Surveying matrix group actions on manifolds.
problem Topological Zimmer's conjecture on matrix group actions on manifolds.
method Surveying existing research and literature.
result Status update on matrix group actions on manifolds.
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48 results for “matrix of action”
Low-dimensional representations of matrix groups and group actions on CAT(0) spaces and manifoldsmath.GT
We study low-dimensional representations of matrix groups over general rings, by considering group actions on CAT(0) spaces, spheres and acyclic manifolds.
New model predicts drug effects across various cell types using causal imputation.
problem Predict drug effects across different cell types given limited data.
method Introduces a novel SCM-based model class with latent factor structure and uses Synthetic Interventions estimator.
result Method outperforms other matrix completion approaches in drug repurposing dataset.
Study -manifolds with a 4-torus action using a symmetric matrix ansatz.
problem Characterize -manifolds with a 4-torus action.
method Provide a Gibbons-Hawking type ansatz using a symmetric -matrix of functions.
result First known -manifolds with a rank 4 symmetry group and full holonomy.
New braid group action defined on projective quantum sl(2) modules.
problem Defining a new braid group action on quantum sl(2) modules.
method Action via R-matrix on tensor powers of simple projective modules.
result The action is faithful for the extended representation.
PSI-LinUCB improves scalability for large recommender systems.
problem Efficiently training and inferring for large action spaces in recommender systems.
method Represent inverse design matrix as diagonal + low-rank correction, derive stable rank-1 and batched updates, use projector-splitting integrator.
result Demonstrated effectiveness on recommender system datasets, achieving scalable training and inference.
The study restricts matrix group actions on CAT(0) spaces and uniquely arcwise connected spaces, proving fixed points are inevitable.
problem Proving the inevitability of fixed points in group actions on specific geometric spaces.
method Analyzing actions of matrix groups and automorphism groups of free groups on CAT(0) and uniquely arcwise connected spaces.
result Fixed points are always present in actions of certain groups on specified geometric spaces.
Identifies latent actions and dynamics from offline data with diverse demonstrators.
problem Recovering latent actions and environment dynamics from action-free trajectories.
method Assumes distinct policies for each demonstrator, identifies latent transitions and policies via matrix factorization.
result Identifies latent transitions and demonstrator policies up to permutation.
In this article we give an explicit description of the representation matrix of a Heisenberg type action constructed by Blanchet, Habegger, Masbaum and Vogel. We give the matrix in terms of a ribbon graph and its admissible colorings. We show that components of the representation matrix satisfies the {\it external edge…
Equivalence proven between equivariant K-theory and K-homology for certain matrix group actions.
problem Establishing Poincaré duality for proper cocompact matrix group actions.
method Using equivariant K-theory and K-homology, with geometric models of Baum and Douglas.
result Poincaré duality holds between equivariant K-theory and K-homology for -spin manifolds with compact quotient.
Algorithm finds isotropy subgroups of orthogonal similarity on symmetric matrices.
problem Computing isotropy subgroups of orthogonal similarity on symmetric matrices.
method Algorithmic procedure solving a Toeplitz matrix equation.
result Structure of isotropy subgroups described.
Computes isotropy subgroups of orthogonal matrices acting on Hermitian matrices.
problem Computing isotropy subgroups of orthogonal matrices acting on Hermitian matrices.
method Algorithm for solving a matrix equation to compute isotropy subgroups.
result Computed isotropy subgroups of orthogonal matrices acting on Hermitian matrices.
Paper defines adapted generating sets and bases for Riemann surfaces.
problem Understanding conformal automorphism groups on compact Riemann surfaces.
method Definition and existence proof of adapted generating sets and bases.
result Existence of adapted generating sets and bases for any conformal group.
We show that for k at least 3, given any matrix in GL(k,Z), there is a hyperbolic fully irreducible automorphism of the free group of rank k whose induced action on Z^k is the given matrix.
Innovates rotation index for matrix pairs, solving group action problems.
problem Solving group actions problems, especially Nielsen realization and higher-rank Anosov actions.
method Rotation index and Milnor--Munkres--Novikov pairing applied to group actions.
result Solved specific group action problems using new matrix pair invariant.
A new RL algorithm POWR learns world models to estimate action-values.
problem Inaccessibility of explicit action-value functions in RL.
method Learning a world model using conditional mean embeddings and deriving action-value function via matrix operations.
result POWR algorithm converges to global optimum with proven rates.
