Mathematical Optimization for Neural Architecture Search

Mathematical Optimization for Neural Architecture Search

Project Overview

This research project develops novel mathematical optimization techniques for Neural Architecture Search (NAS), combining evolutionary algorithms with gradient-based optimization to automatically discover optimal neural network architectures for specific tasks.

Research Contributions

• Hybrid Optimization: Novel combination of evolutionary and gradient-based methods
• Multi-objective Optimization: Balancing accuracy, efficiency, and computational cost
• Theoretical Analysis: Mathematical foundations for convergence guarantees
• Practical Applications: Applied to computer vision and NLP tasks

Mathematical Framework

Optimization Formulation

The NAS problem is formulated as a multi-objective optimization:

minimize f(α) = [f_accuracy(α), f_latency(α), f_memory(α)]
subject to α ∈ A

Where α represents the architecture parameters and A is the feasible architecture space.

Key Algorithms

1. Differentiable Architecture Search (DARTS) with mathematical enhancements
2. Evolutionary Multi-objective Optimization using NSGA-II
3. Bayesian Optimization for hyperparameter tuning
4. Progressive Search with mathematical convergence analysis

Technical Implementation

Core Components

• Search Space Design: Hierarchical cell-based search space
• Performance Estimation: One-shot training with weight sharing
• Optimization Engine: Custom hybrid optimizer combining multiple techniques
• Evaluation Framework: Comprehensive benchmarking suite

Mathematical Models

• Convergence Analysis: Theoretical guarantees for optimization convergence
• Complexity Analysis: Time and space complexity bounds
• Statistical Validation: Rigorous statistical testing of results

Results & Achievements

• Performance: Discovered architectures achieving 96.2% accuracy on CIFAR-10
• Efficiency: 50% reduction in search time compared to baseline methods
• Publications: 2 papers submitted to top-tier ML conferences
• Open Source: Released as open-source framework with 200+ GitHub stars

Applications

The developed techniques have been successfully applied to:

• Image classification tasks
• Natural language processing
• Time series forecasting
• Medical image analysis
• Edge computing optimization

Future Research Directions

• Quantum-inspired Optimization: Exploring quantum algorithms for NAS
• Federated NAS: Distributed architecture search across multiple clients
• Hardware-aware Search: Optimization for specific hardware platforms
• Theoretical Foundations: Deeper mathematical analysis of search dynamics