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Spectral compression of dense retrieval embeddings throws away relevance information, and a closed-form correction recovered 2.34 nDCG points

AspireAI community · arXiv (cs.IR)
Projecting retrieval embeddings onto a smaller principal subspace cuts storage and scoring cost, but corpus-derived weighting rules tie every retained direction to one shared spectral trend instead of accounting for its individual contribution to relevance. Relevance-Guided Residual Calibration estimates margin-based weights from the means and variances of positive and negative score contributions along each retained direction, keeps directions with positive estimated weights, and adds the residual to the compressor's log weights on that support, leaving the overall spectral trend intact. It applies to PCA, Whitening and SpecTemp with no iterative training and no extra inference stage, and on five BRIGHT datasets it improves over SpecTemp by an average of 2.34 nDCG@10 points at 768 dimensions.
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One distance function matched sparse-autoencoder features across layers and compressed feature circuits into supernodes
Two sparse-autoencoder analyses have resisted scaling: matching semantically similar features across layers, and compressing large feature circuits into interpretable supernodes. This paper argues both are the same underlying problem, estimating semantic distances between SAE features that sit on different activation manifolds. Its representation treats each feature not as a single decoder vector but as an activation-weighted distribution over the hidden states expressing it, projects those distributions into a shared reference space, and compares them with Wasserstein distance. The representation is proved invariant to activation rescaling and stable under perturbation, and recovers true matches under finite-sample margin conditions. Empirically it outperformed decoder-vector and LLM-based baselines and captured subtle functional distinctions between related features, and it compressed large feature circuits into interpretable supernodes automatically. The limitation is that this is interpretability tooling: the paper demonstrates better feature matching and circuit compression, not that downstream interpretability claims become more accurate.
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