Hierarchical Representation Learning

Biological visual systems learn from limited experience, unlike deep learning models that rely on millions of training images. What learning principles make this possible? We tested whether efficient coding, the idea that neural representations capture the statistical structure of natural inputs, can build a hierarchy of human-aligned visual features from limited data. We developed an unsupervised learning procedure in which each layer of a deep network compresses its inputs onto the dominant modes of variation in natural images, using only local statistics and no labels, tasks, or backpropagation. This unsupervised procedure yields features that progress from edges and colors to textures and shapes. The features of this deep efficient coding model are readily recognized by human observers and are predictive of image-evoked fMRI responses in human visual cortex. Furthermore, a hybrid learning procedure that combines efficient coding with supervised fine-tuning yields better brain alignment in low-data settings and more rapid category learning. These findings suggest that efficient coding may shape representations across the entire visual hierarchy and help explain the data efficiency of biological vision.

The brain learns abstract representations of high-dimensional sensory input, but the plasticity rules that enable such learning are unknown. We study biologically plausible algorithms on the Random Hierarchy Model (RHM), an artificial dataset designed to investigate how deep neural networks learn the intrinsic hierarchical structure of high-dimensional data. We focus on two types of local learning rules that avoid both a long convergence time and the use of a symmetric error network. The first type uses direct feedback signals to approximate error propagation from the output layer. The second type uses layerwise self-supervised contrastive or non-contrastive loss functions that do not explicitly approximate errors at the output layer. We show that all rules of the first type fail to solve the tasks of the RHM and trace this failure back to input-specific nonlinearities (`masking') that are implemented in full backpropagation and are essential for learning complex tasks. However, algorithms of the second type are able to learn the hierarchical hidden structure of the RHM tasks and are as data-efficient as supervised backpropagation training, while being compatible with known rules of synaptic plasticity in cortex.

Graph Neural Networks and Graph Transformers have become central to graph learning, combining expressive representation learning with sample-efficient inductive biases. Yet they remain fundamentally limited when predictions depend on correlations between distant graph regions. We address this limitation with Graph Hierarchical Recurrence (GHR), a novel framework that jointly operates on the input graph and a pooled hierarchical abstraction. We also show that existing models degrade more sharply under out-of-range generalization, where test instances require interactions across distances exceeding those observed during training. Despite its minimal design, GHR consistently strengthens every tested message-passing backbone, yielding robust performance on long-range dependencies and particularly pronounced gains in out-of-range regimes. Across a broad suite of long-range benchmarks, GHR achieves state-of-the-art or competitive results on multiple tasks, establishing hierarchical recurrence as an effective mechanism for extending graph models beyond their observed interaction range.

As a modern commodity, language has become a vast repository of socially and psychologically significant traits and concepts, reflecting the ways people encode pattern of thoughts, behaviors, and emotions into words. Text-based Automatic Personality Prediction (APP), seeks to infer personality from linguistic behavior, offering a scalable alternative to traditional psychometric assessments. Although text is inherently hierarchical, with the document-level capturing global features, the sentence-level encoding local semantics, and the word-level providing fine-grained lexical information, most existing approaches rely on shallow, sequential, or single-level representations that ignore the multi-level structure of written language. To address this, we propose HyperPersona, a framework that explicitly models the hierarchical organization of text (document, sentence, and word) through hypergraph structure, where a document and its sentences are represented as hyperedges, and the words are represented as nodes, enabling joint modeling of global, local, and lexical dependencies of text. Followed by a transformer-based graph encoder that learns interactions within and across these linguistic layers, yielding context-sensitive and structurally grounded feature representations for personality prediction. Experiments on the Big Five personality dimensions show that, while relying solely on text, HyperPersona effectively integrates multi-level linguistic cues, achieving superior performance compared to state-of-the-art baselines. These findings underscore the critical role of textual hierarchy in advancing human-like personality inference from natural language.

