Expanding on previous work, this note generalizes geometric structures results.
problem Generalizing geometric structures results.
method Generalization to a class of geometric structures including integrable almost-complex structures.
result Main results generalized to a broader class of geometric structures.
A new distance combines features and structure of objects.
problem Comparing structured machine learning objects.
method Fused Gromov-Wasserstein distance combining features and structure.
result Mathematical framework and properties established.
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.
Improves Bayesian optimization by focusing on well-behaved structure in objectives.
problem Bayesian optimization struggles with real-world objectives that are often poorly behaved.
method Proposes surrogate models that focus on well-behaved structure, absorbing challenging structures as irreducible uncertainty.
result Surrogate models with appropriate noise distributions improve reliability and performance in challenging objective functions.
The paper explores how regularization can improve multi-objective learning with high-dimensional data.
problem Improving multi-objective learning with high-dimensional and costly data.
method A two-stage MOL framework that leverages low-dimensional structure.
result Vanilla regularization approaches often fail in multi-objective learning, and a two-stage framework can successfully exploit low-dimensional structure.
Introduces three types of partial bihamiltonian structures.
problem None explicitly stated; focuses on definitions and geometrical objects.
method Definition and study of geometrical objects linked with partial bihamiltonian structures.
result Examples of partial bihamiltonian structures in finite and infinite dimensions.
Introduces VB-structures for geometric objects on manifolds.
problem Properties of higher tangent lifts of geometric structures.
method Introduces weighted structures for various geometric objects on a manifold with a homogeneity structure.
result Proves interesting properties of various weighted structures.
Method designs lightweight, structurally robust shell objects.
problem Designing lightweight, structurally robust shell objects under external forces.
method Shape parametrization based on Laplace's equation for smooth, intersection-free boundaries; gradient-free optimization algorithm.
result Practical solution to structural design of hollow objects with single inner cavity.
A framework evaluates synthetic tabular data quality objectively.
problem Lack of an objective interpretation of tabular data metrics.
method Proposes a single mathematical objective for synthetic tabular data distribution, structurally decomposes it, and unifies existing metrics.
result Synthesizers that represent tabular structure outperform other methods, especially on smaller datasets.
New discrete cobordism category for nested manifolds and relations to algebraic structures.
problem Discrete cobordism category for nested manifolds.
method Stratified Morse theory, Cyl-objects, doubling construction, cylindrical bar construction.
result Relations between Cyl-objects and algebraic structures like Temperley-Lieb algebras.
A new method for optimizing hierarchical multi-objective problems.
problem Symmetry and neglect of objective hierarchy in existing multi-objective methods.
method Priority-Constrained Descent (PCD) framework exploiting hierarchical objective structures.
result Pareto dominance and better per-objective performance with secondary progress guarantees.
CANs improve GANs by enforcing structured constraints during training.
problem Generating valid structured objects like molecules and game maps from examples alone.
method Constrained Adversarial Networks (CANs) embed constraints into the model during training, penalizing invalid structures.
result CANs efficiently generate high-quality and novel valid structures.
The abstract introduces a new cyclic structure for surfaces.
problem Defining a cyclic structure for surfaces.
method Endowing surfaces with a structure of a (co)cyclic object in 3D cobordisms.
result 3D TQFTs induce (co)cyclic modules, which are computed algebraically.
Relational Structural Causal Models enable causal reasoning about unseen object combinations.
problem Developing a model that can reason about causal and combinatorial aspects of unseen object combinations.
method Relational Structural Causal Models extend structural causal models to include relational variables and define identification criteria.
result Proposed relational neural causal models outperform non-relational baselines on simulated traffic scenes.
TOQ-Nets learn to recognize complex temporal events with varying objects and sequences.
problem Recognizing complex relational-temporal events with varying numbers of objects and sequence lengths.
method Neuro-symbolic networks with reasoning layers for finite-domain quantification over objects and time.
result TOQ-Nets can generalize to scenarios with more objects than training data and temporal warpings.
This survey article describes the algorithmic approaches successfully used over the time to construct hyperbolic structures on 3-dimensional topological "objects" of various types, and to classify several classes of such objects using such structures.
