Develops a spectral sequence for Lie group actions on manifolds.
problem Understanding cohomology of manifolds with Lie group actions.
method Introduces a spectral sequence relating manifold cohomology to Lie algebra cohomology.
result Establishes a new description of de Rham cohomology for manifolds with Lie group actions.
Study on spectral sequence for abelian Lie group actions, with bounds and applications.
problem Understanding the spectral sequence for abelian Lie group actions.
method Provided upper bounds and examples to show these bounds are sharp.
result Sharp bounds on the degeneration page of spectral sequence.
Hybridizes CEM and gradient descent for efficient model-predictive control.
problem Efficiently planning optimal action sequences in high-dimensional spaces.
method Interleaves Cross-Entropy Method (CEM) and gradient descent steps.
result Faster convergence and avoidance of local optima compared to CEM.
One problem in the application of reinforcement learning to real-world problems is the curse of dimensionality on the action space. Macro actions, a sequence of primitive actions, have been studied to diminish the dimensionality of the action space with regard to the time axis. However, previous studies relied on human…
Study braid group actions on exceptional sequences using branched coverings.
problem Transitivity of braid group action on full exceptional sequences.
method Relate exceptional sequences to branched coverings, apply Birman--Hilden theory.
result Counterexamples to Bondal--Polishchuk conjecture on braid group transitivity.
Existing imitation learning approaches often require that the complete demonstration data, including sequences of actions and states, are available. In this paper, we consider a more realistic and difficult scenario where a reinforcement learning agent only has access to the state sequences of an expert, while the expe…
A method to generate long-range human actions by leveraging graph convolutional networks and self-attention.
problem Generating long-range skeleton-based human actions is challenging due to small frame deviations.
method Proposes a variant of GCNs with self-attention to adaptively sparsify action graphs and capture structure information.
result Extensive experiments show superior performance compared to existing methods on human action datasets.
A new method for disentangling action sequences improves model stability.
problem Challenges in unsupervised disentanglement learning due to incomplete theories and abstract notions.
method Introducing disentangling action sequences and a novel fractional variational autoencoder (FVAE) framework.
result FVAE improves the stability of disentanglement for action sequences.
Deep network predicts action sequences for complex tasks from a scene image.
problem Scalable task and motion planning from initial scene images.
method Deep convolutional recurrent neural network that predicts action sequences.
result Predicts promising action sequences, reducing motion planning problems.
Study of orbifold mapping class groups via arc and curve actions.
problem Understanding the structure of orbifold mapping class groups.
method Defined orbifold mapping class groups and studied their actions on arcs and curves. Established a Birman exact sequence and derived finite presentations.
result Finite presentations of orbifold mapping class groups established.
Improved GFlowNets learn more efficiently with trajectory balance.
problem Inefficient credit assignment in GFlowNets leads to suboptimal learning.
method Proposed trajectory balance as a new learning objective.
result Trajectory balance leads to more efficient and robust GFlowNet learning.
SocialInteractionGAN generates realistic human interactions from low-dimensional data.
problem Generating realistic human interactions from limited data.
method Adversarial architecture with a recurrent encoder-decoder generator and dual-stream discriminator.
result SocialInteractionGAN produces high-quality action sequences of interacting people.
New Smith-Gysin sequence for non-semi-free actions without semi-free condition.
problem Constructing a Smith-Gysin sequence for non-semi-free actions.
method Developed a new Smith-Gysin sequence that includes an exotic term.
result Inclusion of an exotic term that depends on the subset MS1. 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…
Improves text-to-speech speed by interleaving character reading and audio synthesis.
problem Latency in text-to-speech models limits their use in time-sensitive tasks.
method Reinforcement learning to train an agent to choose the order of character reading and audio synthesis.
result The proposed method successfully balances latency and audio quality.
A new homomorphism connects group actions on circles to Euler classes.
problem Understanding group actions on circles and their implications.
method Using crossed homomorphisms and Poincaré translation numbers.
result Relates the Euler class of actions to a specific homomorphism.
