Algorithm simulates complex-valued Gaussian processes efficiently.
problem Simulating noncircular or improper complex-valued stationary Gaussian processes.
method Circulant embedding method for multivariate Gaussian processes.
result Exact simulation possible except for negative eigenvalues.
Binary embedding of high-dimensional data requires long codes to preserve the discriminative power of the input space. Traditional binary coding methods often suffer from very high computation and storage costs in such a scenario. To address this problem, we propose Circulant Binary Embedding (CBE) which generates bina…
Study on Riemannian manifolds with circulant structures and their properties.
problem Characterizing Riemannian manifolds with specific symmetries.
method Analysis of the covariant derivatives and properties of the circulant structure.
result Conditions for an almost product manifold to belong to specific classes.
The paper uncovers symmetries in large language models through layer-peeled optimization.
problem Understanding geometric structure in large language model weights and context embeddings.
method Constrained layer-peeled optimization program to analyze symmetries in next-token distributions.
result Symmetries in target next-token distributions are transferred to optimal model weights and context embeddings.
Paper studies deep diagonal circulant neural networks and introduces training techniques.
problem Understanding and training deep neural networks with structured weight matrices.
method Theoretical analysis and practical training techniques including initialization and non-linearity use.
result Deep diagonal circulant networks outperform other structured models in accuracy and weight efficiency.
This paper improves binary embeddings and quantized compressed sensing methods.
problem Distance-preserving binary embeddings and quantization for compressed sensing.
method Quantization of fast Johnson-Lindenstrauss embeddings and bounded orthonormal systems.
result Quantization methods yield reconstruction errors that decay polynomially and exponentially in the number of measurements.
Study of a 3D manifold with a circulant structure whose cube is the identity.
problem Characterizing a specific type of Riemannian manifold.
method Analyzing a tensor structure on a 3D manifold with a circulant property and its properties.
result An important characteristic identity for the fundamental tensor is derived.
Study on 4D manifolds with circulant structures and their products.
problem Characterizing 4D Riemannian manifolds with specific tensor structures.
method Investigation of Riemannian product manifolds with circulant structures and analysis of conditions for metric properties.
result Conditions for Riemannian product manifolds to belong to specific classes.
Study on 3D manifolds with circulant structures and their properties.
problem Characterizing 3D almost Einstein manifolds with circulant structures.
method Analyzing the curvature tensor and properties of the Levi-Civita connection.
result Determined geometric characteristics and examples of such manifolds.
Novel Bayesian framework for spatio-temporal neuroimaging data.
problem Inference on multi-task sparse hierarchical regression models with complex spatio-temporal dynamics.
method Flexible hierarchical Bayesian framework with Kronecker product covariance structure, majorization-minimization optimization, and Riemannian geometry.
result Improved performance on synthetic and real M/EEG data.
Study curvature properties of specific Riemannian manifolds with skew-circulant structures.
problem Investigate curvature of Riemannian manifolds with a particular tensor structure.
method Analyze 4D Riemannian manifolds with right skew-circulant tensor S, invariant under S and g, focusing on Ricci tensor and sectional curvatures.
result Obtained properties of curvature tensors and sectional curvatures for specific manifolds.
We have studied the statistical mechanics of money circulation in a closed economic system. An explicit statistical formulation of the circulation velocity of money is presented for the first time by introducing the concept of holding time of money. The result indicates that the velocity is governed by behavior pattern…
This paper tracks coin circulation in Bitcoin to identify miners and analyze mining pool structures.
problem Identifying and understanding Bitcoin miners and their profit distribution schemes.
method Constructs fresh coin circulation networks and uses a heuristic algorithm to compare networks from different mining pools.
result Infers common profit distribution schemes of Bitcoin mining pools and observes an increasing trend in miner numbers.
Paper offers robust recovery for 1-bit sensing with partial Gaussian circulant matrices.
problem Accurately recovering vectors from 1-bit measurements using structured matrices.
method Correlation-based optimization with randomly signed partial Gaussian circulant matrices and generative models.
result Recovery guarantees match those for i.i.d. Gaussian matrices but with faster computation.
Generalizes Kauffman's clock theorem to surfaces.
problem Proving a lattice structure on graph states in various surfaces.
method Using matchings and graph orientations, extending Propp's results.
result Two generalizations of Kauffman's theorem for more surfaces.
