LLVM-optimized matrix computation system for CGA-based AI accelerators with a focus on multiplication and inversion

Abstract

LLVM-optimized matrix computation system (100) for CGA-based KL accelerators with a focus on multiplication and inversion, consisting of: a front-end interface configured to receive CGA-based operations and convert them into matrix representations for compilation; an LLVM IR generator configured to convert the matrix representations into LLVM IR code for optimization; a CGA-specific optimization engine configured to apply LLVM passes that simplify and optimize matrix representations, leveraging algebraic structures to reduce computational complexity; a hardware-specific code generation module configured to generate optimized matrix kernels for execution on various AI accelerators, including GPUs and FPGAs; a backend execution engine configured to deploy the optimized matrix calculations on a target platform for real-time AI applications.

Description

The present invention relates to the field of high performance computing and artificial intelligence hardware acceleration. More particularly, it relates to an LLVM optimized system and method for performing efficient matrix computations - particularly matrix multiplication and inversion - in the context of Clipfford Geometric Algebra (CGA).Califford Geometric Algebra (CGA) provides a powerful mathematical framework for the representation of and computation with geometric objects that uniformizes various operations such as rotations, translations, and projections in a compact and efficient form. CGA is increasingly being used in fields such as robotics, computer vision, physics-based simulations, and geometric deep learning, where high-dimensional multi-vector computations are often required. However, performing matrix operations-in particular multiplication and inversion-in CGA is associated with considerable computational effort due to the high dimensionality and the non-commutative nature of multivector elements. Conventional software libraries and general purpose processors often do not provide the performance and efficiency required for real-time or large scale applications with CGA.While existing AI accelerators are optimized for dense linear algebra (e.g., tensors, matrices in deep learning), they are not specifically matched to the particular characteristics of CGA calculations. Furthermore, the compiler toolcaines used in such environments typically lack algebraic specific optimization strategies, resulting in suboptimal performance. LLVM (Low-Level Virtual Machine) has become a powerful and modular compiler infrastructure capable of generating highly optimized code for multiple hardware platforms. However, LLVM has not yet been systematically expanded to handle domain-specific optimizations for CGA-based matrix operations. There is a need for a specialized system that integrates CGA-specific algebraic transformations, hardware-level optimization, and LLVM-based compilation techniques to speed up matrix operations. Such a system would bypass the performance gap between high-level CGA algorithms and low-level machine execution and allow real-time processing of AI and geometric conclusions in modern computing environments.To solve this problem, the present invention provides an LLVM optimized matrix computation system for CGA-based AI accelerators focusing on multiplication and inversion.The system has been developed to integrate the LLVM compiler infrastructure with CGA-based computation models, enabling efficient translation of high-level multi-vector operations into optimized low-level code for various hardware objectives.The system implements specialized LLVM optimization passes to simplify and merge CGA operations such as external, internal, and geometric products, thereby reducing execution time and memory consumption.The system enables code generation close to hardware, which enables automatic tuning and the use of optimized matrix kernels on AI accelerators such as GPUs, FPGAs, ASICs and domain-specific architectures.The system also aims to enable scalable integration with multiple data sources, including banks, payment gateways, third party accounting tools, and other enterprise systems, to create a unitary financial ecosystem.The system speeds up real-time AI applications that include geometric transformations such as pose estimation, SLAM, 3D object detection, and geometric deep learning by offloading optimized matrix computations to dedicated hardware.The system speeds up real-time AI applications that include geometric transformations such as pose estimation, SLAM, 3D object detection, and geometric deep learning by offloading optimized matrix computations to dedicated hardware.The system provides scalability and extensibility so that advanced matrix decomposition techniques, quantum-injected operations, and compatibility with evolving CGA standards are possible in the future.The system reduces the computational effort and energy consumption in AI hardware systems by optimizing compiler-level matrix operations and thus contributes to more durable and powerful AI workflows.In one embodiment, the present invention provides an LLVM optimized matrix computation system for CGA-based AI accelerators focusing on multiplication and inversion. The system addresses the computational challenges associated with matrix multiplication and inversion in high-dimensional geometric algebra by integrating domain-specific algebraic transformations with compiler-level optimizations. By a modular architecture, the system translates high-level CGA operations into intermediate LLVM representations (IR) and allows application of custom optimization runs that simplify, fuse, and restructure algebraic expressions to achieve maximum execution efficiency.The system also supports near hardware code generation and enables use on a variety of computing platforms, such as GPUs, FPGAs, ASICs, and specialized AI processors. By detecting algebraic structures such as economy and symmetry, the system intelligently optimizes matrix kernels and dynamically tunes them to the underlying hardware. Thanks to these capabilities, the invention is well suited for real-time AI applications involving geometric conclusions such as pose estimation, SLAM, and geometric deep learning, and at the same time promotes energy efficient high performance computations for modern AI workloads.The invention is explained again below with reference to the figure. The following shows: FIG. 1 : an LLVM-optimized matrix calculation system for CGA-based AI accelerators with emphasis on multiplication and inversion.The system (100) provides a novel LLVM optimized matrix computation framework specifically designed for Clipfford Geometric Algebra (CGA)-based Kl accelerators. The system (100) translates high-level multi-vector and CGA operations, such as geometric, external, and internal products, into structured matrix forms, which are then compiled into LLVM Intermediate Representation (IR). It has a user-defined front-end interface that processes CGA-based expressions from domain specific languages (DSLs) or high-level programming APls. The system (100) includes special LLVM passages for simplification and optimization of CGA algebra, utilizing inherent structures such as multivector economy, symmetry, and associative characteristics to reduce redundant computations and memory accesses. This results in a significantly improved execution speed and lower resource consumption compared to conventional matrix calculation methods.The system (100) also includes a hardware aware backend that generates optimized code for various target platforms such as CPUs, GPUs, FPGAs, and custom AI chips. It employs low-level optimization techniques such as loop scrolling, register allocation, vectoring (e.g., AVX or NEON), and memory tiles. The system (100) is also capable of detecting hardware configurations and appropriately adapting the matrix core generation. Optional profile creation and automatic optimization modules allow the system to evaluate multiple configurations and select the most efficient execution path based on runtime metrics. By combining CGA-aware algebraic transformation with platform specific optimization and the extensibility of LLVM, the system enables high performance real-time matrix computations for applications such as pose estimation, geometric deep learning, SLAM, and other AI tasks with complex geometric transformations.List of reference characters100 System

