Hi! I'm Mustehsan.

Building an automatic-differentiation engine and a neural network from nothing but Python’s arithmetic — no PyTorch, no NumPy, no libraries — and the mathematics that makes it work.

A note before you start

I wanted to understand what training a model means at the level of individual numbers, so I built the whole thing from scratch: a tiny automatic-differentiation engine, a neuron, a network of neurons, and the loop that makes them learn — using only Python’s built-in arithmetic, no numerical libraries whatsoever. This post is the account I wish I had been handed. It is written to be self-contained and mathematically explicit: by the end you should be able to derive backpropagation yourself, not merely recognise it.

On desire, the limits of self-knowledge, and what actually makes a person worth something

A note from me before you start

A brief word on scope and intent. This blogpost draws on ideas and evidences from theology, religious texts, and the work of various scholars, and uses them as the raw material for a framework of my own. I am not a scholar or an expert in any of these fields: the sources belong to the people I cite, but the way I have woven them together — and the conclusions I draw from them — are mine, and mine to be wrong about. Read what follows as one person’s attempt to digest these questions, not as a settled account of them.

Abstract

The generative-AI boom of 2021–2025 drove technology stocks to unprecedented highs and raised pressing questions about how extreme downside risk in these high-growth names stacks up against traditional large-value equities. In this thesis, we quantify and compare the one-day 99% Value-at-Risk (VaR) of an equally weighted portfolio of ten AI-growth stocks versus ten large-value stocks, using both nonparametric Historical Simulation (HS) and symmetric GARCH(1,1) models with Gaussian and Student-t innovations. We then subject each VaR estimate to regulatory-style back-tests: Kupiec’s Unconditional Coverage and Christoffersen’s Conditional Coverage, to assess their adequacy for capital calculation. Empirically, the AI portfolio exhibits a mean one-day 99% VaR of 4.997%, more than double the 2.084% observed for the Value portfolio. Violation rates under HS, Student-t GARCH, and Gaussian GARCH are 1.49%, 1.60%, and 1.95% for AI versus 1.03%, 1.26%, and 1.38% for Value. Only HS and Student-t GARCH pass all back-tests. These findings underscore the critical importance of fat-tailed or nonparametric methods when measuring risk for high-growth equity portfolios, with direct implications for setting regulatory capital.

Abstract

This blog post addresses the design of a sustainable logistic network for GreenForwarder—a multinational freight company—by balancing profitability, environmental emissions, and regional reach. A multi-objective network optimization problem is formulated over a graph that represents cities and potential transport connections. Using a modified Minimum Spanning Tree (MST) algorithm that incorporates capacity constraints and investment costs, the approach has been inspired by the Steiner Tree Problem and evaluates candidate edges dynamically by considering cost, emission factors, and a bonus for expanding regional reach. POC and LIVE differ significantly in their approaches, particularly in their starting points. POC begins by simplifying the “full” graph and focusing on optimizing its objective function, whereas LIVE prioritizes satisfying its unique constraint from the outset. For the MVP, two methods are employed to determine which approach would yield a better outcome, as the significance of profit’s contribution was unknown during the project’s initial stages. Detailed experimental results, analysis, and comparisons are provided in later sections.

Abstract

In this blog post, I rigorously analyze the forecasting performance of commodity price inflation models. I compare a conventional univariate autoregressive (AR) model with two mixed frequency models—the unrestricted MiDAS model and the HAR-MiDAS model. By integrating daily stock returns with monthly inflation data, I aim to capture market dynamics that standard techniques overlook. I evaluate model performance using robust statistical tests, RMSE comparisons, and the Diebold-Mariano test, and I explore the benefits of a rolling forecast origin. Throughout the analysis, I include detailed mathematical formulations, estimation results, tables, and graphical visualizations.