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This dissertation introduces executable refinement types, which refine structural types by semi-decidable predicates, and establishes their metatheory and accompanying implementation techniques. These results are useful for undecidable type…
We study how a Reinforcement Learning (RL) system can remain sample-efficient when learning from an imperfect model of the environment. This is particularly challenging when the learning system is resource-constrained and in continual…
In this paper, we set forth a new vision of reinforcement learning developed by us over the past few years, one that yields mathematically rigorous solutions to longstanding important questions that have remained unresolved: (i) how to…
Reinforcement learning (RL) for large language model reasoning is frequently hindered by signal loss, a phenomenon where standard uniform sampling with small group sizes fails to uncover informative learning signals for difficult prompts.…
Semantic data fuels many different applications, but is still lacking proper integration into programming languages. Untyped access is error-prone while mapping approaches cannot fully capture the conceptualization of semantic data. In this…
Confidence calibration is critical for the safe deployment of machine learning models in the real world. However, such issue in vision-language models like CLIP, particularly after fine-tuning, has not been fully addressed. In this work, we…
We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a…
Static resource management in languages remains challenging due to tensions among control, expressiveness, and flexibility. Region-based systems [Grossman et al . 2002; Tofte et al. 2001] offer bulk deallocation via lexically scoped…
Large Language Models (LLMs) have demonstrated remarkable performance across various tasks by effectively utilizing a prompting strategy. However, they are highly sensitive to input perturbations, such as typographical errors or slight…
Prompt learning has become one of the most efficient paradigms for adapting large pre-trained vision-language models to downstream tasks. Current state-of-the-art methods, like CoOp and ProDA, tend to adopt soft prompts to learn an…
Users of program analyses expect that results change predictably in response to changes in their programs, but many analyses fail to provide such robustness. This paper introduces a theoretical framework that provides a unified language to…
This paper presents a new theory, known as robust dynamic pro- gramming, for a class of continuous-time dynamical systems. Different from traditional dynamic programming (DP) methods, this new theory serves as a fundamental tool to analyze…
Insensitivity to semantically-preserving variations of prompts (paraphrases) is crucial for reliable behavior and real-world deployment of large language models. However, language models exhibit significant performance degradation when…
Static verification relying on an automated theorem prover can be very slow and brittle: since static verification is undecidable, correct code may not pass a particular static verifier. In this work we use metaprogramming to generate code…
Refinement transforms an abstract system model into a concrete, executable program, such that properties established for the abstract model carry over to the concrete implementation. Refinement has been used successfully in the development…
We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…
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…
Almost all modern imperative programming languages include operations for dynamically manipulating the heap, for example by allocating and deallocating objects, and by updating reference fields. In the presence of recursive procedures and…
The formal system $\lambda\delta$ is a typed lambda calculus derived from $\Lambda_\infty$, aiming to support the foundations of Mathematics that require an underlying theory of expressions (for example the Minimal Type Theory). The system…
Context Oriented Programming (COP) concerns the ability of programs to adapt to changes in their running environment. A number of programming languages endowed with COP constructs and features have been developed. However, some foundational…