Intuitionistic modal logics (IMLs) extend intuitionistic propositional logic with modalities such as the box and diamond connectives. Advances in the study of IMLs have inspired several applications in programming languages via the development of corresponding type theories with modalities. Until recently, IMLs with diamonds have been misunderstood as somewhat peculiar and unstable, causing the development of type theories with diamonds to lag behind type theories with boxes. In this article, we develop a family of typed-lambda calculi corresponding to sublogics of a peculiar IML with diamonds known as Lax logic. These calculi provide a modal logical foundation for various strong functors in typed-functional programming. We present possible-world and categorical semantics for these calculi and constructively prove normalization, equational completeness and proof-theoretic inadmissibility results. Our main results have been formalized using the proof assistant Agda.

Progress in human behavior modeling involves understanding both implicit, early-stage perceptual behavior, such as human attention, and explicit, later-stage behavior, such as subjective preferences or likes. Yet most prior research has focused on modeling implicit and explicit human behavior in isolation; and often limited to a specific type of visual content. We propose UniAR -- a unified model of human attention and preference behavior across diverse visual content. UniAR leverages a multimodal transformer to predict subjective feedback, such as satisfaction or aesthetic quality, along with the underlying human attention or interaction heatmaps and viewing order. We train UniAR on diverse public datasets spanning natural images, webpages, and graphic designs, and achieve SOTA performance on multiple benchmarks across various image domains and behavior modeling tasks. Potential applications include providing instant feedback on the effectiveness of UIs/visual content, and enabling designers and content-creation models to optimize their creation for human-centric improvements.

We consider the task of producing heatmaps from users' aggregated data while protecting their privacy. We give a differentially private (DP) algorithm for this task and demonstrate its advantages over previous algorithms on real-world datasets. Our core algorithmic primitive is a DP procedure that takes in a set of distributions and produces an output that is close in Earth Mover's Distance (EMD) to the average of the inputs. We prove theoretical bounds on the error of our algorithm under a certain sparsity assumption and that these are essentially optimal.

Everyone is unique. Given the same visual stimuli, people's attention is driven by both salient visual cues and their own inherent preferences. Knowledge of visual preferences not only facilitates understanding of fine-grained attention patterns of diverse users, but also has the potential of benefiting the development of customized applications. Nevertheless, existing saliency models typically limit their scope to attention as it applies to the general population and ignore the variability between users' behaviors. In this paper, we identify the critical roles of visual preferences in attention modeling, and for the first time study the problem of user-aware saliency modeling. Our work aims to advance attention research from three distinct perspectives: (1) We present a new model with the flexibility to capture attention patterns of various combinations of users, so that we can adaptively predict personalized attention, user group attention, and general saliency at the same time with one single model; (2) To augment models with knowledge about the composition of attention from different users, we further propose a principled learning method to understand visual attention in a progressive manner; and (3) We carry out extensive analyses on publicly available saliency datasets to shed light on the roles of visual preferences. Experimental results on diverse stimuli, including naturalistic images and web pages, demonstrate the advantages of our method in capturing the distinct visual behaviors of different users and the general saliency of visual stimuli.

Fitch-style modal lambda calculi enable programming with necessity modalities in a typed lambda calculus by extending the typing context with a delimiting operator that is denoted by a lock. The addition of locks simplifies the formulation of typing rules for calculi that incorporate different modal axioms, but each variant demands different, tedious and seemingly ad hoc syntactic lemmas to prove normalization. In this work, we take a semantic approach to normalization, called normalization by evaluation (NbE), by leveraging the possible-world semantics of Fitch-style calculi to yield a more modular approach to normalization. We show that NbE models can be constructed for calculi that incorporate the K, T and 4 axioms of modal logic, as suitable instantiations of the possible-world semantics. In addition to existing results that handle 𝛽-equivalence, our normalization result also considers 𝜂-equivalence for these calculi. Our key results have been mechanized in the proof assistant Agda. Finally, we showcase several consequences of normalization for proving meta-theoretic properties of Fitch-style calculi as well as programming-language applications based on different interpretations of the necessity modality.

Embedded domain-specific languages (eDSLs) are typically implemented in a rich host language, such as Haskell, using a combination of deep and shallow embedding techniques. While such a combination enables programmers to exploit the execution mechanism of Haskell to build and specialize eDSL programs, it blurs the distinction between the host language and the eDSL. As a consequence, extension with features such as sums and effects requires a significant amount of ingenuity from the eDSL designer. In this paper, we demonstrate that Normalization by Evaluation (NbE) provides a principled framework for building, extending, and customizing eDSLs. We present a comprehensive treatment of NbE for deeply embedded eDSLs in Haskell that involves a rich set of features such as sums, arrays, exceptions and state, while addressing practical concerns about normalization such as code expansion and the addition of domain-specific features.

Categorical combinators offer a simpler alternative to typed lambda calculi for static analysis and implementation. Since categorical combinators are accompanied by a rich set of conversion rules which arise from categorical laws, they also offer a plethora of opportunities for program optimization. It is unclear, however, how such rules can be applied in a systematic manner to eliminate intermediate values such as exponentials, the categorical equivalent of higher-order functions, from a program built using combinators. Exponential elimination simplifies static analysis and enables a simple closure-free implementation of categorical combinators--reasons for which it has been sought after.

The small carrier wavelength at millimeter-wave (mm-Wave) frequencies enables featuring a large number of co-located antennas. This paper exploits the potential of large antenna arrays to develop a low-complexity directional modulation technique, Antenna Subset Modulation (ASM), for point-to-point secure wireless communication. The main idea in ASM is to modulate the radiation pattern at the symbol rate by driving only a subset of antennas in the array. This results in a directional radiation pattern that projects a sharply defined constellation in the desired direction and expanded further randomized constellation in other directions. Two techniques for implementing ASM are proposed. The first technique selects an antenna subset randomly for every symbol. While randomly switching antenna subsets does not affect the symbol modulation for a desired receiver along the main direction, it effectively randomizes the amplitude and phase of the received symbol for an eavesdropper along a sidelobe. Using a simplified statistical model, an expression for the average uncoded symbol error rate (SER) is derived as a function of the observation angle. To overcome the problem of large sidelobes in random antenna subset switching, the second technique uses an optimized antenna subset selection procedure based on simulated annealing to achieve superior performance compared with random selection. Numerical comparisons of the SER performance and secrecy capacity of the proposed techniques against those of conventional array transmission are presented to highlight the potential of ASM.