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Algorithmic decision-making in high-stakes settings can have profound impacts on individuals and populations. While much prior work studies fairness in static settings, recent results show that enforcing static fairness constraints may…
In a previous paper, we have proposed assigning as the value of a physical quantity in quantum theory, a certain kind of set (a sieve) of quantities that are functions of the given quantity. The motivation was in part physical---such a…
A quantitative method is suggested, where meanings of words, and grammatic rules about these, of a vocabulary are represented by real numbers. People meet randomly, and average their vocabularies if they are equal; otherwise they either…
In contrast to conventional, dynamical entanglement, in which particles with definite identity have uncertain properties, in so-called statistical entanglement, which arises between indistinguishable particles because of quantum symmetry…
Normative decision theory proves inadequate for modeling human responses to the social-engineering campaigns of Advanced Persistent Threat (APT) attacks. Behavioral decision theory fares better, but still falls short of capturing…
Traditional studies of memory for meaningful narratives focus on specific stories and their semantic structures but do not address common quantitative features of recall across different narratives. We introduce a statistical ensemble of…
Recent advancements in language models have led to significant improvements in mathematical reasoning across various benchmarks. However, most of these benchmarks rely on automatic evaluation methods that only compare final answers using…
We provide a formal, simple and intuitive theory of rational decision making including sequential decisions that affect the environment. The theory has a geometric flavor, which makes the arguments easy to visualize and understand. Our…
Statistical studies of languages have focused on the rank-frequency distribution of words. Instead, we introduce here a measure of how word ranks change in time and call this distribution \emph{rank diversity}. We calculate this diversity…
The impressive performance of language models is undeniable. However, the presence of biases based on gender, race, socio-economic status, physical appearance, and sexual orientation makes the deployment of language models challenging. This…
Comprehensible explanations of probabilistic reasoning are a prerequisite for wider acceptance of Bayesian methods in expert systems and decision support systems. A study of human reasoning under uncertainty suggests two different…
Agent-based models of the binary naming game are generalized here to represent a family of models parameterized by the introduction of two continuous parameters. These parameters define varying listener-speaker interactions on the…
How intelligence arises from the brain is a central problem in science. A crucial aspect of intelligence is dealing with uncertainty -- developing good predictions about one's environment, and converting these predictions into decisions.…
Do language models make decisions under uncertainty like humans do, and what role does chain-of-thought (CoT) reasoning play in the underlying decision process? We introduce an active probabilistic reasoning task that cleanly separates…
In this work we generalize standard Decision Theory by assuming that two outcomes can also be incomparable. Two motivating scenarios show how incomparability may be helpful to represent those situations where, due to lack of information,…
Mainstream state-of-the-art domain generalization algorithms tend to prioritize the assumption on semantic invariance across domains. Meanwhile, the inherent intra-domain style invariance is usually underappreciated and put on the shelf. In…
In this article, we present a fresh perspective on language, combining ideas from various sources, but mixed in a new synthesis. As in the minimalist program, the question is whether we can formulate an elegant formalism, a universal…
A unified theory of language combines a Bayesian cognitive linguistic model of language processing, with the proposal that language evolved by sexual selection for the display of intelligence. The theory accounts for the major facts of…
A statistical decision problem is hidden in the core of option pricing. A simple form for the price C of a European call option is obtained via the minimum Bayes risk, R_B, of a 2-parameter estimation problem, thus justifying calling C…
Human speech perception involves transforming a countinous acoustic signal into discrete linguistically meaningful units, such as phonemes, while simultaneously causing a listener to activate words that are similar to the spoken utterance…