Decoding visual information from electroencephalography (EEG) signals remains a fundamental challenge in brain-computer interfaces and medical rehabilitation. Existing EEG visual decoding methods mainly focus on learning a single global EEG embedding for cross-modal alignment, but they largely overlook the staged and hierarchical characteristics of human visual processing. To address this limitation, we propose a neuroscience-inspired staged representation learning framework that reformulates EEG visual decoding as a stage-specific representation decomposition problem. The proposed framework organizes EEG representation learning into three complementary phases: low-level visual representation learning, high-level semantic representation learning, and integrative information fusion. To strengthen semantic modeling, we further introduce a multimodal dual-level semantic learning mechanism that separates coarse label-level semantics from fine image-level visual-semantic information. In addition, semantic latent channels are introduced as computational representation channels generated from observed visual EEG signals, expanding the channel-level semantic representation space for structured semantic abstraction and cross-modal alignment. Extensive experiments on the THINGS-EEG benchmark demonstrate that the proposed method achieves superior performance under subject-dependent zero-shot evaluation and improved exact retrieval under subject-independent zero-shot evaluation. Additional analyses, including layer-wise retrieval, temporal accumulation, expanded multi-image retrieval, and ablation studies, further support the effectiveness of staged decomposition and structured semantic modeling. These results suggest that explicitly modeling staged perceptual, semantic, and integrative representations provides an effective neuroscience-inspired framework for EEG-based visual decoding.

Multimodal emotion recognition aims to integrate text, audio, and video sources to understand human affective states. Although multimodal large language models excel at multimodal reasoning, they typically treat emotion categories as independent labels, ignoring the rich hierarchical taxonomy of human psychology. Moreover, lacking external contextual knowledge makes them highly susceptible to over-interpreting noisy cues, further complicating fine-grained emotion classification. To address these issues, we propose \textbf{HyperEmo-RAG}, a retrieval-augmented generation framework that leverages a structured emotional knowledge base. Our framework introduces two key innovations. 1) Hierarchical hyperbolic grounding. Recognizing the inherent hierarchical tree structure of emotion taxonomies, we jointly embed hierarchical emotion labels and multimodal samples into a continuous hyperbolic space (Poincaré ball) and design a hierarchical beam-search deliberation process that progressively retrieves samples from coarse to fine-grained levels. 2) Structured evidence injection. Based on the retrieved evidence, we construct an evidence graph and inject the structured knowledge as explicit cognitive context into the LLM through a Tree-Aware Attention mechanism and an EmotionGraphFormer, preserving the integrity of graph-structured information. Experiments on multiple datasets demonstrate that HyperEmo-RAG significantly outperforms existing methods.

Self-supervised pretraining on molecular graphs has emerged as a promising approach for molecular property prediction, yet most existing methods operate at a single structural granularity and treat bond information as auxiliary edge attributes rather than as an independent semantic layer. In this work, we propose MolCHG, a multi-level self-supervised pretraining framework built upon a novel Compositional Hierarchical Graph that organizes molecular structure into four types of nodes across three semantic levels. By introducing a bond graph that operates in parallel with the atom graph, our architecture elevates bond-level information to independently evolving node representations, enabling fragment nodes to aggregate atom-level and bond-level semantics on an equal footing. We design three level-specific pretraining objectives: an atom-bond cross-view contrastive task that aligns the atom-view and bond-view representations within each fragment, a fragment-level functional group prediction task to inject domain-relevant chemical knowledge, and graph-level structure prediction tasks to encode global molecular topology. Experiments on nine MoleculeNet benchmarks demonstrate that MolCHG achieves the best performance on seven datasets across both classification and regression tasks, remaining competitive with the strongest baselines on the rest. Ablation studies further confirm that the multi-level supervision signals are complementary and that each component contributes to the overall performance.

Humans abstract experiences into structured representations to facilitate pattern inference and knowledge transfer. While the hippocampal-entorhinal (HPC-MEC) circuit is known to represent both spatial and conceptual spaces, the mechanisms for concurrently extracting abstract structures from continuous, high-dimensional dynamics remain poorly understood. We propose a brain-inspired hierarchical model that simultaneously infers latent transitions and constructs a predictive visual world model. Our architecture employs an inverse model for structural extraction alongside an HPC-MEC coupling model that dissociates relational structures (MEC) from integrated episodic scenes (HPC). Using primitive transformation dynamics as a benchmark, we demonstrate the model's capacity for structural abstraction. By leveraging velocity-driven path integration, the framework enables robust prediction and structural reuse across diverse contexts, thereby achieving structural generalization. This work provides a novel computational framework for understanding how brain-inspired, self-supervised learning of world models facilitates the acquisition of reusable abstract knowledge.