Claims

A LLVM optimized matrix computation system (100) for CGA-based Kl accelerators focus on multiplication and inversion, comprising: a front-end interface configured to receive CGA-based operations and convert them into matrix representations for compilation; an LLVM IR generator configured to convert the matrix representations into LLVM IR code for optimization; a CGA-specific optimization engine configured to apply LLVM passes that simplify and optimize the matrix representations, wherein algebraic structures are used to reduce computational complexity; a hardware specific code generation module configured to generate optimized matrix kernels for execution on various AI accelerators including GPUs and FPGAs; a backend execution engine configured to employ the optimized matrix computations on a target platform for real-time AI applications.The system (100) of claim 1, wherein the CGA-specific optimization engine further detects and optimizes multi-vector economy and symmetry in the matrix operations.The system (100) of claim 1, wherein the hardware aware code generation module optimizes matrix cores based on the specific architecture of the target AI accelerator including GPU, FPGA, or ASIC.The system (100) of claim 1, wherein the auto tuning and profiling module dynamically selects the optimal execution path based on runtime profiles and efficiency metrics such as execution time and power consumption.The system (100) of claim 1, wherein the backend execution engine includes a function for real-time inference in AI applications, such as pose estimation, SLAM, or 3D object detection.The system (100) of claim 1, wherein the LLVM IR generator supports the integration of domain specific languages (DSLs) for more intuitive high-level programming of matrix operations.The system (100) of claim 1, wherein the CGA-specific optimization engine performs symbolic simplifications of CGA operations including fusion of geometric products and reduction of redundant matrix terms.