相关论文: Course-of-Value Induction in Cedille

A central method for analyzing the asymptotic complexity of a functional program is to extract and then solve a recurrence that expresses evaluation cost in terms of input size. The relevant notion of input size is often specific to a…

Let T be Goedel's system of primitive recursive functionals of finite type in the lambda formulation. We define by constructive means using recursion on nested multisets a multivalued function I from the set of terms of T into the set of…

This paper extends the dual calculus with inductive types and coinductive types. The paper first introduces a non-deterministic dual calculus with inductive and coinductive types. Besides the same duality of the original dual calculus, it…

Using standard domain-theoretic fixed-points, we present an approach for defining recursive functions that are formulated in monadic style. The method works both in the simple option monad and the state-exception monad of Isabelle/HOL's…

Dedukti is a type-checker for the $\lambda$$\Pi$-calculus modulo rewriting, an extension of Edinburgh's logicalframework LF where functions and type symbols can be defined by rewrite rules. It thereforecontains an engine for rewriting LF…

This paper is a concise and painless introduction to the $\lambda$-calculus. This formalism was developed by Alonzo Church as a tool for studying the mathematical properties of effectively computable functions. The formalism became popular…

A new theory of data types which allows for the definition of types as initial algebras of certain functors Fam(C) -> Fam(C) is presented. This theory, which we call positive inductive-recursive definitions, is a generalisation of Dybjer…

We introduce Reverse Derivative Ascent: a categorical analogue of gradient based methods for machine learning. Our algorithm is defined at the level of so-called reverse differential categories. It can be used to learn the parameters of…

We investigate the possibility of a semantic account of the execution time (i.e. the number of \beta_v-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value {\lambda}-calculus. For…

The use of a necessity modality in a typed $\lambda$-calculus can be used to separate it into two regions. These can be thought of as intensional vs. extensional data: data in the first region, the modal one, are available as code, and…

We define an extension of lambda-calculus with dependents types that enables us to encode transparent and opaque probabilistic programs and prove a strong normalisation result for it by a reducibility technique. While transparent…

This thesis develops methods for causal inference and causal representation learning (CRL) in high-dimensional, time-varying data. The first contribution introduces the Causal Dynamic Variational Autoencoder (CDVAE), a model for estimating…

Curriculum learning can improve neural network training by guiding the optimization to desirable optima. We propose a novel curriculum learning approach for image classification that adapts the loss function by changing the label…

We investigate the possibility of a semantic account of the execution time (i.e. the number of beta-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value lambda-calculus. For this…

This document presents the syntax, classification rules, realizability semantics, and soundness theorem for Cedille, an extrinsic (i.e., Curry-style) type theory extending the Calculus of Constructions, and designed for deriving of…

Probabilistic models such as logistic regression, Bayesian classification, neural networks, and models for natural language processing, are increasingly more present in both undergraduate and graduate statistics and data science curricula…

Deploying machine learning models in safety-related do-mains (e.g. autonomous driving, medical diagnosis) demands for approaches that are explainable, robust against adversarial attacks and aware of the model uncertainty. Recent deep…

There is increasing interest within the research community in the design and use of recursive probability models. Although there still remains concern about computational complexity costs and the fact that computing exact solutions can be…

In this study, we address causal inference when only observational data and a valid causal ordering from the causal graph are available. We introduce a set of flow models that can recover component-wise, invertible transformation of…

Machine learning models play a vital role in making predictions and deriving insights from data and are being increasingly used for causal inference. To preserve user privacy, it is important to enable the model to forget some of its…