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Fractional calculus has become widely studied and applied to physical problems in recent years. As a result, many methods for the numerical computation of fractional derivatives and integrals have been defined. However, these algorithms are…
Discrete Euclidian Spaces (DESs) are the beginning of a journey without return towards the discretization of mathematics. Important mathematical concepts- such as the idea of number or the systems of numeration, whose formal definition is…
The fact that Applicative type class allows one to express simple parsers in a variable-less combinatorial style is well appreciated among Haskell programmers for its conceptual simplicity, ease of use, and usefulness for semi-automated…
Probabilistic programming languages, which exist in abundance, are languages that allow users to calculate probability distributions defined by probabilistic programs, by using inference algorithms. However, the underlying inference…
Writing correct distributed programs is hard. In spite of extensive testing and debugging, software faults persist even in commercial grade software. Many distributed systems, especially those employed in safety-critical environments,…
We present a marriage of functional and structured imperative programming that embeds in pure lambda calculus. We describe how we implement the core of this language in a monadic DSL which is structurally equivalent to our intended source…
Many recent machine learning models show dynamic shape characteristics. However, existing AI compiler optimization systems suffer a lot from problems brought by dynamic shape models, including compilation overhead, memory usage,…
Conic programming has well-documented merits in a gamut of signal processing and machine learning tasks. This contribution revisits a recently developed first-order conic descent (CD) solver, and advances it in three aspects: intuition,…
Applying dynamic logics to program verifications is a challenge, because their axiomatic rules for regular expressions can be difficult to be adapted to different program models. We present a novel dynamic logic, called DLp, which supports…
The first associations to software sustainability might be the existence of a continuous integration (CI) framework; the existence of a testing framework composed of unit tests, integration tests, and end-to-end tests; and also the…
An algorithm is presented that formalizes different steps in a classical Supersymmetric (SUSY) calculation. Based on the algorithm Dill, a symbolic software package, that can perform the calculations, is developed in the Mathematica…
Reinforcement learning with verifiable rewards has emerged as a promising paradigm for enhancing the reasoning capabilities of large language models particularly in mathematics. Current approaches in this domain present a clear trade-off:…
Dynamic programming is a mathematical optimization method and a computer programming method as well. In this paper, the notion of sheaf programming in topological spaces is introduced and it is demonstrated that it relates very well to the…
We present Sleeping-DISCO 9M, a large-scale pre-training dataset for music and song. To the best of our knowledge, there are no open-source high-quality dataset representing popular and well-known songs for generative music modeling tasks…
We present dPASP, a novel declarative probabilistic logic programming framework for differentiable neuro-symbolic reasoning. The framework allows for the specification of discrete probabilistic models with neural predicates, logic…
In recent years, Deep Learning (DL) has found great success in domains such as multimedia understanding. However, the complex nature of multimedia data makes it difficult to develop DL-based software. The state-of-the art tools, such as…
This paper discusses our proposal and implementation of Distill, a domain-specific compilation tool based on LLVM to accelerate cognitive models. Cognitive models explain the process of cognitive function and offer a path to human-like…
Domain-specific high-productivity environments are playing an increasingly important role in scientific computing due to the levels of abstraction and automation they provide. In this paper we introduce Devito, an open-source…
We describe a new library named picasso, which implements a unified framework of pathwise coordinate optimization for a variety of sparse learning problems (e.g., sparse linear regression, sparse logistic regression, sparse Poisson…
The adoption of differential privacy is growing but the complexity of designing private, efficient and accurate algorithms is still high. We propose a novel programming framework and system, Ektelo, for implementing both existing and new…