New method learns action representations for better reinforcement learning.
problem Lack of structured action representations in reinforcement learning.
method Decomposes policy into action representation and action transformation components.
result Action representations improve generalization in large action spaces.
We identify action representations from video data, proving their statistical benefits.
problem Identifying latent action policies from video data.
method Entropy-regularized LAPO objective, formalizing desiderata for action representations.
result Entropy-regularized LAPO identifies action representations satisfying desiderata under suitable conditions.
This study compares global vs local observation and action representations for DRL in RTS games.
problem Improving Deep Reinforcement Learning performance in RTS games.
method Comparing two observation and action representations in μRTS.
result Local representation outperforms global representation in resource harvesting tasks.
A new method learns action representations for reinforcement learning.
problem Efficient action-value estimation in reinforcement learning.
method Action hypergraph networks framework for learning action representations.
result Hypergraph Q-networks show effectiveness on various domains.
The paper explores proper actions and their relation to representation theory, with new quantitative methods.
problem Understanding proper actions and their connection to representation theory.
method Geometric criteria, sharpness measure, and dynamical volume estimates.
result New quantitative methods have established temperedness criteria for unitary representations.
The paper classifies fiber structures of discontinuity domains for Anosov representations.
problem Understanding the topology of discontinuity domains for Anosov representations.
method Explicitly working out a smooth version of Fintushel's classification theorem for S1-actions on 4-manifolds. result The action on the fiber is equivalent to a circle action on a Hirzebruch surface.
Paper learns meaningful state and action representations from MDP trajectories.
problem Learning good state and action representations from MDP trajectories.
method Tensor decomposition, kernelization, importance sampling, low-Tucker-rank approximation.
result The learned state/action abstractions provide accurate approximations to latent block structures.
Linear disentangled representations improve unsupervised action estimation.
problem Learning linear disentangled representations for unsupervised action estimation.
method Developed a method to induce irreducible representations in VAE models without labeled action sequences.
result Linear disentangled representations are a desirable property for unsupervised action estimation.
Study shows mapping class group action is ergodic on specific representations.
problem Ergodicity of mapping class group action on specific representations.
method Applied symplectic methods developed by Goldman and Xia.
result The action is ergodic.
The paper defines cocycles for positive Anosov representations and constructs affine actions with bounded fundamental domains.
problem Positive Anosov representations into SO(2n,2n−1). method Definition of cocycles and construction of affine actions with fundamental domains.
result Quotient manifolds are homeomorphic to handlebodies.
Intelligent agents can learn to represent the action spaces of other agents simply by observing them act. Such representations help agents quickly learn to predict the effects of their own actions on the environment and to plan complex action sequences. In this work, we address the problem of learning an agent's action…
Deroin and Tholozan's representations are mapped to complex projective space via action-angle coordinates.
problem Mapping representations of a punctured sphere into PSL(2,R) to a simpler geometric space. method Polygonal model and chains of triangles to extract action-angle coordinates.
result Action-angle coordinates give an explicit isomorphism and almost global Darboux coordinates.
The paper generalizes deformation results for Fuchsian representations and shows proper affine actions.
problem Infinitesimal deformations of Fuchsian representations do not act properly in certain directions.
method Using results from Labourie--Wentworth, Potrie--Sambarino, and Smilga, the authors introduce affine versions of cross ratios and triple ratios, Margulis invariants, and relate them to infinitesimal Jordan projections.
result A general criterion for existence of proper affine actions in terms of Margulis invariant spectra.
Study subgroup actions on mapping class groups using Heisenberg representations.
problem Untwisting representations of mapping class groups on Heisenberg subgroups.
method Restrict and analyze twisted representations of mapping class groups to Heisenberg subgroups.
result Untwisting representations on Torelli group for any Heisenberg representation.