Identifying the structural priors that enable Deep Neural Networks (DNNs) to overcome the curse of dimensionality is a fundamental challenge in machine learning theory. Existing literature suggests that effective high-dimensional learning is driven by compositional sparsity, where target functions decompose into constituents supported on low-dimensional variable subsets. To investigate this hypothesis, we combine Information Filtering Networks (IFNs), which extract sparse dependency structures via constrained information maximisation, with Homological Neural Networks (HNNs), which map the inferred topology into fixed-wiring sparse neural graphs. We formalise the design principles underlying this construction and present an interpretable pipeline in which abstraction emerges through hierarchical composition. HNNs are orders of magnitude sparser than standard DNNs and require only minimal hyperparameter tuning. On synthetic tasks with known sparse hierarchies, HNNs recover the underlying compositional structure and remain stable in regimes where dense alternatives degrade as dimensionality increases. Across a broad suite of real-world datasets, HNNs consistently match or outperform dense baselines while using far fewer parameters, exhibiting lower variance and showing reduced sensitivity to hyperparameters.

We propose a simple mechanism by which scaling laws emerge from feature learning in multi-layer networks. We study a high-dimensional hierarchical target that is a globally high-degree function, but that can be represented by a combination of latent compositional features whose weights decrease as a power law. We show that a layer-wise spectral algorithm adapted to this compositional structure achieves improved scaling relative to shallow, non-adaptive methods, and recovers the latent directions sequentially: strong features become detectable at small sample sizes, while weaker features require more data. We prove sharp feature-wise recovery thresholds and show that aggregating these transitions yields an explicit power-law decay of the prediction error. Technically, the analysis relies on random matrix methods and a resolvent-based perturbation argument, which gives matching upper and lower bounds for individual eigenvector recovery beyond what standard gap-based perturbation bounds provide. Numerical experiments confirm the predicted sequential recovery, finite-size smoothing of the thresholds, and separation from non-hierarchical kernel baselines. Together, these results show how smooth scaling laws can emerge from a cascade of sharp feature-learning transitions.

Continual learning requires models to adapt to new data while preserving previously acquired knowledge. At its core, this challenge can be viewed as principled one-step adaptation: incorporating new information with minimal interference to existing representations. Most existing approaches address this challenge by modifying model parameters or architectures in a supervised, task-specific manner. However, the underlying issue is representational: tasks require distinct yet structured representations that can be selectively updated without disrupting representations, while structure should reflect intrinsic organization in the data rather than task boundaries. In sequential data, time-delayed dependencies provide a natural signal for uncovering this organization, revealing how fundamental representations give rise to more specific ones. Inspired by the modular organization of the human brain, we propose MoRe, a framework that identifies modularity in the representation itself rather than allocating it at the architectural level. MoRe decomposes knowledge into a hierarchy of fundamental and specific modules with identifiability guarantees, enabling principled module reuse, alignment, and expansion during adaptation while preserving old modules by construction. Experiments on synthetic benchmarks and real-world LLM activations demonstrate interpretable hierarchical structure, improved plasticity-stability trade-offs, suggesting MoRe as a principled foundation for continual adaptation

Understanding how deep neural networks learn useful internal representations from data remains a central open problem in the theory of deep learning. We introduce Neural Low-Degree Filtering (Neural LoFi), a stylized limit of gradient-based training in which hierarchical feature learning becomes an explicit iterative spectral procedure. In this limit, the dynamics at each layer decouple: given the current representation, the next layer selects directions with maximal accessible low-degree correlation to the label. This yields a tractable surrogate mechanism for deep learning, together with a natural kernel-space interpretation. Neural LoFi provides a mathematically explicit framework for studying multi-layer feature learning beyond the lazy regime. It predicts how representations are selected layer by layer, explains how emergence of concepts arises with given sample complexity,and gives a concrete mechanism by which depth progressively constructs new features from old ones through low-degree compositionality. We complement the theory with mechanistic experiments on fully connected and convolutional architectures, showing that Neural LoFi improves over lazy random-feature baselines, recovers meaningful structured filters, and predicts representations aligned with early gradient-descent feature discovery with real datasets.

