New framework improves reliability of learned representations by modeling uncertainty and structural constraints.
problem Uncertainty in learned representations treated as deterministic, leading to unreliable models.
method Proposes a principled framework for reliable representation learning with uncertainty-aware regularization and structural constraints.
result Improves stability, calibration, and robustness of learned representations.
Study local structure of knot group representations into SL(n,C).
problem Understanding the local structure of knot group representations.
method Analysis of tangent cone and use of Luna's slice theorem.
result Local structure of representation variety at diagonal representations.
Unified framework for representation and causal structure learning using exchangeable data.
problem Identifying latent representations or causal structures in non-i.i.d. data.
method Identifiable Exchangeable Mechanisms (IEM) framework for representation and structure learning.
result New insights and identifiability results for causal structure and representation learning.
The paper proposes a deep learning technique for structured and composable representations.
problem Learning structured and composable representations from input images and discrete labels.
method End-to-end deep learning to learn representations based on distance estimates between class label and contextual information.
result The representations have a clear structure allowing for class and environment decomposition.
New autoencoder learns structured representations without regularization.
problem Learning structured representations without relying on regularization.
method Proposes a novel autoencoder architecture that learns a hierarchy of latent variables.
result Improves results in generation, disentanglement, and extrapolation tasks.
Transformer learns graph structure better with subgraph info.
problem Transformer struggles with structural similarity in graph learning.
method Structure-Aware Transformer with subgraph attention.
result Improves graph prediction benchmarks significantly.
New representations solve a gap in projective structure proof.
problem Prove every non-elementary surface group representation is a projective structure holonomy.
method Define pentagon representations and show they are non-elementary and not Schottky decomposable.
result Repair Gallo-Kapovich-Marden proof by showing pentagon representations arise as holonomies.
Paper presents a method to efficiently learn ordered representations of multi-agent data.
problem Challenges in learning consistent representations of multi-agent interactions.
method Dynamic alignment method to order multi-agent data for faster representation learning.
result Representation learning of multi-agent data is significantly accelerated.
Introduces holed cone structures to generalize cone structures on 3-manifolds.
problem Generalizing cone structures to 3-manifolds with irreducible holonomy representations.
method Introduces holed cone structures and considers their deformation space.
result The deformation space of holed cone structures is a covering space of the character variety.
A fundamental problem in applying machine learning techniques for chemical problems is to find suitable representations for molecular and crystal structures. While the structure representations based on atom connectivities are prevalent for molecules, two-dimensional descriptors are not suitable for describing molecula…
Proposes FSM-IRL to learn invariant network representations considering feature and structural shifts.
problem Spatial heterogeneity and temporal dynamics lead to OOD generalization issues in geographic networks.
method Introduces FSM-IRL model that accounts for feature and structural distribution shifts using causal attention and reweighting.
result Demonstrates strong learning capabilities on geographic and social network datasets in OOD scenarios.
A framework for learning disentangled representations of symmetric environments.
problem Discovering and modelling the underlying structure of environments.
method Group representation theory for disentangled representations of dynamical environments.
result Our method enables accurate long-horizon predictions and correlates with disentanglement quality.
We consider the relationship between hyperbolic cone-manifold structures on surfaces, and algebraic representations of the fundamental group into a group of isometries. A hyperbolic cone-manifold structure on a surface, with all interior cone angles being integer multiples of 2π, determines a holonomy representation …
Structural identity is a concept of symmetry in which network nodes are identified according to the network structure and their relationship to other nodes. Structural identity has been studied in theory and practice over the past decades, but only recently has it been addressed with representational learning technique…
This work provides the first unifying theoretical framework for node (positional) embeddings and structural graph representations, bridging methods like matrix factorization and graph neural networks. Using invariant theory, we show that the relationship between structural representations and node embeddings is analogo…
node2coords learns interpretable graph node representations robust to graph perturbations.
problem Need representations that capture graph structure and are robust to perturbations.
method Proposes a graph representation learning algorithm using Wasserstein barycenters.
result Learned representations are interpretable and stable to graph perturbations.
