecommunications, Chongqing, China · College of Information Science and Technology, Beijing University of Chemical Technology, Beijing, China · Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Hong Kong, China +1

Visual Representation Learning EEG-Based Visual Decoding Hierarchical Representation Learning Cross-Modal Retrieval

Sep 21, 2026cs.CV

HDND: Hierarchical Dynamic Neural Decoding for Multilingual Word/Character Retrieval from Non-Invasive Brain Recordings

While deep learning has enabled language decoding from intracranial brain recordings, extending this capability to non-invasive recordings remains an unresolved challenge. Decoding individual words from non-invasive brain recordings is particularly difficult, as word-level neural evidence is weak, temporally distributed, and entangled with acoustic, lexical, and semantic structure. Existing retrieval pipelines often collapse these factors into a single representation, potentially discarding information available at intermediate temporal scales. Here, we introduce Hierarchical Dynamic Neural Decoding (HDND), a hierarchical dynamic decoding framework that treats word decoding as structured refinement rather than flat label retrieval. HDND combines intermediate neural representations, contextual semantic predictions, and, for selected reading conditions, an auxiliary character-form objective. We evaluate HDND across seven electroencephalography (EEG) and magnetoencephalography (MEG) datasets spanning English, Dutch, Mandarin, and Cantonese listening, reading, and reading-aloud conditions. Across the nine-condition word-retrieval benchmark, the proposed HDND yields a higher participant-averaged balanced Top-10 point estimate than the matched contextual word-decoding baseline in every condition and achieves the highest mean among all compared methods in eight of nine conditions. Across the same nine matched conditions, HDND also yields higher token-micro and pooled word-macro Top-10 point estimates in every setting. Sentence retrieval favors HDND in eight of nine conditions, while auditory speech-segment retrieval is mixed across the six listening conditions. These results show that hierarchical residual refinement can improve multilingual word retrieval from heterogeneous non-invasive brain recordings.

Yueyang Li, Shuran Chen, Wai Ting Siok +1

Department of Language Science and Technology, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR, China

Dynamic Neural Networks Neural Decoding EEG Decoding Hierarchical Representation Learning

Sep 21, 2026cs.CV

InterHier: Learning Interconnected Hierarchical Semantics for Open-Vocabulary Object Detection

In this paper, we investigate the limitations of fixed, hand-crafted connectors in hierarchical semantic representations for open-vocabulary object detection. Existing methods establish semantic relationships between base categories and unseen novel categories by placing a fixed connector between adjacent super-/sub-categories. However, such fixed connectors may not optimally capture the relationships within a semantic hierarchy. To address this limitation, we propose interconnected hierarchical semantic representations (InterHier), which utilize a prepended learnable context to globally guide the interpretation of prompts containing hierarchical relationships. InterHier operates in two main stages. First, it constructs a hierarchy-aware prompt by integrating super-/sub-categories and prepending a learnable context. Second, it optimizes this learnable context to align visual region embeddings and textual embeddings. InterHier consistently improves performance over methods that rely on fixed connectors and can be seamlessly integrated into existing open-vocabulary object detection models. Experiments on open-vocabulary object detection benchmarks demonstrate that InterHier achieves competitive performance against state-of-the-art methods.

Yeong-Jin Kim, Ho-Joong Kim, Seong-Whan Lee

Department of Artificial Intelligence, Korea University, Seoul 02841, Republic of Korea

Open-Vocabulary Object Detection Prompt Learning Hierarchical Representation Learning Vision-Language Alignment

Sep 17, 2026cs.LG

Pretrained Medical Representations for the Practical Screening of Drug Repositioning Candidates

