shesha-geometry 0.2.0

Self-consistency metrics for representational stability analysis

Shesha

Self-consistency metrics for representational stability analysis.

Shesha measures the geometric stability of high-dimensional representations by quantifying the self-consistency of their pairwise distance structure (RDMs) under controlled internal perturbations.

Installation

pip install shesha-geometry

Quick Start

import numpy as np
import shesha

# Your embeddings: (n_samples, n_features)
X = np.random.randn(500, 768)

# Feature-split stability (unsupervised)
stability = shesha.feature_split(X, n_splits=30, seed=320)
print(f"Feature-split stability: {stability:.3f}")

With labels:

y = np.random.randint(0, 10, 500)
alignment = shesha.supervised_alignment(X, y)
print(f"Supervised alignment: {alignment:.3f}")

Measuring drift between representations:

X_before = np.random.randn(100, 256)
X_after = X_before + np.random.randn(100, 256) * 0.3  # Add noise

# Compare before/after fine-tuning
similarity = shesha.rdm_similarity(X_before, X_after)
drift = shesha.rdm_drift(X_before, X_after)
print(f"RDM similarity: {similarity:.3f}, drift: {drift:.3f}")

Variants

Unsupervised (no labels required)

feature_split(X, n_splits=30, metric='cosine', seed=None)

Correlates RDMs from random feature partitions. Use for internal consistency and drift detection.

sample_split(X, n_splits=30, subsample_fraction=0.4, seed=None)

Correlates RDMs from bootstrap samples. Use for robustness to sampling.

anchor_stability(X, n_splits=30, n_anchors=100, seed=None)

Distance profile consistency from fixed anchors. Use for large-scale stability.

Supervised (labels required)

variance_ratio(X, y)

Between-class / total variance. Use for quick separability check.

supervised_alignment(X, y, metric='correlation', seed=None)

Correlation with ideal label RDM. Use for task alignment.

class_separation_ratio(X, y, n_bootstrap=50, subsample_frac=0.5)

Between-class to within-class distance ratio.

lda_stability(X, y, n_bootstrap=50, subsample_frac=0.5)

Consistency of discriminant direction under resampling.

Drift Metrics (comparing two representations)

rdm_similarity(X, Y, method='spearman', metric='cosine')

RDM correlation between two representations. Use for comparing models or tracking changes.

rdm_drift(X, Y, method='spearman', metric='cosine')

Representational drift (1 - similarity). Use for quantifying how much geometry has changed.

Similarity Metrics (shesha.sim)

cka(X, Y, debiased=False)

Centered Kernel Alignment - the most popular similarity metric for neural representations. Invariant to orthogonal transformations.

import shesha.sim as sim

# Compare two model layers
similarity = sim.cka(model_layer_12, model_layer_18)

procrustes_similarity(X, Y, center=True, scale=True)

Orthogonal Procrustes alignment. More sensitive to outliers than CKA (6x more false alarms in stable regimes).

rdm_similarity(X, Y, metric='cosine', method='spearman')

RSA-style RDM correlation. Rank-based and robust to transformations.

Examples

Comparing model stability

import numpy as np
import shesha

# Example embeddings from two different models
embeddings_a = np.random.randn(500, 768)  # Model A embeddings
embeddings_b = np.random.randn(500, 768)  # Model B embeddings

models = {'model_a': embeddings_a, 'model_b': embeddings_b}

for name, X in models.items():
    fs = shesha.feature_split(X, seed=320)
    print(f"{name}: {fs:.3f}")

Monitoring fine-tuning drift

import shesha

X_initial = model.encode(data)

for epoch in range(10):
    train_one_epoch(model)
    X_current = model.encode(data)
    
    # Internal stability
    stability = shesha.feature_split(X_current, seed=320)
    
    # Drift from initial
    drift = shesha.rdm_drift(X_initial, X_current)
    
    print(f"Epoch {epoch}: stability={stability:.3f}, drift={drift:.3f}")

