Extracts object-centric frames from unlabeled images.
problem Extracting abstract models of 3D objects from visual measurements.
method Viewpoint factorization and dense equivariant labelling neural network.
result Extracts dense object-centric coordinate frames invariant to deformations.
LORL learns object-centric representations from vision and language.
problem Learning disentangled, object-centric scene representations from vision and language.
method LORL integrates unsupervised object discovery and segmentation with language input to learn object-centric concepts.
result LORL improves unsupervised object discovery methods and aids downstream tasks.
Improved object segmentation and tracking in video using optical flow and initial state conditioning.
problem Challenges in fully unsupervised object-centric learning from video data.
method Weakly-supervised approach using optical flow and initial state conditioning.
result Conditioning the model on simple object location cues significantly improves instance segmentation in realistic synthetic data.
ROOTS learns to represent and render 3D scenes with object-centric models.
problem Learning to represent and render 3D scenes with object-centric compositionality.
method Probabilistic generative model for learning object representations and scene rendering from partial observations.
result The model can infer 3D object representations and render scenes from arbitrary viewpoints.
Graph neural networks detect anomalies in object-centric business processes.
problem Detecting anomalies in graph-like business processes.
method Graph convolutional autoencoder architecture for anomaly detection.
result Promising performance in detecting anomalies at the activity type and attributes level.
Study shows bottlenecks improve image segmentation quality.
problem Robust object discovery in real-world images remains challenging.
method Empirical investigation of reconstruction bottlenecks in GENESIS model.
result Reconstruction bottlenecks determine reconstruction and segmentation quality.
Slot Attention extracts object-centric representations from images.
problem Learning distributed representations that don't capture natural scene composition.
method Slot Attention module interfaces with CNN outputs to produce task-dependent abstract slots.
result Slot Attention enables generalization to unseen compositions.
Object-centric learning improves generalization and robustness in multi-object scenes.
problem Improving generalization and robustness in neural networks for scenes with multiple objects.
method Training state-of-the-art unsupervised models on multi-object datasets and evaluating segmentation metrics and downstream tasks.
result Object-centric representations are useful for downstream tasks and generally robust to most distribution shifts affecting objects, but less so for less structured shifts.
KINet learns object interactions without supervision for robotic pushing.
problem Lack of supervised data for object-centric forward prediction.
method End-to-end unsupervised framework using keypoint representation and contrastive estimation.
result Automatically generalizes to unseen scenarios and accurately predicts future states.
GENESIS generates and samples 3D scenes by capturing object interactions.
problem Lack of models that explicitly capture object interactions in scene generation.
method Object-centric latent variables, spatial GMM, amortized inference, autoregressive prior.
result First object-centric generative model of 3D visual scenes.
Unified model improves object-centric world modeling with new abilities.
problem Integration of recent advances and temporal imagination abilities.
method Generative Structured World Models (G-SWM) framework.
result G-SWM achieves best or comparable performance in temporal generation.
Study explores reinforcement learning in a complex game environment, analyzing rule inference and policy learning.
problem Learning optimal policies in environments with hidden rules.
method Investigated using the Game Of Hidden Rules (GOHR) environment, employing Feature-Centric and Object-Centric state representations with a Transformer-based A2C algorithm.
result Transformer-based A2C models outperform traditional methods in GOHR, demonstrating the effectiveness of representation strategies.
Fastest video anomaly detection via teacher-student distillation.
problem Anomaly detection in video at high speed.
method Adversarial knowledge distillation from object-level teacher models.
result 7-62 times faster than state-of-the-art methods.
Generative model separates objects, positions, and appearances in images.
problem Generating complete images with accurate object positions and appearances.
method Structured latent representation that separates objects, positions, and appearances.
result Generative model can infer object decompositions and accurate depth orderings.
AXIOM learns games quickly with simple object models.
problem Data inefficiency in reinforcement learning.
method Expanding object-centric models with active inference.
result AXIOM learns games in 10,000 steps with minimal parameters.
Soft geometric bias improves physical dynamics predictions.
problem Learning physical dynamics with exact group equivariance can degrade performance.
method Object-centric world models using geometric algebra neural networks.
result Soft geometric inductive bias leads to better physical fidelity predictions.
