Hierarchical Representation Learning

Modern recommender systems leverage ultra-long user behavior sequences to capture dynamic preferences, but end-to-end modeling is infeasible in production due to latency and memory constraints. While summarizing history via interest centers offers a practical alternative, existing methods struggle to (1) identify user-specific centers at appropriate granularity and (2) accurately assign behaviors, leading to quantization errors and loss of long-tail preferences. To alleviate these issues, we propose Hierarchical Sparse Activation Compression (HiSAC), an efficient framework for personalized sequence modeling. HiSAC encodes interactions into multi-level semantic IDs and constructs a global hierarchical codebook. A hierarchical voting mechanism sparsely activates personalized interest-agents as fine-grained preference centers. Guided by these agents, Soft-Routing Attention aggregates historical signals in semantic space, weighting by similarity to minimize quantization error and retain long-tail behaviors. Deployed on Taobao's "Guess What You Like" homepage, HiSAC achieves significant compression and cost reduction, with online A/B tests showing a consistent 1.65% CTR uplift -- demonstrating its scalability and real-world effectiveness.

Graph self-supervised learning (GSSL) has demonstrated strong potential for generating expressive graph embeddings without the need for human annotations, making it particularly valuable in domains with high labeling costs such as molecular graph analysis. However, existing GSSL methods mostly focus on node- or edge-level information, often ignoring chemically relevant substructures which strongly influence molecular properties. In this work, we propose Graph Semantic Predictive Network (GraSPNet), a hierarchical self-supervised framework that explicitly models both atomic-level and fragment-level semantics. GraSPNet decomposes molecular graphs into chemically meaningful fragments without predefined vocabularies and learns node- and fragment-level representations through multi-level message passing with masked semantic prediction at both levels. This hierarchical semantic supervision enables GraSPNet to learn multi-resolution structural information that is both expressive and transferable. Extensive experiments on multiple molecular property prediction benchmarks demonstrate that GraSPNet learns chemically meaningful representations and consistently outperforms state-of-the-art GSSL methods in transfer learning settings.

Hyperbolic spaces provide a natural geometry for representing hierarchical and tree-structured data due to their exponential volume growth. To leverage these benefits, neural networks require intrinsic and efficient components that operate directly in hyperbolic space. In this work, we lift two core components of neural networks, Multinomial Logistic Regression (MLR) and Fully Connected (FC) layers, into hyperbolic space via Busemann functions, resulting in Busemann MLR (BMLR) and Busemann FC (BFC) layers with a unified mathematical interpretation. BMLR provides compact parameters, a point-to-horosphere distance interpretation, batch-efficient computation, and a Euclidean limit, while BFC generalizes FC and activation layers with comparable complexity. Experiments on image classification, genome sequence learning, node classification, and link prediction demonstrate improvements in effectiveness and efficiency over prior hyperbolic layers. The code is available at https://github.com/GitZH-Chen/HBNN.

This paper reformulates Transformer/Attention mechanisms in Large Language Models (LLMs) through measure theory and frequency analysis, theoretically demonstrating that hallucination is an inevitable structural limitation. The embedding space functions as a conditional expectation over a σ-algebra, and its failure to be isomorphic to the semantic truth set fundamentally causes logical consistency breakdown. WavePhaseNet Method The authors propose WavePhaseNet, which explicitly constructs a Semantic Conceptual Hierarchy Structure (SCHS) using Discrete Fourier Transform (DFT). By applying DFT along the sequence dimension, semantic information is decomposed into frequency bands: low-frequency components capture global meaning and intent, while high-frequency components represent local syntax and expression. This staged separation enables precise semantic manipulation in diagonalized space. Dimensionality Reduction GPT-4's 24,576-dimensional embedding space exhibits a 1/f spectral structure based on language self-similarity and Zipf's law. Through cumulative energy analysis, the authors derive that approximately 3,000 dimensions constitute the lower bound for "complete representation." This demonstrates that reduction from 24,576 to 3,000 dimensions preserves meaning and intent while enabling rigorous reasoning and suppressing hallucination. Cohomological Consistency Control The reduced embedding space, constructed via cohomological regularization over overlapping local windows, allows defining a graph structure and cochain complex. This quantifies inconsistencies among local inferences as coboundary-based losses. Applying harmonic projection based on Hodge theory positions cohomology as a computable regularization principle for controlling semantic consistency, extracting maximally consistent global representations.

