A guide simplifies convolutional neural network properties.
problem Understanding and manipulating convolutional neural network architectures.
method Clarifying relationships between properties of convolutional, pooling, and transposed convolutional layers.
result Intuitive relationships between various convolutional and transposed convolutional layers.
Adaptive convolution improves GANs performance on image generation.
problem GANs struggle with generating images of objects with diverse appearances.
method Proposes adaptive convolution to learn upsampling based on local context.
result Adaptive convolution models improve GANs performance on CIFAR-10 and STL-10 datasets.
The paper introduces transposed Poisson superalgebras and their properties.
problem Developing algebraic structures for quantum physics.
method Defining transposed Poisson superalgebras using derivations and proving their identities.
result Six identities are crucial for understanding transposed Poisson superalgebras.
EDAs with matrix transpose improve Bayesian structure learning performance.
problem Improving Bayesian structure learning performance.
method Introducing a matrix transpose mutation operator for EDAs in Bayesian structure learning.
result EDAs with transpose mutation give markedly better performance than conventional EDAs.
Missing data estimation is an important challenge with high-dimensional data arranged in the form of a matrix. Typically this data matrix is transposable, meaning that either the rows, columns or both can be treated as features. To model transposable data, we present a modification of the matrix-variate normal, the mea…
Proposes a fixed smooth convolutional layer to reduce checkerboard artifacts in CNNs.
problem Checkerboard artifacts in CNNs during upsampling and strided convolution.
method Fixed convolutional layer with adjustable smoothness, applied to four CNNs and GANs.
result Significantly improves classification performance and image generation quality.
Improved sample efficiency in semantic segmentation with rotation equivariant CNNs.
problem Efficiently segmenting images with rotation and reflection symmetries.
method Introduced rotation-equivariant CNNs with new equivariant convolutions and transposed convolutions.
result Significant gains in sample efficiency and robustness to symmetry transformations.
New Sasaki-Einstein 7-spheres found via Berglund-Hübsch transpose.
problem Finding new Sasaki-Einstein 7-spheres.
method Berglund-Hübsch transpose rule applied to Kähler-Einstein 3-folds.
result 75 new Sasaki-Einstein rational homology 7-spheres discovered.
Proposes continuous convolution layers for flexible feature map resizing.
problem Fixed stride limitations in discrete convolution layers.
method Introduces Continuous Convolution (CC) layers that use learned continuous functions.
result Dynamic and consistent resizing of feature maps at any scale, non-integer and axis-dependent.
Introduces q-transpose for q-deformed modular group matrices.
problem Understanding q-deformed rational numbers and their properties. method Introduces q-transpose and applies it to refine q-deformed modular group actions. result New proof and refinement of Leclere and Morier-Genoud's trace palindromicity theorem.
This paper addresses graph embedding issues and introduces \strap for scalable, non-linear embeddings.
problem Preserving out-degree distributions and conflicting optimization goals on directed graphs.
method Introduces transpose proximity and \strap, a factorization-based algorithm that handles both directed and undirected graphs.
result Proposes \strap, which outperforms state-of-the-art methods in effectiveness and scalability.
New method improves crowd counting accuracy using inverse k-NN maps and multiscale upsampling.
problem Improving accuracy of crowd density maps for high-density gatherings.
method Developed MUD-ikNN architecture using inverse k-NN maps and multiscale upsampling. result New network architecture outperforms state-of-the-art crowd counting.
We consider the problem of large-scale inference on the row or column variables of data in the form of a matrix. Often this data is transposable, meaning that both the row variables and column variables are of potential interest. An example of this scenario is detecting significant genes in microarrays when the samples…
Study proposes a more accurate method for classifying transposable elements.
problem Classifying transposable elements for understanding their genetic and evolutionary effects.
method Utilized Support Vector Machines (SVM) for hierarchical classification of transposable elements.
result Proposed a robust approach for hierarchical classification of transposable elements with higher accuracy.
Study explores K-means clustering of variables and its relation to PCA.
problem Exploring the relationship between K-means clustering of variables and PCA.
method Apply PCA to original data and K-means to transposed data, quantify variable contributions to principal components.
result Identifies how variable clusters contribute to principal components identified by PCA.
Model disentangles font content and style.
problem Analyzing and reconstructing fonts.
method Variational inference and asymmetric transpose convolutional process.
result Model outperforms state-of-the-art models in font reconstruction.
A new method for higher-order co-occurrences in hypergraphs.
problem Computing higher-order co-occurrences in hypergraphs.
method Face-splitting product or transpose Khatri-Rao product for higher order tuple co-occurrences.
result Demonstrates the utility of the higher order co-occurrence tensor in NLP and hypergraph models.
