Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1706.00231

Automatic Differentiation using Constraint Handling Rules in Prolog

Samer Abdallah
View original source ↗Read source document ↗Export metadata ↓

Abstract

Automatic differentiation is a technique which allows a programmer to define a numerical computation via compositions of a broad range of numeric and computational primitives and have the underlying system support the computation of partial derivatives of the result with respect to any of its inputs, without making any finite difference approximations, and without manipulating large symbolic expressions representing the computation. This note describes a novel approach to reverse mode automatic differentiation using constraint logic programmming, specifically, the constraint handling rules (CHR) library of SWI Prolog, resulting in a very small (50 lines of code) implementation. When applied to a differentiation-based implementation of the inside-outside algorithm for parameter learning in probabilistic grammars, the CHR based implementations outperformed two well-known frameworks for optimising differentiable functions, Theano and TensorFlow, by a large margin.

Explore related subjects

cs.MScs.PLcs.SC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Samer Abdallah. 2017-06-01. Automatic Differentiation using Constraint Handling Rules in Prolog. https://arxiv.org/abs/1706.00231

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Ozaki Scheme II: A GEMM-oriented emulation of floating-point matrix multiplication using an integer modular technique

This paper addresses emulation algorithms for matrix multiplication. General Matrix-Matrix Multiplication (GEMM), a fundamental operation in the Basic Linear Algebra Subprograms (BLAS), is typically optimized for specific hardware architectures. The Ozaki scheme is a well-established GEMM-based emulation method for matrix multiplication, wherein input matrices are decomposed into several low-precision components to ensure that the resulting matrix product is computed exactly through numerical operations. This study proposes a novel GEMM-based emulation method for matrix multiplication that leverages the Chinese Remainder Theorem. The proposed method inherits the computational efficiency of highly optimized GEMM routines and further enables control over the number of matrix multiplications, which can enhance computational accuracy. We present numerical experiments featuring INT8 Tensor Core operations on GPUs and FP64 arithmetic on CPUs as case studies. The results demonstrate that FP64 emulation using the proposed method achieves performance levels of up to 7.4 to 9.8 TFLOPS on the NVIDIA RTX 4090 and 56.6 to 80.2 TFLOPS on the NVIDIA GH200, exceeding the measured performance of native FP64 arithmetic. Furthermore, for FP64 computations on CPUs, the proposed method achieved up to a 2.3x speedup in emulating quadruple-precision arithmetic compared to the conventional Ozaki scheme.

cs.MS↗
arXiv2026

Eigensolvers for polynomial roots and tensor decomposition

Computing eigenvalues and eigenvectors is at the heart of the solution of many non-linear problems. For instance, finding the roots of polynomial systems reduces to computing joint eigenvectors of operators of multiplication. Similarly, tensor decomposition can be performed via the joint diagonalization of submatrices of the Catalecticant of the tensor. We describe and illustrate symbolic-numeric methods for computing the solutions of these algebraic problems from the computation of joint eigenvectors of commuting operators, and for analysing their multiplicity structure, as well as their implementation in the package AlgebraicSolvers.jl.

cs.MS↗
arXiv2026

The Art of Closed-Formula Defaults: Search-Free Code Generation for Tensor Operators

Agentic search and automated optimization of GPU kernels are powerful tools for large language model inference. Their effectiveness, however, depends not on the sophistication of the search itself, but on the clarity of the optimization problem being solved. We provide an application-first approach that drives a hierarchical code generation tool from operator specifi cation down to GPU instructions, and show that a clearly defined computational model makes the optimization problem tractable.

cs.MS↗