UA-LQE improves value function learning by selectively erasing uncertain entries in Q-matrix.
problem Improving value function learning in complex reinforcement learning tasks.
method Uncertainty-aware low-rank Q-matrix estimation (UA-LQE) algorithm.
result UA-LQE selectively erases uncertain entries in Q-matrix to improve value function approximation.
Proposes a new gauge theory for fuzzy geometries using finite-dimensional algebras.
problem Modeling fuzzy geometries in noncommutative geometry.
method Introduces a Yang-Mills-Higgs matrix model based on gauge matrix spectral triples.
result States Yang-Mills-Higgs theory as an explicit random multimatrix model.
Categorifies quantum invariants using cobordism categories and operads.
problem Categorify quantum invariants using cobordism categories and operads.
method Constructs a cobordism category with a colored operad action, categorifies quantum invariants.
result Consistency of the cobordism category and explicit functor to matrix factorizations conjectured.
New framework improves efficiency in low-rank matrix bandit problems.
problem Stochastic contextual low-rank matrix bandit problem with unknown rank matrices.
method G-ESTT and G-ESTS frameworks using Stein's method and regularization.
result Achieved improved regret bounds for low-rank matrix bandit problems.
Designs neural networks on matrix manifolds for improved performance in tasks like human action recognition.
problem Designing neural networks for tasks on non-Euclidean manifolds.
method Develops fully-connected and convolutional layers for SPD manifolds, and MLR on SPSD manifolds.
result Demonstrates improved performance in human action recognition and node classification tasks.
We investigate the analogy between the large N expansion in normal matrix models and the asymptotic expansion of the determinant of the Hilb map, appearing in the study of critical metrics on complex manifolds via projective embeddings. This analogy helps to understand the geometric meaning of the expansion of matrix m…
We show that the Lawrence--Krammer representation is unitary. We explicitly present the non-singular matrix representing the sesquilinear pairing invariant under the action. We show that reversing the orientation of a braid is equivalent to the transposition of its Lawrence--Krammer matrix followed by a certain conjuga…
New algorithms improve on bandit feedback in matrix games with unknown payoff matrices.
problem Improving performance in matrix games with unknown payoff matrices and bandit feedback.
method Regret analyses of variants of UCB and K-learning.
result New algorithms achieve lower regret compared to adversarial bandit algorithms.
New findings reveal discount regularization can be seen as a strong prior, leading to poor performance in unevenly sampled data.
problem Discount regularization leads to poor performance in unevenly sampled data.
method Equivalence theorem showing discount regularization as a strong prior, setting regularization parameters locally for individual state-action pairs.
result Discount regularization can be seen as a strong prior, leading to poor performance in unevenly sampled data.
Paper proposes a new approach to optimal transport for vector and matrix densities.
problem Optimal transport for vector and matrix densities with positivity and action transitivity constraints.
method Gauge-theoretic approach using semi-direct product groups of diffeomorphisms and gauge transformations.
result Bures-type metrics on semi-direct product groups relate to Wasserstein-type metrics on vector and matrix densities via Riemannian submersions.
Study of toric generalized Kähler structures with strong Hamiltonian torus actions.
problem Investigating a subclass of toric generalized Kähler manifolds.
method Introduced a generalized Delzant construction to produce non-abelian examples of strong Hamiltonian actions.
result Found a third canonical complex structure making the manifold toric Kähler.
TRAiL is a linear bandit algorithm that ensures optimal regret and guarantees inference quality.
problem Optimal regret and inference quality in linear bandits with convex action sets.
method TRAiL estimates the parameter through regularized least squares and perturbs the action set along the tangent plane.
result TRAiL achieves an upper bound on cumulative regret with high probability.
Lower bounds on eigenspectrum show rich action spaces force polynomial regret in linear bandits.
problem Understanding the minimum eigenvalue growth in linear bandits with rich action sets.
method Non-asymptotic lower bound on eigenspectrum of design matrix.
result Minimum eigenvalue of expected design matrix grows as for sub-linear regret.
Study -metrics from non-integrable special Lagrangian fibrations.
problem Understanding -metrics from non-integrable special Lagrangian fibrations.
method Decompose -structures into solder 1-forms, connection 1-forms, and equivariant matrix-valued functions.
result Describe regular parts of -manifolds with Lagrangian-type actions.
We show that integration over a -manifold can be reduced to integration over a minimal section with respect to an induced weighted measure and integration over a homogeneous space . We relate our formula to integration formulae for polar actions and calculate some weight functions. In case of a compact …
Generalizes theorem for topological -manifolds with linear Lie groups .
problem Understanding topological -manifolds with linear Lie groups .
method Using countable CW complexes and Palais-proper actions.
result Topological -manifolds have -homotopy type of countable -CW complexes.
