cross-seed-explainability-procrustes-sparse-autoencoders

name	cross-seed-explainability-procrustes-sparse-autoencoders
description	Procrustes-conditioned Joint End-to-end Top-K SAE for extracting cross-seed universal features from independently trained BERT models. Combines Top-K sparsity, end-to-end optimization, and dead-feature revival. Pearson r ≥ 0.70 across seeds. Activation: sparse autoencoder, cross-seed universality, Procrustes alignment, mechanistic interpretability, feature universality.
metadata	{"arxiv_id":"2607.08499","published":"2026-07-09","authors":"Bendegúz Váradi, Zoltán Kmetty","tags":["sparse-autoencoder","cross-seed-universality","procrustes-alignment","mechanistic-interpretability","feature-universality"]}

Cross-seed Explainability using Procrustes-conditioned Joint End-to-end Top-K Sparse Autoencoders

Overview

Cross-seed feature universality is a fundamental challenge in mechanistic interpretability: independently trained networks learn misaligned feature spaces due to random initialization. This paper presents a Procrustes-conditioned Joint End-to-end Top-K Sparse Autoencoder (SAE) that addresses this by computing an orthogonal Procrustes rotation before joint SAE training.

Key Innovations

Procrustes-Conditioned Alignment

• Computes orthogonal Procrustes rotation between seeds' activation spaces before joint training
• Aligns feature spaces that differ by random initialization
• Enables meaningful cross-seed feature comparison

Joint End-to-End Top-K SAE

• Combines Top-K sparsity for representational efficiency
• End-to-end downstream optimization for task-relevant features
• Auxiliary dead-feature revival loss based on prior SAE literature

Universal Feature Extraction

• Evaluated on five independent seed pairs (ten BERT models)
• Three benchmark datasets: SST-2, Stanford Politeness, TweetEval Emotion
• Produces more universal features (Pearson r ≥ 0.70 across seeds) than post-hoc alignment
• High-universality features encode interpretable sociolinguistic patterns

Methodology

1. Procrustes Rotation: Compute orthogonal rotation between seed activation spaces
2. Joint SAE Training: Train Top-K SAE end-to-end with aligned activations
3. Dead-Feature Revival: Auxiliary loss to prevent feature death
4. Universality Evaluation: Measure cross-seed Pearson correlation
5. Qualitative Analysis: Verify interpretable patterns in high-universality features

Implications

• Feature universality across seeds is achievable with proper alignment
• Procrustes conditioning is more effective than post-hoc alignment
• Universal features encode meaningful sociolinguistic patterns
• Advances mechanistic interpretability toward reliable cross-model comparison

Pitfalls

• Procrustes rotation assumes linear alignment which may not hold for all layers
• Top-K sparsity introduces a hyperparameter that affects feature quality
• Evaluation limited to BERT models — generalization to other architectures unclear
• Qualitative analysis is minimal and needs broader validation

Activation Keywords

sparse autoencoder, cross-seed universality, Procrustes alignment, mechanistic interpretability, feature universality, Top-K SAE, BERT, dead-feature revival

Paper Reference

arXiv:2607.08499 - "Cross-seed Explainability using Procrustes-conditioned Joint End-to-end Top-K Sparse Autoencoders" (Jul 2026)