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Single-Core Superscalar Optimization of Clifford Neural Layers

computer-vision › model-architecture

📄 Abstract

Abstract: Within the growing interest in the physical sciences in developing networks with equivariance properties, Clifford neural layers shine as one approach that delivers $E(n)$ and $O(n)$ equivariances given specific group actions. In this paper, we analyze the inner structure of the computation within Clifford convolutional layers and propose and implement several optimizations to speed up the inference process while maintaining correctness. In particular, we begin by analyzing the theoretical foundations of Clifford algebras to eliminate redundant matrix allocations and computations, then systematically apply established optimization techniques to enhance performance further. We report a final average speedup of 21.35x over the baseline implementation of eleven functions and runtimes comparable to and faster than the original PyTorch implementation in six cases. In the remaining cases, we achieve performance in the same order of magnitude as the original library.

Key Contributions

Proposes and implements optimizations for Clifford neural layers, significantly speeding up inference while maintaining correctness. By analyzing Clifford algebra and eliminating redundant computations, the method achieves an average speedup of 21.35x over baseline implementations and matches or exceeds PyTorch performance in many cases.

Business Value

Enables the practical application of powerful equivariant neural networks in fields like computer vision and physics simulations, where computational efficiency is critical for real-time performance and scalability.

Paper Metadata

Innovation Type

Algorithmic Improvement

Deployment Feasibility

High for research and development. Integration into production systems depends on the specific application and availability of optimized libraries.

Limitations Addressed

Computational inefficiency and slow inference of Clifford neural layers,Redundant matrix operations

Performance Gains

Average speedup of 21.35x over baseline implementation; comparable or faster than original PyTorch implementation in many cases.

Technical Tags

Clifford Neural LayersEquivarianceE(n) EquivarianceO(n) EquivarianceInference OptimizationClifford AlgebraMatrix OperationsPerformance SpeedupPyTorchComputational Efficiency

Research Topics

Geometric Deep LearningEquivariant Neural NetworksEfficient Deep LearningComputational MathematicsComputer Vision

Methods & Architectures

Analysis of Clifford algebra computationsElimination of redundant matrix allocationsApplication of optimization techniquesSingle-core superscalar optimization Clifford Neural Layers

Applications & Tasks

Physical Sciences Computer Vision Geometric Deep Learning Computational inefficiency of Clifford neural layersRedundant matrix allocations and computationsSlow inference speed Accelerating inference for Clifford neural layersAchieving E(n) and O(n) equivariancesImproving computational performance

Datasets & Benchmarks

Benchmarks

Eleven functions • PyTorch implementation

Average speedupInference runtimeCorrectness

Related Fields

Machine LearningDeep LearningComputer VisionGeometric Deep LearningComputational MathematicsPhysics

Keywords

Clifford Neural NetworksEquivarianceOptimizationInference SpeedDeep LearningComputer VisionGeometric Deep LearningClifford AlgebraPerformancePyTorchNeural NetworksEfficiency

Academic Context

#Geometric Deep Learning#Equivariant Neural Networks#Efficient Deep Learning#Computational Mathematics#Computer Vision

Technology Stack

Frameworks & Libraries

PyTorch

Commercial Potential

Potential Products

Optimized Libraries for Equivariant NetworksAccelerated Geometric Deep Learning FrameworksSpecialized AI Hardware for Equivariant Computations

Target Industries

Computer VisionRoboticsPhysics SimulationDrug DiscoveryMaterials Science

Use Case Examples

Real-time 3D object recognition with rotational and translational invarianceSimulating physical systems with inherent symmetries

Competitive Edge

Offers significant performance improvements for Clifford neural layers, making them more competitive with other deep learning architectures in terms of speed.

Market Opportunity

Growing interest in geometric deep learning and equivariant models.

Revenue Models

Licensing of optimized librariesconsulting services for implementing equivariant models.

Resource Requirements

Compute Needs

Reduced inference compute requirements due to optimizations.

Data Requirements

Depends on the specific application of Clifford neural layers.

Deployment Constraints

Need for optimized implementations and libraries,Integration into existing deep learning pipelines

Scalability

The optimizations improve the practical scalability of using Clifford neural layers.

Production Readiness

Maturity Level

Research

Time to Market

1-3 years for integration into specialized libraries or frameworks.

Patent Potential

Low to Moderate, depending on specific implementation details.

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