GeoLatent

Geometry-aware, model-intelligent 3-D visualisations for machine learning workflows.

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Overview

Most visualisation libraries for machine learning treat the problem superficially: scatter a few 2-D projections, maybe a confusion matrix, call it done. GeoLatent takes a fundamentally different approach.

It operates as a semantic abstraction layer that understands the intrinsic geometry of models and embeddings. Rather than plotting model outputs directly, it constructs the analytical structures that govern model behaviour — decision manifolds, probability isosurfaces, Mahalanobis confidence regions — and renders them as first-class geometric objects in interactive 3-D scenes.

What makes it different

Capability	Typical wrappers	geolatent
Projection method	Fixed 2-D PCA	PCA · t-SNE · UMAP, auto-selected
Decision surfaces	Axis-aligned slices	True 3-D isosurfaces via PCA inverse-transform
Confidence regions	None	Nested probability shells + Mahalanobis ellipsoids
Model interface	Specific models only	Any predict / predict_proba estimator
Theme	Matplotlib defaults	Dark-scientific, research-publication quality
Notebook support	Requires extra setup	Native Colab/Jupyter inline rendering

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Installation

pip install geolatent

For UMAP support:

pip install "geolatent[umap]"

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Quick Start

Decision geometry of a kernel SVM

from sklearn.svm import SVC
from sklearn.datasets import make_classification
from geolatent import visualize_decision_geometry

X, y = make_classification(
    n_samples=400, n_features=20, n_classes=3,
    n_informative=10, random_state=42
)
model = SVC(kernel="rbf", C=5.0, probability=True).fit(X, y)

fig = visualize_decision_geometry(
    model, X, y,
    title="RBF-SVM — 3-class Decision Geometry",
    show_confidence=True,
    show_ellipsoids=True,
)
fig.show()

Latent-space geometry of high-dimensional embeddings

import numpy as np
from geolatent import inspect_latent_space

# 512 samples of 768-dimensional embeddings (e.g., BERT sentence vectors)
rng = np.random.default_rng(0)
embeddings = np.vstack([
    rng.normal(loc=mu, scale=1.2, size=(128, 768))
    for mu in [0, 4, 8, 12]
])
labels = np.repeat([0, 1, 2, 3], 128)

fig = inspect_latent_space(
    embeddings, labels,
    projection_method="pca",
    title="768-D Embeddings — 4 Topic Clusters",
    class_names={0: "Science", 1: "Politics", 2: "Arts", 3: "Sports"},
)
fig.show()

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Architecture

geolatent separates three orthogonal concerns into dedicated sub-packages:

geolatent/
├── config/
│   └── themes.py          ← ColorPalette · RenderConfig · ProjectionConfig
│                            VisualizationConfig · DARK_SCIENTIFIC
├── core/
│   ├── projector.py       ← DimensionalityProjector (PCA / t-SNE / UMAP)
│   ├── mesh_builder.py    ← MeshBuilder · PredictionMesh
│   └── geometry.py        ← GeometryUtils (ellipsoids · centroids · hulls)
├── rendering/
│   ├── scene.py           ← Scene3D (Plotly figure manager)
│   ├── surfaces.py        ← DecisionSurfaceRenderer (isosurfaces · volumes)
│   └── overlays.py        ← DataOverlay (scatter · centroids · ellipsoids)
└── api/
    ├── decision.py        ← visualize_decision_geometry()
    └── latent.py          ← inspect_latent_space()

The decision-surface pipeline

The key insight that separates geolatent from shallow wrappers is the inverse-transform prediction mesh. For a model trained on n_features- dimensional data:

1. Fit PCA on X → extract top 3 principal components.
2. Construct a regular 3-D grid in the PC space (e.g., 30³ = 27 000 points).
3. Apply PCA.inverse_transform → map each grid point back to the original n_features-dimensional feature space.
4. Query model.predict_proba on the reconstructed feature vectors.
5. Render per-class probability isosurfaces at the P = 0.50 decision boundary, plus optional confidence shells at P = 0.70 and P = 0.85.

