persiscope 0.1.0b5

Topological representations and pairwise comparison of embeddings (persistence + periscope)

persiscope

Topological representations and pairwise comparison of embeddings. The name is persistence + periscope.

persiscope turns embedded data into persistence-based summaries (persistence landscapes and silhouettes) and scores how topologically similar two embedding sets are. It implements the methodology developed in Ashoff (2026); see the Reference section below. Everything runs in memory through a sklearn-style API, with no configuration files and no hidden disk writes.

Install

pip install persiscope                 # core
pip install "persiscope[viz]"          # + matplotlib / plotly plotting
pip install "persiscope[metrics]"      # + DTW and Fréchet curve metrics
pip install "persiscope[frame]"        # + pandas for .to_frame()
pip install "persiscope[all]"          # everything above
pip install "persiscope[reproduce]"    # everything above + jupyter, for the dissertation notebooks

Requires Python ≥ 3.10. Core dependencies: numpy, scipy, networkx, gudhi, tqdm.

Quickstart

compare is the main entry point. It takes a list of embedding arrays and returns an all-pairs comparison:

import numpy as np
import persiscope as ps

embeddings = [emb_gpt2, emb_bert, emb_t5]   # each (n_i, d)

result = ps.compare(
    embeddings,
    method="energy",        # "energy" or a curve metric ("euclidean", "js", ...)
    summary="landscape",    # "landscape" or "silhouette"
    homology_dim=0,
    theta=-3 * np.pi / 8,   # diagram rotation, the method's nonstandard knob (this is the default)
    n_bootstrap=100,
    run_pvalue=False,
    labels=["gpt2", "bert", "t5"],
    random_state=0,
)

result.matrix               # (3, 3) symmetric dissimilarity matrix
result.to_frame()           # labeled pandas DataFrame (needs [frame] extra)
result.representations      # the fitted Representations, reused across all pairs

The pipeline, step by step

compare() chains three stages that you can also drive directly.

1. Embeddings to topological representation

Build a distance graph, compute Vietoris–Rips persistence, and summarize it as landscapes and silhouettes. A subsampling bootstrap makes the result stable and provides confidence bands.

tf = ps.TopologicalTransformer(
    homology_dim=0,
    diagram_transform=ps.RotateScale(theta=-3 * np.pi / 8, alpha=np.sqrt(2) / 2),
    n_bootstrap=100,
    silhouette_power=0.5,
    tenting_resolution=1000,
    random_state=0,
)
rep = tf.fit_transform(emb_gpt2)             # or distance_matrix=..., or graph=...

rep.mean_landscape          # (resolution, 2) bootstrap-mean curve
rep.bootstrapped_landscapes # (n_bootstrap, resolution, 2)
rep.landscape_band          # {"lower_bound", "upper_bound", "half_bound"}
rep.persistence_diagram     # (n, 2), includes the essential class

2. Pairwise scoring

Compare two representations, with an optional permutation p-value.

scorer = ps.Scorer(method="energy", summary="landscape", run_pvalue=True, n_permutations=100)
res = scorer.score(rep_a, rep_b)             # ScoreResult(score, pvalue, perm_scores)

matrix = ps.score_matrix([rep_a, rep_b, rep_c], method="energy")

3. Visualization (optional [viz] extra)

Each helper returns a figure object; you decide whether to show or save it.

The main figure is the baseline report. It compares every model to a reference: overlaid mean landscapes and silhouettes with 95% confidence bands, the energy statistic against the baseline for each summary type with permutation-significance stars, and Wasserstein/JS distance strips annotated the same way.

fig = ps.viz.plot_baseline_report(
    result.representations,
    baseline=0,                          # index of the reference model
    curve_metrics=("wasserstein", "js"),
    n_permutations=200,
)

Individual plotters cover the pieces:

ps.viz.plot_persistence_diagram(rep)         # matplotlib Figure
ps.viz.plot_landscape(rep)                   # matplotlib Figure, with band shading
ps.viz.plot_score_heatmap(result)            # plotly Figure
ps.viz.plot_comparison_report(result.representations)   # all-pairs report figure

Diagram transforms

The rotation applied to a persistence diagram before summaries are built is the nonstandard part of the method, so it is exposed directly alongside homology_dim:

rep = ps.TopologicalTransformer(homology_dim=0, theta=-3 * np.pi / 8).fit_transform(emb)
res = ps.compare(embeddings, theta=-np.pi / 4)   # the conventional rotation, for contrast

If you need more than an angle, pass a full transform object instead: ps.RotateScale, ps.H0Rotate, ps.Identity, or your own implementation of the small DiagramTransform protocol. The rest of the pipeline does not care which one you use.

from persiscope import transforms

tf = ps.TopologicalTransformer(diagram_transform=transforms.H0Rotate(angle=3 * np.pi / 8))

Scoring methods

method	family	compares
energy	distribution	the two bootstrap sets of curves (energy distance)
euclidean, cosine, spectral, chi_squared, kl, js, wasserstein	curve	the two mean curves
dtw, frechet	curve	the two mean curves (needs [metrics] extra)

Larger scores mean more different. The permutation test is one-sided.

Development

pip install -e ".[viz,metrics,frame,dev]"
pytest

During extraction, persiscope's landscapes and silhouettes were verified to match the dissertation's original implementation to numerical tolerance.

Reference

The methodology implemented here (persistence landscapes and silhouettes over embedding graphs, the rotated-diagram construction, and pairwise scoring with permutation tests) is developed in:

Ashoff, T. (2026). Persistent Convolution: A Topological Approach to Formal AI Alignment Testing (PhD dissertation, University of Virginia). DOI: 10.18130/8k9j-9k42

If you use persiscope in academic work, please cite the dissertation (see CITATION.cff).

Reproducing the dissertation results

Notebooks reproducing the dissertation's results live in examples/reproduction/ in this repository. Extras install dependencies, not files, so clone the repository to get the notebooks:

git clone https://github.com/tylerashoff/persiscope.git
cd persiscope
pip install -e ".[reproduce]"
jupyter notebook examples/reproduction/

Reproduced figures are statistically identical to the published ones but not pixel-identical: the bootstrap uses different random draws than the original pipeline.

License

MIT, see LICENSE.