Related papers: Imaging geometry through dynamics: the observable …
A geometric approach to integrability and reduction of dynamical system is developed from a modern perspective. The main ingredients in such analysis are the infinitesimal symmetries and the tensor fields that are invariant under the given…
Learning world models from their sensory inputs enables agents to plan for actions by imagining their future outcomes. World models have previously been shown to improve sample-efficiency in simulated environments with few objects, but have…
This paper is concerned with planning in stochastic domains by means of partially observable Markov decision processes (POMDPs). POMDPs are difficult to solve. This paper identifies a subclass of POMDPs called region observable POMDPs,…
Orthogonally invariant functions of symmetric matrices often inherit properties from their diagonal restrictions: von Neumann's theorem on matrix norms is an early example. We discuss the example of "identifiability", a common property of…
The vast combination of material properties seen in nature are achieved by the complexity of the material microstructure. Advanced characterization and physics based simulation techniques have led to generation of extremely large…
We present a numerical method for learning the dynamics of slow components of unknown multiscale stochastic dynamical systems. While the governing equations of the systems are unknown, bursts of observation data of the slow variables are…
Understanding kinetics and thermodynamics profile of biomolecules is necessary to understand their functional roles which has a major impact in mechanism driven drug discovery. Molecular dynamics simulation has been routinely used to…
We define a class of Markovian parallel dynamics for spin systems on arbitrary graphs with nearest neighbor interaction described by a Hamiltonian function $H(\sigma)$. These dynamics turn out to be reversible and their stationary measure…
Given a visual history, multiple future outcomes for a video scene are equally probable, in other words, the distribution of future outcomes has multiple modes. Multimodality is notoriously hard to handle by standard regressors or…
This work presents a complete geometrical characterisation of divisible and indivisible time-evolution at the level of probabilities for systems with two configurations, open or closed. Our new geometrical construction in the space of…
A fundamental operation in many vision tasks, including motion understanding, stereopsis, visual odometry, or invariant recognition, is establishing correspondences between images or between images and data from other modalities. We present…
In modeling spatial processes, a second-order stationarity assumption is often made. However, for spatial data observed on a vast domain, the covariance function often varies over space, leading to a heterogeneous spatial dependence…
We begin by reviewing a technique to approximate the dynamics of stochastic programs --written in a stochastic process algebra-- by a hybrid system, suitable to capture a mixed discrete/continuous evolution. In a nutshell, the discrete…
A simple geometrical model is presented for the gravity-driven motion of a single particle on a rough inclined surface. Adopting a simple restitution law for the collisions between the particle and the surface, we arrive at a model in which…
In conventional machine learning applications, each data attribute is assumed to be orthogonal to others. Namely, every pair of dimension is orthogonal to each other and thus there is no distinction of in-between relations of dimensions.…
Pretrained Vision Transformers (ViTs) such as DINOv2 and MAE provide generic image features that can be applied to a variety of downstream tasks such as retrieval, classification, and segmentation. However, such representations tend to…
Pedestrian dynamics models have provided valuable insights into pedestrian interactions, collision avoidance, and self-organized crowd behavior using mathematical, computational, AI-based, and heuristic approaches. However, existing models…
Space-Time in general relativity is a dynamical entity because it is subject to the Einstein field equations. The space-time metric provides different geometrical structures: conformal, volume, projective and linear connection. A deep…
This paper presents a heuristic derivation of a geometric minimum action method that can be used to determine most-probable transition paths in noise-driven dynamical systems. Particular attention is focused on systems that violate detailed…
Visual observations of dynamic phenomena, such as human actions, are often represented as sequences of smoothly-varying features . In cases where the feature spaces can be structured as Riemannian manifolds, the corresponding…