Unsupervised Learning of Inter-Object Relationships via Group Homomorphism

• URL: http://arxiv.org/abs/2604.20925v1
• Date: Wed, 22 Apr 2026 07:17:00 GMT
• Title: Unsupervised Learning of Inter-Object Relationships via Group Homomorphism
• Abstract summary: In this study, we propose an unsupervised representation learning method based on a hierarchical relationship in group operations.<n>We experimentally demonstrate that the model can segment multiple objects into individual slots without any ground-truth labels.<n>Results suggest that by introducing algebraic geometric constraints, physically interpretable "disentangled representations" can be acquired.
• Score: 3.8731899020772165
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: While current deep learning models achieve high performance by learning statistical correlations from vast datasets,which stands in stark contrast to human learning. They lack the flexibility of humans-particularly preverbal infants-to autonomously acquire the underlying structure of the world from limited experience and adapt to novel situations. In this study, we propose an unsupervised representation learning method based on a hierarchical relationship in group operations, rather than statistical independence, aiming to build a computational model of the cognitive development of infants. The proposed model features an integrated architecture that simultaneously performs object segmentation and the extraction of motion laws from dynamic image sequences. By introducing the Homomorphism from algebra as a structural constraint within a neural network, the model structurally separates pixel-level changes into meaningful, decomposed transformation components, such as translation and deformation. Using interaction scenes (chasing and evading tasks) based on developmental science findings, we experimentally demonstrate that the model can segment multiple objects into individual slots without any ground-truth labels. Furthermore, we confirmed that relative movements between objects, such as approaching or receding, are accurately mapped and structured into a one-dimensional additive latent space. These results suggest that by introducing algebraic geometric constraints rather than relying solely on statistical correlation learning, physically interpretable "disentangled representations" can be acquired. This study contributes to the understanding of the process by which infants internalize environmental laws as structures and provides a new perspective for constructing artificial systems with developmental intelligence.

Related papers

• Speaking the Language of Science: Toward a General-Purpose Generative Foundation Model for the Natural Sciences [89.71422932447423]
  LOGOS is a scientific generative language model that unifies heterogeneous tasks across the natural sciences.<n>By representing spatial contact and constraint patterns as discrete tokens, the model captures complex structural interactions in a purely sequential manner.<n>Across diverse tasks, LOGOS consistently matches or outperforms domain-specific baselines.
  arXiv  Detail & Related papers  (2026-06-15T16:14:53Z)
• BEHAVE: A Hybrid AI Framework for Real-Time Modeling of Collective Human Dynamics [0.0]
  Existing AI systems fail to capture the collective dynamics that determine whether a group remains stable or transitions into escalation or breakdown.<n>We introduce BEHAVE, a formal framework that models collective dynamics as continuous behavioral fields defined over an interaction space.<n>The same fields, recalibrated, apply to crowd safety, crisis-team dynamics, education, and clinical contexts.
  arXiv  Detail & Related papers  (2026-05-12T20:32:02Z)
• Hierarchical Latent Structures in Data Generation Process Unify Mechanistic Phenomena across Scale [50.33952894976367]
  We use context-free grammars to generate synthetic corpora that are faithful and computationally efficient proxies for web-scale text corpora.<n>We investigate the emergence of three mechanistic phenomena: induction heads, function vectors, and the Hydra effect, under our designed data generation process.<n>Our findings suggest that hierarchical structures in the data generation process serve as the X-factor in explaining the emergence of these phenomena.
  arXiv  Detail & Related papers  (2026-02-04T14:49:13Z)
• Alignment among Language, Vision and Action Representations [0.0]
  We show that linguistic, visual, and action representations converge toward partially shared semantic structures.<n>These findings indicate that linguistic, visual, and action representations converge toward partially shared semantic structures.
  arXiv  Detail & Related papers  (2026-01-30T13:12:07Z)
• A Brain-like Synergistic Core in LLMs Drives Behaviour and Learning [50.68188138112555]
  We show that large language models spontaneously develop synergistic cores.<n>We find that areas in middle layers exhibit synergistic processing while early and late layers rely on redundancy.<n>This convergence suggests that synergistic information processing is a fundamental property of intelligence.
  arXiv  Detail & Related papers  (2026-01-11T10:48:35Z)
• A Markov Categorical Framework for Language Modeling [9.910562011343009]
  Autoregressive language models achieve remarkable performance, yet a unified theory explaining their internal mechanisms, how training shapes their representations, and enables complex behaviors, remains elusive.<n>We introduce a new analytical framework that models the single-step generation process as a composition of information-processing stages using the language of Markov categories.<n>This work presents a powerful new lens for understanding how information flows through a model and how the training objective shapes its internal geometry.
  arXiv  Detail & Related papers  (2025-07-25T13:14:03Z)
• Connecting Neural Models Latent Geometries with Relative Geodesic Representations [21.71782603770616]
  We show that when a latent structure is shared between distinct latent spaces, relative distances between representations can be preserved, up to distortions.<n>We assume that distinct neural models parametrize approximately the same underlying manifold, and introduce a representation based on the pullback metric.<n>We validate our method on model stitching and retrieval tasks, covering autoencoders and vision foundation discriminative models.
  arXiv  Detail & Related papers  (2025-06-02T12:34:55Z)
• Scaling Laws and Representation Learning in Simple Hierarchical Languages: Transformers vs. Convolutional Architectures [49.19753720526998]
  We derive theoretical scaling laws for neural network performance on synthetic datasets.<n>We validate that convolutional networks, whose structure aligns with that of the generative process through locality and weight sharing, enjoy a faster scaling of performance.<n>This finding clarifies the architectural biases underlying neural scaling laws and highlights how representation learning is shaped by the interaction between model architecture and the statistical properties of data.
  arXiv  Detail & Related papers  (2025-05-11T17:44:14Z)
• A Percolation Model of Emergence: Analyzing Transformers Trained on a Formal Language [15.929767234646631]
  Increase in data, size, or compute can lead to sudden learning of specific capabilities by a neural network. "emergence" is a phenomenon often called "emergence"
  arXiv  Detail & Related papers  (2024-08-22T17:44:22Z)
• Bayesian Unsupervised Disentanglement of Anatomy and Geometry for Deep Groupwise Image Registration [59.062085785106234]
  This article presents a general Bayesian learning framework for multi-modal groupwise image registration.<n>We propose a novel hierarchical variational auto-encoding architecture to realise the inference procedure of the latent variables.<n>Experiments were conducted to validate the proposed framework, including four different datasets from cardiac, brain, and abdominal medical images.
  arXiv  Detail & Related papers  (2024-01-04T08:46:39Z)
• Flow Factorized Representation Learning [109.51947536586677]
  We introduce a generative model which specifies a distinct set of latent probability paths that define different input transformations. We show that our model achieves higher likelihoods on standard representation learning benchmarks while simultaneously being closer to approximately equivariant models.
  arXiv  Detail & Related papers  (2023-09-22T20:15:37Z)
• Latent Traversals in Generative Models as Potential Flows [113.4232528843775]
  We propose to model latent structures with a learned dynamic potential landscape. Inspired by physics, optimal transport, and neuroscience, these potential landscapes are learned as physically realistic partial differential equations. Our method achieves both more qualitatively and quantitatively disentangled trajectories than state-of-the-art baselines.
  arXiv  Detail & Related papers  (2023-04-25T15:53:45Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.