Improved Bayesian regret bound for linear Thompson sampling with general distributions.
problem Proving an improved Bayesian regret bound for linear Thompson sampling with general distributions.
method Generalized elliptical potential lemma for non-Gaussian noise and prior distributions.
result Minimax optimal regret bound for changing action sets with general prior and noise distributions.
A CNN-DRL model improves learning in finance with scalable actions.
problem Finance environments with large action scales are hard for MLP-based DRL agents.
method Designed a CNN agent that uses historical data to adapt to large action scales.
result The CNN-DRL model remains stable and learns the environment better than MLP.
Toric geometry of -manifoldsmath.DG
New metrics with holonomy found from torus actions.
problem Finding metrics with holonomy using torus actions.
method Derived a Gibbons-Hawking type ansatz for multi-Hamiltonian -actions, described multi-moment maps.
result Explicit metrics with holonomy derived from torus actions.
Chevalley theorems extended to isotropic functions on matrix spaces.
problem Extending Chevalley theorems to isotropic functions on matrix spaces.
method Proving ultradifferentiable Chevalley restriction theorems for various ultradifferentiable classes.
result Isotropic functions on symmetric matrices have ultradifferentiable regularity if and only if their diagonal restrictions do.
MAGE optimizes policies using action gradients from model-based learning.
problem Lack of direct gradient information from critics in actor-critic methods.
method Model-based actor-critic algorithm that learns action-value gradient.
result MAGE outperforms model-free and model-based baselines on continuous control tasks.
Let SL(n,Z) be the special linear group over integers and , or , products of spheres and tori. We prove that any group action of SL(n,Z) on by diffeomorphims or piecewise linear homeomorphisms is trivial if . This confirms a conjec…
Constructs CAT(0) actions for certain groups without unipotent elements.
problem Understanding actions of certain groups on CAT(0) spaces.
method Constructs an isometric action of a group on a CAT(0) space.
result Fundamental groups of certain 3-manifolds do not admit faithful finite-dimensional unitary representations.
Paper builds neural networks on matrix manifolds using gyrovector spaces.
problem Lack of concepts in gyrovector spaces for matrix manifolds.
method Generalized gyrovector space concepts for SPD and Grassmann manifolds, proposing new neural network models.
result Demonstrated effectiveness in human action recognition and knowledge graph completion.
New method for natural policy gradients converges linearly.
problem Improving natural policy gradient methods for better convergence.
method Fisher-Rao gradient flow applied to state-action distributions.
result Linear convergence rate with geometry-dependent factor.
Expected centre of mass for random embeddings is constant.
problem Understanding the expected centre of mass for random embeddings.
method Analyzing the Haar measure and Gaussian unitary ensemble on SL(N, C).
result The expectation of the centre of mass is a constant multiple of the identity matrix.
Linear recurrent networks explain reinforcement learning performance in partially observable settings.
problem Understanding why linear recurrent networks work in reinforcement learning with partial observability.
method Constructed and studied two linear filters for HMMs and action-controlled HMMs.
result Linear filters serve as sufficient statistics and reduce state ambiguity, explaining empirical reinforcement learning success.
User engagement in social networks depends critically on the number of online actions their users take in the network. Can we design an algorithm that finds when to incentivize users to take actions to maximize the overall activity in a social network? In this paper, we model the number of online actions over time usin…
We reformulate the Poisson structure discovered by Fock and Rosly on moduli spaces of flat connections over marked surfaces in the framework of Poisson structures defined by Lie algebra actions and quasitriangular -matrices, and we show that it is an example of a mixed product Poisson structure associated to pairs o…
We approximate sticky diffusions using Markov chains for efficient simulation.
problem Approximating sticky diffusions for accurate simulation.
method CTMC approximation of sticky diffusions, efficient matrix exponentials, and Euler scheme comparison.
result Second order convergence of CTMC approximation for sticky diffusions.
A new algorithm reduces sample complexity for learning Q-functions in reinforcement learning.
problem Efficiently learning Q-functions in reinforcement learning with continuous state and action spaces.
method Developed a simple, iterative learning algorithm that estimates low-rank Q-functions.
result Achieved exponential improvement in sample complexity for low-rank Q-functions.
Method predicts future rewards from past actions in a linear Gaussian system.
problem Maximizing cumulative reward in a stochastic multi-armed bandit with linear Gaussian dynamics.
method Proposes a method using a modified Kalman filter to predict future rewards based on past rewards.
result Reward from any action can be used to predict another action's future reward.