We simplify matrix computations for block matrices, especially useful for covariance and correlation matrices.
problem Complex computations for block matrices, especially for covariance and correlation matrices.
method Obtained a canonical representation for block matrices, facilitating computation of various matrix operations.
result Simplified computation of matrix operations for block matrices, particularly useful for covariance and correlation matrices.
Paper proposes ABDR for convex subspace clustering with adaptive block diagonal representation.
problem Subspace clustering with block diagonal structure for noisy data.
method ABDR explicitly pursues block diagonality without sacrificing convexity, using a specially designed convex regularizer.
result Experimental results show ABDR outperforms state-of-the-arts.
Constructs six-dimensional braid group representations for knot detection.
problem Detecting braid vertibility of knots and links.
method Constructs six-dimensional block representations of B3 and uses them to detect braid vertibility. result Some representations can detect braid vertibility of known knots and links.
Semisimplicity proven for conformal blocks representations.
problem Semisimplicity of conformal blocks representations.
method Theory of extensions in non-Abelian Hodge theory and Ocneanu rigidity.
result Semisimplicity of braid group and mapping class group representations.
Researchers compute knot invariants in Seifert manifolds using Wilson loops.
problem Calculating BPS invariants for knots in Seifert manifolds.
method Analytically continued Chern-Simons level and representation from Wilson loop operator.
result Homological blocks for knots in Seifert manifolds and Seifert integer homology spheres.
New findings on cusped Borel Anosov representations and their properties.
problem Characterizing and understanding cusped Borel Anosov representations.
method Analyzing representations of lattices in PGL2(R) to PGLd(R). result Cusped Borel Anosov representations with specific properties are Hitchin representations.
Characterizes Anosov reducible representations in terms of eigenvalues.
problem Understanding Anosov representations in reducible settings.
method Characterizes Anosov representations using eigenvalue magnitudes of irreducible block factors.
result Connected components of character varieties do not contain reducible representations for many non-elementary hyperbolic groups.
NoProp learns neural networks without full back-propagation or forward-propagation.
problem Learning hierarchical representations in neural networks.
method NoProp independently learns each block to denoise a noisy target using local targets and back-propagation within the block.
result NoProp is a viable learning algorithm that is easy to use and computationally efficient.
The paper uses deep learning to detect financial market regimes from correlation matrices.
problem Detecting financial market regimes from correlation dynamics.
method Representation learning on block hierarchical SPD correlation matrices using SPDNet, SPD-NetBN, and U-SPDNet models.
result Deep learning models overfit in financial market data, misleading performance metrics.
The excellent performance of representation learning of autoencoders have attracted considerable interest in various applications. However, the structure and multi-local collaborative relationships of unlabeled data are ignored in their encoding procedure that limits the capability of feature extraction. This paper pre…
Unified multilinear model for causal factor disentanglement.
problem Disentangling causal factors from complex data without direct manipulation.
method Hierarchical block multilinear factorization (M-mode Block SVD) and incremental approach.
result Interpretable object representation robust to occlusion and reduced training data.
New method identifies latent variables with sparse perturbations.
problem Identifying latent variables with minimal supervision.
method Weakly supervised representation learning with sparse perturbations.
result Identification of latent variables up to specified blocks.
Spectral embedding is a popular technique for the representation of graph data. Several regularization techniques have been proposed to improve the quality of the embedding with respect to downstream tasks like clustering. In this paper, we explain on a simple block model the impact of the complete graph regularization…
Knowledge distillation (KD) is a popular method for reducing the computational overhead of deep network inference, in which the output of a teacher model is used to train a smaller, faster student model. Hint training (i.e., FitNets) extends KD by regressing a student model's intermediate representation to a teacher mo…
LoCo learns local representations without end-to-end synchronization, improving performance on complex tasks.
problem Learning local representations without end-to-end synchronization constraints.
method Overlap local blocks to increase decoder depth and allow feedback from upper to lower layers.
result LoCo closes the performance gap between local learning and end-to-end contrastive learning.
