arXiv research

DFRot improves LLMs by reducing outlier and massive activation effects.

New method certifies images against transformations like rotations and translations.

DeformRS certifies deep networks against various input deformations.

Federated Learning enables mobile devices to collaboratively learn a shared inference model while keeping all the training data on a user's device, decoupling the ability to do machine learning from the need to store the data in the cloud. Existing work on federated learning with limited communication demonstrates how …

This note gives a simple analysis of a randomized approximation scheme for matrix multiplication proposed by Sarlos (2006) based on a random rotation followed by uniform column sampling. The result follows from a matrix version of Bernstein's inequality and a tail inequality for quadratic forms in subgaussian random ve…

Study optimizes estimation of orthogonal and rotation matrices from noisy data.

RENNs protect input privacy by rotating d-ary features.

In short, our experiments suggest that yes, on average, rotation forest is better than the most common alternatives when all the attributes are real-valued. Rotation forest is a tree based ensemble that performs transforms on subsets of attributes prior to constructing each tree. We present an empirical comparison of c…

Exact optimality achieved in distributed mean estimation with shared randomness.

FibQuant improves KV-cache compression for long-context inference.

The paper analyzes why Gaussianization slows down with higher dimensions and proposes a solution.

Subsampled Randomized Hadamard Transform (SRHT), a popular random projection method that can efficiently project a $d$-dimensional data into $r$-dimensional space ($r \ll d$) in $O(dlog(d))$ time, has been widely used to address the challenge of high-dimensionality in machine learning. SRHT works by rotating the input …

We consider probabilistic PCA and related factor models from a Bayesian perspective. These models are in general not identifiable as the likelihood has a rotational symmetry. This gives rise to complicated posterior distributions with continuous subspaces of equal density and thus hinders efficiency of inference as wel…

In this work, a method of random parameters generation for randomized learning of a single-hidden-layer feedforward neural network is proposed. The method firstly, randomly selects the slope angles of the hidden neurons activation functions from an interval adjusted to the target function, then randomly rotates the act…

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…

We demonstrate that, for a range of state-of-the-art machine learning algorithms, the differences in generalisation performance obtained using default parameter settings and using parameters tuned via cross-validation can be similar in magnitude to the differences in performance observed between state-of-the-art and un…

Most signal processing problems involve the challenging task of multidimensional probability density function (PDF) estimation. In this work, we propose a solution to this problem by using a family of Rotation-based Iterative Gaussianization (RBIG) transforms. The general framework consists of the sequential applicatio…

Study connects covariance cleaning theory to information theory for heavy-tailed distributions.

This chapter introduces quaternion machine learning for 3D rotations.

Expanding self-supervised learning to diverse domains reveals Rotation's semantic superiority.

New TSER algorithms outperform existing methods in time series extrinsic regression.

Study on rotating surfaces in 4D space with matrices.

A new transform links rotating calorons to solutions of a differential equation.

We define general rotational surfaces of elliptic and hyperbolic type in the pseudo-Euclidean 4-space with neutral metric which are analogous to the general rotational surfaces of C. Moore in the Euclidean 4-space. We study Lorentz general rotational surfaces with plane meridian curves and give the complete classificat…

The paper develops a new algorithm for RBMs using dynamical mean-field theory.

The paper defines and analyzes homotopic rotation sets for surfaces of higher genus.

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…

Study of timelike surfaces in Minkowski space with specific geometric properties.

The study characterizes loxodromes on specific rotational surfaces in 3D space.

General rotational surfaces as a source of examples of surfaces in the four-dimensional Euclidean space have been introduced by C. Moore. In this paper we consider the analogue of these surfaces in the Minkowski 4-space. On the base of our invariant theory of spacelike surfaces we study general rotational surfaces with…

This paper explores the trade-off between spatial and adversarial robustness in neural networks.

Rotation systems can't always be drawn in surfaces.

This paper proposes a set of rules to revise various neural networks for 3D point cloud processing to rotation-equivariant quaternion neural networks (REQNNs). We find that when a neural network uses quaternion features under certain conditions, the network feature naturally has the rotation-equivariance property. Rota…

Invariance to nuisance transformations is one of the desirable properties of effective representations. We consider transformations that form a \emph{group} and propose an approach based on kernel methods to derive local group invariant representations. Locality is achieved by defining a suitable probability distributi…

RotEqNet preserves rotation symmetry in fluid systems using high-order tensors.

The rotation prediction (Rotation) is a simple pretext-task for self-supervised learning (SSL), where models learn useful representations for target vision tasks by solving pretext-tasks. Although Rotation captures information of object shapes, it hardly captures information of textures. To tackle this problem, we intr…

The paper applies Clairaut's theorem to rotational surfaces in pseudo-Euclidean 4-space.

Convolutional networks are successful due to their equivariance/invariance under translations. However, rotatable data such as images, volumes, shapes, or point clouds require processing with equivariance/invariance under rotations in cases where the rotational orientation of the coordinate system does not affect the m…

We consider $n$-dimensional discrete motions such that any two neighbouring positions correspond in a pure rotation ("rotating motions"). In the Study quadric model of Euclidean displacements these motions correspond to quadrilateral nets with edges contained in the Study quadric ("rotation nets"). The main focus of ou…

The study examines lower and upper bounds of Wasserstein distances for affine transformations of random vectors.

Minimal sets of moves for rotational Reidemeister diagrams are identified.

A new method for analyzing shapes using FDA techniques.

New method studies moving points on curves using rotating frames.

Study on rotational hypersurfaces with constant Gauss-Kronecker curvature.

In-plane drill rotations are impossible for smooth shells.

Positive factorization found for a specific map on surfaces.

Study of rotation angles in a rotating disc model.

The study disproves rotating ancient flows in 4D space.