New framework predicts diverse, contextually plausible 3D human motions.
problem Predicting multiple plausible future 3D poses given observed poses.
method Developed a new variational framework that conditions latent variable on past observation to encourage relevant information.
result Our approach generates motions of higher quality and preserves contextual information.
Introduces Motion Programs for better video analysis of human motion.
problem Current video analysis focuses on raw pixels or keypoints, missing higher-level motion primitives.
method Introduces Motion Programs as a neuro-symbolic representation of motions as a composition of high-level primitives.
result Motion Programs accurately describe diverse human motions and improve downstream tasks.
Long-term human motion can be represented as a series of motion modes---motion sequences that capture short-term temporal dynamics---with transitions between them. We leverage this structure and present a novel Motion Transformation Variational Auto-Encoders (MT-VAE) for learning motion sequence generation. Our model j…
A new method learns object representations from motion in slot representations.
problem Unsupervised object extraction from low-level visual data.
method Contrastive learning in slot representations, focusing on moving objects and distinct entities.
result Introduced a new evaluation metric to measure diversity of slot vectors.
Human motion prediction is a stochastic process: Given an observed sequence of poses, multiple future motions are plausible. Existing approaches to modeling this stochasticity typically combine a random noise vector with information about the previous poses. This combination, however, is done in a deterministic manner,…
Proposes a new model for predicting future motion of road actors in autonomous vehicles.
problem Forecasting the long-term future motion of road actors for safe autonomous driving.
method Recurrent graph-based attentional approach with interpretable geometric and social relationships.
result Can produce diverse predictions conditioned on hypothetical or 'what-if' scenarios.
RFC enhances humanoid control to imitate complex human motions.
problem Dynamics mismatch between humanoid models and real humans.
method Residual Force Control (RFC) augments control policies with external forces.
result RFC outperforms state-of-the-art methods in convergence speed and motion quality.
Generative Fractional Diffusion Models improve image diversity and quality.
problem Diffusion models struggle with diversity, mode-collapse, and slow convergence.
method Replaces light-tailed BM with fractional Brownian motion (fBM) and its Markov approximation (MA-fBM).
result GFDM achieves greater diversity and quality in image generation.
New method for predicting paths of unpredictable objects with high confidence.
problem Need for dependable uncertainty estimates in motion planning with diverse unpredictable objects.
method Blend online conformal prediction, multiple time series techniques, and heteroscedasticity addressing.
result Simultaneous forecasting bands that cover entire paths with high probability.
Neural networks outperform conventional filters in inertial sensor-based attitude estimation.
problem Limited accuracy in inertial sensor-based attitude estimation due to dynamic and static motion.
method Investigated neural networks versus conventional filters for improving accuracy.
result Neural networks outperform conventional filters only with domain-specific optimizations.
Motion Code models time series dynamics with sparse approximations.
problem Challenges in time series classification and forecasting on noisy data.
method Motion Code views time series as stochastic processes, assigning unique signatures to distinct dynamics.
result Motion Code outperforms benchmarks in noisy datasets, including real-world Parkinson's disease tracking.
The objective of this work is to augment the basic abilities of a robot by learning to use new sensorimotor primitives to enable the solution of complex long-horizon problems. Solving long-horizon problems in complex domains requires flexible generative planning that can combine primitive abilities in novel combination…
Generative model improves safety in self-driving simulators and human motion generation.
problem Improving generative models for constrained domains like safety-critical applications.
method Developed Gen-neG, a denoising diffusion model that uses oracle-assisted guidance.
result Empirically validated Gen-neG for collision avoidance and safety-guarded human motion generation.
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.
New algorithm enhances generative modeling for bounded domains.
problem Ad-hoc thresholding techniques for boundary enforcement in diffusion models.
method Reflected Schrödinger Bridge algorithm for entropy-regularized optimal transport.
result Generative modeling in diverse bounded domains with optimal transport properties.