Given a generalist model, learning a task-relevant specialist representation is fundamental for downstream applications. Identifiability, the asymptotic guarantee of recovering the ground-truth representation, is critical because it sets the ultimate limit of any model, even with infinite data and computation. We study this problem in a completely nonparametric setting, without relying on interventions, parametric forms, or structural constraints. We first prove that the structure between time steps and tasks is identifiable in a fully unsupervised manner, even when sequences lack strict temporal dependence and may exhibit disconnections, and task assignments can follow arbitrarily complex and interleaving structures. We then prove that, within each time step, the task-relevant latent representation can be disentangled from the irrelevant part under a simple sparsity regularization, without any additional information or parametric constraints. Together, these results establish a hierarchical foundation: task structure is identifiable across time steps, and task-relevant latent representations are identifiable within each step. To our knowledge, each result provides a first general nonparametric identifiability guarantee, and together they mark a step toward provably moving from generalist to specialist models.

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.

The Nearest Class Mean (NCM) classifier is widely favored in Class-Incremental Learning (CIL) for its superior resistance to catastrophic forgetting compared to Fully Connected layers. While Neural Collapse (NC) theory supports NCM's optimality by assuming features collapse into single points, non-linear feature drift and insufficient training in CIL often prevent this ideal state. Consequently, classes manifest as complex manifolds rather than collapsed points, rendering the single-point NCM suboptimal. To address this, we propose Hierarchical-Cluster SOINN (HC-SOINN), a novel classifier that captures the topological structure of these manifolds via a ``local-to-global'' representation. Furthermore, we introduce Structure-Topology Alignment via Residuals (STAR) method, which employs a fine-grained pointwise trajectory tracking mechanism to actively deform the learned topology, allowing it to adapt precisely to complex non-linear feature drift. Theoretical analysis and Procrustes distance experiments validate our framework's resilience to manifold deformations. We integrated HC-SOINN into seven state-of-the-art methods by replacing their original classifiers, achieving consistent improvements that highlight the effectiveness and robustness of our approach. Code is available at https://github.com/yhyet/HC_SOINN.

The accurate classification of benign and malignant pulmonary nodules in CT scans is critical for early lung cancer screening, yet remains challenging due to the multi-scale and heterogeneous nature of pulmonary nodules. While deep learning offers potential for auxiliary diagnosis, most existing models act as "black boxes", lacking the transparency and explainability required for trustworthy clinical integration. To address this issue, we propose M3Net, a novel 3D network for pulmonary nodule classification inspired by the hierarchical diagnostic workflow of radiologists, which integrates multi-scale contextual information from fine-grained structures to global anatomical relationships. Our framework constructs a progressive multi-scale input, from fine-grained nodule structures to local semantics and global spatial relationships. M3Net employs scale-specific encoders and ensures cross-scale semantic consistency through latent space projection and mutual information maximization. Extensive experiments on the public LIDC-IDRI dataset and a self-collected clinical dataset (USTC-FHLN) demonstrate that our method achieves state-of-the-art performance, with accuracies of 86.96% and 84.24% respectively, outperforming the best baseline by 3.26% and 2.17%. The results validate that M3Net provides a more robust and clinically relevant solution for pulmonary nodule classification. The code is available at https://github.com/jylEcho/M3-Net.

Online Continual Learning (OCL) aims to learn from endless non\text{-}stationary data streams, yet most existing methods assume a flat label space and overlook the hierarchical organization of real\text{-}world concepts that evolves both horizontally (sibling classes) and vertically (coarse or fine categories). To better reflect this context, we introduce a new problem setting, DHOCL (Online Continual Learning from Dynamic Hierarchies), where taxonomies evolve across granularities and each sample provides supervision at a single hierarchical level. In this setting, we find two fundamental issues: (i) partial supervision under mixed granularities provides only point-wise signals over an evolving path-wise hierarchy, which constrains plasticity and undermines cross-level semantic consistency, and (ii) the dynamically evolving hierarchies induce granularity-dependent interference, destabilizing popular replay and regularization mechanisms and thereby exacerbating catastrophic forgetting. To tackle these issues, we propose HALO (Hierarchical Adaptive Learning with Organized Prototypes), which adaptively combines complementary classification heads, regularized by organized learnable hierarchical prototypes, enabling rapid adaptation, hierarchical consistency, and structured knowledge consolidation as the taxonomy evolves. Extensive experiments on multiple benchmarks demonstrate that HALO consistently outperforms existing methods across hierarchical accuracy, mistake severity, and continual performance.