Complex tables with multi-level headers, merged cells and heterogeneous layouts pose persistent challenges for LLMs in both understanding and reasoning. Existing approaches typically rely on table linearization or normalized grid modeling. However, these representations struggle to explicitly capture hierarchical structures and cross-dimensional dependencies, which can lead to misalignment between structural semantics and textual representations for non-standard tables. To address this issue, we propose an Orthogonal Hierarchical Decomposition (OHD) framework that constructs structure-preserving input representations of complex tables for LLMs. OHD introduces an Orthogonal Tree Induction (OTI) method based on spatial--semantic co-constraints, which decomposes irregular tables into a column tree and a row tree to capture vertical and horizontal hierarchical dependencies, respectively. Building on this representation, we design a dual-pathway association protocol to symmetrically reconstruct semantic lineage of each cell, and incorporate an LLM as a semantic arbitrator to align multi-level semantic information. We evaluate OHD framework on two complex table question answering benchmarks, AITQA and HiTab. Experimental results show that OHD consistently outperforms existing representation paradigms across multiple evaluation metrics.

Understanding how the structure of language can be learned from sentences alone is a central question in both cognitive science and machine learning. Studies of the internal representations of Large Language Models (LLMs) support their ability to parse text when predicting the next word, while representing semantic notions independently of surface form. Yet, which data statistics make these feats possible, and how much data is required, remain largely unknown. Probabilistic context-free grammars (PCFGs) provide a tractable testbed for studying these questions. However, prior work has focused either on the post-hoc characterization of the parsing-like algorithms used by trained networks; or on the learnability of PCFGs with fixed syntax, where parsing is unnecessary. Here, we (i) introduce a tunable class of PCFGs in which both the degree of ambiguity and the correlation structure across scales can be controlled; (ii) provide a learning mechanism -- an inference algorithm inspired by the structure of deep convolutional networks -- that links learnability and sample complexity to specific language statistics; and (iii) validate our predictions empirically across deep convolutional and transformer-based architectures. Overall, we propose a unifying framework where correlations at different scales lift local ambiguities, enabling the emergence of hierarchical representations of the data.

The empirical success of deep learning is often attributed to deep networks' ability to exploit hierarchical structure in data, constructing increasingly complex features across layers. Yet despite substantial progress in deep learning theory, most optimization results sill focus on networks with only two or three layers, leaving the theoretical understanding of hierarchical learning in genuinely deep models limited. This leads to a natural question: can we prove that deep networks, trained with gradient-based methods and standard input-label pairs, can efficiently exploit hierarchical structure? In this work, we consider Random Hierarchy Models -- a hierarchical context-free grammar introduced by arXiv:2307.02129 and conjectured to separate deep and shallow networks. We prove that, under mild conditions, a deep convolutional network can be efficiently trained to learn this function class. Our proof builds on a general observation: if intermediate layers can receive clean signal from the labels and the relevant features are weakly identifiable, then layerwise training each individual layer suffices to hierarchically learn the target function.

Continual learning systems face a fundamental geometric obstacle: as experience accumulates on a fixed-capacity manifold, covering numbers grow linearly with time, eventually forcing representational overlap and catastrophic interference. Prevailing approaches attack this problem by expansion - projecting into higher-dimensional spaces via kernels, overparameterization, or replay. We argue the solution is the opposite: contraction. We formalize abstraction as the Urysohn Ladder, a hierarchy of quotient maps that recursively collapse validated metric neighborhoods into compact tokens, converting unbounded ambient-space search into bounded navigation on a low-dimensional intrinsic scaffold. Geometrically, each collapsed token acts as a shortcut - a region of extreme metric contraction that bridges distant experiences, much like a wormhole in the representational manifold. We establish four results that collectively guarantee separability (metric contraction renders nonlinearly entangled structure linearly separable at each quotient level, and this separability propagates faithfully through the entire hierarchy), bounded capacity (covering numbers remain $O(1)$ per quotient level, independent of stream length), stability (parity-partitioned flow/scaffold subspaces enable unbounded plasticity without catastrophic interference), and scalability (inference cost scales with quotient distance, not ambient distance). We validate each claim empirically with pretrained models and real-world datasets. Moreover, we demonstrate the potential of Urysohn Ladder for scalable continual learning via scaffold amortization.