Comparing two models

import shesha

X_model1 = model1.encode(data)
X_model2 = model2.encode(data)

# How similar are their geometric structures?
similarity = shesha.rdm_similarity(X_model1, X_model2)
print(f"Model similarity: {similarity:.3f}")

Analyzing single-cell perturbations

Measure the geometric consistency of CRISPR/drug screens directly from AnnData objects:

import numpy as np
from shesha.bio import compute_stability, compute_magnitude
from anndata import AnnData


# 1. Setup mock single-cell data (1000 cells, 50 PCA features)
n_cells = 1000
n_genes = 2000  # Original feature space (genes)
n_pcs = 50

# Create a mock AnnData object
# Note: Shesha works best on PCA coordinates (latent space), not raw counts
adata = AnnData(X=np.random.randn(n_cells, n_genes))  # Raw counts (unused)
adata.obsm['X_pca'] = np.random.randn(n_cells, n_pcs)  # PCA embeddings
adata.obs['guide_id'] = ['NT'] * 800 + ['KLF1'] * 200  # Metadata


# Create a proxy for PCA coordinates (Recommended for robust geometry)
adata_pca = AnnData(X=adata.obsm['X_pca'], obs=adata.obs)


# Compute Stability (Consistency of the phenotype)
stability = compute_stability(
    adata_pca, 
    perturbation_key='guide_id', 
    control_label='NT',
    metric='cosine'
)

# Compute Magnitude (Strength of the phenotype)
magnitude = compute_magnitude(
    adata_pca, 
    perturbation_key='guide_id', 
    control_label='NT', 
    metric='euclidean'
)

print(f"KLF1 Stability: {stability['KLF1']:.3f}")  # e.g., 0.85 (High = Consistent)
print(f"KLF1 Magnitude: {magnitude['KLF1']:.3f}")  # e.g., 2.40 (High = Strong)

Tutorials

Explore shesha with these interactive notebooks (each takes < 5 minutes to run):

• LLM Embeddings - Geometric Stability: Analyze embedding stability across layers and models using feature_split.
• Steering Vectors - Consistency Analysis: Compute steering vectors from contrastive pairs and measure their effectiveness and consistency.
• Vision Models - Architecture Comparison: Compare geometric stability and class separability across ResNets, ViTs, and other vision architectures.
• Representational Drift - Perturbation Analysis: Measure drift caused by Gaussian noise injection and LoRA fine-tuning using rdm_drift.
• Training Dynamics - Live Monitoring: Track geometric stability during model training to detect representation collapse or divergence.
• CRISPR (Bio) - Single-Cell Analysis: Use shesha.bio to analyze stability and effect sizes in single-cell CRISPR perturbation experiments.

API Reference

shesha.feature_split(X, n_splits=30, metric='cosine', seed=None, max_samples=1600)

Measures internal geometric consistency by correlating RDMs computed from random, disjoint subsets of feature dimensions.

Parameters:

• X - array of shape (n_samples, n_features)
• n_splits - number of random partitions to average
• metric - 'cosine' or 'correlation'
• seed - random seed for reproducibility
• max_samples - subsample if exceeded

Returns: float in [-1, 1], higher = more stable

shesha.sample_split(X, n_splits=30, subsample_fraction=0.4, metric='cosine', seed=None, max_samples=1500)

Measures robustness to input variation via bootstrap resampling.

Parameters:

• X - array of shape (n_samples, n_features)
• n_splits - number of bootstrap iterations
• subsample_fraction - fraction of samples per bootstrap
• metric - 'cosine' or 'correlation'
• seed - random seed for reproducibility
• max_samples - subsample if exceeded

Returns: float in [-1, 1], higher = more stable

shesha.anchor_stability(X, n_splits=30, n_anchors=100, n_per_split=200, metric='cosine', rank_normalize=True, seed=None, max_samples=1500)

Measures stability of distance profiles from fixed anchor points.

