Paper proposes CNN with SIFT for rotation invariant feature extraction.
problem Max-pooling layer discards rotational information, leading to rotation invariance issues.
method Uses SIFT descriptor to capture orientation and spatial relationships.
result Improves feature extraction on MNIST and fashionMNIST datasets.
Rotation invariant algorithms fail on sparse problems even with noise.
problem Rotation invariant algorithms' suboptimality in sparse linear problems with noise.
method Lower bounds and trajectory analysis of optimization algorithms.
result Rotation invariant algorithms are suboptimal even with noise and many examples.
We introduce a novel class of rotation invariants of two dimensional curves based on iterated integrals. The invariants we present are in some sense complete and we describe an algorithm to calculate them, giving explicit computations up to order six. We present an application to online (stroke-trajectory based) charac…
In recent years, convolutional neural networks (CNN) have played an important role in the field of deep learning. Variants of CNN's have proven to be very successful in classification tasks across different domains. However, there are two big drawbacks to CNN's: their failure to take into account of important spatial h…
We propose a principled method for kernel learning, which relies on a Fourier-analytic characterization of translation-invariant or rotation-invariant kernels. Our method produces a sequence of feature maps, iteratively refining the SVM margin. We provide rigorous guarantees for optimality and generalization, interpret…
Rotation invariant algorithms fail with hard labels sampled from sparse targets.
problem Rotation invariant algorithms fail to learn from hard labels sampled from sparse targets.
method Proving the excess risk of rotation invariant algorithms and proposing a simple non-rotation invariant algorithm.
result Rotation invariant algorithms incur an excess risk of $Ω\left(\frac{d-1}{n}
ight)$, while non-rotation invariant algorithms have an excess risk of $O\left(\frac{s\log d}{n}
ight).
The scalar curvature equation for rotation invariant Kähler metrics on Cn\{0} is reduced to a system of ODEs of order 2. By solving the ODEs, we obtain complete lists of rotation invariant zero or positive csck on Cn\{0} in lower dimensions. We also prove that there doe…
A new rotation invariant method for 3D medical imaging classification.
problem Computational expense and lack of rotation invariance in 3D medical image processing.
method Proposes a rotation invariant convolution operator using hypersphere topology.
result Demonstrates improved classification accuracy and rotation invariance.
We classify Kähler-Einstein manifolds which admit a Kähler immersion into a finite dimensional complex projective space endowed with the Fubini-Study metric, whose codimention is not greater than 3 and whose metric is rotation invariant.
Deep nets improve function approximation and learning in high dimensions.
problem Designing neural networks for rotation-invariant function approximation.
method Developed deep neural networks with multiple hidden layers for radial function approximation.
result Deep nets achieve near-optimal function approximation and learning rates not possible by shallow nets.
GCNNs gain rotation invariance with more training augmentation, making SVD-Universal more effective.
problem Improving robustness of GCNNs to adversarial attacks.
method SVD-Universal technique applied to GCNNs trained with larger rotations.
result SVD-Universal becomes more effective as GCNNs gain rotation invariance.
A new method estimates target images directly from noisy observations in cryo-EM.
problem Estimating target images from noisy, rotated observations in cryo-EM.
method Estimates rotation-invariant features and then images from these features.
result Effectiveness demonstrated on synthetic cryo-EM datasets.
Paper learns to rotate filters for group convolutions.
problem Difficult to rotate 3x3 filters on pixel grids.
method Learn filter basis and rotation-invariant coefficients; switch basis for rotation.
result Produces feature maps insensitive to input rotations.
High-dimensional kernel regression struggles due to rotational invariance.
problem Kernel ridge regression struggles in high dimensions due to rotational invariance.
method Analysis of kernel properties and their impact on high-dimensional data.
result Lower bound on generalization error for high-dimensional kernel regression.
We add prior knowledge to deep networks to make them invariant to transformations.
problem Creating deep networks invariant to transformations like rotation.
method A novel layer based on invariant integration to enforce feature space invariances.
result State-of-the-art performance on the Rotated-MNIST dataset.
We solve Bayesian PCA's rotational symmetry issue by rotation-invariant parameterization.
problem Bayesian PCA's rotational symmetry complicates inference and interpretation.
method Rotation-invariant Householder parameterization using random matrix theory.
result Efficient rotation-invariant probabilistic PCA implementation.