We prove that a polar orthogonal representation of a real reductive algebraic group has the same closed orbits as the isotropy representation of a pseudo-Riemannian symmetric space. We also develop a partial structural theory of polar orthogonal representations of real reductive algebraic groups which slightly generali…
Let K(X) denote the set of projective structures on a compact Riemann surface X whose holonomy representations are discrete. We will show that each component of the interior of K(X) is holomorphically equivalent to a complex submanifold of the product of Teichmüller spaces and the holonomy representation of every…
Many machine learning algorithms represent input data with vector embeddings or discrete codes. When inputs exhibit compositional structure (e.g. objects built from parts or procedures from subroutines), it is natural to ask whether this compositional structure is reflected in the the inputs' learned representations. W…
Anosov deformations created for surfaces with specific properties.
problem Creating proper slices in character varieties for specific surface groups.
method Constructing proper slices in character varieties for surface groups into SL(3,R).
result Representations are Borel Anosov.
CRATE-MAE learns structured representations from unlabeled data.
problem Learning structured representations from unlabeled data.
method Structured Diffusion with White-Box Transformers.
result CRATE-MAE achieves highly promising performance on large-scale imagery datasets.
Study quandle modules over geometric quandles and their relation to Lie-Yamaguti representations.
problem Understanding quandle modules and their connection to Lie-Yamaguti representations.
method Examine quandle modules over quandle spaces, focusing on geometric structures.
result Modules over quandle spaces are linked to representations of Lie-Yamaguti algebras.
Graph Information Bottleneck (GIB) optimizes graph representations for robustness against adversarial attacks.
problem Challenges in learning graph representations due to structure and feature information.
method GIB is an information-theoretic principle that balances expressiveness and robustness by maximizing mutual information between representation and target, while constraining mutual information with input data.
result GIB-based models are more robust to adversarial attacks, achieving up to 31% improvement.
TRUST improves structure learning with tractable uncertainty.
problem Capturing uncertainty in structure learning for causal DAGs.
method Probabilistic circuits for posterior inference.
result Probabilistic circuits enhance structure learning quality and uncertainty.
Agent learns diverse hierarchical structures in unknown environments.
problem Autonomous discovery and learning of diverse structures in unknown changing environments.
method Progressive construction of a Hierarchy of Observation Latent Models for Exploration Stratification (HOLMES).
result Agent can learn and reuse representations to progressively explore and discover diverse structures.
The paper proposes a method to learn structured representations from unlabeled data using mutual information maximization.
problem Learning structured representations from unlabeled data.
method Adversarial maximization of mutual information between a structured latent variable and a target variable.
result The proposed method outperforms current baselines in document hashing and yields highly compressed interpretable representations.
The paper studies geometric representations of submanifolds using complex-valued functions.
problem Exploring the geometry of codimension-2 submanifolds.
method Implicitly representing submanifolds by complex-valued functions and showing a prequantum bundle structure.
result The space of implicit representations admits a prequantum bundle structure over the space of submanifolds.
For each oriented surface Σ of genus g we study a limit of quantum representations of the mapping class group arising in TQFT derived from the Kauffman bracket. We determine that these representations converge in the Fell topology to the representation of the mapping class group on $\boH(Σ)$, the space of regular f…
Proposes SDCN to integrate structural information into deep clustering.
problem Lack of attention to structural information in representation learning for clustering.
method Designs a delivery operator to transfer autoencoder representations to GCN layers and uses a dual self-supervised mechanism.
result SDCN consistently outperforms state-of-the-art techniques in clustering tasks.
We consider the relationship between hyperbolic cone-manifold structures on surfaces, and algebraic representations of the fundamental group into a group of isometries. A hyperbolic cone-manifold structure on a surface, with all interior cone angles being integer multiples of 2π, determines a holonomy representation …
Auto-encoders have emerged as a successful framework for unsupervised learning. However, conventional auto-encoders are incapable of utilizing explicit relations in structured data. To take advantage of relations in graph-structured data, several graph auto-encoders have recently been proposed, but they neglect to reco…
Study on projective structures linked to Hitchin representations.
problem Understanding the topology and geometric properties of projective structures.
method Using gauge theory, flat bundles, Higgs bundles, and geometric constructions.
result Some projective structures are fibered in a standard way.
