What it is for
Hyperstructura makes high-dimensional representations inspectable. A 3-D projection is not the latent space itself; it is an instrument for finding structure worth investigating.
Research focus
Nuisance dimensions provide a concrete example of representational structure that can be visually identified and then tested. Constrained principal component analysis can preserve selected geometric relationships while allowing the remaining projection axes to capture useful variance.
Representation then connects directly to decision architecture: linear, symbolic and deeper neural head-ends expose different trade-offs in explainability, uncertainty, performance and reversibility.
Controls
- Rotate: drag the point cloud.
- Zoom: use the mouse wheel or trackpad.
- Move the focus: use the arrow keys. Hold Shift to move three steps at once.
- Inspect: hover over a point to see its embedded text and metadata.
- Compare: click one point to set the anchor and another to set the comparison. Clicking a third point replaces the comparison; Escape clears both.
- Save a view: use the copy and paste icons beside the coordinates to export or restore the high-dimensional focus, frame and zoom.
Principal Component Analysis
Principal Component Analysis finds orthogonal directions that capture as much variance in the embeddings as possible. Hyperstructura displays three such directions as the x, y and z axes, but the resulting view remains only a projection of the full embedding space.
Constrained PCA
The x, y and z buttons preserve the other two displayed axes and replace the chosen axis with the strongest remaining variance direction orthogonal to them.
After selecting two points, separate makes their difference maximally visible in the screen plane, then uses residual PCA for the remaining directions. join removes their difference direction from the projection, then applies PCA to what remains. Neither operation changes the source embeddings.
The pair constraint is not retained by later PCA operations, although its geometry can remain visible through axes that those operations preserve.