Representation learning from medical code sequences in electronic health records and medical claims data has been successful in various clinical applications, such as those regarding disease prediction. However, significant challenges remain in extending this approach to the discovery of scientific hypotheses. One reason is that many existing BERT-based models fail to adequately capture the hierarchical structure of medical codes and the complex interactions between diagnoses and treatments. To address these limitations, we propose a new unified pre-training framework that explicitly integrates hierarchical sub-token aggregation, partial masking, and cross-reference mechanisms. The proposed model consistently outperformed existing methods on both pre-training objectives and downstream clinical event prediction tasks, including the onset of dementia and hospitalization. We also conducted an in silico drug repositioning case study targeting Alzheimer's disease. In the hypothesis generation step, our approach successfully rediscovered known promising drugs in a data-driven manner without relying on such external knowledge sources as the literature. Subsequently, in the hypothesis prioritization step, we introduced a Task-Adaptive Representation Approach to alleviate the over-encoding of historical prescription information within diagnostic vectors, enabling the robust prioritization of generated hypotheses. This study establishes an exploratory screening workflow for hypothesis generation and prioritization based on observational associations. Importantly, this framework is not intended to provide causal evidence, but rather to identify promising candidates for subsequent rigorous causal inference. Overall, this study demonstrates that domain-informed representation learning combined with task-adaptive representation control can enable a practical hypothesis discovery workflow.

Yuhei Fujioka, Daitaro Misawa, Shingo Fukuma

Cancerscan Inc., Tokyo, Japan · Kyoto University, Graduate School of Medicine, Kyoto, Japan · Hiroshima University, Graduate School of Biomedical and Health Sciences, Hiroshima, Japan

Representation Learning Hierarchical Representation Learning Predictive Representation Learning Longitudinal EHR Modeling

Sep 16, 2026math.NA

HiLNO: A Hierarchical Latent Neural Operator with Multi-Scale Supervision for PDEs on General Geometries

Latent neural operators improve the efficiency of operator learning for partial differential equations (PDEs) by performing the main computation on compact latent representations. However, directly compressing the input representation to obtain such compact representations may discard solution-relevant spatial information, especially for PDE solutions with multiscale structures. To address this problem, we propose HiLNO, a hierarchical latent neural operator that constructs a fine-to-coarse-to-fine latent space and further introduces multi-scale supervision (MSS) and anisotropic Gaussian attention. The hierarchy mitigates potential information loss during compression, while MSS aligns intermediate predictions with downsampled target fields, encouraging solution-relevant structures to be captured across multiple spatial scales. Anisotropic Gaussian attention enables feature transfer across the hierarchy, making HiLNO applicable to general geometries. Experiments on representative PDE benchmarks and a large-scale automotive aerodynamics task show that HiLNO achieves competitive predictive accuracy, while reducing the parameter count by an average of 84.4% and FLOPs by an average of 69.2% compared with LinearNO. Additional experiments demonstrate effective generalization to unseen spatial resolutions. Code is available at https://github.com/JcLimath/HiLNO.

Zhicheng Hu, Jiacheng Li, Min Yang

School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China · Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA), MIIT, Nanjing, 211106, China · School of Mathematics and Information Sciences, Yantai University, Yantai, China

Hierarchical Representation Learning Multi-Scale Feature Fusion PDE Operator Learning Neural Operators

Sep 14, 2026cs.LG

Multi-View Molecular Representation Learning with Hierarchical Graphs and Contextualized Fingerprints

Molecular property prediction requires representations that generalize from limited labeled data to structurally novel compounds. Existing molecular pretraining methods often rely on a single view: graph-based approaches model atom-bond topology but provide limited fragment-level supervision, whereas fingerprint descriptors encode chemical patterns but are typically used as fixed auxiliary features. We propose HiFi-Mol, a multi-view framework that separately pretrains a hierarchical graph encoder and a contextualized fingerprint encoder before downstream integration. The graph branch uses fragment-aware masking with multi-resolution supervision to capture substructure-aware representations, while the fingerprint branch tokenizes active entries from seven fingerprint families and applies masked language modeling to learn contextualized embeddings. During fine-tuning, HiFi-Mol combines projected multi-resolution graph features with fingerprint embeddings for downstream prediction. Evaluated on MoleculeNet benchmarks under the scaffold split, HiFi-Mol achieves a 2.77% improvement in average ROC-AUC over the best baseline across eight classification tasks while maintaining competitive performance on three regression tasks. Further analyses reveal that fragment-aware masking improves graph representation quality, and classification results demonstrate dataset-dependent strengths of the individual graph and fingerprint variants, confirming that the two views provide complementary predictive signals.

