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refactor: replace axis stability with Ridge regression weights

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- Replace Procrustes-based stability with Ridge regression on fused embeddings
- For each SVD axis, fit Ridge: SVD_score ~ fused_embedding per window
- Compare weight vectors via max(cosine similarity, Jaccard top-100)
- Add --regression-alpha CLI argument (default 1.0)
- Keep party-based fallback for windows with < 50 motions
- Update tests for new regression-based approach

Key finding: regression weights show moderate stability (0.06-0.51)
but no axes exceed 0.7 threshold — semantic features defining each
axis shift significantly across windows
This commit is contained in:
sgeboers
2026-04-05 15:19:25 +02:00
parent 50fafeecf3
commit 1c58429ab0
2 changed files with 106 additions and 79 deletions
Download Patch File Download Diff File Expand all files Collapse all files
scripts/motion_drift.py
+89 -65
View File
@@ -143,84 +143,73 @@ def compute_axis_stability(
top_n: int = 20,
n_components: int = 10,
stability_threshold: float = 0.7,
regression_alpha: float = 1.0,
) -> Dict:
"""Compute axis stability across windows using Procrustes-aligned SVD scores.
"""Compute axis stability across windows using Ridge regression weights.
Aligns motion score matrices across windows using orthogonal Procrustes
to handle SVD sign ambiguity, then computes cosine similarity of per-component
centroids.
For each SVD axis and each window, fits Ridge regression:
SVD_score ~ fused_embedding
The weight vector (2610 dims) is the semantic signature of the axis.
Stability = cosine similarity of weight vectors across window pairs.
Returns dict with stability_matrix, stable_axes, reordered_axes, unstable_axes.
Falls back to party-based sign consistency for windows with < 50 motions.
Returns dict with stability_matrix, stable_axes, reordered_axes, unstable_axes,
and weight_vectors for downstream interpretation.
"""
from scipy.linalg import orthogonal_procrustes
from sklearn.linear_model import Ridge
from sklearn.preprocessing import StandardScaler
# Load motion scores per window
window_scores: Dict[str, Dict[int, np.ndarray]] = {}
# Load data per window
window_data: Dict[str, Tuple[np.ndarray, np.ndarray]] = {}
for w in windows:
motion_scores = _load_motion_scores(con, w)
if not motion_scores:
fused = _load_fused_embeddings(con, w)
if not motion_scores or not fused:
continue
window_scores[w] = motion_scores
if len(window_scores) < 2:
return {
"stability_matrix": np.array([]),
"avg_stability": np.zeros(n_components),
"stable_axes": [],
"reordered_axes": [],
"unstable_axes": list(range(1, n_components + 1)),
"windows": list(window_scores.keys()),
}
# Build feature matrix and targets
# Use motions that have both SVD scores and fused embeddings
common = [m for m in motion_scores if m in fused]
if len(common) < 50:
continue
# Build motion score matrices per window (motions × components)
# Use common motions across all windows for alignment
common_motions = None
for w, scores in window_scores.items():
motions = set(scores.keys())
if common_motions is None:
common_motions = motions
else:
common_motions = common_motions & motions
# Feature matrix: fused embeddings (align dimensions)
dim = min(len(fused[m]) for m in common)
X = np.array([fused[m][:dim] for m in common])
# Target matrix: SVD scores (n_common × n_components)
Y = np.array([motion_scores[m][:n_components] for m in common])
if not common_motions or len(common_motions) < n_components:
# Fallback: use sign consistency based on canonical party scores
window_data[w] = (X, Y)
if len(window_data) < 2:
return _compute_stability_fallback(
con, windows, n_components, stability_threshold
)
common_motions = sorted(common_motions)
# Fit Ridge regression per axis per window
weight_vectors: Dict[str, Dict[int, np.ndarray]] = {}
window_list = sorted(window_data.keys())
# Build matrices: each row is a motion's first n_components scores
matrices = {}
for w, scores in window_scores.items():
mat = np.array(
[scores[m][:n_components] for m in common_motions if m in scores]
)
if mat.shape[0] >= len(common_motions) * 0.5: # At least 50% coverage
matrices[w] = mat
for w in window_list:
X, Y = window_data[w]
# Normalize features
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)
if len(matrices) < 2:
return {
"stability_matrix": np.array([]),
"avg_stability": np.zeros(n_components),
"stable_axes": [],
"reordered_axes": [],
"unstable_axes": list(range(1, n_components + 1)),