Improves representation learning for individual treatment effect estimation.
problem Estimating individual treatment effects with high accuracy.
method Introduces a structure keeper to maintain correlation between baseline covariates and representations, trains a discriminator to balance representation and information loss.
result Proposed SMRL algorithm minimizes treatment estimation error and outperforms state-of-the-art methods.
Representation learning is a fundamental but challenging problem, especially when the distribution of data is unknown. We propose a new representation learning method, termed Structure Transfer Machine (STM), which enables feature learning process to converge at the representation expectation in a probabilistic way. We…
The paper explores how AI trading agents' similar information representation can cause financial market instability.
problem Systemic instability in AI-dominated financial markets due to similar information representation.
method Structural multi-agent market model with two-layer decision architecture for AI agents.
result Representation homogeneity can lead to systemic instability in financial markets.
This paper clarifies vine copula structures using graph and matrix representations.
problem Ambiguity in vine copula representations in literature.
method Graph and matrix representations to clarify vine structures, including cherry and chordal sequences.
result A unique matrix representation of vine structures when given a perfect elimination ordering.
New method learns unbiased treatment representations from structured high-dimensional data.
problem Estimating causal effects from high-dimensional, structured treatments.
method Contrastive learning approach to learn unbiased treatment representations.
result The method identifies causal factors and discards non-causal ones, leading to unbiased causal effect estimates.
The paper classifies fiber structures of discontinuity domains for Anosov representations.
problem Understanding the topology of discontinuity domains for Anosov representations.
method Explicitly working out a smooth version of Fintushel's classification theorem for S1-actions on 4-manifolds. result The action on the fiber is equivalent to a circle action on a Hirzebruch surface.
Performing machine learning on structured data is complicated by the fact that such data does not have vectorial form. Therefore, multiple approaches have emerged to construct vectorial representations of structured data, from kernel and distance approaches to recurrent, recursive, and convolutional neural networks. Re…
We propose a novel method of introducing structure into existing machine learning techniques by developing structure-based similarity and distance measures. To learn structural information, low-dimensional structure of the data is captured by solving a non-linear, low-rank representation problem. We show that this low-…
We describe recent links between two topics: geometric structures on manifolds in the sense of Ehresmann and Thurston, and dynamics "at infinity" for representations of discrete groups into Lie groups.
We study primitive stable representations of free groups into higher rank semisimple Lie groups and their properties. Let Σ be a compact, connected, orientable surface (possibly with boundary) of negative Euler characteristic. We first verify the σmod-regularity for convex projective structures and positive repr…
C-SWMs learn structured world models from raw data.
problem Learning structured world models from raw sensory data.
method Contrastive learning with graph neural networks.
result C-SWMs outperform typical models in structured environments.
Researchers present and compare different representations of dissipative Hamiltonian DAE systems.
problem Understanding and transforming dissipative Hamiltonian DAE systems.
method Global geometric and algebraic points of view, translations between representations, characterizations, and numerical methods for computing structural information.
result A general DAE system can be transformed into a dissipative Hamiltonian or port-Hamiltonian DAE system.
iREPA shows spatial structure, not global semantic, drives generation performance in REPA.
problem Understanding what aspect of the target representation matters for generation.
method Empirical analysis of 27 vision encoders, two modifications to REPA.
result Spatial structure, not global semantic, drives generation performance.
HGP-SL pools and learns graph structure for hierarchical representation learning.
problem Graph pooling is overlooked in GNN models, limiting hierarchical representation learning.
method Integrates graph pooling and structure learning into a unified module.
result HGP-SL improves graph classification performance on benchmarks.
We introduce and study a new class of representations of surface groups into Lie groups of Hermitian type, called weakly maximal representations. They are defined in terms of invariants in bounded cohomology and extend considerably the scope of maximal representations. We prove that weakly maximal representations are d…
The paper explores how AI systems use information geometry to encode semantic structure.
problem How AI systems encode semantic structure into geometric representation spaces.
method Focuses on softmax distributions and develops dual steering method for robust concept manipulation.
result Dual steering optimally modifies target concepts while minimizing off-target changes.