Affine actions fail for Hitchin linear parts, except flat pseudo-Riemannian cases.
problem Properly discontinuous affine actions of surface groups with Hitchin linear part.
method Analysis of representations and pseudo-Riemannian metrics.
result Hitchin linear parts in SO(n,n−1) lead to non-properly discontinuous affine actions. Autoencoder learns group representations from actions, improving future prediction accuracy.
problem Learning internal models of interactions with the real world.
method Homomorphism autoencoder with group representation trained on equivariance-derived loss.
result Agents can predict future actions with improved accuracy.
Representation of human actions as a sequence of human body movements or action attributes enables the development of models for human activity recognition and summarization. We present an extension of the low-rank representation (LRR) model, termed the clustering-aware structure-constrained low-rank representation (CS…
Programmatic Motion Concepts learn human actions from paired videos.
problem Learning motion concepts from paired video and action sequences.
method Semi-supervised learning architecture for hierarchical motion representation.
result Outperforms established baselines, especially in small data settings.
We prove in this paper that the action of the mapping class group on the complex of curves has noncommensurable stabilizers. Following a method due to Burger and de la Harpe, this action leads to constructions of irreducible unitary representations of the mapping class group.
Study geometric and representation theory of statistical transformation models.
problem Understand relationships between induced structures and actions on measure spaces.
method Investigate geometric properties and symplectic actions on induced structures.
result Show equivariance of action and relationships between tangent bundles and projectivizations.
This work uses action equivariance to learn structured latent spaces for reinforcement learning.
problem Learning structured latent spaces for reinforcement learning.
method Introduced a contrastive loss function to enforce action equivariance on learned representations.
result Optimal policies in the abstract MDP can be successfully lifted to the original MDP.
We introduce a new integral invariant for isometric actions of compact Lie groups, the copolarity. Roughly speaking, it measures how far from being polar the action is. We generalize some results about polar actions in this context. In particular, we develop some of the structural theory of copolarity k representations…
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.
Classifies actions on Minkowski space up to orbit equivalence.
problem Classifying actions on Minkowski space up to orbit equivalence.
method Classifying actions up to orbit equivalence, providing representations and orbit spaces.
result Orbits and orbit spaces determined for proper actions.
We study low-dimensional representations of matrix groups over general rings, by considering group actions on CAT(0) spaces, spheres and acyclic manifolds.
This paper learns actionable representations for reinforcement learning.
problem Learning comprehensive representations in reinforcement learning.
method Focuses on goal-conditioned policies to learn salient, actionable representations.
result Actionable representations improve exploration and hierarchical reinforcement learning.
The paper defines conditions for proper actions and relates them to Margulis spacetimes.
problem Understanding proper actions on specific geometric spaces.
method Analyzes Anosov representations and their infinitesimal versions.
result Interprets Margulis spacetimes as quotient manifolds of Hn,n−1. Given a knot K in an integral homology sphere with exterior N_K, there is a natural action of the cyclic group Z/n on the space of SL(n,C) representations of the knot group π_1(N_K), and this induces an action on the SL(n,C) character variety. We identify the fixed points of this action in terms of characters of metabe…
New representations of Lie algebras via monoidal category actions.
problem Constructing representations of Lie algebras using monoidal categories.
method Using crossed homomorphisms and monoidal categories to generate representations.
result Established new bifunctor for weak and admissible representations of Lie-Rinehart algebras.
Identifies LA-groups via VB-group structure and complementary actions.
problem Understanding the structure and integrability of LA-groups.
method Identifies LA-groups via VB-group structure and complementary actions up to homotopy.
result Establishes an equivalence between LA-groups and LA-matched pairs.
Conditions for equivariant bundles on 4-manifolds with cyclic actions.
problem Existence of equivariant bundles on 4-manifolds with cyclic actions.
method Conditions derived from the twisted signature formula and congruence relations between fixed point data and isotropy representations.
result Necessary and sufficient conditions for the existence of equivariant bundles.
