Related papers: Tight Typings and Split Bounds

In this paper we investigate the $\lambda$ -calculus, a $\lambda$-calculus enriched with resource control. Explicit control of resources is enabled by the presence of erasure and duplication operators, which correspond to thinning and…

Large Language Models (LLMs) have demonstrated remarkable progress in reasoning across diverse domains. However, effective reasoning in real-world tasks requires adapting the reasoning strategy to the demands of the problem, ranging from…

Motivated by recent results of Kapron and Steinberg (LICS 2018) we introduce new forms of iteration on length in the setting of applied lambda-calculi for higher-type poly-time computability. In particular, in a type-two setting, we…

Lagrangian decomposition (LD) is a relaxation method that provides a dual bound for constrained optimization problems by decomposing them into more manageable sub-problems. This bound can be used in branch-and-bound algorithms to prune the…

We show how systems of session types can enforce interactions to be bounded for all typable processes. The type system we propose is based on Lafont's soft linear logic and is strongly inspired by recent works about session types as…

We show how systems of sessions types can enforce interactions to be bounded for all typable processes. The type system we propose is based on Lafont's soft linear logic and is strongly inspired by recent works about session types as…

Intersection types have been originally developed as an extension of simple types, but they can also be used for refining simple types. In this survey we concentrate on the latter option; more precisely, on the use of intersection types for…

This abstract aims at presenting an ongoing effort to apply a novel typing mechanism stemming from Implicit Computational Complexity (ICC), that tracks dependencies between variables in three different ways, at different stages of…

Temporal difference (TD) methods constitute a class of methods for learning predictions in multi-step prediction problems, parameterized by a recency factor lambda. Currently the most important application of these methods is to temporal…

This paper introduces a new methodology for the complexity analysis of higher-order functional programs, which is based on three components: a powerful type system for size analysis and a sound type inference procedure for it, a ticking…

Large language models (LLMs) have achieved notable success in code generation. However, they still frequently produce uncompilable output because their next-token inference procedure does not model formal aspects of code. Although…

In large-scale classification problems, the data set always be faced with frequent updates when a part of the data is added to or removed from the original data set. In this case, conventional incremental learning, which updates an existing…

Large Language Models (LLMs) have achieved significant advances in reasoning tasks. A key approach is tree-based search with verifiers, which expand candidate reasoning paths and use reward models to guide pruning and selection. Although…

Multimodal deep neural networks enhance deep comprehension by integrating diverse data modalities. Data from different modalities are typically projected into a shared latent space for similarity computation, but this process is resource…

Multi-step reasoning tasks like mathematical problem solving are vulnerable to cascading failures, where a single incorrect step leads to complete solution breakdown. Current LLM routing methods assign entire queries to one model, treating…

We present a type system to guarantee termination of pi-calculus processes that exploits input/output capabilities and subtyping, as originally introduced by Pierce and Sangiorgi, in order to analyse the usage of channels. We show that our…

In multiparameter quantum metrology, the ultimate precision of joint estimation is dictated by the Holevo Cram\'er-Rao bound. In this paper, we discuss and analyze in detail an alternative approach: the stepwise estimation strategy. In this…

Dynamic languages (such as Python and JavaScript) offer flexibility and simplified type handling for programming, but this can also lead to an increase in type-related errors and additional overhead for compile-time type inference. As a…

Large Language Models (LLMs) have demonstrated strong reasoning capabilities in solving complex problems. However, current approaches primarily enhance reasoning through the elaboration of thoughts while neglecting the diversity of…

Despite a growing body of work at the intersection of deep learning and formal languages, there has been relatively little systematic exploration of transformer models for reasoning about typed lambda calculi. This is an interesting area of…