Gwang-Hyeon Yun, Jong-Hoon Park, Bing Hu +3

Yonsei University · Wonju-si, Republic of Korea · University of Waterloo +1

Graph SSL Hierarchical Representation Learning Multi-View Learning Molecular Property Prediction Molecular Representation Learning

Sep 14, 2026cs.AI

CMA-OT: Hierarchical Expert Supervision for Dance-to-Music Generation

Dance-to-music (D2M) generation aims to synthesize music that is rhythmically and stylistically aligned with dance videos. A key challenge arises from the semantic mismatch between sparse dance cues, such as rhythm and style, and the dense information required for music composition, including structure, instrumentation, and expressive dynamics. Existing methods typically rely on these sparse cues and supervise only the final audio output, resulting in poorly learned music representations and generated music with limited musicality and structural coherence. To address these issues, we propose Curriculum-guided Multi-scale representation Alignment with scale-aware Optimal Transport (CMA-OT), a novel paradigm that leverages an external music expert to provide hierarchical supervision for the generator's latent features, bridging the semantic gap and enhancing representation learning. To effectively incorporate hierarchical supervision, we introduce a curriculum-guided multi-scale learning strategy that progressively transfers musical knowledge from the expert to the music generator, enabling stable and effective representation learning. Moreover, to accommodate the semantic and structural variations across different expert scales and achieve fine-grained alignment under temporal mismatch, we propose a scale-aware optimal transport alignment mechanism, which models soft correspondences between hierarchical expert representations and the generator's latent features. Extensive experiments on two datasets demonstrate that CMA-OT achieves state-of-the-art performance in rhythmic synchronization, perceptual quality, and overall music generation.

Jinting Wang, Chenxing Li, Dong Yu +1

HKUST(GZ) · Tencent

Cross-Modal Alignment Hierarchical Representation Learning

Sep 11, 2026cs.AI

Diffusion Models and Concept Formation

Humans organize knowledge into a taxonomy of concepts with nested levels of abstraction and a \emph{basic level} at which people recognize and name objects with the least cognitive effort. Cobweb is a classic cognitive account of this ability, an incremental learner that builds a probabilistic concept hierarchy by maximizing category utility. We argue that diffusion models, although designed for image synthesis, implicitly perform the same computation. The noisy marginals of a diffusion model are Gaussian smoothings of the data distribution, and the modes of these marginals form a hierarchy that corresponds to a Cobweb tree of probabilistic prototypes in four respects. Both are hierarchical density models, both are hierarchical-Bayesian models with Gaussian prototypes, both treat categorization as score-following that reduces uncertainty, and in both a basic level emerges. We locate this basic level for a diffusion model at an intermediate noise level, where recent analyses show that the reverse process commits to the class identity of a sample. The two models differ mainly in how they represent and learn the taxonomy. Cobweb learns a discrete tree incrementally, whereas a diffusion model encodes a continuous, interpolable hierarchy in a single learned score field fit to the data distribution. We test the correspondence on MNIST and Fashion-MNIST by recovering the diffusion hierarchy through mode-finding and comparing the basic levels of the two models. This reframes diffusion as a cognitive model of concept formation and offers Cobweb a continuous, scalable instantiation.

