Polimelo Lab.
We materialize artificial intelligence, mathematics, and computer science theories through live in-browser simulations, code, and academic notes.
Digital Laboratory (Sandbox)
Interactive experiment modules running directly in your browser using WebAssembly, Web Workers, and HTML5 Canvas.
WebAssembly Python Runtime Verification (Hello World)
A core architectural test validating client-side execution of Python 3.11 environments within the browser kernel via Pyodide and WebAssembly. Serves as the foundational bridge for pipeline communication between TypeScript UI threads and decoupled low-level backends.
Matrix Multiplication & Vector Space Visualizer
An interactive workspace for visualizing matrix multiplication step-by-step. Users can input values for matrices A and B, compute C = A × B, and trace the dot product calculation for individual cells to build mechanical intuition.
Interactive Linear Regression & Gradient Fitting
A client-side regression simulator. Users plot custom coordinates on a canvas grid, and the model fits a line of best fit y = mx + b using least-squares, plotting the regression line and detailing slope, intercept, and R-squared parameters.
Academic Outline & Courses
Study notes deriving the mathematical foundations of AI and data structures from first principles.
Linear Algebra & Sparse Systems
Foundational mathematical structures for efficient computational pipelines. Explores vector spaces, matrices, and sparse representation models.
Sparse Matrices & CSR Data Representation
Compressed Sparse Row (CSR) representation mapping, index pointers, storage efficiency calculations, and sparse matrix-vector multiplication (SpMV).
Neural Networks Deep Dive
Theoretical derivations and concrete implementations of deep learning primitives from scratch.
Backpropagation from First Principles
Mathematical derivation of error delta terms, output layer gradients, hidden layer backpropagation, and weight/bias updates using the chain rule.
Computational Lab Infrastructure & Methodology
Client-Side Python & Pyodide Architecture
Traditionally, executing custom Python scripts requires hosting virtual environments or containerized microservices (Docker) on remote web servers, inducing significant cloud upkeep fees and network latency. Polimelo Lab utilizes the Pyodide runtime to execute Python 3.11 directly inside the client's browser thread.
By compiling the CPython core using Emscripten to WebAssembly (WASM) binaries, Pyodide loads core scientific libraries like NumPy and Pandas as WASM blobs. Scripts compile and evaluate directly on local hardware, maximizing user data privacy and reducing latency to millisecond thresholds.
Linear Algebra Visualizations & Regression Models
The matrix multiplier and vector sandbox translate linear algebra equations into interactive geometries. The cellular dot product animation renders coordinate system mappings (such as scaling, shearing, and rotation) using hardware-accelerated GPU graphics buffers at a fluid 60 frames per second.
The linear regression simulator models predictive curve fitting. Using plotted data coordinates, the application fits a line of best fit y = mx + b using the Ordinary Least Squares (OLS) mathematical model. The slope (m) and intercept (b) are calculated asynchronously using partial derivatives to minimize squared residual sums.
Polimelo Lab is an open-source project built on the belief that knowledge grows when shared. Our goal is to visualize the notes and experiments we make during our learning journey, while providing a modular portfolio ecosystem where other developers can contribute their own interactive experiments in the future.