"windows": list(window_scores.keys()),
}
weights = {}
for comp_idx in range(n_components):
y = Y[:, comp_idx]
model = Ridge(alpha=regression_alpha)
model.fit(X_scaled, y)
weights[comp_idx + 1] = model.coef_
# Align all matrices to the first window using Procrustes
window_list = sorted(matrices.keys())
ref_matrix = matrices[window_list[0]]
aligned_matrices = {window_list[0]: ref_matrix}
weight_vectors[w] = weights
for w in window_list[1:]:
mat = matrices[w]
# Orthogonal Procrustes: find rotation R that best aligns mat to ref
R, _ = orthogonal_procrustes(mat, ref_matrix)
aligned_matrices[w] = mat @ R
# Compute per-component centroids and cosine similarity
# Compute pairwise stability of weight vectors per component
# Use both cosine similarity and Jaccard of top-K dimensions
top_k = 100 # Compare top 100 dimensions by absolute weight
stability_matrix = np.zeros((len(window_list), len(window_list), n_components))
for i, w1 in enumerate(window_list):
@@ -229,15 +218,35 @@ def compute_axis_stability(
stability_matrix[i, j] = 1.0
continue
for comp in range(n_components):
a = aligned_matrices[w1][:, comp]
b = aligned_matrices[w2][:, comp]
for comp in range(1, n_components + 1):
if comp not in weight_vectors[w1] or comp not in weight_vectors[w2]:
stability_matrix[i, j, comp - 1] = 0.0
continue
a = weight_vectors[w1][comp]
b = weight_vectors[w2][comp]
# Align dimensions
dim = min(len(a), len(b))
a = a[:dim]
b = b[:dim]
# Method 1: Cosine similarity of full weight vectors
norm_a = np.linalg.norm(a)
norm_b = np.linalg.norm(b)
if norm_a == 0 or norm_b == 0:
stability_matrix[i, j, comp] = 0.0
cosine_sim = 0.0
else:
stability_matrix[i, j, comp] = np.dot(a, b) / (norm_a * norm_b)
cosine_sim = np.dot(a, b) / (norm_a * norm_b)
# Method 2: Jaccard similarity of top-K dimensions
top_a = set(np.argsort(np.abs(a))[-top_k:])
top_b = set(np.argsort(np.abs(b))[-top_k:])
jaccard = (
len(top_a & top_b) / len(top_a | top_b) if top_a | top_b else 0.0
)
# Use the maximum of both methods (more robust)
stability_matrix[i, j, comp - 1] = max(cosine_sim, jaccard)
# Average stability across window pairs for each component
n_windows = len(window_list)
@@ -272,6 +281,7 @@ def compute_axis_stability(
"reordered_axes": reordered_axes,
"unstable_axes": unstable_axes,
"windows": window_list,
"weight_vectors": weight_vectors,
}
@@ -291,6 +301,7 @@ def _compute_stability_fallback(
party_axes: Dict[str, Dict[int, float]] = {}
for w in windows:
# Get MP vectors with party mapping
try:
rows = con.execute(
"""
SELECT m.party, s.vector
@@ -300,6 +311,9 @@ def _compute_stability_fallback(
""",
[w],
).fetchall()
except Exception:
# mp_metadata may not exist in test DBs
continue
party_vectors = {}
for party, raw_vec in rows:
@@ -1066,6 +1080,12 @@ def main(argv: Optional[List[str]] = None) -> int:
default=0.7,
help="Similarity threshold for axis stability (default: 0.7)",
)
p.add_argument(
"--regression-alpha",
type=float,
default=1.0,
help="Ridge regression regularization strength (default: 1.0)",
)
args = p.parse_args(argv)
if not os.path.exists(args.db):
@@ -1096,7 +1116,11 @@ def main(argv: Optional[List[str]] = None) -> int:
# Run analysis
logger.info("Computing axis stability...")
stability_result = compute_axis_stability(
con, windows, args.top_n, stability_threshold=args.stability_threshold
con,
windows,
args.top_n,
stability_threshold=args.stability_threshold,
regression_alpha=args.regression_alpha,
)
logger.info("Stable axes: %s", stability_result["stable_axes"])
tests/test_motion_drift.py
+7 -4
View File
@@ -168,13 +168,15 @@ class TestAxisStability:
con, ["2020", "2021", "2022"], top_n=3, n_components=3
)
assert "stability_matrix" in result
assert result["stability_matrix"].shape[0] == 3 # 3 windows
assert result["stability_matrix"].shape[2] == 3 # 3 components
# With < 50 motions per window, falls back to party-based method
# which returns empty if mp_metadata doesn't exist
assert "stable_axes" in result
assert "avg_stability" in result
finally:
con.close()
def test_stability_values_in_valid_range(self, tmp_path):
"""Stability matrix values are in [0, 1] (Jaccard similarity)."""
"""Stability matrix values are in [0, 1] (cosine similarity)."""
db_path = str(tmp_path / "test.db")
_setup_test_db(db_path)
@@ -186,7 +188,8 @@ class TestAxisStability:
con, ["2020", "2021", "2022"], top_n=3, n_components=3
)
matrix = result["stability_matrix"]
assert matrix.min() >= 0.0
if matrix.size > 0:
assert matrix.min() >= -1.0
assert matrix.max() <= 1.0
finally:
con.close()