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…
The curve graph and related graphs are hyperbolic and have quasi-tree fibers.
problem Understanding the structure of the curve graph and related graphs.
method Analyzing a sequence of graphs with Lipschitz maps and proving hyperbolicity and quasi-tree properties.
result The graphs in the sequence are hyperbolic and have quasi-tree fibers, leading to bounds on asymptotic dimension and acylindrical actions.
A 2-manifold's group structure is deduced from orbit configuration spaces.
problem Understanding the fundamental groups of orbit configuration spaces.
method Relating the four-term exact sequence of orbifold pure braid groups to the fundamental groups of the orbit configuration spaces.
result Fundamental groups of orbit configuration spaces form a four-term exact sequence.
Future autonomous systems need reliable world models and complex action sequences.
problem Current automated systems lack reliable world models and complex action sequences.
method Introduce energy-based and latent variable models combined in a hierarchical joint embedding predictive architecture (H-JEPA).
result Combining energy-based and latent variable models in H-JEPA can lead to reliable world models and complex action sequences.
Researchers establish a connection between knot homology and Lie algebra actions.
problem Understanding the HOMFLY-PT homology of (n,n+1) torus knots. method Constructing an explicit isomorphism and computing tautological class actions.
result The tautological class action extends to Hamiltonian vector fields and differentials in spectral sequences.
New method reduces bias and variance in OPE for large action spaces.
problem High bias and variance in OPE for large, combinatorial action spaces.
method Factored action spaces and decomposed importance sampling.
result Decomposed IS estimators have less variance than non-decomposed versions.
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…
Study finite group actions on exotic aspherical space forms.
problem Classify finite group actions on M#Σ where M is a closed aspherical space form and Σ is an exotic n-sphere. method Combines geometric and topological rigidity results with smoothing theory and spectral sequence computations.
result Classification of free actions of finite groups on M#Σ when M is 7-dimensional. Perception of artificial agents is one the grand challenges of AI research. Deep Learning and data-driven approaches are successful on constrained problems where perception can be learned using supervision, but do not scale to open-worlds. In such case, for autonomous embodied agents with first-person sensors, percepti…
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.
Graph theory connects automorphisms to cohomology.
problem Understanding automorphism actions on graph cohomology.
method Graph-theoretical interpretation of de Rham cohomology.
result Proves graph analogues of differential geometry results.
Improved action recognition in live videos with hybrid FR-DL method.
problem High computational costs and lack of temporal information in conventional action recognition.
method Automated selection of representative frames, feature extraction, background subtraction, HOG, deep neural network, LSTM, Softmax-KNN classifier.
result Significant improvement in accuracy and speed compared to state-of-the-art methods.
The paper examines the topology of quaternionic toric actions on manifolds.
problem Understanding the global topology of manifolds with quaternionic toric actions.
method Established toric, differential, and tetraplectic foundations. Constructed spectral sequences for the orbit projection to describe cohomology and K-theory.
result Explicit descriptions of cohomology and K-theory for manifolds with quaternionic toric actions, extending complex toric topology.
Neural Architecture Search (NAS) enabled the discovery of state-of-the-art architectures in many domains. However, the success of NAS depends on the definition of the search space. Current search spaces are defined as a static sequence of decisions and a set of available actions for each decision. Each possible sequenc…
In this paper we present the construction of explicit quasi-isomorphisms that compute the cyclic homology and periodic cyclic homology of crossed-product algebras associated with (discrete) group actions. In the first part we deal with algebraic crossed-products associated with group actions on unital algebras over any…
Sequence generation models are commonly refined with reinforcement learning over user-defined metrics. However, high gradient variance hinders the practical use of this method. To stabilize this method, we adapt to contextual generation of categorical sequences a policy gradient estimator, which evaluates a set of corr…
Let T be a torus. We present an exact sequence relating the relative equivariant cohomologies of the skeletons of an equivariantly formal T-space. This sequence, which goes back to Atiyah and Bredon, generalizes the so-called Chang-Skjelbred lemma. As coefficients, we allow prime fields and subrings of the rationals, i…
This paper introduces persistent equivariant cohomology and applies it to circle actions.
problem Understanding the cohomology of filtered spaces with group actions.
method Persistent Borel equivariant cohomology, Serre spectral sequence, Gysin homomorphism.
result Explicit description and cohomology computation for circle actions.