Shared workspace improves neural module coordination in deep learning.
problem Pairwise interactions in deep learning models lack global coordination.
method Introduce a shared global workspace with bandwidth limitations among neural modules.
result Capacity limitations encourage specialization and synchronization.
GENESIS-V2 infers unordered object representations without iterative refinement.
problem Unsupervised learning of unordered object representations for complex images.
method Stochastic stick-breaking process for clustering pixel embeddings.
result GENESIS-V2 outperforms recent baselines in unsupervised image segmentation and scene generation.
OP3 models entities for better task generalization in reinforcement learning.
problem Generalizing to unseen physical tasks with combinatorial complexity.
method Object-centric perception, prediction, and planning (OP3) framework.
result OP3 outperforms oracle models and state-of-the-art video prediction models.
Bertrand framed surfaces defined in Euclidean 3-space with applications.
problem Defining and characterizing Bertrand framed surfaces.
method Using moving frames to define Bertrand framed surfaces and analyzing their caustics and involutes.
result Conditions for caustics and involutes to be inverse operations of framed surfaces.
Quaternionic frames' admissibility and homotopy proven.
problem Existence and interpolation of quaternionic frames.
method Interpreting frames as adjoint orbits.
result Spaces of quaternionic frames are path-connected.
Introduces hyperbolic generalized framed surfaces and their properties.
problem None explicitly stated; focuses on introducing new geometric objects.
method Generalization of hyperbolic framed surfaces and curves.
result Established conditions for a surface to be a hyperbolic generalized framed base surface and explored their singularities.
Images seen during test time are often not from the same distribution as images used for learning. This problem, known as domain shift, occurs when training classifiers from object-centric internet image databases and trying to apply them directly to scene understanding tasks. The consequence is often severe performanc…
Study of generalized Bishop frames on curves in 4D space.
problem Understanding frames on curves in 4D space.
method Introducing and studying four types of generalized Bishop frames on curves in E4. result Every regular curve in E4 admits all four types of generalized Bishop frames. The main drawback of the Frenet frame is that it is undefined at those points where the curvature is zero. Further- more, in the case of planar curves, the Frenet frame does not agree with the standard framing of curves in the plane. The main drawback of the Bishop frame is that the principle normal vector N is not in …
New framed moves extend classical knot theory results.
problem Extending classical knot theory to framed braids.
method Introduced framed versions of L-moves, Hilden, Pure Hilden groups, and framed versions of the Birman theorem.
result Proved a framed version of the Birman theorem for framed links in plat representation.
Study on Bertrand lightcone framed curves in Lorentz-Minkowski 3-space.
problem Analyzing mixed types of curves with singular points in Lorentz-Minkowski 3-space.
method Using lightcone frame to consider Bertrand types for lightcone framed curves.
result Existence conditions of Bertrand lightcone framed curves in all cases.
The paper extends BPS invariants for framed knots and links.
problem Investigating BPS invariants for framed knots and links.
method Using the dual A-polynomial and framing change formula, the paper extends the relationship between algebraic curves and BPS invariants to framed knots and links.
result Explicit formulas for extremal A-polynomials and BPS invariants of framed knots, and numerical calculations for framed Whitehead links and Borromean rings.
Gradient descent constructs tight fusion frames.
problem Constructing tight fusion frames from prescribed subspaces.
method Gradient descent and symplectic geometry.
result Gradient descent can be used to construct tight fusion frames.
Simply connected spaces of tight frames identified.
problem Understanding the connectivity of spaces of tight frames.
method Viewing tight frames as elements of Stiefel manifolds and identifying simply connected spaces.
result Spaces of tight frames, including finite unit-norm tight frames, are simply connected.
New invariants defined for framed knots and links.
problem Defining invariants for framed knots and links.
method Introducing birack brackets and categorifying their multiset.
result Quiver-valued invariant defined for framed knots and links.
Study reveals LLM personas have two distinct components: frame-robust aggregated traits and frame-dependent geometric features.
problem Evaluation of LLM personas via psychometric questionnaires discards within-instance correlation structure.
method Constructed within-instance correlation matrices from IPIP-50 responses and analyzed geometry on SPD manifolds under manipulated question orderings.
result Persona expression comprises two dissociable components: aggregated features (Big Five scores) and geometric features (SPD manifold).
