Related papers: On Locally Rationalizable Social Choice Functions
The proliferation of social media platforms, recommender systems, and their joint societal impacts have prompted significant interest in opinion formation and evolution within social networks. We study how local edge dynamics can drive…
Mechanistic interpretability is the program of explaining what AI systems are doing in terms of their internal mechanisms. I analyze some aspects of the program, along with setting out some concrete challenges and assessing progress to…
We describe an algorithm to decompose rational functions from which we determine the poset of groups fixing these functions.
We provide sufficient conditions under which a utility function may be recovered from a finite choice experiment. Identification, as is commonly understood in decision theory, is not enough. We provide a general recoverability result that…
Modern logics of dependence and independence are based on team semantics, which means that formulae are evaluated not on a single assignment of values to variables, but on a set of such assignments, called a team. This leads to high…
As large language models (LLMs) like GPT become increasingly prevalent, it is essential that we assess their capabilities beyond language processing. This paper examines the economic rationality of GPT by instructing it to make budgetary…
Automated Machine Learning-based systems' integration into a wide range of tasks has expanded as a result of their performance and speed. Although there are numerous advantages to employing ML-based systems, if they are not interpretable,…
Recently, several claims have been made that certain fundamental problems of distributed computing, including Leader Election and Distributed Consensus, begin to admit feasible and efficient solutions when the model of distributed…
Recent years have witnessed the introduction and development of extremely fast rational function algorithms. Many ideas in this realm arose from polynomial-based linear-algebraic algorithms. However, polynomial approximation is occasionally…
It is well-known that if one assumes quantum theory to hold locally, then processes with indefinite causal order and cyclic causal structures become feasible. Here, we study qualitative limitations on causal structures and correlations…
We study how linear orders can be employed to realise choice functions for which the set of potential choices is restricted, i.e., the possible choice is not possible among the full powerset of all alternatives. In such restricted settings,…
The desirable gambles framework provides a foundational approach to imprecise probability theory but relies heavily on linear utility assumptions. This paper introduces function-coherent gambles, a generalization that accommodates…
Local learning methods are a popular class of machine learning algorithms. The basic idea for the entire cadre is to choose some non-local model family, to train many of them on small sections of neighboring data, and then to `stitch' the…
We say that a control system is locally controllable if the attainable set from any state $x$ contains an open neighborhood of $x$, while it is controllable if the attainable set from any state is the entire state manifold. We show in this…
We formulate some problems and conjectures about semigroups of rational functions under composition. The considered problems arise in different contexts, but most of them are united by a certain relationship to the concept of amenability.
This paper proposes a unique optimization approach for estimating the minimax rational approximation and its application for evaluating matrix functions. Our method enables the extension to generalized rational approximations and has the…
It is well known that options can make planning more efficient, among their many benefits. Thus far, algorithms for autonomously discovering a set of useful options were heuristic. Naturally, a principled way of finding a set of useful…
Over an algebraically closed field of positive characteristic, there exist rational functions with only one critical point. We give an elementary characterization of these functions in terms of their continued fraction expansions. Then we…
The $\beta\gamma$ system is generalized by complex(rational) powers of the fields, which leads to a corresponding extension on the Fock space. Two different approaches to compute the Green functions of the physical operators are proposed.…
We analyze the precise modal commitments of several natural varieties of set-theoretic potentialism, using tools we develop for a general model-theoretic account of potentialism, building on those of Hamkins, Leibman and L\"owe, including…