HOMER learns latent states to explore rich environments efficiently.
problem Exploration in rich observation environments with unknown latent states.
method Interleaves representation learning and strategic exploration to identify kinematic states.
result Provably efficient exploration with polynomial sample complexity in latent states and time horizon.
We define partial differential (PD in the following), i.e., field theoretic analogues of Hamiltonian systems on abstract symplectic manifolds and study their main properties, namely, PD Hamilton equations, PD Noether theorem, PD Poisson bracket, etc.. Unlike in standard multisymplectic approach to Hamiltonian field the…
New kinematic model for a spin-rolling sphere using Darboux frame.
problem Control and planning of an underactuated sphere on a plane.
method Darboux frame transformation to fully-actuated model.
result Underactuated sphere model transformed into fully-actuated model.
In this contribution we review results on the kinematics of a quantum system localized on a connected configuration manifold and compatible dynamics for the quantum system including external fields and leading to non-linear Schrödinger equations for pure states.
Self-driving vehicles (SDVs) hold great potential for improving traffic safety and are poised to positively affect the quality of life of millions of people. To unlock this potential one of the critical aspects of the autonomous technology is understanding and predicting future movement of vehicles surrounding the SDV.…
Model predicts multi-agent trajectories using a differentiable simulator.
problem Predicting future positions of multiple interacting agents.
method Conditional recurrent variational neural networks (CVRNNs) with a kinematic bicycle model.
result Achieves state-of-the-art results on INTERACTION dataset.
A famous theorem of Weyl states that if M is a compact submanifold of euclidean space, then the volumes of small tubes about M are given by a polynomial in the radius r, with coefficients that are expressible as integrals of certain scalar invariants of the curvature tensor of M with respect to the induced metr…
Proves a special case of the Gaussian kinematic formula using large sphere limits.
problem Proving a special case of the Gaussian kinematic formula.
method Viewing the GKF as the limit of spherical kinematic formulas for large dimension spheres.
result Proves a special case of the Gaussian kinematic formula.
In this research, Artificial Neural Networks (ANNs) have been used as a powerful tool to solve the inverse kinematic equations of a parallel robot. For this purpose, we have developed the kinematic equations of a Tricept parallel kinematic mechanism with two rotational and one translational degrees of freedom (DoF). Us…
Proposes KStar Diffuser for kinematics-aware bimanual robotic manipulation.
problem Challenges in applying imitation learning to bimanual robotic tasks.
method Integrates physical robot structure into action prediction using a dynamic spatial-temporal graph and differentiable kinematics.
result Effective generation of kinematics-aware actions in both simulation and real-world environments.
This paper simplifies OPE in large state spaces using state abstractions.
problem Accurately evaluating policies offline in large state spaces.
method Developed a backward-model-irrelevance condition and an iterative state abstraction procedure.
result Deeply-abstracted states substantially simplify OPE sample complexity.
Algorithm finds latent structure in value functions for improved reinforcement learning.
problem Finding latent structure in value functions for efficient reinforcement learning.
method Proposes a practical algorithm using two posterior distributions over state abstractions and abstract-state values.
result Substantial performance gains in multi-task settings where tasks share a common, low-dimensional representation.
This paper explores non-periodic folding of Spidron units, revealing nonlinear dynamics.
problem Understanding the kinematics and nonlinear phenomena of Spidron units.
method Analysis of single unit cell kinematics and recursive construction of multiple cells.
result Non-periodic folding restricts isotropic folding as the number of unit cells increases.
Tabular Q-Learning with learned state abstractions solves continuous control tasks.
problem Challenging reinforcement learning problems in continuous control.
method Learned state abstraction to transform continuous state-space into discrete.
result Tabular Q-Learning with learned abstractions achieves efficient learning in unseen tasks.
Abstract MDPs enable strategic exploration and fast reward transfer in complex environments.
problem Challenging to learn accurate MDPs for high-dimensional states.
method Learn an abstract MDP over low-dimensional coarse states, using an abstraction function.
result Achieves superhuman performance on Pitfall! and higher reward with fewer samples.
A novel controller for wheeled robots handles joystick inputs for smooth steering.
problem Steering control for differential-drive wheeled robots from indirect joystick inputs.
method Developed a geometric controller based on Darboux frame kinematics.
result Smooth trajectories achieved with safety constraints and no desired states.
