Related papers: Isotonic conditional laws

This work initiates a general study of learning and generalization without the i.i.d. assumption, starting from first principles. While the traditional approach to statistical learning theory typically relies on standard assumptions from…

The algorithmic independence of conditionals, which postulates that the causal mechanism is algorithmically independent of the cause, has recently inspired many highly successful approaches to distinguish cause from effect given only…

In-context learning (ICL) has emerged as a powerful capability for large language models (LLMs) to adapt to downstream tasks by leveraging a few (demonstration) examples. Despite its effectiveness, the mechanism behind ICL remains…

In-Context Learning (ICL) has emerged as an important new paradigm in natural language processing and large language model (LLM) applications. However, the theoretical understanding of the ICL mechanism remains limited. This paper aims to…

Existential rules are an expressive knowledge representation language mainly developed to query data. In the literature, they are often supposed to be in some normal form that simplifies technical developments. For instance, a common…

We determine all composition-closed equational classes of Boolean functions. These classes provide a natural generalization of clones and iterative algebras: they are closed under composition, permutation and identification…

Scoring rules measure the deviation between a probabilistic forecast and reality. Strictly proper scoring rules have the property that for any forecast, the mathematical expectation of the score of a forecast p by the lights of p is…

We discuss conditionalisation for Accept-Desirability models in an abstract decision-making framework, where uncertain rewards live in a general linear space, and events are special projection operators on that linear space. This abstract…

In-context learning (ICL) has shown impressive results in few-shot learning tasks, yet its underlying mechanism is still not fully understood. A recent line of work suggests that ICL performs gradient descent (GD)-based optimization…

We introduce First-Order Coalition Logic ($\mathsf{FOCL}$), which combines key intuitions behind Coalition Logic ($\mathsf{CL}$) and Strategy Logic ($\mathsf{SL}$). Specifically, $\mathsf{FOCL}$ allows for arbitrary quantification over…

Instance-incremental learning (IIL) focuses on learning continually with data of the same classes. Compared to class-incremental learning (CIL), the IIL is seldom explored because IIL suffers less from catastrophic forgetting (CF). However,…

Conditional language models are predominantly trained with maximum likelihood estimation (MLE), giving probability mass to sparsely observed target sequences. While MLE trained models assign high probability to plausible sequences given the…

In-context Learning (ICL) empowers large language models (LLMs) to swiftly adapt to unseen tasks at inference-time by prefixing a few demonstration examples before queries. Despite its versatility, ICL incurs substantial computational and…

In-context learning (ICL) exhibits dual operating modes: task learning, i.e., acquiring a new skill from in-context samples, and task retrieval, i.e., locating and activating a relevant pretrained skill. Recent theoretical work investigates…

Large language models (LLMs) like transformers demonstrate impressive in-context learning (ICL) capabilities, allowing them to make predictions for new tasks based on prompt exemplars without parameter updates. While existing ICL theories…

Recently, Forr\'e (arXiv:2104.11547, 2021) introduced transitional conditional independence, a notion of conditional independence that provides a unified framework for both random and non-stochastic variables. The original paper establishes…

In-context learning (ICL) emerges as a promising capability of large language models (LLMs) by providing them with demonstration examples to perform diverse tasks. However, the underlying mechanism of how LLMs learn from the provided…

Linear structural error-in-variables models with univariate observations are revisited for studying modified least squares estimators of the slope and intercept. New marginal central limit theorems (CLT's) are established for these…

In this paper a conditional logic is defined and studied. This conditional logic, DmBL, is constructed as a deterministic counterpart to the Bayesian conditional. The logic is unrestricted, so that any logical operations are allowed. A…

We study two axioms for social choice functions that capture the impact of similar candidates: independence of clones (IoC) and composition consistency (CC). We clarify the relationship between these axioms by observing that CC is strictly…