Neuroligence Inc. conducts ongoing research and prototyping across AI, robotics, sensing, mathematics, and scientific computing.
Below are selected internal projects, proof-of-concept systems, and experimental simulations showcasing our technical capabilities and research direction.

These projects demonstrate how we approach complex problems through mathematics, AI, simulation, and engineering rigor.

1. MathRAG — Retrieval-Augmented Mathematical Reasoning

Domain: AI Research, Formal Reasoning, Mathematics
Status: Active R&D

MathRAG is our flagship research initiative that integrates:

• Graph-based knowledge retrieval
• Symbolic mathematics (Lean4, expression trees)
• Neural models
• Formal verification

Objectives:

• Build intelligent agents capable of structured mathematical reasoning
• Retrieve definitions, theorems, and lemmas from complex knowledge graphs
• Generate explainable reasoning chains
• Assist researchers and engineers with mathematical problem solving

Highlights:

• Early prototypes demonstrate graph-based retrieval of mathematical concepts
• Integration with Lean4 and symbolic AST structures
• Foundation for future hybrid symbolic-neural AI systems

2. Autonomous Robotics Simulation Environment

Domain: Robotics, Autonomy, ROS2, Control Theory
Status: Prototype Complete — Iterative Development

A modular simulation framework built in ROS2 + Gazebo to test:

• SLAM and perception algorithms
• Navigation and mapping
• Sensor fusion (LiDAR, IMU, radar)
• Control strategies (PID, MPC, RL-based)
• Multi-agent behaviors

Outcomes:

• Developed reusable simulation worlds
• Built initial control stacks and perception modules
• Demonstrated autonomous navigation under uncertainty

This environment supports future robotics research and DoD-relevant autonomy.

3. Multimodal Signal Processing & Sensing Pipeline

Domain: Signal Processing, Acoustics, Sensor Fusion
Status: Active Experimentation

A flexible signal-processing toolkit designed for:

• Acoustic waveform analysis
• Radar/LiDAR modeling
• Spectral and time-frequency transforms
• ML-enhanced detection and classification
• Multi-sensor integration

Key Features:

• Supports both simulated and real-world sensor datasets
• Early models show effective classification on noisy signals
• Extensible for defense-grade sensing applications

4. Quantitative Market Simulation Engine

Domain: Finance, Multi-Agent Systems, Cognitive Modeling
Status: Ongoing Research

A mathematical and computational framework that simulates financial markets as interacting agents.

Capabilities:

• Time-series forecasting
• Factor model generation
• Behavioral & narrative-based prediction
• Agent-based simulation of market microstructure
• Stress-testing and scenario analysis

Applications:

• Trading research
• Risk modeling
• Market structure analysis
• Predictive intelligence tools

5. Optimization & Operations Research Toolkit

Domain: Mathematical Optimization, OR, Scientific Computing
Status: Prototype

A suite of optimization modules used across robotics, finance, and engineering models.

Includes:

• Linear / nonlinear / integer optimization solvers
• MPC and trajectory optimization components
• Routing, scheduling, and allocation algorithms
• Stochastic and robust optimization frameworks

Use Cases:

• Autonomous path planning
• Resource allocation
• Decision optimization
• Multi-objective tradeoff analysis

6. Neural-Symbolic Cognitive Agent Prototype

Domain: Cognitive Modeling, Hybrid AI, Decision Intelligence
Status: Research Prototype

A hybrid agent that integrates:

• Symbolic reasoning
• Neural language models
• Cognitive decision frameworks
• Narrative and sentiment analysis

Purpose:

• Understand complex human decision patterns
• Support strategic reasoning under uncertainty
• Bridge human-machine collaboration in defense or financial applications

7. Scientific Computing & System Dynamics Models

Domain: Simulation, Differential Equations, Complex Systems
Status: Active R&D

Internal models exploring:

• ODE/PDE dynamics
• Parameter estimation and system identification
• Monte Carlo and stochastic simulation
• Stability analysis and bifurcation studies
• Multi-agent and game-theoretic dynamics

These models support robotics, sensing, finance, and scientific applications.

How We Build Projects

Every project at Neuroligence follows a research-driven process:

1. Mathematical framing of the problem
2. Simulation-first prototypes
3. Data-driven and model-driven integration
4. Iterative refinement using evaluation benchmarks
5. Transparent reporting and scientific documentation

This ensures reliability, clarity, and real-world usefulness.