Related papers: Resource-Bounded Martin-L\"of Type Theory: Composi…
The inference cost of Large Language Models (LLMs) has become a critical factor in determining their commercial viability and widespread adoption. This paper introduces a quantitative ``economics of inference'' framework, treating the LLM…
Recent studies explored integrating state-space search algorithms with Language Models (LM) to perform look-ahead on the token generation process, the ''Tree-of-Thoughts'' (ToT), generated by LMs, thereby improving performance on…
We present new induction principles for the syntax of dependent type theories, which we call relative induction principles. The result of the induction principle relative to a functor F into the syntax is stable over the codomain of F. We…
In this paper, we explore a connection between type universes and memory allocation. Type universe hierarchies are used in dependent type theories to ensure consistency, by forbidding a type from quantifying over all types. Instead, the…
Ontologies of research topics are crucial for structuring scientific knowledge, enabling scientists to navigate vast amounts of research, and forming the backbone of intelligent systems such as search engines and recommendation systems.…
We study the problem of fitting ontologies and constraints to positive and negative examples that take the form of a finite relational structure. As ontology and constraint languages, we consider the description logics $\mathcal{E\mkern-2mu…
We propose the first framework for defining relational program logics for arbitrary monadic effects. The framework is embedded within a relational dependent type theory and is highly expressive. At the semantic level, we provide an…
This paper provides the first systematic economic analysis of token pricing in the large language model (LLM) inference market. Assembling a novel dataset integrating OpenRouter API data (318 models), Epoch AI records (3,237 models), and 62…
As modern artificial intelligence (AI) systems become more advanced and capable, they can leverage a wide range of tools and models to perform complex tasks. The task of orchestrating these models is increasingly performed by Large Language…
We define and develop two-level type theory (2LTT), a version of Martin-L\"of type theory which combines two different type theories. We refer to them as the inner and the outer type theory. In our case of interest, the inner theory is…
The standard oracle model for matroid algorithms assumes that each independence query can be answered in constant time, regardless of the size of the queried set. While this abstraction has underpinned much of the theoretical progress in…
Pretrained large Language Models (LLMs) are able to answer questions that are unlikely to have been encountered during training. However a diversity of potential applications exist in the broad domain of reasoning systems and considerations…
We develop a static complexity analysis for a higher-order functional language with structural list recursion. The complexity of an expression is a pair consisting of a cost and a potential. The former is defined to be the size of the…
We present a novel general resource analysis for logic programs based on sized types. Sized types are representations that incorporate structural (shape) information and allow expressing both lower and upper bounds on the size of a set of…
Large language models (LLMs) are increasingly recognized for their exceptional generative capabilities and versatility across various tasks. However, the high inference costs associated with these models have not received adequate…
Large language models (LLMs) achieve state-of-the-art accuracy on complex reasoning tasks by generating multiple chain-of-thought (CoT) traces, but using a fixed token budget per query leads to over-computation on easy inputs and…
While information from the field of linguistic typology has the potential to improve performance on NLP tasks, reliable typological data is a prerequisite. Existing typological databases, including WALS and Grambank, suffer from…
We present an extensive mechanization of the meta-theory of Martin-L\"of Type Theory (MLTT) in the Coq proof assistant. Our development builds on pre-existing work in Agda to show not only the decidability of conversion, but also the…
Following the types-as-sets paradigm, we present a mechanized embedding of dependent function types with a hierarchy of universes into schematic first-order logic with equality, with axiom schemas of Tarski-Grothendieck set theory. We carry…
Understanding and quantifying causal relationships between variables is essential for reasoning about the physical world. In this work, we develop a resource-theoretic framework to do so. Here, we focus on the simplest nontrivial setting --…