Related papers: Facticity as the amount of self-descriptive inform…
Factuality evaluation of large language model (LLM) outputs requires decomposing text into discrete "atomic" facts. However, existing definitions of atomicity are underspecified, with empirical results showing high disagreement among…
The \emph{index set} of a computable structure $\mathcal{A}$ is the set of indices for computable copies of $\mathcal{A}$. We determine the complexity of the index sets of various mathematically interesting structures, including arbitrary…
The amount of information in satisfiability problem (SAT) is considered. SAT can be polynomial-time solvable when the solving algorithm holds an exponential amount of information. It is also established that SAT Kolmogorov complexity is…
Fact verification based on structured data is challenging as it requires models to understand both natural language and symbolic operations performed over tables. Although pre-trained language models have demonstrated a strong capability in…
The problem of verifying whether a textual hypothesis holds based on the given evidence, also known as fact verification, plays an important role in the study of natural language understanding and semantic representation. However, existing…
Can we learn more from data than existed in the generating process itself? Can new and useful information be constructed from merely applying deterministic transformations to existing data? Can the learnable content in data be evaluated…
The difficulty of explaining non-local correlations in a fixed causal structure sheds new light on the old debate on whether space and time are to be seen as fundamental. Refraining from assuming space-time as given a priori has a number of…
We develop a novel formal theory of finite structures, based on a view of finite structures as a fundamental artifact of computing and programming, forming a common platform for computing both within particular finite structures, and in the…
Compositionality is a widely discussed property of natural languages, although its exact definition has been elusive. We focus on the proposal that compositionality can be assessed by measuring meaning-form correlation. We analyze…
I discuss several aspects of information theory and its relationship to physics and neuroscience. The unifying thread of this somewhat chaotic essay is the concept of Kolmogorov or algorithmic complexity (Kolmogorov Complexity, for short).…
The task of finding a criterion allowing to distinguish a text from an arbitrary set of words is rather relevant in itself, for instance, in the aspect of development of means for internet-content indexing or separating signals and noise in…
Originally conceived as a theory of consciousness, integrated information theory (IIT) provides a theoretical framework intended to characterize the compositional causal information that a system, in its current state, specifies about…
Let $X$ be a smooth projective variety of dimension $n\geq 2$. It is shown that a finite configuration of points on $X$ subject to certain geometric conditions possesses rich inner structure. On the mathematical level this inner structure…
We prove that the satisfaction relation $\mathcal{N}\models\varphi[\vec a]$ of first-order logic is not absolute between models of set theory having the structure $\mathcal{N}$ and the formulas $\varphi$ all in common. Two models of set…
We characterize the communication complexity of truthful mechanisms. Our departure point is the well known taxation principle. The taxation principle asserts that every truthful mechanism can be interpreted as follows: every player is…
This is a chapter in the Encyclopedia of Robotics. It is devoted to the study of complexity of complete (or exact) algorithms for robot motion planning. The term ``complete'' indicates that an approach is guaranteed to find the correct…
The existence of string functions, which are not polynomial time computable, but whose graph is checkable in polynomial time, is a basic assumption in cryptography. We prove that in the framework of algebraic complexity, there are no such…
We present some new results which relate information to chaotic dynamics. In our approach the quantity of information is measured by the Algorithmic Information Content (Kolmogorov complexity) or by a sort of computable version of it…
We introduce The FACTS Leaderboard, an online leaderboard suite and associated set of benchmarks that comprehensively evaluates the ability of language models to generate factually accurate text across diverse scenarios. The suite provides…
String diagrams are an increasingly popular algebraic language for the analysis of graphical models of computations across different research fields. Whereas string diagrams have been thoroughly studied as semantic structures, much less…