Solves classical problem with Kähler-Einstein metrics in complex projective spaces.
problem Classical problem of non-isometric bidimensional Kähler-Einstein submanifolds.
method Listed complete non-isometric bidimensional rotation invariant Kähler-Einstein submanifolds.
result Solves the classical problem in the specified case.
Graph-based CNN for spherical data with equivariance.
problem Efficiently learning from non-uniformly distributed spherical data.
method Discretized sphere as graph, graph convolutions, equivariance using Defferrard's graph neural network.
result Good performance on rotation-invariant learning problems.
Feature engineering plays an important role in the success of a machine learning model. Most of the effort in training a model goes into data preparation and choosing the right representation. In this paper, we propose a robust feature engineering method, Randomized Union of Locally Linear Subspaces (RULLS). We generat…
New MCMC method improves sampling efficiency across diverse structural models.
problem Low sampling efficiency in generic MCMC methods for specific problems.
method Adaptive Principal-Component (PC) Meta-learning Stochastic Gradient Hamiltonian Monte Carlo (APM-SGHMC) algorithm.
result Universal samplers achieve zero-shot generalization across structurally distinct models.
Optimal square matrices for image approximation under translation and rotation.
problem Approximating images with translation and rotation invariant subspaces.
method Abstract harmonic analysis for constructing optimal square matrices.
result Optimal approximation of images with minimal quadratic error.
Recent work by Cohen \emph{et al.} has achieved state-of-the-art results for learning spherical images in a rotation invariant way by using ideas from group representation theory and noncommutative harmonic analysis. In this paper we propose a generalization of this work that generally exhibits improved performace, but…
Paper relaxes symmetry conditions for universal feature selection in noisy data.
problem Feature selection in noisy data with weak symmetry.
method Developed a universal feature selection framework using singular value decomposition of canonical dependence matrix.
result Selected features achieve asymptotically optimal error exponents up to a residual term.
A new sliced IGW distance for Gromov-Wasserstein alignment.
problem Scalability issues in Gromov-Wasserstein alignment for high-dimensional problems.
method Proposed a sliced IGW distance with rotational invariance.
result Natural rotational invariance of the sliced IGW distance.
We investigate the problem of estimating a given real symmetric signal matrix C from a noisy observation matrix M in the limit of large dimension. We consider the case where the noisy measurement M comes either from an arbitrary additive or multiplicative rotational invariant perturbati…
New method learns disentangled discrete representations using categorical variational autoencoders.
problem Learning disentangled representations from discrete latent spaces.
method Replaced standard Gaussian VAE with a categorical VAE to mitigate rotational invariance.
result Categorical distributions improve learning of disentangled representations.
The paper develops a new algorithm for RBMs using dynamical mean-field theory.
problem Learning in Restricted Boltzmann Machines (RBMs) with complex dependencies.
method Dynamical mean-field theory applied to RBMs with rectangular coupling matrices drawn from a bi-rotation invariant ensemble.
result The algorithm converges globally under a stability criterion, with rates matching numerical simulations.
LassoFlexNet improves deep learning performance on tabular data.
problem Deep learning underperforms tree-based models on tabular data.
method Incorporates five inductive biases and uses Tied Group Lasso for variable selection.
result LassoFlexNet matches or outperforms leading tree-based models on 52 datasets.
A Minkowski class is a closed subset of the space of convex bodies in Euclidean space Rn which is closed under Minkowski addition and non-negative dilatations. A convex body in Rn is universal if the expansion of its support function in spherical harmonics contains non-zero harmonics of all orders. If K is universal, t…
Translating or rotating an input image should not affect the results of many computer vision tasks. Convolutional neural networks (CNNs) are already translation equivariant: input image translations produce proportionate feature map translations. This is not the case for rotations. Global rotation equivariance is typic…
We prove two results on the classification of trivial Legendrian embeddings g:G→(S3,ξstd) of planar graphs. First, the oriented Legendrian ribbon Rg and rotation invariant rotg are a complete set of invariants. Second, if G is 3-connected or contains K4 as a minor, then the unique t…
A new Wasserstein distance method for comparing incomparable distributions.
problem Comparing distributions that are not supported on the same metric space.
method Distributional slicing, embeddings, and closed-form computation of Wasserstein distance.
result HWD preserves properties like rotation-invariance and can be efficiently learned.