Parameters:

• X - array of shape (n_samples, n_features)
• n_splits - number of random splits
• n_anchors - number of fixed anchor points
• n_per_split - samples per split
• metric - 'cosine' or 'euclidean'
• rank_normalize - rank-normalize distances within each anchor
• seed - random seed for reproducibility
• max_samples - subsample if exceeded

Returns: float in [-1, 1], higher = more stable

shesha.variance_ratio(X, y)

Ratio of between-class to total variance.

Parameters:

• X - array of shape (n_samples, n_features)
• y - array of shape (n_samples,) with class labels

Returns: float in [0, 1], higher = better class separation

shesha.supervised_alignment(X, y, metric='correlation', seed=None, max_samples=300)

Spearman correlation between model RDM and ideal label-based RDM.

Parameters:

• X - array of shape (n_samples, n_features)
• y - array of shape (n_samples,) with class labels
• metric - 'cosine' or 'correlation'
• seed - random seed for reproducibility
• max_samples - subsample if exceeded (RDM is O(n^2))

Returns: float in [-1, 1], higher = better task alignment

shesha.class_separation_ratio(X, y, n_bootstrap=50, subsample_frac=0.5, metric='euclidean', seed=None)

Ratio of between-class to within-class distances with bootstrap subsampling.

Parameters:

• X - array of shape (n_samples, n_features)
• y - array of shape (n_samples,) with class labels
• n_bootstrap - number of bootstrap iterations
• subsample_frac - fraction of samples per bootstrap
• metric - 'cosine' or 'euclidean'

Returns: float > 0, higher = better class separation. Typically in [0.5, 5.0].

shesha.lda_stability(X, y, n_bootstrap=50, subsample_frac=0.5, seed=None)

Consistency of LDA discriminant direction under resampling. Binary classification only.

Parameters:

• X - array of shape (n_samples, n_features)
• y - array of shape (n_samples,) with binary class labels (exactly 2 classes)
• n_bootstrap - number of bootstrap iterations
• subsample_frac - fraction of samples per bootstrap

Returns: float in [0, 1], higher = more stable discriminant. Predicts steerability (ρ=0.89-0.96).

shesha.rdm_similarity(X, Y, method='spearman', metric='cosine')

Computes RDM correlation between two representations. Useful for comparing models, tracking drift during training, or measuring the effect of interventions.

Parameters:

• X - array of shape (n_samples, n_features_x), first representation
• Y - array of shape (n_samples, n_features_y), second representation (same n_samples)
• method - 'spearman' (rank-based, default) or 'pearson' (linear)
• metric - 'cosine', 'correlation', or 'euclidean'

Returns: float in [-1, 1], higher = more similar geometric structure

shesha.rdm_drift(X, Y, method='spearman', metric='cosine')

Computes representational drift as 1 - rdm_similarity. Useful for quantifying how much a representation has changed.

Parameters:

• X - array of shape (n_samples, n_features_x), baseline representation
• Y - array of shape (n_samples, n_features_y), comparison representation
• method - 'spearman' (rank-based, default) or 'pearson' (linear)
• metric - 'cosine', 'correlation', or 'euclidean'

Returns: float in [0, 2], where 0 = identical, 1 = uncorrelated, 2 = inverted

Biological Perturbation Analysis

The shesha.bio module provides metrics for single-cell perturbation experiments (e.g., Perturb-seq, CRISPR screens).

shesha.bio.perturbation_stability(X_control, X_perturbed, method='standard', metric='cosine', k=50, regularization=1e-6, seed=None, max_samples=1000)

Unified interface for measuring consistency of perturbation effects across samples.

Parameters:

• X_control - array of shape (n_control, n_features), control population
• X_perturbed - array of shape (n_perturbed, n_features), perturbed population
• method - 'standard' (default), 'whitened', or 'knn'
  • 'standard': Global control centroid (fastest)
  • 'whitened': Mahalanobis-scaled for batch effects
  • 'knn': Local k-NN matched controls for heterogeneity
• metric - 'cosine' (default) or 'euclidean' (for standard/knn methods)
• k - number of neighbors (only for method='knn')
• regularization - covariance regularization (only for method='whitened')
• seed - random seed for reproducibility
• max_samples - subsample perturbed population if exceeded

Returns: float in [-1, 1], higher = more consistent perturbation

shesha.bio.perturbation_effect_size(X_control, X_perturbed)

Cohen's d-like effect size measuring magnitude of perturbation shift.

