相关论文: Extending valuations to formal completions
Large Language Models (LLMs) frequently hallucinate to long-form questions, producing plausible yet factually incorrect answers. A common mitigation strategy is to provide attribution to LLM outputs. However, existing benchmarks primarily…
In this paper, we give a valuation formula for rational top differential forms of function fields in characteristic zero for arbitrary Abhyankar places generalizing the classical valuation at prime divisors. This enables us to define log…
We extend many theorems from the context of solid angle sums over rational polytopes to the context of solid angle sums over real polytopes. Moreover, we consider any real dilation parameter, as opposed to the traditional integer dilation…
Argumentation is based on the exchange and valuation of interacting arguments, followed by the selection of the most acceptable of them (for example, in order to take a decision, to make a choice). Starting from the framework proposed by…
These notes contain an introduction to proofs of Farrell-Jones Conjecture for some groups and are based on talks given in Ohio, Oxford, Berlin, Shanghai, M\"unster and Oberwolfach in 2011 and 2012.
Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…
This volume contains the proceedings of the 3rd International Workshop on Formal Aspects of Virtual Organisations (FAVO 2011). The workshop was held in Sao Paulo, Brazil on October 18th, 2011 as a satellite event to the 12th IFIP Working…
Based on the work of Hahn, Baer, Ostrowski, Krull, Kaplansky and the Artin-Schreier theory, and stimulated by a paper of S. Lang in 1953, the theory of real places and convex valuations has witnessed a remarkable development and has become…
This is a revised version of the preprint which has been available electronically for a while. The paper will now appear in J. Ramanujan Math. Soc.
Author's generalization of one-dimensional class field theory to theory of abelian totally ramified p-extensions of a complete discrete valuation field with arbitrary non-separably p-closed residue field and its applications are described.
Natural language semantics has recently sought to combine the complementary strengths of formal and distributional approaches to meaning. More specifically, proposals have been put forward to augment formal semantic machinery with…
Evaluating the factuality of long-form output generated by large language models (LLMs) remains challenging, particularly when responses are open-ended and contain many fine-grained factual statements. Existing evaluation methods primarily…
One of the aims of this paper is to better explain the philosophy behind the computations in [E.Bifet, C.De Concini,C.Procesi Cohomology of Regular Embeddings ] and to place them in a wider conceptual setting. Another aim of the paper is to…
Understanding how policy is debated and justified in parliament is a fundamental aspect of the democratic process. However, the volume and complexity of such debates mean that outside audiences struggle to engage. Meanwhile, Large Language…
By considering probability distributions over the set of assignments the expected truth values assignment to propositional variables are extended through linear operators, and the expected truth values of the clauses at any given…
This article provides an accessible introduction to fractional derivatives, a concept that extends classical calculus by allowing derivatives of non-integer order. It explores both the fundamental definitions and some of the most relevant…
Recent advancements in Large Language Models (LLMs) have revealed new capabilities and opportunities across the technological landscape. However, the practicality of very large LLMs is challenged by their high compute cost, which does not…
Using valuation rings and valued fields as examples, we discuss in which ways the notions of "topological IFS attractor" and "fractal space" can be generalized to cover more general settings.
The monograph "Invitation to higher local fields" is the result of the conference on higher local fields held in Muenster, August 29 to September 5, 1999. The aim is to provide an introduction to higher local fields (more generally complete…
Fix a set-theoretic universe $V$. We look at small extensions of $V$ as generalised degrees of computability over $V$. We also formalise and investigate the complexity of certain methods one can use to define, in $V$, subclasses of degrees…