In web environments, user preferences are often refined progressively as users move from browsing broad categories to exploring specific items. However, existing generative recommenders overlook this natural refinement process. Generative recommendation formulates next-item prediction as autoregressive generation over tokenized user histories, where each item is represented as a sequence of discrete tokens. Prior models typically fuse heterogeneous attributes such as ID, category, title, and description into a single embedding before quantization, which flattens the inherent semantic hierarchy of items and fails to capture the gradual evolution of user intent during web interactions. To address this limitation, we propose CoFiRec, a novel generative recommendation framework that explicitly incorporates the Coarse-to-Fine nature of item semantics into the tokenization process. Instead of compressing all attributes into a single latent space, CoFiRec decomposes item information into multiple semantic levels, ranging from high-level categories to detailed descriptions and collaborative filtering signals. Based on this design, we introduce the CoFiRec Tokenizer, which tokenizes each level independently while preserving structural order. During autoregressive decoding, the language model is instructed to generate item tokens from coarse to fine, progressively modeling user intent from general interests to specific item-level interests. Experiments across multiple public benchmarks and backbones demonstrate that CoFiRec outperforms existing methods, offering a new perspective for generative recommendation. Theoretically, we prove that structured tokenization leads to lower dissimilarity between generated and ground truth items, supporting its effectiveness in generative recommendation. Our code is available at https://github.com/YennNing/CoFiRec.

Class-Incremental Learning (CIL) enables models to learn new classes continually while preserving past knowledge. Recently, vision-language models like CLIP offer transferable features via multimodal pre-training, making them well-suited for CIL. However, real-world visual and linguistic concepts are inherently hierarchical: a textual concept like "dog" subsumes fine-grained categories such as "Labrador" and "Golden Retriever," and each category is associated with corresponding images. Nevertheless, existing CLIP-based CIL methods fail to explicitly capture this inherent hierarchy, leading to feature drift of fine-grained classes during incremental updates and ultimately to catastrophic forgetting. To address this challenge, we propose HASTEN (Hierarchical Semantic Tree Anchoring), a hierarchy-aware framework that uses semantic structure to stabilize CLIP-based CIL. Rather than treating classes as isolated labels, HASTEN leverages external hierarchical knowledge as structured supervision to organize visual and textual features in hyperbolic space, helping maintain parent--child relations as new tasks arrive and mitigating feature drift. Since the shared hyperbolic mapper is updated across tasks, we further stabilize it by constraining its updates to a null space induced by prior-task features, reducing interference with previous mappings while retaining adaptability to new classes. Extensive experiments on nine benchmarks show that HASTEN consistently outperforms existing methods while reducing feature drift and catastrophic forgetting. Code is available at: https://github.com/LAMDA-CL/NeurIPS2026-HASTEN.

We argue that training autoencoders to reconstruct inputs from noised versions of their encodings, when combined with perceptually motivated losses, yields encodings that are structured according to a perceptual hierarchy. We demonstrate the emergence of this hierarchy by showing that, after training an audio autoencoder in this manner, perceptually salient information is captured in coarser representation structures than with conventional training. Furthermore, we show that such perceptual hierarchies improve latent diffusion decoding in the context of estimating pitch surprisal in music and predicting EEG-brain responses to music listening. In both cases, our results surpass those of previous methods. Pretrained weights are available on github.com/CPJKU/pa-audioic.

