Related papers: Normalisation by Traversals
We introduce a first proofs-as-parallel-programs correspondence for classical logic. We define a parallel and more powerful extension of the simply typed lambda calculus corresponding to an analytic natural deduction based on the excluded…
We develop a technique for normalization for $\infty$-type theories. The normalization property helps us to prove a coherence theorem: the initial model of a given $\infty$-type theory is $0$-truncated. The coherence theorem justifies…
A type assignment system for lambda-calculus enjoys the principal typing property if every typable term M has a special typing, called principal, from which all typings for M can be obtained via suitable operations. The existence of…
Perfect sorting by reversals, a problem originating in computational genomics, is the process of sorting a signed permutation to either the identity or to the reversed identity permutation, by a sequence of reversals that do not break any…
In this paper we introduce a typed, concurrent $\lambda$-calculus with references featuring explicit substitutions for variables and references. Alongside usual safety properties, we recover strong normalization. The proof is based on a…
We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms…
We study the strict type assignment for lambda-mu that is presented in [van Bakel'16]. We define a notion of approximants of lambda-mu-terms, show that it generates a semantics, and that for each typeable term there is an approximant that…
We introduce a way of implementing Wilson renormalization within the context of the theory of effective Hamiltonians. Our renormalization scheme involves manipulations at the level of the generalized $G$--matrix and is independent of any…
Modern meta-learning approaches for image classification rely on increasingly deep networks to achieve state-of-the-art performance, making batch normalization an essential component of meta-learning pipelines. However, the hierarchical…
In this paper we use the framework of algebraic effects from programming language theory to analyze the Beta-Bernoulli process, a standard building block in Bayesian models. Our analysis reveals the importance of abstract data types, and…
Lambda-calculi come with no fixed evaluation strategy. Different strategies may then be considered, and it is important that they satisfy some abstract rewriting property, such as factorization or normalization theorems. In this paper we…
We propose TANDA, an effective technique for fine-tuning pre-trained Transformer models for natural language tasks. Specifically, we first transfer a pre-trained model into a model for a general task by fine-tuning it with a large and…
We describe the extension of normal iteration strategies with appropriate condensation properties to strategies for stacks of normal trees, with full normalization. Given a regular uncountable cardinal $\Omega$ and an…
In this paper we develop a formal system called Natural Term Logic (NTL). NTL aims to represent key aspects of the logical and grammatical mechanisms of natural language as well as grammatical transformations which preserve core logical…
Question Answering (QA) is a task in natural language processing that has seen considerable growth after the advent of transformers. There has been a surge in QA datasets that have been proposed to challenge natural language processing…
Current benchmark tasks for natural language processing contain text that is qualitatively different from the text used in informal day to day digital communication. This discrepancy has led to severe performance degradation of…
On the topic of probabilistic rewriting, there are several works studying both termination and confluence of different systems. While working with a lambda calculus modelling quantum computation, we found a system with probabilistic…
Bayesian meta-learning enables robust and fast adaptation to new tasks with uncertainty assessment. The key idea behind Bayesian meta-learning is empirical Bayes inference of hierarchical model. In this work, we extend this framework to…
In this paper, we define a new realizability semantics for the simply typed lambda-mu-calculus. We show that if a term is typable, then it inhabits the interpretation of its type. We also prove a completeness result of our realizability…
Transformer models have recently achieved impressive performance on NLP tasks, owing to new algorithms for self-supervised pre-training on very large text corpora. In contrast, recent literature suggests that simple average word models…