Parameters:

• X_control - array of shape (n_control, n_features)
• X_perturbed - array of shape (n_perturbed, n_features)

Returns: float >= 0, higher = larger perturbation effect

Scanpy / AnnData Integration

For single-cell analysis, Shesha provides high-level wrappers that work directly with AnnData objects.

shesha.bio.compute_stability(adata, perturbation_key, control_label, layer=None, method='standard', **kwargs)

Computes the geometric stability for every perturbation in the dataset. Unified interface supporting multiple methods.

Parameters:

• adata - AnnData object.
• perturbation_key - Column in adata.obs identifying the perturbation (e.g., 'guide_id').
• control_label - The label in that column representing control cells (e.g., 'NT').
• layer - (Optional) Layer to use (e.g., 'pca'). If None, uses .X.
• method - 'standard' (default), 'whitened', or 'knn'.
• **kwargs - Additional arguments: k=50 for knn, regularization=1e-6 for whitened, metric='cosine' for standard/knn.

Returns: Dictionary {perturbation_name: stability_score}.

shesha.bio.compute_magnitude(adata, perturbation_key, control_label, layer=None, metric='euclidean')

Computes the magnitude (effect size) for every perturbation.

Parameters:

• adata - AnnData object.
• metric - 'euclidean' (default, raw distance) or 'cohen' (standardized effect size).

Returns: Dictionary {perturbation_name: magnitude_score}.

Enhanced Perturbation Methods

shesha.bio.perturbation_stability(X_control, X_perturbed, method='standard', ...)

Unified interface with three methods for computing perturbation stability:

• method='standard' - Global control centroid (default, fastest)
• method='whitened' - Mahalanobis-scaled for batch effects
• method='knn' - k-NN matched for heterogeneous controls

shesha.bio.compute_stability(adata, perturbation_key, method='standard', ...)

AnnData wrapper supporting all three methods.

import shesha.bio as bio

# Standard stability
stability = bio.compute_stability(adata, "perturbation", method="standard")

# Whitened (for batch effects)
stability_white = bio.compute_stability(adata, "perturbation", method="whitened")

# k-NN (for heterogeneous controls)
stability_knn = bio.compute_stability(adata, "perturbation", method="knn", k=50)

# Low-level API also supports method parameter
from shesha.bio import perturbation_stability
score = perturbation_stability(X_ctrl, X_pert, method="whitened")

Backward compatibility: Old function names (perturbation_stability_whitened, perturbation_stability_knn, compute_stability_whitened, compute_stability_knn) still work as convenience wrappers.

Testing

Shesha has a comprehensive test suite to ensure scientific reliability and correctness.

Running Tests Locally

Install development dependencies:

pip install -e .[dev]

Run all tests:

pytest tests/

Run with coverage report:

pytest tests/ --cov=shesha --cov-report=term

Continuous Integration

All tests are automatically run on:

• Multiple Python versions: 3.8, 3.9, 3.10, 3.11, 3.12
• Multiple operating systems: Ubuntu, macOS, Windows

See the Tests workflow for current status.

Citation

If you use shesha-geometry, please cite:

@software{shesha2026,
  title = {Shesha: Self-Consistency Metrics for Representational Stability},
  author = {Raju, Prashant C.},
  year = {2026},
  howpublished = {Zenodo},
  doi = {10.5281/zenodo.18227453},
  url = {https://doi.org/10.5281/zenodo.18227453},
  copyright = {MIT License}
}

@article{raju2026geometric,
  title = {Geometric Stability: The Missing Axis of Representations},
  author = {Raju, Prashant C.},
  journal = {arXiv preprint arXiv:2601.09173},
  year = {2026}
}

License

MIT

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