Vision-language models (VLMs) have advanced multimodal perception, demonstrated by open-vocabulary object detection with simple language queries. State-of-the-art VLMs still struggle to handle complex queries involving descriptive attributes and relational clauses. To address this problem, we propose restructuring linguistic representations according to the hierarchical relations within sentences for language-based object detection. A key insight is that textual tokens should be disentangled into core components-objects, attributes, and relations-and aggregated into hierarchically structured sentence-level representations. Building on this principle, we introduce the TaSe (Talk in Pieces, See in Whole) framework with three main contributions: (1) a hierarchical synthetic captioning dataset spanning three tiers from category names to descriptive sentences; (2) the three-component disentanglement module guided by a novel disentanglement loss function, transforms text embeddings into subspace compositions; and (3) aggregating disentangled components into hierarchically structured embeddings guided by the proposed hierarchical objectives. Experimental results under the OmniLabel benchmark show a 24% performance improvement, demonstrating the importance of linguistic compositionality.

Class-Incremental Learning (CIL) aims to endow models with the ability to continuously adapt to evolving data streams. Recent advances in pre-trained vision-language models (e.g., CLIP) provide a powerful foundation for this task. However, existing approaches often rely on simplistic templates, such as "a photo of a [CLASS]", which overlook the hierarchical nature of visual concepts. For example, recognizing "cat" versus "car" depends on coarse-grained cues, while distinguishing "cat" from "lion" requires fine-grained details. Similarly, the current feature mapping in CLIP relies solely on the representation from the last layer, neglecting the hierarchical information contained in earlier layers. In this work, we introduce HiErarchical Representation MAtchiNg (HERMAN) for CLIP-based CIL. Our approach leverages LLMs to recursively generate discriminative textual descriptors, thereby augmenting the semantic space with explicit hierarchical cues. These descriptors are matched to different levels of the semantic hierarchy and adaptively routed based on task-specific requirements, enabling precise discrimination while alleviating catastrophic forgetting in incremental tasks. Extensive experiments on multiple benchmarks demonstrate that our method consistently achieves state-of-the-art performance.

The representation of urban trajectory data plays a critical role in effectively analyzing spatial movement patterns. Despite considerable progress, the challenge of designing trajectory representations that can capture diverse and complementary information remains an open research problem. Existing methods struggle in incorporating trajectory fine-grained details and high-level summary in a single model, limiting their ability to attend to both long-term dependencies while preserving local nuances. To address this, we propose HiT-JEPA (Hierarchical Interactions of Trajectory Semantics via a Joint Embedding Predictive Architecture), a unified framework for learning multi-scale urban trajectory representations across semantic abstraction levels. HiT-JEPA adopts a three-layer hierarchy that progressively captures point-level fine-grained details, intermediate patterns, and high-level trajectory abstractions, enabling the model to integrate both local dynamics and global semantics in one coherent structure. Extensive experiments on multiple real-world datasets for trajectory similarity computation show that HiT-JEPA's hierarchical design yields richer, multi-scale representations. Code is available at: https://anonymous.4open.science/r/HiT-JEPA.

Sparse Autoencoders (SAEs) decompose language-model activations into sparse, interpretable features, but standard encoders usually treat the latent dictionary as a flat set of independent coordinates, leaving hierarchy and feature interactions to emerge only implicitly. We propose KronSAE, a design that factorizes the latent space into heads and forms post-latent features as pairwise compositions of lower-dimensional pre-latents using mAND, a differentiable AND-like interaction. This imposes a compositional co-activation prior while remaining compatible with standard SAE objectives and variants such as TopK, Matryoshka, and Switch SAEs. KronSAE matches strong baselines on the EV-FLOPs frontier, improves interpretability of the latents, better captures the underlying correlated feature structure, and reduces encoder computational cost as an additional benefit. Code is available at https://github.com/corl-team/kronsae.

