Related papers: Fixed Point Explainability

We prove a general finite convergence theorem for "upward-guarded" fixpoint expressions over a well-quasi-ordered set. This has immediate applications in regular model checking of well-structured systems, where a main issue is the eventual…

In order to ensure the reliability of the explanations of machine learning models, it is crucial to establish their advantages and limits and in which case each of these methods outperform. However, the current understanding of when and how…

We propose new definitions of (causal) explanation, using structural equations to model counterfactuals. The definition is based on the notion of actual cause, as defined and motivated in a companion paper. Essentially, an explanation is a…

Calibration strengthens the trustworthiness of black-box models by producing better accurate confidence estimates on given examples. However, little is known about if model explanations can help confidence calibration. Intuitively, humans…

Changepoint detection is commonly formulated by minimizing the sum of in-sample losses to quantify the model's overall fit. However, for flexible modeling procedures -- especially those involving high-dimensional parameter spaces or…

A useful sampling-reconstruction model should be stable with respect to different kind of small perturbations, regardless whether they result from jitter, measurement errors, or simply from a small change in the model assumptions. In this…

Explainable question answering systems predict an answer together with an explanation showing why the answer has been selected. The goal is to enable users to assess the correctness of the system and understand its reasoning process.…

As the application of deep neural networks proliferates in numerous areas such as medical imaging, video surveillance, and self driving cars, the need for explaining the decisions of these models has become a hot research topic, both at the…

We use fixed point theory to analyze nonnegative neural networks, which we define as neural networks that map nonnegative vectors to nonnegative vectors. We first show that nonnegative neural networks with nonnegative weights and biases can…

This paper establishes a formal framework, grounded in mathematical logic and order theory, to analyze the inherent limitations of radical transparency. We demonstrate that self-referential disclosure policies inevitably encounter…

The increasing number of regulations and expectations of predictive machine learning models, such as so called right to explanation, has led to a large number of methods promising greater interpretability. High demand has led to a…

In this paper, we show a series of abstract results on fixed point regularity with respect to a parameter. They are based on a Taylor development taking into account a loss of regularity phenomenon, typically occurring for composition…

Logic programming with fixed-point definitions is a useful extension of traditional logic programming. Fixed-point definitions can capture simple model checking problems and closed-world assumptions. Its operational semantics is typically…

While explainability is a desirable characteristic of increasingly complex black-box models, modern explanation methods have been shown to be inconsistent and contradictory. The semantics of explanations is not always fully understood - to…

We introduce the notions of weakly *-concave and weakly naturally quasi-concave correspondence and prove fixed point theorems and continuous selection theorems for these kind of correspondences. As applications in the game theory, by using…

The celebrated Kleene fixed point theorem is crucial in the mathematical modelling of recursive specifications in Denotational Semantics. In this paper we discuss whether the hypothesis of the aforementioned result can be weakened. An…

Integrating free-text explanations to in-context learning of large language models (LLM) is shown to elicit strong reasoning capabilities along with reasonable explanations. In this paper, we consider the problem of leveraging the…

In this paper, we prove several generalizations and applications of a fixed point theorem. This theorem is used to prove the existence and uniqueness of solutions of the linear sparse matrix problem considered.

In this paper, we explore connections between interpretable machine learning and learning theory through the lens of local approximation explanations. First, we tackle the traditional problem of performance generalization and bound the…

Two possible definitions of fixed points in the self-similar analysis of time series are considered. One definition is based on the minimal-difference condition and another, on a simple averaging. From studying stock market time series, one…