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Recent studies have examined the computational complexity of computing Shapley additive explanations (also known as SHAP) across various models and distributions, revealing their tractability or intractability in different settings.…
Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…
High-dimensional time series are common in many domains. Since human cognition is not optimized to work well in high-dimensional spaces, these areas could benefit from interpretable low-dimensional representations. However, most…
Multimodal alignment constructs a joint latent vector space where modalities representing the same concept map to neighboring latent vectors. We formulate this as an inverse problem and show that, under certain conditions, paired data from…
It is known that the so-called monadic decomposition, applied to the adjunction connecting the category of bialgebras to the category of vector spaces via the tensor and the primitive functors, returns the usual adjunction between…
Recently, Multimodal Large Language Models (MLLMs) have demonstrated impressive performance on instruction-following tasks by integrating pretrained visual encoders with large language models (LLMs). However, existing approaches often…
Classes of set functions along with a choice of ground set are a bedrock to determine and develop corresponding variants of greedy algorithms to obtain efficient solutions for combinatorial optimization problems. The class of approximate…
In the quest to give a formal compositional semantics to natural languages, semanticists have started turning their attention to phenomena that have been also considered as parts of pragmatics (e.g., discourse anaphora and presupposition…
In this paper, a visual language, VCP, for queries on complex-value databases is proposed. The main strength of the new language is that it is purely visual: (i) It has no notion of variable, quantification, partiality, join, pattern…
ML5 is a programming language for spatially distributed computing, based on a Curry-Howard correspondence with the modal logic S5. Despite being designed by a correspondence with S5 modal logic, the ML5 programming language differs from the…
Making quantum mechanical equations and concepts come to life through interactive simulation and visualization are commonplace for augmenting learning and teaching. However, graphical visualizations nearly always exhibit a set of hard-coded…
Inductive families provide a convenient way of programming with dependent types. Yet, when it comes to compilation, their default linked-tree runtime representations, as well as the need to convert between different indexed views of the…
Reynold's parametricity theory captures the property that parametrically polymorphic functions behave uniformly: they produce related results on related instantiations. In dependently-typed programming languages, such relations and…
In the semantics of programming languages one can view programs as state transformers, or as predicate transformers. Recently the author has introduced state-and-effect triangles which capture this situation categorically, involving an…
Modal types -- types that are derived from proof systems of modal logic -- have been studied as theoretical foundations of metaprogramming, where program code is manipulated as first-class values. In modal type systems, modality corresponds…
We present a geometric framework for understanding Transformer-based language models, drawing an explicit analogy to General Relativity. Queries and keys induce an effective metric on representation space, and attention acts as a discrete…
We introduce a generalization of monads, called relative monads, allowing for underlying functors between different categories. Examples include finite-dimensional vector spaces, untyped and typed lambda-calculus syntax and indexed…
While modern software development heavily uses versioned packages, programming languages rarely support the concept of versions in their semantics, which makes software updates more bulky and unsafe. This paper proposes a programming…
Linearity and dependency analyses are key to several applications in computer science, especially, in resource management and information flow control. What connects these analyses is that both of them need to model at least two different…
We consider a method for conformalizing a stacked ensemble of predictive models, showing that the potentially simple form of the meta-learner at the top of the stack enables a procedure with manageable computational cost that achieves…