The Berglund-Hübsch rule connects Calabi-Yau orbifolds to Sasakian manifolds.
problem Connecting Calabi-Yau orbifolds to Sasakian manifolds.
method Applying the Berglund-Hübsch transpose rule to associate Sasaki manifolds.
result Four seven-dimensional Sasakian manifolds of positive Ricci curvature are associated with a K3 orbifold.
A hybrid ASR system using conformer architecture improves word-error-rate and training speed.
problem Improving word-error-rate and training efficiency for hybrid ASR systems.
method Used conformer architecture, applied time downsampling, and transposed convolutions.
result Conformer-based hybrid model achieves competitive results and significantly outperforms BLSTM-based hybrid model.
Bayesian deep learning counts crowds robustly despite occlusions and scale variations.
problem Accurately counting individuals in crowded scenes with occlusions and varying sizes.
method Proposes a Bayesian multi-scale neural network with a ResNet feature extractor, dilated convolutions, and a Perspective-aware Aggregation Module.
result Achieves superior performance on crowd counting benchmarks with uncertainty estimates.
Orthogonium offers unified, efficient layers for robust deep learning.
problem Fragmented and computationally demanding implementations of orthogonal and 1-Lipschitz layers.
method Unified, efficient PyTorch library providing orthogonal and 1-Lipschitz layers.
result Reduced overhead and standardized tools for robust experimentation.
Transposable data represents interactions among two sets of entities, and are typically represented as a matrix containing the known interaction values. Additional side information may consist of feature vectors specific to entities corresponding to the rows and/or columns of such a matrix. Further information may also…
Language models fail to process hallucinated responses, and this study diagnoses the failure.
problem Language models fail to process hallucinated responses, leading to over-concentration or diffuse attention.
method The study uses forced scoring of benchmark-labeled responses to compute attention shapes and analyze the symmetric component of the degree-normalized attention operator.
result The study proves that every transpose-invariant spectral diagnostic of the attention operator is orientation-blind and bounds the sensitivity of any Lipschitz diagnostic by the asymmetry coefficient \(G\).
Given a knot and an SL(n,C) representation of its group that is conjugate to its dual, the representation that replaces each matrix with its inverse-transpose, the associated twisted Reidemeister torsion is reciprocal. An example is given of a knot group and SL(3,Z) representation that is not conjugate to its dual for …
New examples show Sasaki manifolds without extremal metrics.
problem Finding Sasaki manifolds without extremal metrics.
method Using Berglund-Hübsch transpose rule and relative K-stability.
result Examples of Sasaki manifolds without extremal metrics.
Combines gradient-based and competitive learning for unsupervised feature extraction.
problem Handling input data without supervision and replicating input manifold topology.
method Integrates gradient-based and competitive learning approaches to learn topological structures.
result The dual competitive layer outperforms the vanilla layer in high-dimensional datasets.
This paper studies iteration convergence of Kronecker graphical lasso (KGLasso) algorithms for estimating the covariance of an i.i.d. Gaussian random sample under a sparse Kronecker-product covariance model and MSE convergence rates. The KGlasso model, originally called the transposable regularized covariance model by …
We study Nijenhuis structures on Courant algebroids in terms of the canonical Poisson bracket on their symplectic realizations. We prove that the Nijenhuis torsion of a skew-symmetric endomorphism N of a Courant algebroid is skew-symmetric if the square of N is proportional to the identity, and only in this case when t…
The interior polynomial of a bipartite graph's hypergraph equals its Ehrhart polynomial of its root polytope.
problem Understanding the relationship between the interior polynomial of a bipartite graph and its root polytope.
method Proving equivalence between the interior polynomial of a bipartite graph's hypergraph and the Ehrhart polynomial of its root polytope.
result The interior polynomials of a bipartite graph and its transpose agree.
The paper extends Gray's result to quaternion-Kähler manifolds.
problem Understanding quaternion-Kähler manifolds with non-negative quaternionic sectional curvature.
method Introducing quaternionic sectional curvature, proving Wolf spaces have non-negative curvature, and using nearly Kähler twistor spaces.
result Every quaternion-Kähler manifold with non-negative quaternionic sectional curvature is a Wolf space.
New Sliced-Wasserstein distances for non-Euclidean data.
problem Computational burden of Wasserstein distance on non-Euclidean manifolds.
method Derive Sliced-Wasserstein distances and flows on Cartan-Hadamard manifolds.
result General constructions and non-parametric schemes for minimizing new distances.