Zekun Wang, Karthik Singaravadivelan, Christopher J. MacLellan

College of Computing, Georgia Institute of Technology, Atlanta, GA 30332 USA

Cognitive Modeling Hierarchical Representation Learning Hierarchical Bayesian Modeling Diffusion Models

Sep 9, 2026cs.LG

Hierarchical and Permutation-Invariant Feature Transformation Learning via Policy-Guided Embedding Search

Feature transformation improves predictive performance on tabular data by constructing informative abstractions from raw features. Recent generative approaches encode transformation knowledge into continuous embedding spaces for efficient exploration of candidate strategies, but face three key limitations: (1) overlooking hierarchical relationships between low-level features, operations, and high-level abstractions; (2) enforcing order-sensitive embeddings on inherently permutation-invariant transformation sequences, thereby introducing systematic bias; and (3) relying on gradient-based search, which is ill-suited to non-convex transformation spaces. We propose a framework with two complementary components. First, a permutation-invariant hierarchical module captures interactions across features, operations, and abstraction levels, with a self-attention pooling mechanism that maps semantically equivalent structures to consistent embeddings aligned with downstream performance. Second, a policy-guided multi-objective reinforcement learning strategy initializes the search from empirically strong seeds and jointly optimizes predictive accuracy and transformation efficiency. Extensive experiments on diverse tabular benchmarks demonstrate the effectiveness and robustness of our framework against strong baselines. Our code and data are publicly available at: https://github.com/RayLiu1103/PHER.

Rui Liu, Tao Zhe, Yanyong Huang +5

University of Kansas Lawrence, United States · Southwest University of Finance and Economics Chengdu, China · University of Wisconsin–Madison Madison, United States +3

Representation Learning Hierarchical Representation Learning Permutation-Invariant Learning Automated Feature Engineering

Sep 8, 2026cs.LG

HypLTSF: A Hyperbolic Geometric View of Multi-Scale Hierarchies for Long-Term Time Series Forecasting

Multi-scale modeling has become an effective approach for long-term time series forecasting, capturing temporal patterns that range from fine-grained local dynamics to coarse global trends. Representations across these temporal scales are inherently hierarchical, with coarser scales abstracting and aggregating information from finer ones. While existing approaches readily exchange information across these scales, the hierarchy itself is typically left as an emergent byproduct of such interactions rather than captured as a geometric structure in its own right. In this paper, we introduce HypLTSF, a framework that endows the multi-scale hierarchy with a concrete geometric form by embedding scale-wise representations into the Poincaré ball, whose exponentially expanding volume naturally accommodates hierarchical structures. To align this geometry with the temporal hierarchy, HypLTSF imposes two constraints: (1) a radial constraint that orders embeddings by their level of abstraction, and (2) an angular constraint that groups fine-scale patterns sharing a common coarser-scale ancestor. Extensive experiments on long-term time series forecasting benchmarks show that HypLTSF achieves state-of-the-art performance, suggesting that explicitly modeling the multi-scale hierarchy as a geometric structure is effective for forecasting.

Namwoo Kim, Hyungryul Baik, Yoonjin Yoon

Urban AI Institute, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea · Department of Mathematical Science, KAIST, Daejeon, Republic of Korea · Department of Civil and Environmental Engineering, KAIST, Daejeon, Republic of Korea

Long-Term Time Series Forecasting Hierarchical Representation Learning Multiscale Time-Series Modeling Hyperbolic Representation Learning

Sep 2, 2026cs.LG

ProbeMatchDTI: Probe-Driven Multi-Scale Biochemical Pattern Matching for Drug-Target Interaction Prediction