The main results on the theory of conformal and almost Grassmann structures are presented. The common properties of these structures and also the differences between them are outlined. In particular, the structure groups of these structures and their differential prolongations are found. A complete system of geometric …
We obtain variational formulas for holomorphic objects on Riemann surfaces with respect to arbitrary local coordinates on the moduli space of complex structures. These formulas are written in terms of a canonical object on the moduli space which corresponds to the pairing between the space of quadratic differentials an…
Deep generative models have shown promising results in generating realistic images, but it is still non-trivial to generate images with complicated structures. The main reason is that most of the current generative models fail to explore the structures in the images including spatial layout and semantic relations betwe…
Stochastic structured prediction under bandit feedback follows a learning protocol where on each of a sequence of iterations, the learner receives an input, predicts an output structure, and receives partial feedback in form of a task loss evaluation of the predicted structure. We present applications of this learning …
A thesis submitted for the degree of Doctor of Philosophy of The Australian National University. In this work we introduce several new optimisation methods for problems in machine learning. Our algorithms broadly fall into two categories: optimisation of finite sums and of graph structured objectives. The finite sum pr…
Shows flexible sheaves as fibrant objects for Gromov's h-principle.
problem Applying the h-principle to partial differential relations.
method Interprets flexible sheaves as fibrant objects in a model structure.
result Flexible sheaves can be understood as fibrant objects.
Learning automatically the structure of object categories remains an important open problem in computer vision. In this paper, we propose a novel unsupervised approach that can discover and learn landmarks in object categories, thus characterizing their structure. Our approach is based on factorizing image deformations…
Generative model for discrete objects using Markov chains with valid transitions.
problem Generating valid discrete objects with unique construction histories.
method Markov chain with restricted local operations that preserve validity.
result Generative model produces valid discrete objects and compares favorably to alternatives.
UOLO detects and segments objects in medical images, achieving state-of-the-art performance.
problem Automatic detection and segmentation of objects in medical images.
method UOLO combines object segmentation and detection using a novel loss function.
result UOLO achieves state-of-the-art performance on optic disc and fovea detection and segmentation from retinal images.
We define the beta diffusion tree, a random tree structure with a set of leaves that defines a collection of overlapping subsets of objects, known as a feature allocation. A generative process for the tree structure is defined in terms of particles (representing the objects) diffusing in some continuous space, analogou…
Paper identifies invariant structures for object perception.
problem Understanding how agents perceive objects in dynamic environments.
method Sensorimotor Contingencies Theory inspired unsupervised predictive model.
result Agents can identify invariant structures in sensorimotor experiences.
Unified tensor model disentangles object appearance factors.
problem Representing hierarchical intrinsic and extrinsic causal factors of object appearance.
method Compositional hierarchical tensor factorization.
result Interpretable object representation robust to occlusion and reduced training data requirements.
Paper develops a differentiable approach for 3D imaging models using Fourier slice theorem.
problem Uncertainty in 3D structure modeling and pose estimation in scientific imaging.
method Differentiable probabilistic models in Fourier space with backpropagation through projection.
result Validates approach on 3D protein reconstruction and extends to probabilistic models.
RICH models scenes as hierarchical tree to learn and generate complex compositions.
problem Learning compositional structures between parts and objects in natural scenes.
method RICH uses a latent scene graph to organize entities into a tree structure and employs a top-down inference approach.
result RICH learns and generates complex scene hierarchies from unlabeled data.
A modular object in a symmetric monoidal bicategory is a Frobenius algebra object whose product and coproduct are biadjoint, equipped with a braided structure and a compatible twist, satisfying rigidity, ribbon, pivotality, and modularity conditions. We prove that the oriented 3-dimensional bordism bicategory of 1-, 2-…
We discuss corks, and introduce new objects which we call plugs. Though plugs are fundamentally different objects, they also detect exotic smooth structures in 4-manifolds like corks. We discuss relation between corks, plugs and rational blow-downs. We show how to detect corks and plugs inside of some exotic manifolds.…
GraLSP improves graph neural networks by incorporating local structural patterns.
problem GNNs struggle with identifying common structural patterns in graphs.
method GraLSP uses random anonymous walks to capture local graph structures and incorporates these into feature aggregation mechanisms.
result GraLSP outperforms other models in various prediction tasks on multiple datasets.
