arXiv research

Convex cores found for group actions on median spaces.

Reduces proper actions to simpler core actions for analysis.

We prove that every slim double Lie groupoid with proper core action is completely determined by a factorization of a certain canonically defined "diagonal" Lie groupoid.

Efficiently plans large MDPs with weak function approximations.

We provide abelianizations of differentiable actions of finite groups on smooth real manifolds. De Concini-Procesi wonderful models for (local) subspace arrangements and a careful analysis of linear actions on real vector spaces are at the core of our construction. In fact, we show that our abelianizations have stabili…

A core novelty of Alpha Zero is the interleaving of tree search and deep learning, which has proven very successful in board games like Chess, Shogi and Go. These games have a discrete action space. However, many real-world reinforcement learning domains have continuous action spaces, for example in robotic control, na…

Equivariant cohomology simplifies symplectic manifold integrals with group actions.

New statistical convex-cocompactness found for non-orientable surfaces.

Unique entropy measure found for convex projective manifolds.

An action of a compact Lie group is called equivariantly formal, if the Leray--Serre spectral sequence of its Borel fibration degenerates at the E_2-term. This term is as prominent as it is restrictive. In this article, also motivated by the lack of junction between the notion of equivariant formality and the concept o…

We study discrete group actions on coarse Poincare duality spaces, e.g. acyclic simplicial complexes which admit free cocompact group actions by Poincare duality groups. When G is an (n-1) dimensional duality group and X is a coarse Poincare duality space of formal dimension n, then a free simplicial action of G on X d…

A core operation in reinforcement learning (RL) is finding an action that is optimal with respect to a learned value function. This operation is often challenging when the learned value function takes continuous actions as input. We introduce deep radial-basis value functions (RBVFs): value functions learned using a de…

Imitation learning targets deriving a mapping from states to actions, a.k.a. policy, from expert demonstrations. Existing methods for imitation learning typically require any actions in the demonstrations to be fully available, which is hard to ensure in real applications. Though algorithms for learning with unobservab…

Let R be a compact oriented surface of genus g with one boundary component. Homology cylinders over R form a monoid IC into which the Torelli group I of R embeds by the mapping cylinder construction. Two homology cylinders M and M' are said to be Y_k-equivalent if M' is obtained from M by "twisting" an arbitrary surfac…

DRL agents perform poorly at high decision frequencies, but a new algorithm improves performance.

This paper establishes an equivalence between transitive double Lie algebroids and core diagrams.

The affine diffeomorphism group $\mathrm{Aff}(S,q)$ of a half-translation surface $(S,q)$ comprise the self-diffeomorphisms with constant differential away from the singularities. This group coincides with the stabiliser of the associated Teichmüller disc under the action of the mapping class group on Teichmüller space…

New peripheral structure for core groups detects noninvertible knots.

In various application areas, networked data is collected by measuring interactions involving some specific set of core nodes. This results in a network dataset containing the core nodes along with a potentially much larger set of fringe nodes that all have at least one interaction with a core node. In many settings, t…

AL$\ell_0$CORE tensor decomposition reduces computational cost for sparse count data.

Interbank markets are often characterised in terms of a core-periphery network structure, with a highly interconnected core of banks holding the market together, and a periphery of banks connected mostly to the core but not internally. This paradigm has recently been challenged for short time scales, where interbank ma…

We introduce the notion of the visual core of a hyperbolic 3-manifold N and explore its basic properties. The visual core can be thought of as a harmonic analysis analogue of the convex core. We investigate circumstances in which the visual core of a cover N' of N embeds under the covering map from N' to N. We apply th…

New combinatorial structures represent subgroups of surface groups, analogous to Stallings core graphs.

Paper introduces a core-periphery model for identifying informative network structures.

MO2 learns useful behaviours from past experience for new tasks.

A new RL method improves performance on Atari games without complex techniques.

Novel multisymplectic framework for pseudo-Fueter curves in Hamiltonian field theory.

Estimates covariance matrices for matrix-variate data via core covariance geometry.

Smarter applications are making better use of the insights gleaned from data, having an impact on every industry and research discipline. At the core of this revolution lies the tools and the methods that are driving it, from processing the massive piles of data generated each day to learning from and taking useful act…

Probabilistic programming aids in automatically dating ice cores, reducing manual error and uncertainty.

Compactifies maximal component of surface group representations into a closed ball.

Classifies stability of flat-core $p$-elasticae pinned at boundaries.

System learns optimizer hyperparameters to generalize across tasks.

The term "CoRE kernel" stands for correlation-resemblance kernel. In many applications (e.g., vision), the data are often high-dimensional, sparse, and non-binary. We propose two types of (nonlinear) CoRE kernels for non-binary sparse data and demonstrate the effectiveness of the new kernels through a classification ex…

Recent work has noted that all bad local minima can be removed from neural network loss landscapes, by adding a single unit with a particular parameterization. We show that the core technique from these papers can be used to remove all bad local minima from any loss landscape, so long as the global minimum has a loss o…

Efficient RL algorithm for multinomial logistic MDPs with provable guarantees.

We obtain upper and lower bounds on the difference between the renormalized volume and the volume of the convex core of a convex cocompact hyperbolic 3-manifold which depend on the injectivity radius of the boundary of the universal cover of the convex core and the Euler characteristic of the boundary of the convex cor…

New algorithm detects cores in graphs with community structure, improving vertex selection for better clustering.

Kernel method estimates long-term effects from short-term data.

We consider non-elementary representations of two generator free groups in $PSL(2,\mathbb{C})$, not necessarily discrete or free, $G = < A, B >$. A word in $A$ and $B$, $W(A,B)$, is a palindrome if it reads the same forwards and backwards. A word in a free group is {\sl primitive} if it is part of a minimal generating …

Deep learning predicts nuclear equation of state from rotating core collapse GW signals.

New method deforms function algebras on manifolds using spectral decomposition.

The study allows for connected sums in manifolds with positive intermediate Ricci curvature.

This study examines cores within superclusters, highlighting their transitional nature and dynamical state.

Study signatures of torus links and their cores using Neumann's equivariant signatures and Hirzebruch's formula.

Proves NP and co-NP status for knot core recognition in solid torus.

Core groups are link invariants defined by arc or region presentations.

Empty core found in max-loss non-centroid clustering.