Related papers: Three representations of the Ising model
The well-known Ising model used in statistical physics was adapted to a social dynamics context to simulate the adoption of a technological innovation. The model explicitly combines (a) an individual's perception of the advantages of an…
Forsstr\"om et al. [8] recently introduced a large class of $\{0,1\}$-valued processes that they named Poisson representable. In addition to deriving several interesting properties for these processes, their main focus was determining which…
Inspired by empirical work in neuroscience for Bayesian approaches to brain function, we give a unified probabilistic account of various types of symbolic reasoning from data. We characterise them in terms of formal logic using the…
We provide a concise exposition with original proofs of combinatorial formulas for the 2D Ising model partition function, multi-point fermionic observables, spin and energy density correlations, for general graphs and interaction constants,…
As machine learning and algorithmic decision making systems are increasingly being leveraged in high-stakes human-in-the-loop settings, there is a pressing need to understand the rationale of their predictions. Researchers have responded to…
The results here presented are a continuation of the algebraic research line which attempts to find properties of multiple-valued systems based on a poset of two agents. The aim of this paper is to exhibit two relationships between some…
The Ising model was generalized to a system of cells interacting exclusively by presence of shared spins. Within the cells there are interactions of any complexity, the simplest intracell interactions come down to the Ising model. The…
Mechanistic interpretability (MI) is an emerging framework for interpreting neural networks. Given a task and model, MI aims to discover a succinct algorithmic process, an interpretation, that explains the model's decision process on that…
Many questions of fundamental interest in todays science can be formulated as inference problems: Some partial, or noisy, observations are performed over a set of variables and the goal is to recover, or infer, the values of the variables…
This document presents the material of two lectures on statistical physics and neural representations, delivered by one of us (R.M.) at the Fundamental Problems in Statistical Physics XIV summer school in July 2017. In a first part, we…
We develop the information-theoretical concepts required to study the statistical dependencies among three variables. Some of such dependencies are pure triple interactions, in the sense that they cannot be explained in terms of a…
Note: Accepted version, published in Statistical Papers, https://doi.org/10.1007/s00362-023-01414-3. It is shown that some theoretically identifiable parameters cannot be empirically identified, meaning that no consistent estimator of them…
Machine learning models have had discernible achievements in a myriad of applications. However, most of these models are black-boxes, and it is obscure how the decisions are made by them. This makes the models unreliable and untrustworthy.…
Causal discovery from observational data is a challenging task that can only be solved up to a set of equivalent solutions, called an equivalence class. Such classes, which are often large in size, encode uncertainties about the orientation…
The use of models, even if efficient, must be accompanied by an understanding at all levels of the process that transforms data (upstream and downstream). Thus, needs increase to define the relationships between individual data and the…
Inferring causal models from observed correlations is a challenging task, crucial to many areas of science. In order to alleviate the computational effort when sifting through possible causal explanations for some given observations, it is…
In this study the magnetization phenomenon has been investigated as a behavior of interacting elementary moments ensemble, with the help of Ising model [1] in the frame of non-extensive statistical mechanics. To investigate the physical…
A multi-level model of opinion formation is presented which takes into account that attitudes on different issues are usually not independent. In the model, agents exchange beliefs regarding a series of facts. A cognitive structure of…
We propose a Statistical-Mechanics inspired framework for modeling economic systems. Each agent composing the economic system is characterized by a few variables of distinct nature (e.g. saving ratio, expectations, etc.). The agents…
High-dimensional representations for words, text, images, knowledge graphs and other structured data are commonly used in different paradigms of machine learning and data mining. These representations have different degrees of…