Related papers: Code subspaces for LLM geometries
Ontologies are useful for automatic machine processing of domain knowledge as they represent it in a structured format. Yet, constructing ontologies requires substantial manual effort. To automate part of this process, large language models…
Large language models (LLMs) have demonstrated remarkable capabilities across various NLP tasks and have recently expanded their impact to coding tasks, bridging the gap between natural languages (NL) and programming languages (PL). This…
Using ideas from the gauge theory approach to the geometric Langlands program, we revisit supersymmetric localization with monopole operators in 3d $\mathcal{N} = 4$ supersymmetric gauge theories subject to $\Omega$-deformation. The key…
These lectures review some of the basic properties of $N=2$ superconformal field theories and the corresponding topological field theories. One of my basic aims is to show how the techniques of topological field theory can be used to…
Supersymmetric nonlinear sigma models are obtained from linear sigma models by imposing supersymmetric constraints. If we introduce auxiliary chiral and vector superfields, these constraints can be expressed by D-terms and F-terms depending…
We analyze the soft supersymmetry breaking parameters obtained in grand unified theories after integrating out the heavy GUT-states. The superfield formalism greatly simplifies the calculations and allows us to derive the low-energy…
We review and extend the vertex algebra framework linking gauge theory constructions and a quantum deformation of the Geometric Langlands Program. The relevant vertex algebras are associated to junctions of two boundary conditions in a 4d…
Large Language Models (LLMs) drive current AI breakthroughs despite very little being known about their internal representations. In this work, we propose to shed the light on LLMs inner mechanisms through the lens of geometry. In…
N = 2 supersymmetry in four space-time dimensions is intimately related to hyperkahler and quaternionic Kahler geometries. On one hand, the target spaces for rigid supersymmetric sigma-models are necessarily hyperkahler manifolds. On the…
We construct the differential geometry of smooth manifolds equipped with an algebraic curvature map acting as an area measure. Area metric geometry provides a spacetime structure suitable for the discussion of gauge theories and strings,…
We construct a new class of supersymmetric surface operators in N=4 SYM and find the corresponding dual supergravity solutions. We show that the insertion of the surface operator - which is given by a WZW model supported on the surface -…
We introduce a framework for internal topological symmetries in quantum field theory, including "noninvertible symmetries" and "categorical symmetries". This leads to a calculus of topological defects which takes full advantage of…
Subsystem codes protect quantum information by encoding it in a tensor factor of a subspace of the physical state space. Subsystem codes generalize all major quantum error protection schemes, and therefore are especially versatile. This…
The subject of this thesis are various ways to construct four-dimensional quantum field theories from string theory. In a first part we study the generation of a supersymmetric Yang-Mills theory, coupled to an adjoint chiral superfield,…
Superstring theory, and a recent extension called M theory, are leading candidates for a quantum theory that unifies gravity with the other forces. As such, they are certainly not ordinary quantum field theories. However, recent duality…
A central question in cognitive science is whether conceptual representations converge onto a shared manifold to support generalization, or diverge into orthogonal subspaces to minimize task interference. While prior work has discovered…
Large-scale fault-tolerant quantum computation requires compiling logical circuits into physical operations tailored to a given architecture. Prior work addressing this challenge has mostly focused on the surface code and lattice surgery…
We introduce geometric consideration into the theory of formal languages. We aim to shed light on our understanding of global patterns that occur on infinite strings. We utilise methods of geometric group theory. Our emphasis is on large…
Supersymmetric models based on the scenario of gague mediation often suffer from the well-known $\mu$ problem. In this paper, we reconsider this problem in low-scale gauge mediation in terms of effective field theory analysis. In this…
Performing multiple computations within the same system, without spatial or temporal separation of tasks, requires encoding multiple data items into a well-defined physical state. The most widely explored mechanism for such encoding is the…