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

Differentiable Architecture Search (DARTS) with mathematical enhancements
Evolutionary Multi-objective Optimization using NSGA-II
Bayesian Optimization for hyperparameter tuning
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