The study examines when MAML's objective has a benign landscape.
problem Understanding when MAML's objective landscape is benign.
method Analyzing the landscape of MAML objective on LQR tasks.
result The benign landscape of the MAML objective depends on task similarities.
Paper proposes ASR framework to improve image generation by incorporating human knowledge.
problem Deep generative models struggle to capture rich structures and relations in multi-object images.
method Introduces amortized structural regularization (ASR) framework using posterior regularization (PR) to embed human knowledge.
result Empirical results show ASR significantly outperforms DGM baselines in inference accuracy and sample quality.
This work considers the problem of computing distances between structured objects such as undirected graphs, seen as probability distributions in a specific metric space. We consider a new transportation distance (i.e. that minimizes a total cost of transporting probability masses) that unveils the geometric nature of …
Designs a framework to transfer causal models between similar environments.
problem Transferability of causal models between different but similar environments.
method Object-oriented representations and continuous optimization for structure learning.
result Demonstrates advantages in gridworld settings using reinforcement learning.
In this work, we introduce a deep-structured conditional random field (DS-CRF) model for the purpose of state-based object silhouette tracking. The proposed DS-CRF model consists of a series of state layers, where each state layer spatially characterizes the object silhouette at a particular point in time. The interact…
SPARTAN learns sparse interaction graphs between objects in scenes.
problem Capturing structured interactions between entities in complex settings remains challenging.
method SPARTAN is a Transformer-based world model that learns sparse, context-dependent interaction graphs through sparsity regularization on attention patterns.
result SPARTAN achieves significantly improved few-shot adaptation to dynamics changes and robustness against distractors.
A group, defined as set with associative multiplication and inverse, is a natural structure describing the symmetry of a space. The concept of group generalizes to group objects internal to other categories than sets. But there are yet more general objects that can still be thought of as groups in many ways, such as qu…
Bayesian framework learns latent preference archetypes for many-objective optimization.
problem Expanding space of trade-offs and context-dependent human values.
method Dirichlet-process mixture model for latent preference archetypes, hybrid queries for efficient information.
result Mixture-aware Bayesian optimization outperforms standard methods on synthetic and real-world benchmarks.
Graph-to-Tree Neural Networks improve structured input-output translation in tasks like semantic parsing and math word problems.
problem Improving performance on tasks like semantic parsing and math word problem solving.
method Graph-to-Tree Neural Networks, consisting of a graph encoder and a hierarchical tree decoder.
result Graph2Tree model outperforms or matches state-of-the-art models on neural semantic parsing and math word problem tasks.
This paper studies node embeddings of networks, revealing their geometric properties.
problem Understanding the geometric properties of node embeddings in random networks.
method Characterization of ergodic limits, generalization, and convex relaxations of random walk node embedding objectives.
result The optimal node embedding Grammians have rank 1 for a nuclear norm relaxation of the non-randomized objective.
New tensor kernels reduce mismatch between clustering and reconstruction objectives in deep learning.
problem Objective Function Mismatch in deep clustering.
method Proposed Unsupervised Companion Objectives (UCOs) with tensor kernels to address mismatch.
result Reduced OFM between clustering and reconstruction objectives, leading to improved clustering performance.
The main contribution of this article is a new prior distribution over directed acyclic graphs, which gives larger weight to sparse graphs. This distribution is intended for structured Bayesian networks, where the structure is given by an ordered block model. That is, the nodes of the graph are objects which fall into …
Model learns disentangled object location and appearance representations.
problem Learning disentangled representations of object location and appearance.
method Probabilistic generative model with amortized variational inference.
result Fully disentangled object location and appearance representations.
Variational approach to basic manifold structures.
problem Understanding basic differential geometric structures.
method Variational description of geometric structures.
result Variational formulation of manifold structures.
An absolute parallelism (AP-) space having Finslerian properties is called FAP-space. This FAP-structure is more wider than both conventional AP and Finsler structures. In the present work, more geometric objects as curvature and torsion tensors are derived in the context of this structure. Also second order tensors, u…