Deep neural network learns discrete state abstractions for efficient planning.
problem Efficient sequential decision making in large state spaces.
method Information bottleneck method for learning approximate bisimulations using deep neural encoders and action-conditioned HMM.
result Trained method efficiently plans for unseen goals in multi-goal reinforcement learning.
The paper uses complex-valued functions to simplify plane differential geometry and kinematics.
problem Simplifying complex problems in plane differential geometry and kinematics.
method Consistent use of complex-valued functions of a real variable.
result Derives results in a particularly simple, uniform, and transparent way.
New formulas for measuring geometric properties of definable sets.
problem Measuring geometric properties of definable sets in a non-standard setting.
method Proved two kinematic formulas integrating on SO(n)imesSn−1. result Generalized Cauchy-Crofton and infinitesimal linear kinematic formulas.
Paper proposes a smart neck-band for detecting neck postures using integrated kinematic and kinetic data.
problem Improper neck postures lead to musculoskeletal disorders requiring therapy and rehabilitation.
method Integrated use of kinematic and kinetic data with machine learning algorithms.
result 100% accuracy in predicting neck postures using the proposed platform.
The paper proposes a principle for dynamically adjusting the granularity of reinforcement learning abstractions.
problem Lack of general principles for dynamically adjusting the granularity of reinforcement learning abstractions.
method The paper proposes a principle based on rate-distortion theory, formalized through a performance certificate decomposing value error into learning and abstraction error bounds.
result Soft state-action abstractions can achieve near-optimal performance under substantial lossy compression of state and action information.
The thesis explores kinematical symmetries beyond Lorentzian spacetime.
problem Exploring symmetries beyond standard Lorentzian spacetime.
method Algebraic and geometric classification of kinematical, super-kinematical, and super-Bargmann symmetries.
result Classification of kinematical Lie algebras and superalgebras in 3D spacetime.
Proposes method to learn state abstractions that generalize across environments.
problem Learning abstractions that generalize in block MDPs.
method Invariant causal prediction to learn model-irrelevant state abstractions (MISA).
result Proves high probability of outputting a state abstraction corresponding to causal feature set for return.
Given a compact manifold with boundary with unknown Riemannian metric. The problem is to reconstruct the metric in a class of conformal metrics from knowledge of lengths of all closed geodesics (kinematic data). An integral inequality is stated which implies uniqueness and stability for this problem. If the conformal c…
Explains non-lorentzian theories and their dynamics.
problem Understanding non-lorentzian kinematics and dynamics.
method Review of kinematical spacetimes, construction of particle dynamics actions, discussion of gravity theories and field theories.
result Introduction and analysis of non-lorentzian gravity and field theories.
The paper introduces a method to learn Markov state abstractions for reinforcement learning.
problem Learning Markov state representations in complex environments.
method The paper introduces a novel set of conditions and a training procedure combining inverse model estimation and temporal contrastive learning.
result The approach learns representations that capture the underlying structure of the domain and improve sample efficiency.
We introduce different bases for the vector space of Sp(2)Sp(1)-invariant, translation invariant continuous valuations on the quaternionic plane and determine a complete set of kinematic formulas.
Study explores kinematics of surfaces under metric restrictions.
problem Understanding the kinematics of surfaces under metric constraints.
method Analyzed three energy contents: stretching, drilling, and bending.
result Metric restrictions can hinder the elastic response of a shell.
Study the geometry and dynamics of skew evolutes and involutes, related to bicycle kinematics.
problem Understanding the geometry and dynamics of skew evolutes and involutes.
method Investigate the skew evolute and involute maps, comparing them to bicycle kinematics.
result The skew evolute and involute maps have properties analogous to bicycle kinematics.
Researchers prove formulas for flag area measures, extending previous work.
problem Proving additive kinematic formulas for flag area measures.
method Introducing an algebraic framework to compute these formulas explicitly.
result Existence and explicit computation of additive kinematic formulas for flag area measures.
The algebra of transactions as fundamental measurements is constructed on the basis of the analysis of their properties and represents an expansion of the Boolean algebra. The notion of the generalized economic measurements of the economic quantity and quality of objects of transactions is introduced. It has been shown…
A new method shapes reinforcement learning environments by abstracting large state spaces.
problem Learning in large, noisy environments with sparse feedback.
method Environment shaping using state abstraction.
result Agent's policy in shaped environment preserves near-optimal behavior in original environment.