This produces genuine decision boundaries that reflect the model's actual behaviour in the subspace spanned by the top 3 principal directions — not an approximation based on a 2-D axis-aligned slice.

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Configuration

All styling and algorithmic parameters are controlled through VisualizationConfig, a nested dataclass that can be customised via fluent helpers:

from geolatent import VisualizationConfig, DARK_SCIENTIFIC

cfg = (
    DARK_SCIENTIFIC
    .with_method("tsne")                  # t-SNE projection
    .with_title("GBM Latent Geometry")    # figure title
    .with_resolution(1200, 800)           # canvas size
    .with_opacity(surface=0.4, scatter=0.9)
)

fig = inspect_latent_space(embeddings, labels, config=cfg)

Colour palette

The default DARK_SCIENTIFIC theme uses a GitHub Dark–inspired palette with eight class colours chosen for accessibility and contrast on dark backgrounds:

#58a6ff  #3fb950  #f78166  #d2a8ff
#ffa657  #79c0ff  #56d364  #ff7b72

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Advanced usage

Custom pipeline (lower-level API)

For research workflows that need fine-grained control:

from geolatent.core.projector import DimensionalityProjector
from geolatent.core.mesh_builder import MeshBuilder
from geolatent.rendering.scene import Scene3D
from geolatent.rendering.surfaces import DecisionSurfaceRenderer
from geolatent.rendering.overlays import DataOverlay
from geolatent import DARK_SCIENTIFIC

cfg = DARK_SCIENTIFIC.copy()
cfg.projection.method = "pca"

# 1. Project
projector = DimensionalityProjector(cfg.projection)
result = projector.fit_transform(X)

# 2. Build mesh
mesh = MeshBuilder(resolution=35).build_prediction_mesh(clf, projector, result.coordinates)

# 3. Compose scene
scene = Scene3D(cfg)
scene.set_axis_labels(result.axis_labels)
scene.add_traces(DecisionSurfaceRenderer(cfg).render(mesh))
scene.add_traces(DataOverlay(cfg).render_scatter(result.coordinates, y))
scene.add_trace(DataOverlay(cfg).render_centroids(result.coordinates, y))
scene.add_variance_annotation(result.explained_variance_ratio)
fig = scene.render()
fig.show()

Optimisation trajectories

from geolatent.rendering.overlays import DataOverlay

overlay = DataOverlay(cfg)
# waypoints: projected coordinates of gradient-descent iterates
trajectory_traces = overlay.render_trajectory(waypoints, name="SGD path")
scene.add_traces(trajectory_traces)

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Design principles

Semantic over syntactic. The API speaks in ML concepts — models, embeddings, decision boundaries, confidence regions — not in Plotly trace types.

Modularity over monolithism. Projection, mesh construction, geometry, and rendering are four independent modules with clearly defined interfaces. Each can be replaced, extended, or tested in isolation.

Correctness over speed. The decision-surface computation is geometrically exact within the PCA subspace; we do not approximate boundaries by sampling random projections or evaluating only on 2-D slices.

Research-grade aesthetics. The dark-scientific theme is designed to produce figures suitable for ML conference supplementary materials without any post-processing.

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Requirements

Dependency	Version
Python	≥ 3.9
NumPy	≥ 1.23
SciPy	≥ 1.9
scikit-learn	≥ 1.1
Plotly	≥ 5.13
umap-learn (optional)	≥ 0.5.3

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Citation

If geolatent contributes to published research, please acknowledge it:

@software{geolatent2026,
  title  = {GeoLatent: Geometry-aware 3-D Visualisations for Machine Learning},
  year   = {2026},
  url    = {https://pypi.org/project/geolatent/},
}

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License

MIT — see LICENSE.