motief/docs/research/2026-04-05-svd-overtone-shift-deep-dive.md

title	date	module	problem_type	component	tags
SVD Axis Overtone Shift Analysis: Deep Dive	2026-04-05	analysis	research	motion-analysis	[svd overtone-shift semantic-drift time-series parliamentary-analysis]

SVD Axis Overtone Shift: Deep Dive Analysis

Executive Summary

This analysis explores the relationship between axis stability (structural consistency of SVD components over time) and overtone shift (semantic drift of motion content within those stable axes). The key finding is that these are independent phenomena: axes can be structurally stable (same parties voting similarly) while their semantic content drifts dramatically.

Key Finding: Stability vs. Semantic Content are Independent

Phenomenon	What it Measures	Typical Value	Interpretation
Axis Stability	Consistency of which motions load on an axis	0.70-0.83	Structural alignment of semantic signatures
Overtone Shift	How motion content evolves over time	1.30-1.97	Semantic drift within stable structure

Why This Matters

A stable axis (e.g., "Rechts kabinetsbeleid versus links oppositiebeleid") means:

• The same coalition/opposition voting pattern persists across years
• Parties maintain consistent relative positions

But high overtone shift means:

• The specific topics that define "coalition" vs "opposition" change substantially
• Motions discussed in 2026 are semantically different from 2016 even though they occupy the same axis position

Detailed Findings

Axis Stability Results (Lasso Regression, alpha=0.1)

Axis	Avg Stability	Classification	Interpretation
1	0.83	Stable	Coalition vs opposition voting pattern is consistent
2	0.75	Stable	PVV/FVD populist positioning vs mainstream
3	0.78	Stable	Welfare state vs market liberalisation
4	0.72	Stable	NSC/BBB vs D66/CDA/JA21
5	0.70	Stable	Christian-social vs progressive-individual
6	0.35	Reordered	Migration/culture axis most volatile
7	0.77	Stable	Administrative pragmatism
8	0.79	Stable	Healthcare/education/regional housing
9	0.76	Stable	System reform vs practical governance
10	0.74	Stable	Regulation vs deregulation

Overtone Shift Results

Axis	Avg Shift	Max Shift	Inflection Points
1	1.47	1.97	0
2	1.42	1.79	0
3	1.38	1.83	0
4	1.39	1.89	0
5	1.43	1.93	0
7	1.31	1.84	0
8	1.30	1.89	0
9	1.38	1.93	0
10	1.30	1.72	0

Critical observation: ALL stable axes show high overtone shift (1.3-1.97), with no inflection points detected. This indicates gradual, continuous semantic drift rather than sudden shifts.

Interpretation Framework

The "Axis Stability" Metric

Axis stability uses Lasso regression to learn the semantic signature of each axis:

SVD_score ~ fused_embedding

The learned weight vector (2610 dimensions) represents which embedding dimensions are most predictive of an axis score. Stability is measured by comparing these weight vectors across windows using:

• Cosine similarity of full weight vectors
• Jaccard similarity of top-100 weighted dimensions

Why Lasso (alpha=0.1)? The L1 regularization produces sparse weight vectors, concentrating on the most important semantic dimensions. This makes cross-window comparison more robust than dense Ridge regression.

The "Overtone Shift" Metric

Overtone shift computes semantic gravity — the weighted mean fused embedding of all motions on an axis:

gravity = weighted_mean(fused_embeddings, weights=abs(SVD_scores))

The cosine distance between gravity vectors of consecutive windows measures how the "center of mass" of motion content moves. High shift values (1.3-1.9) indicate the motion topics that define each axis change substantially over time.

Implications for Interpretation

For Users of the Stemwijzer

1. Axis labels are temporally bounded — The label "Rechts kabinetsbeleid versus links oppositiebeleid" accurately describes the 2016-2026 period, but the specific motions that exemplify this axis have changed.

2. Cross-temporal comparison is valid structurally but not semantically — Party positions along Axis 1 are comparable across years (stable structure), but the meaning of extreme positions has shifted (high overtone).

3. Axis 6 (Migration/Culture) is an exception — Low stability (0.35) suggests this axis may have fundamentally changed meaning or composition over the period.

For Analysts Studying Parliamentary Evolution

1. Coalition/opposition as a dimension is remarkably stable — Despite changes in coalition composition (Rutte III, Rutte IV, Schoof), the first axis consistently captures this dynamic.

2. Policy content evolves within stable voting patterns — What constitutes "coalition policy" in 2026 differs semantically from 2016, even if the voting alignment remains.

3. The 2022-2023 period may be significant — Gap in windows (2020-2021) coincides with COVID and government crises, potentially affecting overtone patterns.

Methodological Notes

Why Lasso (alpha=0.1)?

Three alternatives were evaluated and rejected:

Approach	Problem
Jaccard similarity of top-N motion IDs	Motions are unique per window — 0% overlap
Cosine similarity of embedding centroids	Near-zero similarity due to varying embedding dimensions
Ridge regression weights	Dense weights less interpretable; Lasso concentrates signal

Lasso (alpha=0.1) was chosen for:

• Interpretability: Sparse weights identify key semantic dimensions
• Robustness: Top-K dimension matching captures structural similarity
• Stability: Results are less sensitive to embedding dimension changes

Dimension Alignment Challenge

Fused embeddings have varying dimensions across windows (typically 768-2610). All comparisons use minimum common dimension alignment to ensure valid cosine similarity computation.

Inflection Point Detection

Inflection points are defined as shift/drift rates exceeding 2× median rate. The absence of detected inflection points suggests gradual, continuous drift rather than sudden semantic shifts — consistent with how policy debates evolve incrementally.

Recommendations

For Stemwijzer Maintenance

1. Re-run overtone analysis after SVD recomputation — Current themes may drift further from the underlying data
2. Monitor Axis 6 specifically — Low stability warrants closer attention during axis updates
3. Consider temporal weighting in visualizations — Recent windows may better represent current semantics

For Future Research

1. Correlate overtone shift with political events — External factors (elections, crises) may explain inflection patterns
2. Analyze dimension-level drift patterns — Which specific embedding dimensions drive the shift?
3. Extend to party-level analysis — Do individual parties show consistent voting semantics over time?

Related Files

• scripts/motion_drift.py — Analysis script
• reports/drift/report.md — Generated report
• reports/drift/axis_stability.png — Stability heatmaps
• reports/drift/semantic_drift.png — Drift timelines
• reports/drift/party_trajectories.png — Party position plots