We study --both in theory and practice-- the use of momentum motions in classic iterative hard thresholding (IHT) methods. By simply modifying plain IHT, we investigate its convergence behavior on convex optimization criteria with non-convex constraints, under standard assumptions. In diverse scenaria, we observe that …
This paper develops a two-dimensional structural framework for valuing credit default swaps and corporate bonds in the presence of default contagion. Modelling the values of related firms as correlated geometric Brownian motions with exponential default barriers, analytical formulae are obtained for both credit default…
This work improves autonomous racing by creating diverse opponents and adapting risk.
problem Balancing performance and safety in autonomous racing environments.
method Developed a self-play method using replica-exchange Markov chain Monte Carlo for diverse opponents and a distributionally robust bandit optimization for adaptive risk adjustment.
result Demonstrated real-time motion-planning methods achieving speeds comparable to Formula One racecars.
Study motion planning for points avoiding obstacles in a plane.
problem Avoiding collisions for multiple points in a plane with unknown obstacles.
method Algebraic and topological tools for motion planning.
result New topological complexity for planar motion planning.
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.
DeepONets enhance spatial-temporal surrogates for structural dynamics.
problem Creating full spatial-temporal surrogates for dynamical systems under uncertainty.
method Proposed Full-Field Extended DeepONet (FExD) to learn full solution operator across multiple degrees of freedom.
result FExD achieves superior accuracy and computational efficiency compared to other models.
Unified framework for human motion generation on Riemannian manifolds.
problem Learning valid human motion in Euclidean spaces.
method Riemannian Motion Generation (RMG) on product manifolds, Riemannian flow matching.
result Achieves state-of-the-art FID (0.043) on HumanML3D and surpasses strong baselines on MotionMillion.
Study on determinants of unitary Brownian motion and their asymptotic laws.
problem Understanding determinants of unitary Brownian motion and their behavior over time.
method Using Stiefel fibration and skew-product decomposition of the Stiefel Brownian motion.
result Prove asymptotic laws for determinants of block entries of unitary Brownian motion.
Data-driven modelling and synthesis of motion is an active research area with applications that include animation, games, and social robotics. This paper introduces a new class of probabilistic, generative, and controllable motion-data models based on normalising flows. Models of this kind can describe highly complex d…
Jointly trains images and videos using residual vectors.
problem Generating high-quality videos from images and vice versa.
method Simultaneously learns latent variables for images and videos using residual vectors.
result Improves sample quality and diversity in video generation and image generation.
Study refracted skew Brownian motion, find densities and asymptotics.
problem Modeling and analyzing refracted skew Brownian motion.
method Perturbation approach to find potential densities, transition density, and asymptotic behaviors.
result Expressions and asymptotic behaviors of refracted skew Brownian motion.
Neural network predicts vessel motions with high accuracy.
problem Real-time prediction of heave and surge motions for improved performance and safety.
method Developed an LSTM-based machine learning model trained on measured waves and motion data.
result The model predicts vessel motions up to 46.5 seconds into the future with an average accuracy of 90%.
Study fractal dimension for motion without crossing a subset.
problem Fractal dimension of a subset X in R^n for motion without crossing.
method Analyzes fractal dimension of subset X in R^n.
result Determines conditions for motion without crossing a subset.
Let E E E be a closed set in the Riemann sphere C ^ \widehat{\mathbb{C}} C . We consider a holomorphic motion φ φ φ of E E E over a complex manifold M M M , that is, a holomorphic family of injections on E E E parametrized by M M M . It is known that if M M M is the unit disk Δ Δ Δ in the complex plane, then any holomorphic motion of E E E ove…
Study cohomological equation for robotic screw motions on SE(3).
problem Understanding obstruction phenomena in robotic rigid-body motion.
method Combining Fourier analysis and Peter-Weyl theory, reduce to finite-dimensional linear transport systems.
result Explicit screw motion illustrates resonance conditions and finite-dimensional obstructions.
New approach for obstacle avoidance in robotics using learned representations.
problem Challenges in sensor-based motion planning for new and dynamic environments.
method Proposes a new obstacle representation using PointNet architecture trained jointly with policies for obstacle avoidance.
result Significant improvements in accuracy and efficiency compared to state of the art.
Paper defines multi-dimensional fractional Brownian motion under volatility uncertainty.
problem Volatility uncertainty in fractional Brownian motion.
method Definition and study of multi-dimensional fractional Brownian motion (G-fBm) with Hurst index.
result First results on stochastic calculus for G-fBm with Hurst index > 0.5.