This paper extends the evolution operator to contact mechanics, linking Lagrangian and Hamiltonian formulations.
problem Translating the evolution operator to contact mechanics for mechanical systems with dissipation.
method Using the evolution operator K to connect Lagrangian and Hamiltonian formalisms in contact mechanics.
result The evolution operator provides a geometric description of evolution equations and relates constraints.
RFSVM uses learned RF similarity for HDLSS classification.
problem High dimension, low sample size classification problems.
method Transposes RFD approach to HDLSS classification using RF similarity as SVM kernel.
result RFSVM outperforms existing methods for HDLSS problems.
New JPEG algorithm corrects biases in endogenously truncated data.
problem Correcting biases in data with endogenous truncation.
method Semiparametric wavelet-based approach, avoiding matrix computations.
result Corrects both endogenous truncation and covariate shifts biases.
Kernel clustering algorithm improved for large datasets using incomplete Cholesky factorization.
problem Large memory usage in kernel-based clustering for large-scale datasets.
method Approximate the kernel matrix using incomplete Cholesky factorization and apply linear k-means clustering. result The proposed method achieves similar performance to kernel k-means clustering but handles large-scale datasets efficiently. Legendrian invariant studied in knot lattice homology.
problem Legendrian invariant in knot lattice homology.
method Defined Alexander grading and used filtered chain homotopy.
result Alexander grading of Legendrian invariant is invariant under blow-ups.
Tensor programs prove neural network limits for any architecture.
problem Understanding the limits of neural networks of any architecture.
method Prove convergence of neural network's Tangent Kernel (NTK) to a deterministic limit as network widths increase.
result Identify conditions for correct NTK limit calculation based on gradient independence assumption.
Variables in many massive high-dimensional data sets are structured, arising for example from measurements on a regular grid as in imaging and time series or from spatial-temporal measurements as in climate studies. Classical multivariate techniques ignore these structural relationships often resulting in poor performa…
A new VAE adds a classifier to generate music in different keys.
problem Generating music in different keys using VAEs.
method Classifying VAE with LSTM for sequential data.
result The Classifying VAE+LSTM models generate music in different keys better than non-classifying models.
DeepCAM learns convolutional dictionaries for image processing.
problem Processing high-dimensional signals like images efficiently.
method Introduces a Deep Convolutional Analysis Dictionary Model (DeepCAM) using convolutional dictionaries.
result DeepCAM achieves performance comparable to other methods on single image super-resolution.
Improved generative models using flexible convolutions.
problem Generating high-quality images efficiently.
method Generalized 1 x 1 convolutions to d x d convolutions, chaining autoregressive and periodic convolutions.
result Flexible d x d convolutions significantly improve generative flow models' performance.
Proposes a new interpretation of separable convolutions.
problem Lack of a thorough explanation for the efficacy of separable convolutions.
method Hybrid interpretation combining depthwise and pointwise convolutions.
result Proposes a new model for understanding separable convolutions.
Introduces Finslerian convolution metrics and their properties.
problem No specific problem stated; focuses on new metric concept.
method Definition and study of Finslerian convolution metrics.
result Characterization of Finslerian convolution metrics of Riemannian, Minkowskian, and Randers types.
DSGC unifies graph and grid convolutions.
problem Lack of understanding between graph and grid convolutions.
method Depthwise separable graph convolution.
result DSGC outperforms existing methods on benchmark datasets.
This work bridges competitive learning with gradient-based learning for faster feature extraction.
problem Lack of powerful feature extractors in competitive learning methods.
method Introduces gradient-based competitive layers for feature extraction.
result Demonstrates theoretical equivalence and faster convergence of gradient-based competitive layers.
TAGCN improves graph CNN performance without approximation.
problem Performance loss in spectral graph convolutional neural networks.
method Topology adaptive graph convolutional network (TAGCN) with adaptive filters.
result TAGCN outperforms existing spectral CNNs on various datasets.
New PTC convolution preserves properties of Euclidean convolutions on manifolds.
problem Lack of generalizable convolutions on curved domains with desirable properties.
method Parallel transport convolution (PTC) on Riemannian manifolds.
result PTC preserves compactly supported filters and directionality.
VC dimensions of group CNNs are infinite for certain kernels and groups.
problem Estimating the generalization capacity of group convolutional neural networks.
method Identifying precise VC dimension estimates for simple sets of group CNNs.
result Two-parameter families of convolutional neural networks have an infinite VC dimension for infinite groups and certain kernels.