Related papers: Probabilistic interpretation of mechanical motion
The transition from microscopic to macroscopic in quantum mechanics can be seen from various points of view. It is often not merely a transition from quantum to classical mechanics in the sense of the Correspondence Principle. The fact that…
Analytical and numerical studies on many-body stochastic processes with multiplicative interactions are reviewed. The method of moment relations is used to investigate effects of asymmetry and randomness in interactions. Probability…
Recognizing spatial relations and reasoning about them is essential in multiple applications including navigation, direction giving and human-computer interaction in general. Spatial relations between objects can either be explicit --…
We provide a mathematically rigorous derivation of the first order expansion of the motion of a charged particle in a strong magnetic field. In contrast to the derivations that can be found in the physics literature we solely assume…
Definitions and notations with historical references are given for some numerical coefficients commonly used to quantify relations among collections of objects for the purpose of expressing approximate knowledge and probabilistic reasoning.
Probabilistic frames are a generalization of finite frames into the Wasserstein space of probability measures with finite second moment. We introduce new probabilistic definitions of duality, analysis, and synthesis and investigate their…
Dynamics of systems of structured particles consisting of potentially interacting material points is considered in the framework of classical mechanics. Equations of interaction and motion of structured particles have been derived. The…
The Bayesian approach to machine learning amounts to computing posterior distributions of random variables from a probabilistic model of how the variables are related (that is, a prior distribution) and a set of observations of variables.…
The Bayesian posterior probability of the true state is stochastically dominated by that same posterior under the probability law of the true state. This generalizes to notions of "optimism" about posterior probabilities.
Transition path theory provides a statistical description of the dynamics of a reaction in terms of local spatial quantities. In its original formulation, it is limited to reactions that consist of trajectories flowing from a reactant set A…
We present a probabilistic extension of action language BC+. Just like BC+ is defined as a high-level notation of answer set programs for describing transition systems, the proposed language, which we call pBC+, is defined as a high-level…
Computational mechanics, an approach to structural complexity, defines a process's causal states and gives a procedure for finding them. We show that the causal-state representation--an $\epsilon$-machine--is the minimal one consistent with…
A probabilistic propositional logic, endowed with an epistemic component for asserting (non-)compatibility of diagonizable and bounded observables, is presented and illustrated for reasoning about the random results of projective…
A distribution shift can have fundamental consequences such as signaling a change in the operating environment or significantly reducing the accuracy of downstream models. Thus, understanding distribution shifts is critical for examining…
Transformer-based models generate hidden states that are difficult to interpret. In this work, we analyze hidden states and modify them at inference, with a focus on motion forecasting. We use linear probing to analyze whether interpretable…
Most expressivity results for transformers treat them as language recognizers -- devices that accept or reject strings -- rather than as they are used in practice: as language models that generate strings autoregressively and…
The author's opinion on the interpretation of quantum mechanics is further elucidated. Not only may quantum mechanics be a description of the sub-microscopic world that is profoundly different from what is often asserted, particularly…
Inspired by the need for effective stochastic models to describe the complex behavior of biological motor proteins that move on linear tracks exact results are derived for the velocity and dispersion of simple linear sequential models (or…
By using straightforward frequency arguments we classify transformations of probabilities which can be generated by transition from one preparation procedure (context) to another. There are three classes of transformations corresponding to…
Probabilistic Movement Primitives (ProMPs) are a widely used representation of movements for human-robot interaction. They also facilitate the factorization of temporal and spatial structure of movements. In this work we investigate a…