Related papers: Cocon: Computation in Contextual Type Theory

We establish a computation-substrate-agnostic inference architecture in which domain is an explicit first-class computational parameter. This produces domain-scoped pruning that reduces per-query search space from O(N) to O(N/K),…

Chain-of-thought responses from language models improve performance across most benchmarks. However, it remains unclear to what extent these performance gains can be attributed to human-like task decomposition or simply the greater…

Recent advances in programming languages study and design have established a standard way of grounding computational systems representation in category theory. These formal results led to a better understanding of issues of control and…

Research on LLM technologies is rapidly emerging, with most of them employ a 'fast thinking' approach to inference. Most LLMs generate the final result based solely on a single query and LLM's reasoning capabilities. However, with the…

Understanding architectural differences in language models is challenging, especially at academic-scale pretraining (e.g., 1.3B parameters, 100B tokens), where results are often dominated by noise and randomness. To overcome this, we…

Dependent Object Types (DOT) is intended to be a core calculus for modelling Scala. Its distinguishing feature is abstract type members, fields in objects that hold types rather than values. Proving soundness of DOT has been surprisingly…

We propose a new type-theoretic approach to SLD-resolution and Horn-clause logic programming. It views Horn formulas as types, and derivations for a given query as a construction of the inhabitant (a proof-term) for the type given by the…

Chain-of-Thought (CoT) reasoning enhances the problem-solving ability of large language models (LLMs) but leads to substantial inference overhead, limiting deployment in resource-constrained settings. This paper investigates efficient CoT…

Chain-of-Thought (CoT) prompting has shown promise in enhancing the reasoning capabilities of large language models (LLMs) on text-attributed graphs (TAGs). This work reframes CoT-based graph learning through the principle of clustering as…

We argue that locally Cartesian closed categories form a suitable doctrine for defining dependent type theories, including non-extensional ones. Using the theory of sketches, one may define syntactic categories for type theories in a style…

Chain-of-Thought (CoT) prompting helps models think step by step. But naive CoT breaks down in visually grounded social tasks, where models must perceive, understand, and judge all at once; bridging perception with norm-grounded reasoning.…

Generalization to novel compound tasks under distribution shift is important for deploying transformer-based language models (LMs). This work investigates Chain-of-Thought (CoT) reasoning as a means to enhance OOD generalization. Through…

Several approaches exist to data-mining big corpora of formal proofs. Some of these approaches are based on statistical machine learning, and some -- on theory exploration. However, most are developed for either untyped or simply-typed…

We propose to use Church encodings in typed lambda-calculi as the basis for an automata-theoretic counterpart of implicit computational complexity, in the same way that monadic second-order logic provides a counterpart to descriptive…

General mathematical reasoning is computationally undecidable, but humans routinely solve new problems. Moreover, discoveries developed over centuries are taught to subsequent generations quickly. What structure enables this, and how might…

With the remarkable success of Multimodal Large Language Models (MLLMs) in perception tasks, enhancing their complex reasoning capabilities has emerged as a critical research focus. Existing models still suffer from challenges such as…

This paper aims at carrying out termination proofs for simply typed higher-order calculi automatically by using ordering comparisons. To this end, we introduce the computability path ordering (CPO), a recursive relation on terms obtained by…

Intensional computation derives concrete outputs from abstract function definitions; extensional computation defines functions through explicit input-output pairs. In formal semantics: intensional computation interprets expressions as…

Latent Chain-of-Thought (Latent-CoT) aims to enable step-by-step computation without emitting long rationales, yet its mechanisms remain unclear. We study CODI, a continuous-thought teacher-student distillation model, on strictly sequential…

Modern causal language models, followed by rapid developments in discrete diffusion models, can now produce a wide variety of interesting and useful content. However, these families of models are predominantly trained to output tokens with…