DeepSpatial Density Explorer

An interactive comparison between statistical estimators and neural density regressors.
Click inside the canvas to drop points. The environment will instantly train both models via a PyTorch microservice and synchronize the updates across all user sessions in real time.

Canvas | Click to Add Points

Kernel Density Evaluation

Neural Density Regressor

Methodological Breakdown

Data Persistence Pipeline

Every coordinate transaction generated from the Canvas viewport normalizes raw pixels into mathematical boundaries ranging between $[0, 1]$. These coordinate values are instantly transmitted via JSON payload to a lightweight SQLite database managed by an asynchronous FastAPI wrapper. When a new agent joins, the system pulls the full historical telemetry array to guarantee identical visualization states.

Traditional Kernel Density Estimation

The center panel visualizes a standard Scikit-Learn Gaussian Kernel Density model. It acts as a non-parametric baseline by placing a continuous normal probability curve over each individual point token. This statistical method calculates density directly without explicit structural optimization, making it responsive but prone to strict hyperparameter boundaries.

Deep Spatial Normalization Network

The rightmost graph visualizes a custom Deep Multi-Layer Perceptron optimized in PyTorch. Unlike standard models, it converts coordinate boundaries directly into continuous spatial density scores. To prevent overfitting to sharp points, it adds smooth Gaussian jitter to the target batch arrays, while a numeric LogSumExp partition layer maps the space into a valid probability distribution.