New geometric structures on Lie groups discovered.
problem Understanding geometric properties of Lie groups.
method Investigated 4D Riemannian manifolds with specific endomorphisms.
result Found new Lie groups with circulant structure.
In this paper, we examine the problem of approximating a general linear dimensionality reduction (LDR) operator, represented as a matrix A∈Rm×n with m<n, by a partial circulant matrix with rows related by circular shifts. Partial circulant matrices admit fast implementations via Fourier tra…
We prove that Pareto theory of circulation of elites results from our wealth evolution model, Kelly criterion for optimal betting and Keynes' observation of "animal spirits" that drive the economy and cause that human financial decisions are prone to excess risk-taking.
Investigates neural codes and their embeddings, proving conjectures and introducing new code types.
problem Analyzing neural codes and their embedding dimensions.
method Combinatorial, topological, and algebraic analysis; proving conjectures; introducing new neural code types.
result Proves conjectures about neural codes and their embeddings, introduces new code types.
Adaptive activity monitoring framework for wearable sensors.
problem Efficiently monitor human activities with low power consumption.
method Switching Gaussian process model with block circulant embedding and FFT for inference.
result Optimized trade-off between sensor power consumption and prediction performance.
C-OPH improves One Permutation Hashing by using a shorter circulant permutation.
problem Improving the accuracy of One Permutation Hashing (OPH) for Jaccard similarity estimation.
method Develops a new densification method using a shorter circulant permutation.
result Achieves the smallest estimation variance for Jaccard similarity.
Study finds equations for spheres and circles on a specific manifold.
problem Equations for spheres and circles on a manifold with circulant structures.
method Analyzes a 3D manifold with Riemannian and additional indefinite metrics.
result Equations for spheres and circles defined with respect to the associated metric.
CirCNN compresses deep neural networks using block-circulant matrices.
problem Efficiency and accuracy trade-offs in large-scale deep neural networks.
method CirCNN uses block-circulant matrices for weight representation and processing, reducing computational and storage complexity.
result CirCNN achieves high energy efficiency and performance with negligible accuracy loss.
Study of spheres and circles on a manifold with a specific metric structure.
problem Understanding geometric objects on a manifold with a skew-circulant structure.
method Analyzing hyper-spheres, spheres, and circles in a tangent space of a 4D manifold with a skew-circulant tensor structure.
result Characterization of geometric objects under an indefinite metric.
A new Riemannian manifold with skew-circulant structures and its associated locally conformal Kähler manifold are studied.
problem Exploring new Riemannian manifolds with specific tensor structures.
method Defined a tensor on a 4D Riemannian manifold with skew-circulant properties, constructed a Lie group, and studied associated Hermitian manifolds.
result The associated Hermitian manifold is a locally conformal Kähler manifold.
New model identifies anticyclonic patterns causing drought and heat.
problem Identifying atmospheric drivers of drought and heat.
method Smoothed convolutional neural network classifier for anticyclonic circulations.
result Helps identify important drivers of hot and dry extremes in climate simulations.
In the present paper it is considered a class V of 3-dimensional Riemannian manifolds M with a metric g and two affinor tensors q and S. It is defined another metric \bar{g} in M. The local coordinates of all these tensors are circulant matrices. It is found: 1)\ a relation between curvature tensors R and \bar{R} of g …
We introduce preferential behavior into the study on statistical mechanics of money circulation. The computer simulation results show that the preferential behavior can lead to power laws on distributions over both holding time and amount of money held by agents. However, some constraints are needed in generation mecha…
We consider a 3-dimensional Riemannian manifold V with a metric g and an affinor structure q. The local coordinates of these tensors are circulant matrices. In V we define an almost conformal transformation. Using that definition we construct an infinite series of circulant metrics which are successively almost conform…
We consider a 3-dimensional Riemannian manifold M with two circulant structures -- a metric g and an endomorphism q whose third power is identity. The structure q is compatible with g such that an isometry is induced in any tangent space of M. We obtain some curvature properties of this manifold (M, g, q) and give an e…
We consider a three-dimensional Riemannian manifold equipped with two circulant structures - a metric g and a structure q, which is an isometry with respect to g and the third power of q is minus identity. We discuss some curvature properties of this manifold, we give an example of such a manifold and find a condition …
We consider a 4-dimensional Riemannian manifold M equip\-ped with a circulant structure q, which is an isometry with respect to the metric g and $q^{4}=\id$, $q^{2}\neq \pm \id$. For such a manifold (M,g,q) we obtain some assertions for the sectional curvatures of 2-planes. We construct an example of such…
New algorithms for learning shift-invariant components and aligning signals.
problem Learning shift-invariant components and aligning signals.
method Formulated optimization problems using circulant and convolutional matrices, proposed efficient solutions.
result Effective algorithms for learning shift-invariant components and aligning signals.
