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The Constraint Satisfaction Problem (CSP) has been intensively studied in many areas of computer science and mathematics. The approach to the CSP based on tools from universal algebra turned out to be the most successful one to study the…
For Boolean satisfiability problems, the structure of the solution space is characterized by the solution graph, where the vertices are the solutions, and two solutions are connected iff they differ in exactly one variable. In 2006, Gopalan…
For Boolean satisfiability problems, the structure of the solution space is characterized by the solution graph, where the vertices are the solutions, and two solutions are connected iff they differ in exactly one variable. For this…
This thesis investigates two key phenomena in large language models (LLMs): in-context learning (ICL) and model collapse. We study ICL in a linear transformer with tied weights trained on linear regression tasks, and show that minimising…
String theory in 4 dimensions has the unique feature that a topological term, the oriented self-intersection number, can be added to the usual action. It has been suggested that the corresponding theory of random surfaces wold be free from…
Quantum contextuality is the key concept which explains the fact that the result of a measurement is not independent of the context in which it is found. It is observed to be an intrinsic feature, i.e., neither entanglement nor spatial…
Large Language Models (LLMs) frequently prioritize conflicting in-context information over pre-existing parametric memory, a phenomenon often termed sycophancy or compliance. However, the mechanistic realization of this behavior remains…
An independent transversal of a graph $G$ with a vertex partition $\mathcal P$ is an independent set of $G$ intersecting each block of $\mathcal P$ in a single vertex. Wanless and Wood proved that if each block of $\mathcal P$ has size at…
In-Context Learning (ICL) is a technique by which language models make predictions based on examples provided in their input context. Previously, their context window size imposed a limit on the number of examples that can be shown, making…
Many problems in static program analysis can be modeled as the context-free language (CFL) reachability problem on directed labeled graphs. The CFL reachability problem can be generally solved in time $O(n^3)$, where $n$ is the number of…
Large-scale neural language models exhibit a remarkable capacity for in-context learning (ICL): they can infer novel functions from datasets provided as input. Most of our current understanding of when and how ICL arises comes from LMs…
A conflict-free coloring of a graph $G$ is a (partial) coloring of its vertices such that every vertex $u$ has a neighbor whose assigned color is unique in the neighborhood of $u$. There are two variants of this coloring, one defined using…
In this paper, we consider contention resolution on a multiple-access communication channel. In this problem, a set of nodes arrive over time, each with a message it intends to send. In each time slot, each node may attempt to broadcast its…
Large language models (LLMs) exhibit remarkable flexibility: they can adapt to novel tasks from in-context examples without any parameter updates, a capability known as in-context learning (ICL). Prior work on synthetic tasks has shown that…
A recent study on structural properties of regular and context-free languages has greatly promoted our basic understandings of the complex behaviors of those languages. We continue the study to examine how regular languages behave when they…
Every system that maintains a large language model conversation beyond a single session faces two inescapable constraints: the context window is finite, and information quality degrades with accumulated volume. We formalize these…
Contextuality is a natural generalization of nonlocality which does not need composite systems or spacelike separation and offers a wider spectrum of interesting phenomena. Most notably, in quantum mechanics there exist scenarios where the…
The conflict-free chromatic index of a graph $G$ is the minimum number of colours in an edge colouring of $G$ such that the neighbourhood of every edge contains a colour appearing exactly once. Its vertex analogue is the conflict-free…
The classical Cantor's intersection theorem states that in a complete metric space $X$, intersection of every decreasing sequence of nonempty closed bounded subsets, with diameter approaches zero, has exactly one point. In this article, we…
The paper is about a class of languages that extends context-free languages (CFL) and is stable under shuffle. Specifically, we investigate the class of partially-commutative context-free languages (PCCFL), where non-terminal symbols are…