Drug-target interaction (DTI) prediction is an important task in AI-driven drug discovery. Although recent biochemical representation learning methods have improved DTI prediction, their passive feature aggregation tends to favor dominant molecular patterns while suppressing weak yet binding-relevant signals, such as functional groups and residue-context patterns, limiting the modeling of multi-scale biochemical correspondences. To address this issue, we propose ProbeMatchDTI, a pattern-probe-driven framework comprising IterProbe and BindingProbe. IterProbe explicitly retains contextual states across refinement depths and uses learnable probes to select them at each position before cross-entity matching, thereby preserving weak biochemical patterns and strengthening associations among functional groups, local motifs, and molecular scaffolds. BindingProbe then characterizes cross-entity drug-protein complementarity at local biochemical-unit and whole-pair levels, jointly modeling fine-grained interactions and multi-scale correspondences while preserving weaker binding-relevant associations. Extensive experiments demonstrate the superiority of ProbeMatchDTI, achieving 2.0% and 0.5% higher AUC-ROC on BindingDB and DrugBank, respectively. Feature-level pattern analyses further characterize its probe-driven behavior in cross-scale biochemical pattern matching. We further connect ProbeMatchDTI predictions with an evidence-guided downstream drug-discovery workflow, demonstrating their utility for candidate refinement and validation planning. Our code is available at https://github.com/developer-hq/ProbeMatchDTI

Quan Hao, Mengyue Fan, Zifan Dong +8

School of Computer Science and Engineering, University of New South Wales, Sydney, Australia

Drug Discovery AI-Assisted Scientific Research Hierarchical Representation Learning

Sep 1, 2026cs.AI

H2Table: Hierarchical Hypergraph-Enhanced Large Language Models for Complex Table Reasoning

Tables are ubiquitous across diverse domains, yet reasoning over them remains a significant challenge for modern large language models (LLMs). Current approaches typically linearize tables into sequences, inherently overlooking their intrinsic two-dimensional and hierarchical structure. To address this, we propose H2Table (Hierarchical Hypergraph-Enhanced Table Reasoning), a novel framework that represents complex tables as hierarchical nested hypergraphs. To process this representation, we design a tailored hypergraph encoder to facilitate message passing between hyperedges (headers) and nodes (cells), thereby perceiving the semantic entailment relationships between them within complex tables. Furthermore, we introduce a set of learnable query vectors acting as a lightweight bridge to extract representative structural embeddings from the encoder into the LLM. Experimental results demonstrate that our approach effectively handles complex table question answering tasks with hierarchical nested headers. Notably, on the HiTab dataset, H2Table achieves an average improvement of 22.88% over state-of-the-art baselines on highly complex tables with a nesting depth of four. Our code is available at: https://github.com/lila120/h2table.

Jia Ling, Yangfan Wang, Chen Tang +4

Harbin Institute of Technology · AI Research Center, Midea Group (Shanghai) Co., Ltd. · Changchun University of Science and Technology +1

Table QA Hierarchical Representation Learning Hypergraph Neural Networks Tabular Representation Learning

Aug 30, 2026cs.AI

Spatial Matryoshka Training for Multi-Granularity Visual Document Retrieval

Multi-modal late-interaction retrievers achieve strong retrieval on visually rich documents by representing each page as per patch embeddings and matching at the token level. However, this approach incurs high storage costs. Existing compression methods typically fix a single compression level at indexing time, limiting flexibility. We present ColSNAP (Spatial Nested Average Pooling)1, a training method that generates a nested hierarchy of compression levels directly from a backbone's patch grid. By spatially pooling patch embeddings into pro- gressively coarser tiers and training all tiers simultaneously, a single model learns to support retrieval at multiple compression levels without architectural changes. Crucially, a single encoding pass yields every tier, enabling the accuracy-storage trade-off to be configured at indexing time to match avail- able storage budgets, rather than being fixed during training. We demonstrate that models trained using ColSNAP maintain near full-resolution retrieval performance under substantial compression and that ColSNAP transfers effectively across multiple late-interaction backbones, and achieves most of its improvements via a lightweight adaptation stage applied to a pre-trained retriever.

