Educational
Fourier Neural Operators (FNOs)
A step by step guide through the architecture of Fourier Neural Operators, their applications, and how they efficiently process global information through the Fourier transform.
Blog Posts
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14 posts
Educational
The Fourier Transform, explained for Neural Operators
A semi-deep dive into the Fourier transform and its applications in signal processing and neural networks.
Educational
Neural Operators and DeepONet
An introduction to neural operators, DeepONet, and how they can be used to learn mappings between function spaces.
Educational
The CFL Condition of the Wave Equation
A deep dive into the Von Neumann stability analysis of the wave equation and its connection to the CFL condition.
Educational
Von Neumann Stability Analysis
A deep dive into the von Neumann stability analysis, its connection to the CFL condition, and how it determines the stability of numerical schemes.
Educational
Neural Networks as Wave Equation Approximators
A deep dive into the wave equation, its reformulation for neural network approximation, and the challenges of learning dynamics with finite speed.
Educational
Deriving the Wave Equation
A step-by-step derivation of the wave equation from first principles, exploring how tension and mass density lead to wave propagation with finite speed.
Educational
Partial Differential Equations and Neural PDEs
From the mathematics of change to neural networks that learn dynamics — understanding PDEs, numerical solvers, and how modern generative models are PDEs in disguise.
Educational
Ordinary Differential Equations and Neural ODEs
From the mathematics of change to neural networks that learn dynamics — understanding ODEs, numerical solvers, and how modern generative models are ODEs in disguise.
Educational
The Mathematics Behind Flow and Diffusion Models
A deep dive into the mathematical foundations of flow-based models and diffusion processes in deep learning.
Research Paper
Context-Parametric Inversion
A controlled faithfulness study on how QASPER fine-tuning affects context reliance across a RAG pipeline for NLP research papers.
Project Recap
Dual-MIDI Transformer
A recap of my work on the Dual-Midi Transformer project, which aims to generate music from MIDI data.
Literature Review
An Introduction to Artificial Music Generation
A comprehensive overview of the current state of music generation techniques
Educational
Introduction to Gradient Descent and Backpropagation
An introduction into Neural Networks, Gradient Descent and Backpropagation.