Related papers: Behavioral Metrics via Functor Lifting
The Wasserstein distance between two probability measures on a metric space is a measure of closeness with applications in statistics, probability, and machine learning. In this work, we consider the fundamental question of how quickly the…
The collective motion of self-driven agents is a phenomenon of great interest in interacting particle systems. In this paper, we develop and analyze a model of agent motion in one dimension with periodic boundaries using a stochastic…
Hilbert space combines the properties of two fundamentally different types of mathematical spaces: vector space and metric space. While the vector-space aspects of Hilbert space, such as formation of linear combinations of state vectors,…
We study reinforcement learning with function approximation for large-scale Partially Observable Markov Decision Processes (POMDPs) where the state space and observation space are large or even continuous. Particularly, we consider Hilbert…
Multidimensional fitting (MDF) method is a multivariate data analysis method recently developed and based on the fitting of distances. Two matrices are available: one contains the coordinates of the points and the second contains the…
Despite their success in numerous fields, the potential of foundation models for modeling and understanding human behavior remains largely unexplored. We introduce Be.FM, one of the first open foundation models designed for human behavior…
In this paper, we establish sharp upper and lower bounds on the convergence rate of the empirical measures of point processes under the Wasserstein distance. To this end, we first introduce a new metric on the space of counting measures…
Steering vectors are a lightweight method for controlling language model behavior by adding a learned bias to the activations at inference time. Although effective on average, steering effect sizes vary across samples and are unreliable for…
It is shown how it is possible to reconstruct the initial state of a one-dimensional system by measuring sequentially two conjugate variables. The procedure relies on the quasi-characteristic function, the Fourier-transform of the Wigner…
We introduce a Cucker-Smale-type model for flocking, where the strength of interaction between two agents depends on their relative separation (called "topological distance" in previous works), which is the number of intermediate…
We define a metric in the space of quantum states taking the Monge distance between corresponding Husimi distributions (Q--functions). This quantity fulfills the axioms of a metric and satisfies the following semiclassical property: the…
This paper presents a state representation framework for Markov decision processes (MDPs) that can be learned solely from state trajectories, requiring neither reward signals nor the actions executed by the agent. We propose learning the…
Learning-based control approaches have shown great promise in performing complex tasks directly from high-dimensional perception data for real robotic systems. Nonetheless, the learned controllers can behave unexpectedly if the trajectories…
Differential logical relations are a method to measure distances between higher-order programs. They differ from standard methods based on program metrics in that differences between functional programs are themselves functions, relating…
Alignment faking (AF) refers to a model strategically complying with a training objective to avoid behavioural modification while preserving its deployment preferences. Understanding when and why AF arises matters as models grow better at…
In genome-wide epigenetic studies, exposures (e.g., Single Nucleotide Polymorphisms) affect outcomes (e.g., gene expression) through intermediate variables such as DNA methylation. Mediation analysis offers a way to study these intermediate…
A growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions. Approximate Bayesian computation (ABC) has become a popular approach to overcome this issue, in which one simulates…
We develop a comprehensive axiomatic framework for quantum-inspired distance metrics on projective Hilbert spaces, providing a unified foundation that organizes and generalizes existing measures in quantum information theory. Starting from…
Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently…
We propose a new class of metrics on sets, vectors, and functions that can be used in various stages of data mining, including exploratory data analysis, learning, and result interpretation. These new distance functions unify and generalize…