Non-Euclidean Deep Learning Framework

Overview

A monolithic, high-performance computing (HPC) pipeline designed to resolve the three-dimensional bottlenecks of enterprise-grade AI: Compute Costs, Stealthy Threat Vectors, and Data Saturation.

By re-engineering deep neural networks from Euclidean flat projections into non-Euclidean curved manifolds, this framework achieves superior pattern separation and threat isolation.

Technical Architecture

• Dynamic Kernel Projection: Utilizes Hilbert space mapping to un-warp topological anomalies via vectorized pairwise distances.
• Invariant Parameter Trajectory: Constrains latent transformations to the compact Lie Group $SO(n)$ via continuous skew-symmetric tangent matrices, neutralizing gradient explosions.
• Kinetic Damping Optimization: Implements custom GPU-bound velocity buffers to smooth backpropagation traces, reducing hardware training overhead.

Production Utility

• Autonomous Security Auditing: Extracts and isolates Zero-Day exploits and APT anomalies from standard network traffic without signature-based bottlenecks.
• HPC Data Archiving (LedgerCompressor): Achieves 70% to 90% space reduction by mapping unstructured logs into compact PyTorch LongTensors on the GPU.

Project Repository

https://github.com/Nossari/Non-Euclidean-Deep-Learning-Framework/tree/main

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Principal Architect: Eng. Ryan Nssr Naji Nusari (ريان نصر ناجي نصاري) 2. Hidden Layer (Geodesic Trajectory): The features are processed by the RotationalLinearLayer, which restricts continuous parameter modifications to the compact Lie Group $SO(n)$ using clean matrix exponentials ($\exp(\mathbf{\Omega})$), keeping matrix Frobenius norms mathematically invariant. 3. Optimization Engine (Kinetic Damping): Stateful momentum velocity buffers are maintained directly inside GPU device memory, applying dynamic kinetic damping forces to computed first-order gradients to eliminate parameter trajectory oscillations.

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⚡ Hardware & Execution Metrics

• Stateful Buffer Registries: Velocity profiles are bound as model tensor buffers, eliminating CPU-GPU memory context switching during high-rate updates.
• Vectorized Pairwise Geometry: Relies on the high-speed linear matrix expansion property ($A^2 + B^2 - 2AB^T$) to enable complete execution coalescing across NVIDIA streaming multiprocessors.

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📜 License

This integrated ecosystem is open-sourced under the strict terms of the MIT License.