Trishan Singha Roy, Arkadeep Acharya, Vishwajeet Kumar +2

IIT Delhi · IBM

Hierarchical Representation Learning Matryoshka Representation Learning Multi-Vector Retrieval Visual Document Retrieval Visual Token Compression

Aug 11, 2026cs.CV

Multiple Scale Latents for Learned Image Compression

Most learned image compression systems rely on a single latent representation combined with a hyperprior, which limits their ability to efficiently capture image structure across spatial scales. In this work, we propose a hierarchical latent representation to improve the efficiency of the entropy model. By using multiple latents at different scales, each with its own entropy model, we better capture the spatial structure of the latent representation. Our experiments show that this approach achieves a 17.9% BD-rate reduction over VVC on Kodak, demonstrating the effectiveness of multi-scale latent representations. Furthermore, the approach is orthogonal to other advances in learned image compression, making it a versatile addition to existing methods.

Jonas Brenig, Radu Timofte

Learned Image Compression Representation Learning Hierarchical Representation Learning

Aug 10, 2026cs.LG

Hierarchical rank-evolving representation for physics-informed neural networks

Recently, tensor-based physics-informed neural networks (T-PINNs) have received increasing attention. However, existing T-PINNs still face a fundamental challenge: they mainly rely on pre-specified low-rank tensor decompositions with manually tuned ranks, which limits their ability to capture the underlying structures of multivariate solution functions and hinders their practical deployment. To address this challenge, we propose a hierarchical rank-evolving (abbreviated as HRE) representation for multivariate functions, which endows us to faithfully capture the underlying structure of the targeted multivariate function accompanying with automatic rank determination. Concretely, in the hierarchical design of HRE representation, the target multivariate function is decomposed as a small-scale inner tensor with a set of univariate functions along each mode, where a customized tensor network decomposition can be readily deployed to capture the underlying structure of the small-scale inner tensor. In HRE representation, the crucial hyperparameters, ranks, can be adaptively revealed during the decomposition, freeing us from manual rank tuning and making HRE practically applicable to real-world problems. Besides, we build the HRE-PINNs correspondingly. Extensive numerical experiments, including high-dimensional static problems (Helmholtz equation and Poisson equation), nonlinear time-dependent problems (Klein-Gordon equation), and complex fluid-dynamics problems (flow mixing equation and Navier-Stokes equation), demonstrate that HRE-PINNs consistently outperform existing state-of-the-art approaches in terms of accuracy.

Ruoyang Su, Xi-Le Zhao, Kun Li +1

University of Electronic Science and Technology of China, No.2006, Xiyuan Ave, West Hi-Tech Zone, Chengdu, 611731, Sichuan, P.R.China · Southwestern University of Finance and Economics, 555, Liutai Avenue, Wenjiang District, Chengdu, 611130, Sichuan, P.R.China

Tensor Networks Neural PDE Solvers Hierarchical Representation Learning Tensor Decomposition Physics-Informed ML

Aug 8, 2026cs.LG

FreSH: Frequency-Segmented Hierarchical Multi-Expert Framework for Multivariate Time Series Classification

Multivariate Time Series Classification (MTSC) demands models that can effectively capture complex temporal patterns across multiple scales while remaining computationally efficient. However, existing approaches generally struggle to reconcile fine-grained representation learning, especially under class imbalance and real-world constraints. In this paper, we present FreSH, a Frequency-Segmented Hierarchical Multi-Expert Framework designed to address these challenges. FreSH introduces a new perspective for MTSC by enabling adaptive, multi-scale analysis of temporal signals, allowing different aspects of the data to be modeled in a complementary and coordinated manner. By combining localized specialization with holistic context modeling, FreSH achieves strong representational capacity without incurring excessive computational overhead. An adaptive fusion strategy further enhances flexibility, enabling the model to dynamically emphasize the most informative components of the input. In addition, we incorporate a more robust optimization objective that improves learning stability across varying sample difficulties and class distributions. Extensive evaluations on 30 UEA benchmark datasets and real-world vibration data demonstrate that FreSH consistently outperforms state-of-the-art methods in classification accuracy, while substantially reducing model size and efficiency.

