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To interpret deep models' predictions, attention-based visual cues are widely used in addressing \textit{why} deep models make such predictions. Beyond that, the current research community becomes more interested in reasoning \textit{how}…
A standard informal method for analyzing the asymptotic complexity of a program is to extract a recurrence that describes its cost in terms of the size of its input, and then to compute a closed-form upper bound on that recurrence. We give…
We develop necessary and sufficient conditions and a novel provably consistent and efficient algorithm for discovering topics (latent factors) from observations (documents) that are realized from a probabilistic mixture of shared latent…
Large Language Models (LLMs) excel at many tasks but often falter on complex problems that require structured, multi-step reasoning. We introduce the Diagram of Thought (DoT), a framework that enables a single LLM to build and navigate a…
Programs written in dynamic languages make heavy use of features --- run-time type tests, value-indexed dictionaries, polymorphism, and higher-order functions --- that are beyond the reach of type systems that employ either purely syntactic…
Two distinct research approaches have been proposed for assigning a purely extensional semantics to higher-order logic programming. The former approach uses classical domain theoretic tools while the latter builds on a fixed-point…
We develop domain theory in constructive and predicative univalent foundations (also known as homotopy type theory). That we work predicatively means that we do not assume Voevodsky's propositional resizing axioms. Our work is constructive…
Dynamic languages such as Python and JavaScript widely use function decorators to extend behavior. In TypeScript, a common way to type such patterns uses Parameters<T> and ReturnType<T>. In practice, this idiom relies on a function-type…
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 programming languages allow sophisticated properties of data to be expressed within the type system. Of particular use in dependently typed programming are indexed types that refine data by computationally useful…
We propose some slight additions to O-O languages to implement the necessary features for using Deductive Object Programming (DOP). This way of programming based upon the manipulation of the Production Tree of the Objects of Interest,…
Many empirical studies have provided evidence for the emergence of algorithmic mechanisms (abilities) in the learning of language models, that lead to qualitative improvements of the model capabilities. Yet, a theoretical characterization…
In previous deep-learning-based methods, semantic segmentation has been regarded as a static or dynamic per-pixel classification task, \textit{i.e.,} classify each pixel representation to a specific category. However, these methods only…
The depth-bounded fragment of the pi-calculus is an expressive class of systems enjoying decidability of some important verification problems. Unfortunately membership of the fragment is undecidable. We propose a novel type system,…
We study a cost-aware programming language for higher-order recursion dubbed $\textbf{PCF}_\mathsf{cost}$ in the setting of synthetic domain theory (SDT). Our main contribution relates the denotational cost semantics of…
Gradual dependent types can help with the incremental adoption of dependently typed code by providing a principled semantics for imprecise types and proofs, where some parts have been omitted. Current theories of gradual dependent types,…
A non-deterministic recursion scheme recognizes a language of finite trees. This very expressive model can simulate, among others, higher-order pushdown automata with collapse. We show decidability of the diagonal problem for schemes. This…
Discrete structures are currently second-class in differentiable programming. Since functions over discrete structures lack overt derivatives, differentiable programs do not differentiate through them and limit where they can be used. For…
This paper investigates how global decision problems over arithmetically represented domains acquire reflective structure through class-quantification. Arithmetization forces diagonal fixed points whose verification requires reflection…
A more realistic object detection paradigm, Open-World Object Detection, has arisen increasing research interests in the community recently. A qualified open-world object detector can not only identify objects of known categories, but also…