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

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…

Deep learning models have achieved remarkable success in different areas of machine learning over the past decade; however, the size and complexity of these models make them difficult to understand. In an effort to make them more…

Let G be a connected reductive group defined over a finite field F_q and let L be the Levi subgroup (defined over F_q) of a parabolic subgroup P of G. We define a linear map from class functions on L(F_q) to class functions on G(F_q). This…

A theory of recursive and corecursive definitions has been developed in higher-order logic (HOL) and mechanized using Isabelle. Least fixedpoints express inductive data types such as strict lists; greatest fixedpoints express coinductive…

We introduce an operational rewriting-based semantics for strictly positive nested higher-order (co)inductive types. The semantics takes into account the "limits" of infinite reduction sequences. This may be seen as a refinement and…

We develop a dependent type theory that is based purely on inductive and coinductive types, and the corresponding recursion and corecursion principles. This results in a type theory with a small set of rules, while still being fairly…

Rule-induction models have demonstrated great power in the inductive setting of knowledge graph completion. In this setting, the models are tested on a knowledge graph entirely composed of unseen entities. These models learn relation…

Over twenty years ago, Abadi et al. established the Dependency Core Calculus (DCC) as a general purpose framework for analyzing dependency in typed programming languages. Since then, dependency analysis has shown many practical benefits to…

As mathematical induction is applied to prove statements on natural numbers, {\it continuous induction} (or, {\it real induction}) is a tool to prove some statements in real analysis.(Although, this comparison is somehow an overstatement.)…

Human written source code in imperative programming languages exhibits typical patterns for variable use such as flags, loop iterators, counters, indices, bitvectors etc. Although it is widely understood by practitioners that these variable…

This paper introduces Whittemore, a language for causal programming. Causal programming is based on the theory of structural causal models and consists of two primary operations: identification, which finds formulas that compute causal…

When humans perform inductive learning, they often enhance the process with background knowledge. With the increasing availability of well-formed collaborative knowledge bases, the performance of learning algorithms could be significantly…

Substructural type systems, such as affine (and linear) type systems, are type systems which impose restrictions on copying (and discarding) of variables, and they have found many applications in computer science, including quantum…

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 pose causal inference as the problem of learning to classify probability distributions. In particular, we assume access to a collection $\{(S_i,l_i)\}_{i=1}^n$, where each $S_i$ is a sample drawn from the probability distribution of $X_i…

We provide a method to identify system parameters of dynamical systems, called ID-ODE -- Inference by Differentiation and Observing Delay Embeddings. In this setting, we are given a dataset of trajectories from a dynamical system with…

Object-oriented programming languages such as Java and Objective C have become popular for implementing agent-based and other object-based simulations since objects in those languages can {\em reflect} (i.e. make runtime queries of an…

We focus on control constructs that allow programmers define actions to be performed when respective conditions are met without requiring the explicit evaluation and testing of conditions as part of an imperative algorithm. Such elements…

We present new induction principles for the syntax of dependent type theories, which we call relative induction principles. The result of the induction principle relative to a functor F into the syntax is stable over the codomain of F. We…

We study instancewise feature importance scoring as a method for model interpretation. Any such method yields, for each predicted instance, a vector of importance scores associated with the feature vector. Methods based on the Shapley score…