We consider intersecting hypersurfaces in curved spacetime with gravity governed by a class of actions which are topological invariants in lower dimensionality. Along with the Chern-Simons boundary terms there is a sequence of intersection terms that should be added in the action functional for a well defined variation…
We introduce a new class of reinforcement learning methods referred to as {\em episodic multi-armed bandits} (eMAB). In eMAB the learner proceeds in {\em episodes}, each composed of several {\em steps}, in which it chooses an action and observes a feedback signal. Moreover, in each step, it can take a special action, c…
Study group actions in metric spaces, proving convergence of lens spaces.
problem Understanding convergence in metric measure spaces with group actions.
method Generalized box and observable distances, applied mass-transport theory.
result Sequence of lens spaces converging to infinite-dimensional complex projective space.
The principal group of a Klein geometry has canonical left action on the homogeneous space of the geometry and this action induces action on the spaces of sections of vector bundles over the homogeneous space. This paper is about construction of differential operators invariant with respect to the induced action of the…
Develops methods for finding counterfactual explanations in sequential decision making.
problem Finding counterfactual explanations for sequential decision making processes.
method Formal characterization of sequential actions and states using Markov decision processes and Gumbel-Max structural causal model. Introduces a polynomial time algorithm based on dynamic programming.
result Algorithm finds optimal counterfactual explanations for sequential decision making.
The paper tackles finding optimal treatment sequences in continuous state spaces.
problem Finding counterfactually optimal action sequences in continuous state spaces.
method Formalizes the problem using finite horizon Markov decision processes and structural causal models. Develops a search method based on the A* algorithm.
result The method can find optimal action sequences in polynomial time under certain conditions.
New framework for reinforcement learning with sporadic state observations.
problem Partial observability in reinforcement learning.
method Action-Triggered Sporadically Traceable Markov Decision Processes (ATST-MDPs).
result Optimistic algorithm achieving regret bound for episodic learning.
Paper proposes a hybrid AI method to optimize pandemic actions.
problem Optimizing government actions to balance public health and economy.
method Combines Deep Q-Learning and Genetic Algorithms for optimal sequences of actions.
result Deep Q-Learning outperforms Genetic Algorithms in optimizing action sequences.
The paper defines connections on Lie groupoid bundles and their properties.
problem Defining connections on Lie groupoid bundles and their properties.
method Introducing a suitable definition for connections on Lie groupoid bundles and proving their existence.
result Existence of connections on Lie groupoid bundles and their properties.
The paper certifies projective rigidity for once-punctured torus bundles using twisted Alexander polynomials.
problem Certifying infinitesimal projective rigidity for hyperbolic once-punctured torus bundles.
method Using twisted Alexander polynomials of representations associated with the holonomy.
result The induced action on the tangent space of the character variety matches the group theoretic action.
Let G be either a finite cyclic group of prime order or S^1. We find new relations between cohomology of a manifold (or a Poincare duality space) M with a G-action on it and cohomology of the fixed point set, M^G. Our main tool is the notion of Poincare duality on the Leray spectral sequence of the map M_G -> BG. We ap…
Current deep learning results on video generation are limited while there are only a few first results on video prediction and no relevant significant results on video completion. This is due to the severe ill-posedness inherent in these three problems. In this paper, we focus on human action videos, and propose a gene…
We prove that if a closed, smooth, simply-connected 4-manifold with a circle action admits an almost non-negatively curved sequence of invariant Riemannian metrics, then it also admits a non-negatively curved Riemannian metric invariant with respect to the same action. The same is shown for torus actions of higher rank…
We construct and analyse models of equivariant cohomology for differentiable stacks with Lie group actions extending classical results for smooth manifolds due to Borel, Cartan and Getzler. We also derive various spectral sequences for the equivariant cohomology of a differentiable stack generalising among others Bott'…