Pingping Liu, Muyao Wang, Zijian Zhang +5

1Jilin University · 2Hong Kong Polytechnic University · 3Pengcheng Laboratory +1

Multivariate Time Series Classification Time Series Classification Mixture of Experts Frequency-Domain Feature Learning Hierarchical Representation Learning Multiscale Time-Series Modeling

Aug 7, 2026cs.CV

H2AL: Hyperbolic Hierarchy-aware Aggregative Learning for Registration-based Few-shot Medical Image Segmentation

Registration-based Few-shot medical image segmentation (RFMIS) aims to generate pseudo-labels for unlabeled images by warping a labeled image through registration. However, existing methods primarily perform pixel-level optimization and inference in Euclidean space, treating anatomical structures as flat and disjoint. This neglect of inherent hierarchies degrades pseudo-label quality and weakens the discrimination of ambiguous regions, limiting the segmentation performance. To overcome this challenge, we propose a Hyperbolic Hierarchy-aware Aggregative Learning framework for RFMIS, termed H2AL, that enhances both deformation plausibility and anatomical discrimination for dual-task learning. Specifically, we introduce a Hyperbolic Hierarchy-aware Infusion (H2I) module, which leverages the hierarchical modeling capability of hyperbolic space to learn precise hierarchy-aware representations via transformation-guided supervised hyperbolic contrastive learning, and injects such hierarchical priors into Euclidean space through a gated infusion block while preserving semantic richness. Furthermore, we propose an end-to-end joint optimization algorithm by gradient aggregation, where the gradients from the registration and segmentation decoders, embedding semantic and hierarchical cues, are aggregated to update the shared encoder to promote collaborative learning across tasks. Extensive experiments on two anatomical regions, with five experimental settings, demonstrate the effectiveness and efficiency of our method in both registration and segmentation. The code is publicly available at https://github.com/JiamingCai469/H2AL.

Jia Wang, Jiaming Cai, Zunying Hu +4

Hierarchical Representation Learning Medical Image Registration Few-Shot Medical Image Segmentation Hyperbolic Representation Learning

Aug 6, 2026q-bio.NC

Convergent Evolution in Neural Representation Space: Emergent Order in Deep Belief Networks

Deep Belief Networks (DBNs) learn hierarchical generative models without class supervision. Here, we ask whether this purely unsupervised process nevertheless organizes internal representations according to the unknown data classes. We analyze successive layers of DBNs trained on MNIST, Fashion-MNIST, and KMNIST using the Generalized Discrimination Value (GDV), supervised probes applied only after training, a reconstruction-based measure of abstraction distance, effective dimensionality, and free sample generation. Remarkably, class-specific clustering generally increases with depth across datasets and network widths, although no label information is available during DBN training. Control experiments show that this effect depends on the learned feature structure and cannot be explained by random transformations, weight marginals, dimensionality reduction, or sigmoid saturation. The first hidden layers also frequently make class identity more accessible to linear and nonlinear probes. With greater depth, representations become increasingly compact and prototype-like as neurons acquire correlated feature directions. At the same time, GDV and probe accuracy reveal complementary aspects of class structure: improved average clustering can coexist with reduced accessibility for a few difficult class pairs. These findings demonstrate that layer-wise generative learning can spontaneously uncover and progressively amplify class-related structure in unlabeled data.