Rare semantic innovations in high-dimensional, mission-critical domains are often obscured by dense background contexts, a challenge we define as \textit{feature density conflict}. We introduce the \textbf{Hybrid Hierarchical SAE (HH-SAE)} to resolve this by factorizing manifolds into a nested hierarchy of \textbf{Contextual} ($L_0$), \textbf{Atomic} ($f_1$), and \textbf{Compository} ($f_2$) tiers. Evaluating across disparate manifolds, HH-SAE demonstrates superior resolution by \textbf{``fracturing'' administrative clinical labels into physiological modes} and achieving a peak \textbf{cross-domain zero-shot AUC of 0.9156 in fraud detection}. Path ablation confirms the architecture's structural necessity, revealing a 13.46% utility collapse when contextual subtraction is removed. Finally, knowledge-steered synthesis achieves a +9.9% AUPRC lift over state-of-the-art generators, proving that HH-SAE effectively prioritizes high-order mechanistic innovation over environmental proxies to enable high-precision discovery in high-stakes environments.

We study the information-theoretic limits of learning a one-hidden-layer teacher network with hierarchical features from noisy queries, in the context of knowledge transfer to a smaller student model. We work in the high-dimensional regime where the teacher width $k$ scales linearly with the input dimension $d$ -- a setting that captures large-but-finite-width networks and has only recently become analytically tractable. Using a heuristic leave-one-out decoupling argument, validated numerically throughout, we derive asymptotically sharp characterizations of the Bayes-optimal generalization error and individual feature overlaps via a system of closed fixed-point equations. These equations reveal that feature learnability is governed by a sequence of sharp phase transitions: as data grows, teacher features become recoverable sequentially, each through a discontinuous jump in overlap. This sequential acquisition underlies a precise notion of \textit{effective width} $k_c$ -- the number of learnable features at a given data budget $n$ -- which unifies two distinct scaling regimes: a feature-learning regime in which the Bayes-optimal generalization error $\varepsilon^{\rm BO}$ scales as $n^{1/(2β)-1}$, and a refinement regime in which it scales as $n^{-1}$, where $β>1/2$ is the exponent of the power-law feature hierarchy. Both laws collapse to the single relation $\varepsilon^{\rm BO}=Θ(k_c d/n)$. We further show empirically that a student trained with \textsc{Adam} near the effective width $k_c$ achieves these optimal scaling laws (up to a small algorithmic gap), and provide an information-theoretic account of the associated scaling in model size.

Wearable sensors enable the continuous acquisition of high-resolution physiological waveforms, such as photoplethysmography and accelerometry, under free-living conditions. However, inferring health-related phenotypes from these signals presents significant challenges due to high sampling frequencies, multimodal dependencies, and extreme sequence lengths (e.g., weeks of recordings), compounded by a scarcity of ground-truth labels. To address these challenges, existing self-supervised learning (SSL) methodologies typically follow two paradigms: (1) learning rich morphological representations from short waveform segments while collapsing longitudinal dynamics through simple aggregation, or (2) modeling behavioral patterns from coarse, hand-crafted features (e.g. heart rate, step counts) spanning longer horizons but foregoing subtle, predictive signatures in raw waveforms. To bridge this gap, we propose WavesFM, a foundation model utilizing a two-stage SSL framework for longitudinal physiological data. Specifically, we decompose the learning problem into two stages: first, a segment-level encoder is pretrained to extract local embeddings from short waveforms; subsequently, a temporal encoder is trained to model the sequence of these embeddings across a multi-day horizon. This hierarchical approach overcomes the computational complexity of high-resolution, long-sequence data, allowing the overall model to capture both local signal semantics and the complex circadian and inter-day variations governing physiological dynamics. Pretrained on over 6.8M hours (N=324k individuals) of recordings for the first stage and 5.3M hours (N=10k) for the second stage, WavesFM demonstrates superior performance across 58 diverse tasks spanning demographics, lifestyle, health conditions, and medications.

