相关论文: A Framework for Dependent Types and Effects

We introduce a formal meta-language for probabilistic programming, capable of expressing both programs and the type systems in which they are embedded. We are motivated here by the desire to allow an AGI to learn not only relevant knowledge…

This paper explores two topics at once: the use of denotational semantics to bound the evaluation length of functional programs, and the semantics of strong (that is, possibly under abstractions) call-by-value evaluation. About the first,…

Understanding interaction effects among variables is important for regression modeling in various applications. The conventional approach of quantifying interactions as the product of variables often lacks clear interpretability, especially…

This paper develops a more general theory of sequences of dependent categorical random variables, extending the works of Korzeniowski (2013) and Traylor (2017) that studied first-kind dependency in sequences of Bernoulli and categorical…

The aim of this paper is to present an elementary computable theory of random variables, based on the approach to probability via valuations. The theory is based on a type of lower-measurable sets, which are controlled limits of open sets,…

Nominal abstract syntax is an approach to representing names and binding pioneered by Gabbay and Pitts. So far nominal techniques have mostly been studied using classical logic or model theory, not type theory. Nominal extensions to simple,…

We present gradual type theory, a logic and type theory for call-by-name gradual typing. We define the central constructions of gradual typing (the dynamic type, type casts and type error) in a novel way, by universal properties relative to…

We introduce causal Markov Decision Processes (C-MDPs), a new formalism for sequential decision making which combines the standard MDP formulation with causal structures over state transition and reward functions. Many contemporary and…

Enhanced sampling simulations make the computational study of rare events feasible. A large family of such methods crucially depends on the definition of some collective variables (CVs) that could provide a low-dimensional representation of…

Constraint-based (CB) learning is a formalism for learning a causal network with a database D by performing a series of conditional-independence tests to infer structural information. This paper considers a new test of independence that…

Languages may encode similar meanings using different sentence structures. This makes it a challenge to provide a single set of formal rules that can derive meanings from sentences in many languages at once. To overcome the challenge, we…

Dependently typed lambda calculi such as the Logical Framework (LF) are capable of representing relationships between terms through types. By exploiting the "formulas-as-types" notion, such calculi can also encode the correspondence between…

The defunctionalization translation that eliminates higher-order functions from programs forms a key part of many compilers. However, defunctionalization for dependently-typed languages has not been formally studied. We present the first…

Inductive datatypes in programming languages allow users to define useful data structures such as natural numbers, lists, trees, and others. In this paper we show how inductive datatypes may be added to the quantum programming language QPL.…

Conditional independence and graphical models are crucial concepts for sparsity and statistical modeling in higher dimensions. For L\'evy processes, a widely applied class of stochastic processes, these notions have not been studied. By the…

Dropout has been demonstrated as a simple and effective module to not only regularize the training process of deep neural networks, but also provide the uncertainty estimation for prediction. However, the quality of uncertainty estimation…

Dijkstra monads enable a dependent type theory to be enhanced with support for specifying and verifying effectful code via weakest preconditions. Together with their closely related counterparts, Hoare monads, they provide the basis on…

Graded Type Theory provides a mechanism to track and reason about resource usage in type systems. In this paper, we develop GraD, a novel version of such a graded dependent type system that includes functions, tensor products, additive…

The concept bottleneck model (CBM) is an interpretable-by-design framework that makes decisions by first predicting a set of interpretable concepts, and then predicting the class label based on the given concepts. Existing CBMs are trained…

Conditional Random Fields (CRFs) are undirected graphical models, a special case of which correspond to conditionally-trained finite state machines. A key advantage of these models is their great flexibility to include a wide array of…