Related papers: ForeignFunctions package for Macaulay2
Compound AI applications, which compose calls to ML models using a general-purpose programming language like Python, are widely used for a variety of user-facing tasks, from software engineering to enterprise automation, making their…
LIBS2ML is a library based on scalable second order learning algorithms for solving large-scale problems, i.e., big data problems in machine learning. LIBS2ML has been developed using MEX files, i.e., C++ with MATLAB/Octave interface to…
We present FUEL (Fractional Universal Evaluation Library), a C++ library for performing rational function arithmetic with a flexible choice of third-party computer algebra systems as simplifiers. FUEL is an outgrowth of a C++ interface to…
The ramification method in Implicit Computational Complexity has been associated with functional programming, but adapting it to generic imperative programming is highly desirable, given the wider algorithmic applicability of imperative…
Adapting pretrained large language models (LLMs) to various downstream tasks in tens or hundreds of human languages is computationally expensive. Parameter-efficient fine-tuning (PEFT) significantly reduces the adaptation cost, by tuning…
This paper introduces the bicomplex Prabhakar derivative, extending fractional calculus to four-dimensional bicomplex spaces. Using the generalized kernel involving bicomplex Prabhakar function, we construct the bicomplex Prabhakar…
In this manuscript, we generalize F-calculus to apply it on fractal Tartan spaces. The generalized standard F-calculus is used to obtain the integral and derivative of the functions on the fractal Tartan with different dimensions. The…
Machine learning (ML) research and application often involve time-consuming steps such as model architecture prototyping, feature selection, and dataset preparation. To support these tasks, we introduce the Deep Fast Machine Learning Utils…
While enabling large language models to implement function calling (known as APIs) can greatly enhance the performance of Large Language Models (LLMs), function calling is still a challenging task due to the complicated relations between…
We introduce DiffOpt.jl, a Julia library to differentiate through the solution of optimization problems with respect to arbitrary parameters present in the objective and/or constraints. The library builds upon MathOptInterface, thus…
We describe efficient differentiation methods for computing Jacobians and gradients of a large class of matrix functions including the matrix logarithm $\log(A)$ and $p$-th roots $A^{\frac{1}{p}}$. We exploit contour integrals and conformal…
We briefly describe what tau-functions in integrable systems are. We then define a collection of tau-functions given as matrix elements for the action of $\widehat{GL_2}$ on two-component Fermionic Fock space. These tau-functions are…
We use the recently introduced factorization of motion polynomials for constructing overconstrained spatial linkages with a straight line trajectory. Unlike previous examples, the end-effector motion is not translational and the link graph…
High-fidelity simulators that connect theoretical models with observations are indispensable tools in many sciences. When coupled with machine learning, a simulator makes it possible to infer the parameters of a theoretical model directly…
Standard library implementations of functions like sin and exp optimize for accuracy, not speed, because they are intended for general-purpose use. But applications tolerate inaccuracy from cancellation, rounding error, and…
This paper introduces LLM2Fx-Tools, a multimodal tool-calling framework that generates executable sequences of audio effects (Fx-chain) for music post-production. LLM2Fx-Tools uses a large language model (LLM) to understand audio inputs,…
In a recent paper \cite{ft} a new powerful method to calculate Feynman diagrams was proposed. It consists in setting up a Taylor series expansion in the external momenta squared. The Taylor coefficients are obtained from the original…
In the previous papers \cite{L1, L2} the author constructed Mabuchi and Aubin-Yau functionals over any complex surfaces and three-folds, respectively. Using the method in \cite{L2}, we construct those functionals over any complex manifolds…
\textbf{FlexBox} is a flexible MATLAB toolbox for finite dimensional convex variational problems in image processing and beyond. Such problems often consist of non-differentiable parts and involve linear operators. The toolbox uses a…
This note describes a package for computing seminormalization of rings within Macaulay2.