Few-shot action recognition (FSAR) aims to recognize novel action categories with few exemplars. Existing methods typically learn frame-level representations for each video by designing inter-frame temporal modeling strategies or inter-video interaction at the coarse video-level granularity. However, they treat each episode task in isolation and neglect fine-grained temporal relation modeling between videos, thus failing to capture shared fine-grained temporal patterns across videos and reuse temporal knowledge from historical tasks. In light of this, we propose HR2G-shot, a Hierarchical Relation-augmented Representation Generalization framework for FSAR, which unifies three types of relation modeling (inter-frame, inter-video, and inter-task) to learn task-specific temporal patterns from a holistic view. Going beyond conducting inter-frame temporal interactions, we further devise two components to respectively explore inter-video and inter-task relationships: i) Inter-video Semantic Correlation (ISC) performs cross-video frame-level interactions in a fine-grained manner, thereby capturing task-specific query features and enhancing both intra-class consistency and inter-class separability; ii) Inter-task Knowledge Transfer (IKT) retrieves and aggregates relevant temporal knowledge from the bank, which stores diverse temporal patterns from historical episode tasks. Extensive experiments on five benchmarks show that HR2G-shot outperforms current top-leading FSAR methods.

Over the past decade, deep learning has proven to be a highly effective tool for learning meaningful features from raw data. However, it remains an open question how deep networks perform hierarchical feature learning across layers. In this work, we attempt to unveil this mystery by investigating the structures of intermediate features. Motivated by our empirical findings that linear layers mimic the roles of deep layers in nonlinear networks for feature learning, we explore how deep linear networks transform input data into output by investigating the output (i.e., features) of each layer after training in the context of multi-class classification problems. Toward this goal, we first define metrics to measure within-class compression and between-class discrimination of intermediate features, respectively. Through theoretical analysis of these two metrics, we show that the evolution of features follows a simple and quantitative pattern from shallow to deep layers when the input data is nearly orthogonal and the network weights are minimum-norm, balanced, and approximate low-rank: Each layer of the linear network progressively compresses within-class features at a geometric rate and discriminates between-class features at a linear rate with respect to the number of layers that data have passed through. To the best of our knowledge, this is the first quantitative characterization of feature evolution in hierarchical representations of deep linear networks. Empirically, our extensive experiments not only validate our theoretical results numerically but also reveal a similar pattern in deep nonlinear networks which aligns well with recent empirical studies. Moreover, we demonstrate the practical implications of our results in transfer learning. Our code is available at https://github.com/Heimine/PNC_DLN.

For deep learning problems on graph-structured data, pooling layers are important for down sampling, reducing computational cost, and to minimize overfitting. We define a pooling layer, nervePool, for data structured as simplicial complexes, which are generalizations of graphs that include higher-dimensional simplices beyond vertices and edges; this structure allows for greater flexibility in modeling higher-order relationships. The proposed simplicial coarsening scheme is built upon partitions of vertices, which allow us to generate hierarchical representations of simplicial complexes, collapsing information in a learned fashion. NervePool builds on the learned vertex cluster assignments and extends to coarsening of higher dimensional simplices in a deterministic fashion. While in practice the pooling operations are computed via a series of matrix operations, the topological motivation is a set-theoretic construction based on unions of stars of simplices and the nerve complex.

Hierarchical classification aims to sort the object into a hierarchical structure of categories. For example, a bird can be categorized according to a three-level hierarchy of order, family, and species. Existing methods commonly address hierarchical classification by decoupling it into a series of multi-class classification tasks. However, such a multi-task learning strategy fails to fully exploit the correlation among various categories across different levels of the hierarchy. In this paper, we propose Label Hierarchy Transition (LHT), a unified probabilistic framework based on deep learning, to address the challenges of hierarchical classification. The LHT framework consists of a transition network and a confusion loss. The transition network focuses on explicitly learning the label hierarchy transition matrices, which has the potential to effectively encode the underlying correlations embedded within class hierarchies. The confusion loss encourages the classification network to learn correlations across different label hierarchies during training. The proposed framework can be readily adapted to any existing deep network with only minor modifications. We experiment with a series of public benchmark datasets for hierarchical classification problems, and the results demonstrate the superiority of our approach beyond current state-of-the-art methods. Furthermore, we extend our proposed LHT framework to the skin lesion diagnosis task and validate its great potential in computer-aided diagnosis. The code of our method is available at https://github.com/renzhenwang/label-hierarchy-transition.