We introduce block-tree graphs as a framework for deriving efficient algorithms on graphical models. We define block-tree graphs as a tree-structured graph where each node is a cluster of nodes such that the clusters in the graph are disjoint. This differs from junction-trees, where two clusters connected by an edge al…
Contrastive learning harms minority group representations, affecting downstream tasks.
problem Representation harm in contrastive learning, especially affecting minority groups.
method Causal mediation analysis and stochastic block model explanation.
result Representation harm in contrastive learning is partly responsible for allocation harm in downstream tasks.
Based on projective representations of smooth Deligne cohomology groups, we introduce an analogue of the space of conformal blocks to compact oriented (4k+2)-dimensional Riemannian manifolds with boundary. For the standard (4k+2)-dimensional disk, we compute the space concretely to prove that its dimension is finite.
BEGIN network models binary data without parametric assumptions.
problem Conditional independence in non-parametric families of binary data.
method BEGIN network models binary data using sparse linear representations and block factorizations.
result BEGIN network captures conditional independence for arbitrary binary and multinomial variables.
We explain an elementary topological construction of the Springer representation on the homology of (topological) Springer fibers of types C and D in the case of nilpotent endomorphisms with two Jordan blocks. The Weyl group and component group actions admit a diagrammatic description in terms of cup diagrams which app…
Unsupervised deep learning is one of the most powerful representation learning techniques. Restricted Boltzman machine, sparse coding, regularized auto-encoders, and convolutional neural networks are pioneering building blocks of deep learning. In this paper, we propose a new building block -- distributed random models…
This paper introduces GLT for better input data representation in BNN and proposes a compact topology with block pruning.
problem Improving input data representation for Binary Neural Networks (BNN).
method Generic Learned Thermometer (GLT) for encoding, block pruning and Knowledge Distillation for compact topology.
result Significant accuracy gains and lightweight fully-binarized models with limited accuracy degradation.
New method finds balanced clusters in graphs using auxiliary information.
problem Finding balanced clusters in graphs with population-level constraints.
method Proposes individual-level balancing constraint and develops spectral clustering algorithms.
result Establishes first statistical consistency result for constrained spectral clustering.
Improved ResNets and DenseNets models for better feature reuse.
problem Diminishing feature reuse in ResNets and DenseNets.
method ResNEsts and DenseNEsts are block-based DNN models with improved representation guarantees.
result Wide ResNEsts with bottleneck blocks can guarantee desirable training properties.
Deep latent-variable models learn representations of high-dimensional data in an unsupervised manner. A number of recent efforts have focused on learning representations that disentangle statistically independent axes of variation by introducing modifications to the standard objective function. These approaches general…
In this work, we propose an end-to-end block-based auto-encoder system for image compression. We introduce novel contributions to neural-network based image compression, mainly in achieving binarization simulation, variable bit rates with multiple networks, entropy-friendly representations, inference-stage code optimiz…
New invariants for 3-manifolds derived from supergroup representations.
problem Developing invariants for 3-manifolds using supergroup analogues.
method Introducing supergroup analogues of 3-manifold invariants for superunitary groups, focusing on SU(2|1). Calculating q-series for specific 3-manifolds and studying their properties.
result Explicit calculation and study of q-series for certain 3-manifolds, providing a formula relating new invariants to quantum invariants.
Subspace clustering is a useful technique for many computer vision applications in which the intrinsic dimension of high-dimensional data is often smaller than the ambient dimension. Spectral clustering, as one of the main approaches to subspace clustering, often takes on a sparse representation or a low-rank represent…
Geometrically connects theta functions and WZNW blocks.
problem Identifying connections between theta functions and WZNW blocks.
method Constructing flat connections on bundles of theta functions and WZNW blocks.
result The Tsuchiya-Ueno-Yamada and Knizhnik-Zamolodchikov connections are identified.
We adapt tools from information theory to analyze how an observer comes to synchronize with the hidden states of a finitary, stationary stochastic process. We show that synchronization is determined by both the process's internal organization and by an observer's model of it. We analyze these components using the conve…
Entity resolution seeks to merge databases as to remove duplicate entries where unique identifiers are typically unknown. We review modern blocking approaches for entity resolution, focusing on those based upon locality sensitive hashing (LSH). First, we introduce k-means locality sensitive hashing (KLSH), which is b…
Calculates Dehn twist actions on conformal blocks for modular categories.
problem Order of Dehn twists on spaces of conformal blocks.
method Quantum representations of mapping class groups, ribbon twists, monoidal powers.
result Order of Dehn twists generalizes previous results for small quantum group.