The paper presents a method to reduce arm motion complexity for prosthetics and robotics.
problem Reducing the complexity of human arm motions for robotic and prosthetic control.
method Data-driven techniques including DTW, DBA, Ward's distance, batch-DTW, and fPCA.
result Representative motion clusters and averages for different arm DOF levels.
Researchers calculate the Laplace transform of a geometric Brownian motion integral.
problem Calculating the Laplace transform of a specific integral functional of geometric Brownian motion.
method Analytical calculation of the Laplace transform of the cumulative distribution and probability density functions.
result The Laplace transform of the integral functional of geometric Brownian motion is derived.
We consider n n n -dimensional discrete motions such that any two neighbouring positions correspond in a pure rotation ("rotating motions"). In the Study quadric model of Euclidean displacements these motions correspond to quadrilateral nets with edges contained in the Study quadric ("rotation nets"). The main focus of ou…
Researchers created a continuous Markov martingale that mimics Brownian motion but lacks the strong Markov property.
problem Constructing a continuous Markov martingale with Brownian marginals that misses the strong Markov property.
method Developed a new approach to create a continuous Markov martingale that differs from Brownian motion in terms of the strong Markov property.
result A continuous Markov martingale with Brownian marginals that lacks the strong Markov property was successfully constructed.
Improved vehicle motion prediction with uncertainty estimation.
problem Robust motion prediction for autonomous vehicles, especially under distributional shift.
method Presented an approach significantly improving the benchmark and taking 2nd place on the leaderboard.
result Significantly improved motion prediction and uncertainty measurement.
The paper explores representations of graph manifolds to Seifert motion groups.
problem Existence of faithful representations of graph manifolds to Seifert motion groups.
method Discussion and proof of non-existence of certain representations.
result Graph manifolds can have virtually no faithful representations to the Seifert motion group.
Geodesic walks converge to Brownian motion on Finsler manifolds.
problem Understanding random walks on Finsler manifolds.
method Analyzing convergence of geodesic random walks to diffusion processes.
result The Brownian motion on a Riemannian metric is a key result.
A framework for computing holonomy groups of hybrid systems to achieve forward motion.
problem Achieving forward motion from periodic leg motion.
method Developing a framework for computing holonomy groups of hybrid systems.
result Computing holonomy groups of hybrid systems to achieve non-zero net motion.
Study homotopy motions of surfaces in 3-manifolds.
problem Understanding the behavior of surfaces under continuous deformations in 3-manifolds.
method Introduce and study homotopy motions of surfaces in closed orientable 3-manifolds.
result Systematic study of homotopy motions of surfaces in 3-manifolds.
The paper proposes a model to forecast traffic motion from sensor data.
problem Accurately predicting traffic motion for safe vehicle maneuvers.
method Implicit latent variable model using interaction graphs and graph neural networks.
result Achieves state-of-the-art motion forecasting and interaction understanding.
New SDEs use G G G -Brownian motion, extending mean-field models.
problem Extending mean-field models to new types of stochastic processes.
method Introduced G G G -SDEs with coefficients dependent on current state and solution as random variable. result Validated new SDE framework for complex stochastic systems.
A new model captures option price dynamics using sub-fractional Brownian motion.
problem Capturing the complex price dynamics of financial options.
method Developed a CEV model driven by a mixed sub-fractional Brownian motion.
result Empirical tests show the model effectively captures option price dynamics.
Study shows not all ML models are uniquely identifiable from data.
problem Identifiability issues in machine learning models.
method Investigated through a case study on gait dynamics using a bipedal-spring mass model.
result Some parameters can be identified, but others remain unidentifiable.
Equations for minimal surfaces from rigid motions in high dimensions.
problem Finding minimal surfaces from rigid motions in R N \mathbb{R}^N R N . method Derives equations for minimal surfaces using rigid motions in R N \mathbb{R}^N R N . result Equations for minimal surfaces in R N \mathbb{R}^N R N . New model uses generalized fractional Brownian motion for stock price prediction.
problem Traditional models fail to accurately predict stock price fluctuations.
method Introduces generalized fractional Brownian motion as a new stochastic process for price modeling.
result Validates the new model for option pricing and risk assessment.
This paper derives the non-analytic solution to the Fokker-Planck equation of fractional Brownian motion using the method of Laplace transform. Sequentially, by considering the fundamental solution of the non-analytic solution, this paper obtains the transition probability density function of the random variable that i…