Research & Innovation
Pioneering breakthroughs in AI development methodologies, optimization algorithms, and human-AI collaboration patterns
Featured Research
QQN: Quadratic Quasi-Newton Optimization Methods
Comprehensive research on the Quadratic-Quasi-Newton (QQN) algorithm, a novel optimization method that combines gradient descent and quasi-Newton directions through quadratic interpolation. QQN began as an experimental optimizer inside the MindsEye Java deep learning framework, was formally published alongside a purpose-built Rust benchmarking framework, and is now available as reference implementations for three mainstream Python deep learning frameworks (JAX, PyTorch, and TensorFlow). QQN achieves statistically significant dominance across 62 benchmark problems, winning 72.6% of test cases with 50-80% fewer function evaluations than traditional methods.
Rational Certificate Complexity (RCC Trilogy)
A three-essay research program that treats every convergent sequence as a rational certificate engine, measures its bit-length against the demanded tolerance ε, and stratifies mathematical constants into cost classes. RCC establishes the vocabulary, PI_RCC stress-tests the boundary with a cubic-convergent non-hypergeometric iteration for π, and NAM builds the executable substrate: a generator-based numerics library where every number is a forkable, deterministic nano-VM emitting an infinite digit stream.
Unit Testing for Neural Networks
Pioneering research on applying test-driven development methodologies to neural network development. Introduces comprehensive unit testing frameworks for neural network layers, gradient validation, and A/B testing methodologies for model comparison.
DeepArtist: Symmetric Neural Style Transfer
Research and platform development for making neural style transfer with experimental methods and integrated UI and reporting.
Volumetry: Multidimensional Probability Modeling
Research project focused on volumetric probability distribution modeling and visualization. Implements novel techniques for modeling complex multidimensional distributions using gaussian kernels, decision trees, and equipotential surface analysis.
Modeling Network Latency
Research on modeling network latency for distributed systems as a real-world case study of various distribution families. Explores statistical modeling approaches for understanding and predicting network performance in distributed computing environments.
Research Areas
Enterprise AI/ML Frameworks
Pioneering JVM-based machine learning frameworks. Focus on GPU acceleration, memory optimization, and production deployment patterns as part of a complete AI development suite.
Key Contributions:
- Comprehensive test-driven development methodology for ML systems
- QQN optimization algorithm achieving 72.6% win rate across comprehensive benchmark suite
- Enterprise-friendly deployment patterns with Maven Central distribution
- First production-grade neural network framework in Java with full GPU acceleration and support for large-scale models
- Cross-language integration (Interop layers and API design)
- Rust-based benchmarking framework for reproducible optimization research
Developer Productivity
Creating sophisticated developer tools that leverage AI for code generation, task automation, and intelligent assistance as part of a complete AI development suite. Emphasis on privacy-first architecture and user control as alternatives to proprietary solutions.
Key Contributions:
- Various integrated tools for generating code, documentation, and tests
- Capable of generating large-scale applications with minimal user input
- Supports automatic bug fixing and iterative automation
- Full user oversight and control over AI-activity (optional)
- BYOK architecture eliminating vendor lock-in and subscription fees
- Production-grade IntelliJ plugin competing with commercial alternatives
- Privacy-first design addressing enterprise security requirements
AI Testing and Quality Assurance
Developing comprehensive testing methodologies for AI systems, including unit testing frameworks for neural networks, statistical validation approaches, and quality assurance practices. Essential quality control component of the complete AI development suite.
Key Contributions:
- First comprehensive unit testing framework for neural network components
- Gradient validation through automated finite difference testing
- A/B testing methodologies for statistically rigorous model comparison
- Test-driven development practices adapted for machine learning workflows
- Statistical benchmarking frameworks for optimization algorithm evaluation
Computational Mathematics
Original mathematical research conducted and published as live, in-browser experiments: geometry treated as computation, discrete problems given continuous relaxations, and an explicit accounting of what cannot be decided or distinguished. Published as 16 interactive labs and 6 formal essays at math.cognotik.com.
Key Contributions:
- Rational Certificate Complexity: cost classes for computing real numbers, with a running reference implementation
- Pentagonal Lattice Geometry: fractional dimension and spinor-like holonomy from exact ℚ(√5) arithmetic
- Geometric Entropy: a continuous analogue of the Erdős distinct-distance problem on arbitrary manifolds
- Irrational Lattice: deterministic, provably aperiodic, spectrally tunable lattice noise in pure integer arithmetic
- Optimizer fingerprinting on degenerate landscapes — Adam, L-BFGS, and QQN leave distinguishable geometry
- Computational verification via Maxima batch scripts, BFS dimension sweeps, and KPM spectral estimation
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