Related papers: Resource-Bounded Martin-L\"of Type Theory: Composi…

This paper introduces a new family of models of intensional Martin-L\"of type theory. We use constructive ordered algebra in toposes. Identity types in the models are given by a notion of Moore path. By considering a particular gros topos,…

Recurrence equations have played a central role in static cost analysis, where they can be viewed as abstractions of programs and used to infer resource usage information without actually running the programs with concrete data. Such…

We define a general class of dependent type theories, encompassing Martin-L\"of's intuitionistic type theories and variants and extensions. The primary aim is pragmatic: to unify and organise their study, allowing results and constructions…

We present a type theory combining both linearity and dependency by stratifying typing rules into a level for logics and a level for programs. The distinction between logics and programs decouples their semantics, allowing the type system…

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…

A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…

Structured reasoning can improve the inference performance of large language models (LLMs), but it also introduces computational cost and control constraints. When additional reasoning structure helps, and when it instead reduces efficiency…

Safe reinforcement learning (RL) agents accomplish given tasks while adhering to specific constraints. Employing constraints expressed via easily-understandable human language offers considerable potential for real-world applications due to…

Rankings derived from pairwise comparisons are central to many economic and computational systems. In the context of large language models (LLMs), rankings are typically constructed from human preference data and presented as leaderboards…

This article presents liquid resource types, a technique for automatically verifying the resource consumption of functional programs. Existing resource analysis techniques trade automation for flexibility -- automated techniques are…

Type checking algorithms and theorem provers rely on unification algorithms. In presence of type families or higher-order logic, higher-order (pre)unification (HOU) is required. Many HOU algorithms are expressed in terms of…

We present two Dialectica-like constructions for models of intensional Martin-L\"of type theory based on G\"odel's original Dialectica interpretation and the Diller-Nahm variant, bringing dependent types to categorical proof theory. We set…

We consider a framework for structured prediction based on search in the space of complete structured outputs. Given a structured input, an output is produced by running a time-bounded search procedure guided by a learned cost function, and…

Scaling large language models (LLMs) leads to an emergent capacity to learn in-context from example demonstrations. Despite progress, theoretical understanding of this phenomenon remains limited. We argue that in-context learning relies on…

Large language models (LLMs) have rapidly progressed into general-purpose agents capable of solving a broad spectrum of tasks. However, current models remain inefficient at reasoning: they apply fixed inference-time compute regardless of…

In recent years, foundation models have become very popular due to their exceptional performance, mainly in natural language (NLP) tasks where they were first introduced. These models usually consist of hundreds of millions, or even…

The exponential growth of financial research has rendered traditional systematic literature reviews (SLRs) increasingly impractical, as manual screening and narrative synthesis struggle to keep pace with the scale and complexity of modern…

Structured output from large language models (LLMs) has enhanced efficiency in processing generated information and is increasingly adopted in industrial applications. Prior studies have investigated the impact of structured output on LLMs'…

We present a new model of Guarded Dependent Type Theory (GDTT), a type theory with guarded recursion and multiple clocks in which one can program with, and reason about coinductive types. Productivity of recursively defined coinductive…

Training LLMs to think and reason for longer has become a key ingredient in building state-of-the-art models that can solve complex problems previously out of reach. Recent efforts pursue this in different ways, such as RL fine-tuning to…