Learned representations are often invariant to rotational transformations, leaving individual dimensions non-identifiable and interchangeable. We study how Matryoshka Representation Learning (MRL) induces a task-aligned privileged basis distinct from variance-based or regularizer-induced orderings. In the linear setting, we prove that full-prefix MRL recovers the ordered principal directions, and can be computed efficiently using shared statistics. Empirically, we demonstrate that MRL yields consistent per-dimension structure aligned with task signal, where coordinate magnitude reflects informativeness.

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.

Graphs with heterophily, where adjacent nodes carry different labels, are prevalent in real-world applications, from social networks to molecular interactions. However, existing spectral Graph Neural Network (GNN) approaches tailored for heterophilous graph classification suffer from hub-dominated (node with large degree) aggregation and oversmoothing, as their suboptimal polynomial filters introduce approximation errors and blend distant signals. To address the degree-biased aggregation and suboptimal polynomial filtering, we introduce a Hierarchical Multi-view HAAR (HMH), a novel spectral graph-learning framework that scales in near-linear time . HMH first learns feature- and structure-aware signed affinities via a heterophily-aware encoder, then constructs a soft graph hierarchy guided by these embeddings. At each hierarchical level, HMH constructs a sparse, orthonormal, and locality-aware Haar basis to apply learnable spectral filters in the frequency domain. Finally, skip-connection unpooling layers combine outputs from all hierarchical levels back into the original graph, effectively preventing hub domination and long-range signal bottleneck (over-squashing). Experimentation shows that HMH outperforms state-of-the-art spectral baselines, achieving up to a 3% improvement on node classification and 7% points on graph classification datasets, all while maintaining linear scalability.

Learning hierarchical features in Sparse Autoencoders (SAEs) is essential for capturing the structured nature of real-world data and mitigating issues like feature absorption or splitting. Existing works attempt to identify hierarchical relationships within independent feature sets by relying on activation coverage, the assumption that child feature should only activate when its parent feature activates. However, we demonstrate that this condition alone is insufficient; that is, it often produces false positives where parent and child concepts are semantically unrelated. To address this, we introduce a novel reconstruction condition that enforces a deeper functional link between hierarchical levels. By combining both activation and reconstruction constraints, we propose the Tree SAE, a model designed to learn hierarchical structures directly from within the feature set. Our results demonstrate that Tree SAEs significantly surpass the existing SAEs at learning hierarchical pairs while maintaining competitive performance to the state-of-the-art on several key benchmarks. Finally, we demonstrate the practical utility of our Tree SAE in mapping the geometry of child feature subspaces and uncovering the complex hierarchical concept structures encoded within large language models.

With the rise in scale for deep learning models to billions of parameters, the computational cost of fine-tuning remains a significant barrier to deployment. While Low-Rank Adaptation (LoRA) has become the standard for parameter-efficient fine-tuning, the need to set a predefined, static rank $r$ requires exhaustive grid searches to balance efficiency and performance. Existing rank-adaptive solutions such as DyLoRA mitigate this by sampling ranks during the training from a predefined distribution. However, they often yield sub-optimal results at higher ranks due to lack of consistent gradient signals across the full hierarchy of ranks, thus making these methods data-inefficient. In this paper, we propose MatryoshkaLoRA, a general, Matryoshka-inspired training framework for LoRA that learns accurate hierarchical low-rank representations by inserting a fixed, carefully crafted diagonal matrix $P$ between the existing LoRA adapters to scale their sub-ranks accordingly. By introducing this simple modification, our general framework recovers LoRA and DyLoRA only by changing $P$ and ensures all sub-ranks embed the available gradient information efficiently. Our MatryoshkaLoRA supports dynamic rank selection with minimal degradation in accuracy. We further propose Area Under the Rank Accuracy Curve (AURAC), a metric that consistently evaluates the performance of hierarchical low-rank adapters. Our results demonstrate that MatryoshkaLoRA learns more accurate hierarchical low-rank representations than prior rank-adaptive approaches and achieves superior accuracy-performance trade-offs across ranks on the evaluated datasets. Our code is available at https://github.com/IST-DASLab/MatryoshkaLoRA.