Consider a lattice Γ in a group G=SL2(R),SO(1,n),SU(1,n), $SL_2(\Q_p)$. We discuss actions of Γ by affine isometric transformations of Hilbert spaces. We show that for irreducible affine isometric action of G its restriction to Γ is irreducible. We prove the existence of canonical irreducible affine iso…
The paper constructs TQFTs and Schrödinger representations for Heisenberg group.
problem Constructing TQFTs and Schrödinger representations for Heisenberg group.
method Using Lagrangian correspondences and q-deformation of U(1).
result Normalization of Schrödinger bimodule action reproduces abelian TQFT.
Study mapping class groups' action on surface homology.
problem Characterize mapping class groups' homology representation.
method Precise characterization of induced homology representation.
result Characterized the image of the homology representation.
The paper studies mapping class group actions on character varieties of surfaces.
problem Understanding the dynamics of mapping class group actions on relative extPSL(2,R)-character varieties. method Definition and proof of simple-stability and primitive-stability of representations.
result Holonomies of hyperbolic cone surfaces are simple-stable and primitive-stable.
We establish several characterizations of Anosov representations of word hyperbolic groups into real reductive Lie groups, in terms of a Cartan projection or Lyapunov projection of the Lie group. Using a properness criterion of Benoist and Kobayashi, we derive applications to proper actions on homogeneous spaces of red…
In this note we observe that the notion of an induced representation has an analog for quasi-actions. We then use induced quasi-actions to refine some earlier rigidity results for product spaces.
We discuss how the global geometry and topology of manifolds depend on different group actions of their fundamental groups, and in particular, how properties of a non-trivial compact 4-dimensional cobordism M whose interior has a complete hyperbolic structure depend on properties of the variety of discrete representa…
Paper introduces SALE for better state-action learning in RL.
problem Challenges in representation learning for low-level states in RL.
method Introduces SALE, a novel approach for learning embeddings of state-action interactions.
result TD7 algorithm significantly outperforms existing continuous control algorithms.
Temporal-difference (TD) networks are a class of predictive state representations that use well-established TD methods to learn models of partially observable dynamical systems. Previous research with TD networks has dealt only with dynamical systems with finite sets of observations and actions. We present an algorithm…
We study actions of finite groups on moduli spaces of stable holomorphic vector bundles and relate the fixed-point sets of those actions to representation varieties of certain orbifold fundamental groups.
Deformation spaces Hom(π,G)/G of representations of the fundamental group π of a surface Σ in a Lie group G admit natural actions of the mapping class group ModΣ, preserving a Poisson structure. When G is compact, the actions are ergodic. In contrast if G is noncompact semisimple, the associated deformat…
Minimal action of mapping class group on character variety.
problem Character variety of Deroin-Tholozan representations.
method Geometric perspective using symplectic structure.
result Infinite mapping class group orbits are dense.
Classifies symmetries of knots using group actions and orthogonal representation theory.
problem Classifying symmetries of knots in 3-sphere.
method Using geometrization and orthogonal representation theory, constructing examples, and distinguishing symmetries.
result Cyclic and dihedral families of symmetries of prime knots and composite knots.
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.
This paper investigates learning sparse representations and action-value functions simultaneously in deep reinforcement learning.
problem Mitigating catastrophic interference and improving cumulative reward in deep reinforcement learning agents.
method Employing regularization techniques to learn sparse representations and action-value functions incrementally.
result Learning sparse representations can improve performance and robustness in deep reinforcement learning agents.
We prove that any rigid representation of π1Σg in Homeo+(S1) with Euler number at least g is necessarily semi-conjugate to a discrete, faithful representation into PSL(2,R). Combined with earlier work of Matsumoto, this precisely characterizes Fuchsian actions by a topological rig…
We define a fuchsian affine action of a surface group to be such that the linear part factors through a representation of SL(2,R). We prove a fuchsian affine action of a surface group is never proper.