Enhances ocean floor mapping with adaptive uncertainty estimates.
problem Inaccurate bathymetric data for precise ocean modeling.
method Block-based conformal prediction with VQ-VAE architecture.
result Significant improvements in reconstruction quality and uncertainty estimation reliability.
Generates high-quality images using sparse DCT representations.
problem Challenges in generating images due to high dimensionality.
method Transformers trained on sparse DCT block sequences.
result Competitive image generation quality with state-of-the-art methods.
Graph learning categorizes DeFi services into similar functionalities.
problem Identifying similar financial services in decentralized finance protocols.
method Graph representation learning (GRL) to categorize smart contract blocks into clusters.
result Purity of clustering reaches .888 in the best-case scenario.
This paper evaluates various representations for robotics tasks, improving performance in lifting, stacking, and pushing.
problem Improving data-efficiency in reinforcement learning for robotics with limited data.
method Systematic evaluation of common representations in three robotics tasks: lifting, stacking, and pushing.
result Some representations can perform as well as simulator states as agent inputs, challenging common intuitions.
Improved singular value approximation for convolutional layers.
problem Improving accuracy of singular value approximation for linear convolutional layers.
method Developed a new spectral density matrix method for singular value approximation with improved accuracy and reduced computational complexity.
result Obtained moderate improvement in singular value distribution compared to circular approximation.
Many statistical methods for network data parameterize the edge-probability by attributing latent traits to the vertices such as block structure and assume exchangeability in the sense of the Aldous-Hoover representation theorem. Empirical studies of networks indicate that many real-world networks have a power-law dist…
We propose a mixture of latent trait models with common slope parameters (MCLT) for model-based clustering of high-dimensional binary data, a data type for which few established methods exist. Recent work on clustering of binary data, based on a d-dimensional Gaussian latent variable, is extended by incorporating com…
Sound event detection systems typically consist of two stages: extracting hand-crafted features from the raw audio waveform, and learning a mapping between these features and the target sound events using a classifier. Recently, the focus of sound event detection research has been mostly shifted to the latter stage usi…
CGRL improves graph neural networks' OOD generalization by blocking spurious correlations.
problem Graph Neural Networks struggle with out-of-distribution data due to learning spurious correlations.
method Formulates a causal graph, uses backdoor adjustment, and introduces a loss replacement strategy.
result Significantly improves OOD generalization of GNNs, stabilizing mutual information learning.
Interventional data helps identify latent factors without distributional assumptions.
problem Identifying latent factors from interventional data without distributional assumptions.
method Leveraging geometric signatures of latent factors' support from interventional data.
result Latent causal factors can be identified up to permutation and scaling given data from perfect do-interventions.
Community detection is an important task in network analysis, in which we aim to learn a network partition that groups together vertices with similar community-level connectivity patterns. By finding such groups of vertices with similar structural roles, we extract a compact representation of the network's large-scale …
DAM with MRL improves relational reasoning in MANNs.
problem Limited performance of associative memory networks on complex relational reasoning tasks.
method Distributed Associative Memory architecture with Memory Refreshing Loss.
result Enhanced relation reasoning performance of MANNs on long temporal sequence data.
This work tackles representation learning by introducing stochastic competition-based activations.
problem Learning diversified representations in deep learning models.
method Combining information-theoretic arguments with stochastic competition-based activations, using Stochastic Local Winner-Takes-All (LWTA) units.
result The proposed method yields significant discriminative representation learning abilities and allows for a principled investigation of intermediate network representations.
A new framework for robot block-stacking tasks using causal probabilistic models.
problem Robots fail outside controlled environments due to uncertainty and lack of explicit design for all scenarios.
method Causal probabilistic framework combining causal models and probabilistic representations of noise.
result Robots can perceive, reason about, and explain their environment for block-stacking tasks.
New method builds hyperbolic spheres with controlled holonomy.
problem Creating hyperbolic spheres with specific holonomy properties.
method Gluing simple building blocks to form hyperbolic cone spheres.
result Any Deroin-Tholozan representation can be realized as cone sphere holonomy.
We show how to define invariants of graphs related to quantum sl(2) when the graph has more then one connected component and components are colored by blocks of representations with zero quantum dimensions.