We consider decomposition spaces R3/G that are manifold factors and admit defining sequences consisting of cubes-with-handles. Metrics on R3/G constructed via modular embeddings into Euclidean spaces promote the controlled topology to a controlled geometry. The quasisymmetric parametrizability of the metric spa…
Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good kernel has to be chosen. Picking a good kernel is a very challenging problem in its…
We investigate nodal sets of magnetic Schroedinger operators with zero magnetic field, acting on a non simply connected domain in $\r^2$. For the case of circulation 1/2 of the magnetic vector potential around each hole in the region, we obtain a charactisation of the nodal set, and use this to obtain bounds on the mul…
We consider a four dimensional Riemannian manifold M with a metric g and an affinor structure q. We note the local coordinates of g and q are circulant matrices. Their first orders are (A, B, C, B), A, B, C \in FM and (0, 1, 0, 0), respectively. Let \nabla be the connection of g. Further, let mu_{1}, mu_{2},mu_{3}, mu_…
A graph theory approach defines curl and decomposes vector fields.
problem Defining curl for vector fields on graphs and decomposing them.
method Definition of curl as orthogonal complement of circulation-free fields, proving analogues of vector field theorems.
result Helmholtz-Hodge decomposition on graphs: gradient, curl, and harmonic fields.
The dynamics of an ideal fluid or plasma is constrained by topological invariants such as the circulation of (canonical) momentum or, equivalently, the flux of the vorticity or magnetic fields. In the Hamiltonian formalism, topological invariants restrict the orbits to submanifolds of the phase space. While the coadjoi…
Recursive Feature Machines show grokking in modular arithmetic without neural networks.
problem Grokking in modular arithmetic tasks.
method Recursive Feature Machines (RFM) with Average Gradient Outer Product (AGOP).
result RFM and neural networks learn block-circulant features to solve modular arithmetic.
C-MinHash reduces the number of permutations needed for MinHash from thousands to just two.
problem Approximating Jaccard similarity in large binary datasets using many permutations.
method Initial permutation followed by circulant shifting of a second permutation to generate hashes.
result C-MinHash achieves unbiased Jaccard similarity estimation with uniformly smaller variance.
We consider a class (M, g, q) of four-dimensional Riemannian manifolds M, where besides the metric g there is an additional structure q, whose fourth power is the unit matrix. We use the existence of a local coordinate system such that there the coordinates of g and q are circulant matrices. In this system q has consta…
New algorithms for efficient learning with long-term rewards in contextual bandits.
problem Efficient learning with long-term rewards in contextual bandits.
method Proposes new algorithms leveraging sparsity to discover dependence patterns and arm parameters.
result Regret upper bounds for data-poor and data-rich regimes, showing improved sample complexity.
New approach uses deep learning to control SAI for climate mitigation.
problem Catastrophic regional consequences of naive SAI control.
method Treats SAI as a high-dimensional control problem using Deep Reinforcement Learning (DRL).
result First application of DRL to climate sciences.
UGConvs improve CNN accuracy with unitary transforms.
problem Improving CNN accuracy with richer representations.
method UGConvs combine group convolutions with unitary transforms.
result HadaNets achieve similar accuracy to circulant networks with lower complexity.
Sublinear time kernel approximations using structured matrices.
problem Efficiently approximating kernel functions in sublinear time.
method Structured matrices and random embeddings for Gaussian vectors.
result Structured matrices can approximate kernel functions in sublinear time.
Deep learning improves probabilistic river discharge forecasting for hydroelectric power.
problem Uncertain river discharges due to climate variability.
method Modified recurrent neural network architecture conditioned on global circulation model projections.
result Generates parameterized probability distributions for realistic long-term discharge scenarios.
Game-theoretic flow allocation models network dynamics.
problem Maximizing flow through a network with strategic node allocations.
method Game-theoretic analysis of flow allocation strategies in a network.
result Existence and computational complexity of Nash and strong equilibria.