Constructed a Vanilla Recurrent Neural Network using only linear algebra primitives. Addressed the vanishing gradient problem through explicit eigenvalue analysis of weight matrices during Backpropagation Through Time (BPTT).

First Principles: Derived Jacobian matrices for hidden state vectors to analyze gradient flow across temporal sequences.

Architected a Multi-Layer Perceptron (MLP) from scratch to classify MNIST data. Manually derived chain rules for ReLU and SoftMax activation functions.

First Principles: Manual implementation of Stochastic Gradient Descent (SGD) without automatic differentiation libraries.

Engineered a stochastic predictive model to decompose financial data into trend, seasonality, and holographic noise components.

Methodology: Additive regression models to identify non-linear growth saturations and variance shifts in time-series data.

Architected a multi-agent quantitative trading terminal using DeepSeek R1 and V3. The system executes core-satellite portfolio construction by synthesizing technical indicators, macro-regime detection (VIX & yield curves), and Kelly criterion sizing.

Methodology: Separated alpha generation from risk management to enforce checks and balances. Includes a live backend that serves dynamic Monte Carlo simulations and strictly controls drawdown probabilities.

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