Understanding how molecular alterations propagate across biological systems to drive disease remains a central challenge. Although high-throughput profiling enables comprehensive characterization of tumor states, most models neglect structured biological relationships or lack interpretability across scales. Here we present PPI-Net, a hierarchical graph neural network that integrates protein-protein interaction (PPI) networks with pathway-level representations to model disease from molecular interactions to functional processes. Patient-specific molecular profiles are embedded within a shared interaction network from STRING and propagated through a multi-layer Reactome hierarchy using graph attention, enabling aggregation of gene-level signals into higher-order biological programs. Across RNA-seq data from ten cancer types from The Cancer Genome Atlas, PPI-Net achieves robust predictive performance, with balanced accuracy exceeding 90% in multiple cohorts. Comparative analysis on RNA-Seq data from breast cancer demonstrated that PPI-Net's integration of the Reactome hierarchy improved balanced accuracy by 6.7% relative to a PPI-only model, while hierarchical multi-level supervision improved balanced accuracy by 12.3% relative to using only a single top-level prediction head. Applying a multi-omics approach using RNA-seq and methylation data improves model interpretation, recovering canonical oncogenic modules, including TP53-AKT signaling and stress response pathways, while revealing convergence onto coherent programs such as ion signaling and cellular responses to stimuli. These results demonstrate that integrating interaction networks with pathway hierarchies enables accurate prediction while providing mechanistic insight into cancer biology.

Classical clustering methods usually return either a finite partition of the observed data or a finite dendrogram over it. This finite-sample view is inadequate when the hierarchy of interest is a recursive geometric object with fine-scale refinements that continue beyond the levels directly observed. We introduce classification fields: infinite-depth hierarchical cluster structures on $\mathbb{R}^d$ generated by a local parent-to-child refinement rule. A classification field generator maps each parent centre to an ordered, bounded, and separated tuple of child residuals. Together with a root and a scale factor, this rule recursively generates cluster centres, Voronoi cells, and a metric DAG encoding the hierarchy. Given only a finite prefix of such a hierarchy, we learn a classification field predictor that approximates the generator and can be rolled out to unseen depths. We prove exponential truncation convergence in the completed cell metric and ReLU realizability with width $O(\varepsilon^{-γ})$ and depth $\widetilde O(\varepsilon^{-3γ/2})$, where $γ=\log K/(-\log s)$, up to finite-window aspect-ratio factors. The approximation holds at the level of the induced compact metric structures, measured in the completed cell-metric Hausdorff distance. Experimental validation on matched CFG-generated hierarchies, IFS fractals, and image-induced recursive clustering hierarchies shows that learned predictors preserve ordered child slots, unordered geometry, and hierarchy-level path metrics under recursive rollout. These results support the claim that finite hierarchical observations can reveal local refinement rules capable of generating substantially deeper classification fields.

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.

We present a method for finding hierarchy-aware embeddings of knowledge graphs (KGs) using graph neural networks (GNNs) enriched with a semantic loss derived from underlying ontologies. This method yields embeddings that better reflect domain knowledge. To demonstrate their utility, we predict and interpret the effects of gene deletions in the yeast Saccharomyces cerevisiae and learn box embeddings for KGs in the absence of a prediction task. We further show how box embeddings can serve as the basis for evaluating KG revisions. Our yeast KG is constructed from community databases and ontology terms. Low-dimensional box embeddings combined with GNNs are used to predict cell growth for double gene knockouts. Over 10-fold cross validation, these predictions have a mean $R^2$scoreof~0.360, significantly higher than baseline comparisons, demonstrating that high-level qualitative knowledge is informative about experimental outcomes. Incorporating semantic loss terms in the training of the models improves their predictive performance ($R^2$=0.377) by aligning embeddings with ontology structure. This shows that class hierarchies from ontologies can be exploited for quantitative prediction. We also test the trained models on triple gene knockouts, showing they generalise to data beyond those seen in training. Additionally, by identifying co-occurring relations in the yeast KG important for the cell-growth predictions, we construct hypotheses about interacting traits in yeast. A biological experiment validates one such finding, revealing an association between inositol utilisation and osmotic stress resistance, highlighting the model's potential to guide biological discovery.

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.