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The evolution of grammatical systems of syntactic and semantic composition is modeled here with a novel application of reinforcement learning theory. To test the functionalist thesis that speakers' expressive purposes shape their language,…

We study monads resulting from the combination of nondeterministic and probabilistic behaviour with the possibility of termination, which is essential in program semantics. Our main contributions are presentation results for the monads,…

We consider the common setting where one observes probability estimates for a large number of events, such as default risks for numerous bonds. Unfortunately, even with unbiased estimates, selecting events corresponding to the most extreme…

The classic paradigms for learning and memory recall focus on strengths of synaptic couplings and how these can be modulated to encode memories. In a previous paper [A. K. Behera, M. Rao, S. Sastry, and S. Vaikuntanathan, Physical Review X…

It is typically understood that the training of modern neural networks is a process of fitting the probability distribution of desired output. However, recent paradoxical observations in a number of language generation tasks let one wonder…

We propose a framework for general Bayesian inference. We argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the…

Many mathematical models of synaptic plasticity have been proposed to explain the diversity of plasticity phenomena observed in biological organisms. These models range from simple interpretations of Hebb's postulate, which suggests that…

The sequential order of utterances is often meaningful in coherent dialogues, and the order changes of utterances could lead to low-quality and incoherent conversations. We consider the order information as a crucial supervised signal for…

Learning a sequence of tasks without access to i.i.d. observations is a widely studied form of continual learning (CL) that remains challenging. In principle, Bayesian learning directly applies to this setting, since recursive and one-off…

We study education as a remedy for misspecified beliefs in a canonical sequential social-learning model. Uneducated agents misinterpret action histories - treating actions as if they were independent signals and, potentially, overstating…

We develop a theory of estimation when in addition to a sample of $n$ observed outcomes the underlying probabilities of the observed outcomes are known, as is typically the case in the context of numerical simulation modeling, e.g. in…

Calibration is a classical notion from the forecasting literature which aims to address the question: how should predicted probabilities be interpreted? In a world where we only get to observe (discrete) outcomes, how should we evaluate a…

In a Bayesian setting, inverse problems and uncertainty quantification (UQ) - the propagation of uncertainty through a computational (forward) model - are strongly connected. In the form of conditional expectation the Bayesian update…

We examine three probabilistic concepts related to the sentence "two variables have no bearing on each other". We explore the relationships between these three concepts and establish their relevance to the process of constructing similarity…

In the hypothesis testing framework, p-value is often computed to determine rejection of the null hypothesis or not. On the other hand, Bayesian approaches typically compute the posterior probability of the null hypothesis to evaluate its…

In recent years there has been a spate of papers describing systems for probabilisitic reasoning which do not use numerical probabilities. In some cases the simple set of values used by these systems make it impossible to predict how a…

The plasticity of the conduction delay between neurons plays a fundamental role in learning. However, the exact underlying mechanisms in the brain for this modulation is still an open problem. Understanding the precise adjustment of…

Bayes' theorem incorporates distinct types of information through the likelihood and prior. Direct observations of state variables enter the likelihood and modify posterior probabilities through consistent updating. Information in terms of…

Our goal is to understand how post-training methods, such as fine-tuning, alignment, and unlearning, modify language model behavior and representations. We are particularly interested in the brittle nature of these modifications that makes…

We analyze selected iterated conditionals in the framework of conditional random quantities. We point out that it is instructive to examine Lewis's triviality result, which shows the conditions a conditional must satisfy for its probability…