Patrick Krauss, Achim Schilling, Andreas Maier +2

Cognitive Computational Neuroscience Group, Pattern Recognition Lab, Friedrich-Alexander-University Erlangen-Nürnberg (FAU), Germany · Neuromodulation and Neuroprosthetics, University Hospital Mannheim, University Heidelberg, Germany · Neuroscience Lab, University Hospital Erlangen, Germany +1

Representation Geometry Hierarchical Representation Learning Unsupervised Clustering Unsupervised Representation Learning

Aug 3, 2026cs.CV

SWINSleepNet: A Hierarchical Context-Aware Framework for Sleep Staging (v2)

Automatic sleep staging is a critical role in sleep disorder diagnosis, sleep quality assessment, and long-term health monitoring; however, existing approaches suffer poor performance on ambiguous and transition-related sleep stages, caused by inadequate modeling of fine-grained intra-epoch structures and complex cross-region spectral dependencies. Traditional epoch-level encoders commonly fail to extract subtle temporal microstructures and intra-epoch cross-region interactions, resulting in unsatisfactory recognition accuracy for hard categories such as the N1 stage. To tackle these drawbacks, we propose SwinSleepNet, a hierarchical context-aware dual-stream framework that separately optimizes intra-epoch representation learning and inter-epoch contextual modeling. Concretely, we characterize each sleep epoch from two complementary perspectives: raw time-domain EEG signal and its time-frequency transformation. The time-domain branch adopts convolutional encoders to capture fine waveform temporal details, and the time-frequency branch uses Swin Transformer to extract local spectro-temporal features, hierarchical multi-scale information and long-range spatial dependencies. The multi-branch extracted features are fused into integrated embeddings, which are optimized by a bidirectional context module to capture cross-epoch temporal dependencies for final sleep stage classification. Comprehensive experiments on Sleep-EDF-20, Sleep-EDF-78 and SHHS datasets verify that our method achieves competitive overall performance, and exhibits stronger robustness and stability on difficult N1 stages and transitional epochs. The results prove that optimized intra-epoch representation learning based on hierarchical architecture greatly benefits automatic sleep staging tasks.

Chongjian Wang, Junjie Gao

School of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, China · School of Artificial Intelligence, Shandong Women’s University, Jinan 250352, Shandong, China

Sleep Stage Classification Hybrid CNN-Transformer Architectures Hierarchical Representation Learning

Aug 1, 2026cs.LG

HP-JEPA: Hierarchical Partitioning for Multi-Resolution Graph Joint-Embedding Predictive Learning

Graph self-supervised learning aims to learn transferable representations from large-scale unlabeled graph data. Joint-embedding predictive architectures (JEPAs) avoid explicit negative-pair construction and raw-input reconstruction by predicting masked targets directly in latent space. However, existing graph JEPAs typically rely on a single predefined graph partition, biasing the learned representations toward one structural granularity and limiting their ability to capture complementary patterns at different graph scales. To address this limitation, we propose HP-JEPA, a hierarchical partitioning framework for multi-resolution graph joint-embedding prediction. HP-JEPA organizes each graph into an ordered bank of coarse-to-fine partition resolutions and performs context-target latent prediction separately at each resolution using an online encoder, an exponential-moving-average target encoder, and a latent predictor. The resulting resolution-specific graph representations are subsequently integrated through concatenation or task-specific resolution weighting, allowing downstream models to combine complementary local, regional, and global structural information. Experiments on seven graph classification benchmarks and one graph regression benchmark show that HP-JEPA outperforms the fixed-resolution Graph-JEPA baseline on 6 of 8 tasks, improving upon Graph-JEPA on most evaluated benchmarks. Size-stratified analyses further show that HP-JEPA achieves higher accuracy than Graph-JEPA in most evaluated graph-size quartiles on three representative datasets. These results highlight the effectiveness of hierarchical multi-resolution partitioning for transferable graph representation learning.

Ruichen Xu, Jingxiang Qu, Wenhan Gao +5

Department of Applied Mathematics and Statistics Stony Brook University Stony Brook, NY, USA · Department of Computer Science Stony Brook University Stony Brook, NY, USA · TikTok Bellevue, WA, USA +2

Graph Representation Learning Graph SSL Joint-Embedding Predictive Architecture Hierarchical Representation Learning Graph Classification