The paper develops GPR models for hyperelastic materials, improving accuracy and rotational invariance.
problem Modeling stress tensors of hyperelastic materials with fewer training examples and higher accuracy.
method Developed three approaches: direct stress tensor modeling, embedding rotational invariance, and recovering strain-energy density.
result Improved GPR models achieve higher accuracy and rotational invariance with fewer training examples.
A novel approach learns goal-conditioned policies for locomotion using batch RL.
problem Training goal-conditioned policies for rotation invariant locomotion.
method Data augmentation and Siamese framework for invariance.
result Our approach outperforms existing RL algorithms on 3D locomotion agents.
Study connects covariance cleaning theory to information theory for heavy-tailed distributions.
problem Optimizing covariance matrices for heavy-tailed distributions using information theory.
method Minimizing Frobenius norm and information loss between true and estimated covariance matrices.
result Asymptotic regime of large matrices minimizes information loss for Student's t distributions.
A new method calculates intrinsic effective sample size for manifold-valued data.
problem Challenges in choosing effective sample size for manifold-valued data.
method Proposes an intrinsic effective sample size based on kernel discrepancy.
result Establishes an exact finite-sample risk interpretation and consistency of the estimator.
New method simplifies tomographic reconstruction using RKHS.
problem Tomographic reconstruction challenges.
method RKHS framework for X-ray transform.
result Sharp stability results without Fourier transform.
A new method for density estimation using mixture discrepancy and moments.
problem Generalizing histogram statistics to higher dimensions.
method Density estimation via mixture discrepancy and moments (DSP-mix and MSP).
result DSP-mix and MSP are computationally tractable and maintain accuracy with increased speed.
The paper classifies invariant gradient k-Yamabe solitons in pseudo-Euclidean spaces.
problem Characterizing invariant gradient k-Yamabe solitons in pseudo-Euclidean spaces. method Characterization through the action of an (n−1)-dimensional translation group and classification of rotational invariant solutions. result Infinitely many explicit examples of geodesically complete steady gradient k-Yamabe solitons are constructed. Bayes-optimal limits in PCA with structured noise are determined.
problem Analyzing statistical dependencies in measurement noise for high-dimensional inference.
method Study of spiked matrix model with low-order polynomial orthogonal noise, providing Bayes-optimal limits and proposing a novel AMP.
result A novel AMP algorithm reaches the information-theoretic limits for more general priors.
A machine learning model with approximate rotational symmetry is tested and found stable.
problem The effects of broken symmetries in machine learning models.
method Testing a model with approximate rotational symmetry in various physical scenarios.
result The model remains stable even with noticeable symmetry artifacts, suggesting potential benefits.
A simple 2-layer linear network outperforms neural networks in learning sparse targets.
problem Learning sparse targets from a sparse input with gradient descent.
method A 2-layer linear network with fully connected input layer and sparse targets.
result The 2-layer linear network achieves a lower expected square loss than neural networks.
Performance of neural networks can be significantly improved by encoding known invariance for particular tasks. Many image classification tasks, such as those related to cellular imaging, exhibit invariance to rotation. We present a novel scheme using the magnitude response of the 2D-discrete-Fourier transform (2D-DFT)…
A neural network speeds up bond-associated peridynamics simulations.
problem High computational costs in bond-associated peridynamics.
method Message-passing neural network (MPNN) for bond-associated peridynamic material correspondence formulation.
result Significantly reduces computation time via GPU acceleration.
All knots in R3 possess Seifert surfaces, and so the classical Thurston-Bennequin and rotation (or Maslov) invariants for Legendrian knots in a contact structure on R3 can be defined. The definitions extend easily to null-homologous knots in any 3-manifold M endowed with a contact structure ξ. We generalize…
Let $M\subset{\complex}^n$ be a complex domain of ${\complex}^n$ endowed with a rotation invariant \K form ωΦ=2i∂∂ˉΦ. In this paper we describe sufficient conditions on the \K potential Φ for (M,ωΦ) to admit a symplectic embedding (explicitely described in terms of Φ) into a compl…
Spectral clustering performance depends on eigenvector fluctuations, shown to be Gaussian.
problem Predicting the performance of spectral clustering.
method General spike random matrix model and rotational invariance of noise.
result Fluctuations of eigenvector entries are Gaussian in large-dimensional regime.
Whitening, or sphering, is a common preprocessing step in statistical analysis to transform random variables to orthogonality. However, due to rotational freedom there are infinitely many possible whitening procedures. Consequently, there is a diverse range of sphering methods in use, for example based on principal com…