Higher-dimensional Milnor frames are characterized and contrasted with 3D Heisenberg and 4D nilpotent Lie algebras.
problem Characterizing higher-dimensional Milnor frames and their properties.
method Definition and classification of higher-dimensional Milnor frames and their relationship to known Lie algebras.
result Higher-dimensional Milnor frames are isomorphic to direct sums of 3D Heisenberg and 4D nilpotent Lie algebras and an abelian Lie algebra.
Canonical framings and stable framings for the tangent bundle of a spin 3-manifold are introduced, and illustrated by a number of familiar examples. Methods for constructing canonical framings, and for comparing them with other naturally defined framings, are discussed.
Study on focal surfaces of lightcone framed surfaces in Lorentz-Minkowski 3-space.
problem Investigate differential geometry properties of focal surfaces of lightcone framed surfaces.
method Introduced lightcone frame to define lightcone framed surfaces, then investigated their differential geometry properties.
result Investigated differential geometry properties of focal surfaces of lightcone framed surfaces.
The paper shows that random frames have full spark with high probability.
problem The probability of a random frame having full spark.
method Relating frame spaces to toric symplectic manifolds to analyze geometric and spectral properties.
result The probability of a random frame having full spark is one.
The paper connects hyperbolic spinors to non-null framed curves in Minkowski 3-space.
problem Understanding geometric properties of non-null framed curves.
method Developed new adapted frames for non-null framed curves and investigated their hyperbolic spinor representations.
result Found geometric results and interpretations for non-null framed curves.
This note is dedicated to the study of a Hopf module structures on the space of framed chord diagrams and framed graphs. We also introduce a framed version of the chromatic polynomial and propose two methods to construct framed weight systems.
Clarifies Einstein-Cartan gravitation with Dirac spinor on generalized frame bundle.
problem Formulating Einstein-Cartan gravitation on a frame bundle.
method Integrates Dirac spinor into the Einstein-Cartan spacetime structure.
result Variational equations imply standard field equations under standard frame bundle condition.
Generates coherent 3D scenes from monocular videos without supervision.
problem Lack of 3D scene modeling in video generation models.
method Trains a model to generate 3D scenes with moving objects and a background from monocular videos.
result Trained model generates coherent 3D scenes with multiple moving objects and a background.
Model removes objects from general scenes using weak supervision.
problem Automatic object removal from general scene images with weak supervision.
method Two-stage editor architecture with mask generator and image in-painter; novel GAN prior for mask generator.
result Effectively removes a wide variety of objects from general scenes using weak supervision.
Defined Fermi-Walker derivative in Galilean space and its applications.
problem Defining and applying Fermi-Walker derivative in Galilean space.
method Defined Fermi-Walker derivative in Galilean space G3, and investigated conditions for Fermi-Walker transport and non-rotating frame along curves. result Conditions for Fermi-Walker transport and non-rotating frame were investigated in Galilean space.
Generalized Frenet frames for singular space curves
problem Revisiting the Frenet frame for singular space curves
method Introducing a generalized Frenet frame and frame sequence
result Unified framework for Frenet and Bishop frames
Introduces formal frames for manifolds and their properties.
problem Understanding and generalizing frames and connections on manifolds.
method Introduces formal frames, canonical forms, and torsions.
result Equivalence of vanishing torsions to realizability of formal frames as ordinary frames.
Study of lightcone framed surfaces in Lorentz-Minkowski 3-space, focusing on curvature behavior.
problem Investigate differential geometric properties of lightcone framed surfaces.
method Introduced modified frame to study the properties of lightcone framed surfaces.
result Showed behavior of Gaussian and mean curvatures at lightlike and singular points.
Frame-spun knots are constructed by spinning a knot of lower dimension about a framed submanifold of S^n. We show that all frame-spun knots are slice (null-cobordant).
Modified knotoids with framing and coframing for quantum invariants.
problem Defining and classifying knotoids with framing.
method Defining framed and biframed knotoids, showing topological correspondence, and constructing quantum invariants.
result Generalized quantum knotoid invariants constructed.
The paper studies circular evolutes and involutes of framed curves in Euclidean space.
problem Investigating properties of framed curves and their evolutes and involutes.
method Definition and analysis of circular evolutes and involutes of framed curves, properties of normal surfaces, and their relations.
result Circular evolutes and involutes of framed curves are opposite operations under suitable assumptions, similar to fronts in the Euclidean plane.