The existence of kinematic formulas for area measures with respect to any connected, closed subgroup of the orthogonal group acting transitively on the unit sphere is established. In particular, the kinematic operator for area measures is shown to have the structure of a co-product. In the case of the unitary group the…
New formalism solves kinematical constraints in curved backgrounds and non-trivial states.
problem Solving kinematical constraints due to Weyl invariance in curved backgrounds and non-trivial states.
method Constructing Weyl covariant geometric objects and identifying them as building blocks of correlation functions.
result Exact agreement with thermal OPEs and holographic computations for thermal 2-point functions.
A kinematics of the motion of a car is reformulated in terms of the theory of gauge potentials (connection on principal bundle). E(2)-connection originates in the no-slipping contact of the car with a road.
We consider the kinematics of specific fluid spacetimes admitting timelike congruences of Ricci Solitons. These fluids includes string cloud, string fluid, perfect fluid, radially symmetric fluid, anisotropic fluid and relativistic magneto-fluid. Results are obtained and important physical aspects are discussed.
We discuss some aspects about the computation of kinematic, spectroscopic, Fermi and astrometric relative velocities that are geometrically defined in general relativity. Mainly, we state that kinematic and spectroscopic relative velocities only depend on the 4-velocities of the observer and the test particle, unlike F…
A method uses RL to learn abstractions for planning, improving robot navigation and manipulation tasks.
problem Planning requires suitable abstractions for states and transitions, which RL struggles with for temporally extended tasks.
method Goal-conditioned policies learned with RL are incorporated into planning, with a latent variable model representing valid states.
result Our method significantly outperforms prior work on image-based robot navigation and manipulation tasks.
We prove that higher moment maps on area measures of a euclidean vector space are injective, while the kernel of the centroid map equals the image of the first variation map. Based on this, we introduce the space of smooth dual area measures on a finite-dimensional euclidean vector space and prove that it admits a natu…
Frustration causes buckling-like behavior in tubular foldable mechanisms.
problem Kinematic coupling and geometric confinement in tubular foldable mechanisms.
method Analytical and numerical solutions of exact kinematics.
result Frustration propagates axially as if by buckling in tubular states.
STAR framework reduces OPE variance by distilling complex problems into discrete ARPs.
problem High variance and bias in off-policy evaluation methods.
method STAR framework that includes various OPE estimators and leverages state abstraction.
result Predictions from ARPs estimated from off-policy data are asymptotically correct.
Paper generates synthetic radar signatures for motion classification.
problem Lack of large training datasets for radar-based human activity recognition.
method Adversarial learning for synthetic data generation, kinematic sifting for consistency.
result 93% overall accuracy achieved on diverse aspect angles.
Generalizes kinematical Lie algebras for isotropic spacetimes.
problem Classifying relativity algebras in isotropic spacetimes.
method Elementary proof and Lie group analysis.
result Symplectic involutive Lie algebras always exist.
Robust visual tracking for long video sequences is a research area that has many important applications. The main challenges include how the target image can be modeled and how this model can be updated. In this paper, we model the target using a covariance descriptor, as this descriptor is robust to problems such as p…
We consider the problem of inverse kinematics (IK), where one wants to find the parameters of a given kinematic skeleton that best explain a set of observed 3D joint locations. The kinematic skeleton has a tree structure, where each node is a joint that has an associated geometric transformation that is propagated to a…
We develop a new approach on the (1+3) threading of spacetime (M,g) with respect to a congruence of curves defined by an arbitrary timelike vector field. The study is based on spatial tensor fields and on the Riemannian spatial connection ∇⋆, which behave as 3D geometric objects. We obtain new formul…
Generative models use latent abstractions to create images.
problem Understanding how generative models create high-dimensional data like images.
method Developed a theoretical framework using SDE and information theory.
result Diffusion models can be seen as a non-linear filter driven by latent abstractions.
We revisit the contact measures introduced by Firey, and further developed by Schneider and Teufel, from the perspective of the theory of valuations on manifolds. This reveals a link between the kinematic formulas for area measures studied by Wannerer and the integral geometry of curved isotropic spaces. As an applicat…