Kernel Affine Hull Machines for Compute-Efficient Query-Side Semantic Encoding
Mohit Kumar, Somayeh Kargaran, Bernhard A. Moser, Manuela Gei{\ss}

TL;DR
This paper introduces Kernel Affine Hull Machines (KAHMs), a lightweight, explicit estimator for semantic encoding that replaces costly neural inference, achieving high retrieval accuracy and efficiency in fixed-teacher regimes.
Contribution
KAHMs provide a transparent, analytically explicit method for semantic encoding that maintains retrieval quality while significantly reducing per-query latency.
Findings
KAHMs outperform learned adapters in teacher-space reconstruction (MSE 0.000091, R^2 0.9071).
KAHMs achieve higher rank-sensitive metrics like MRR@20, Hit@20, and Top-1 accuracy.
KAHMs reduce per-query latency by a factor of 8.5 compared to direct transformer encoding.
Abstract
Transformer-based semantic retrieval is highly effective, yet in many deployments the dominant cost lies in online query encoding rather than corpus indexing. We study the fixed-teacher query-adaptation problem and ask whether repeated neural inference can be replaced by a lightweight, analytically explicit estimator without degrading decision-relevant retrieval quality. We propose Kernel Affine Hull Machines (KAHMs), which map inexpensive lexical features into a frozen semantic embedding space by estimating prototype-mixture weights in a rigorously specified RKHS and refining prototypes via normalized least-mean-squares, yielding a transparent decomposition of encoding error into posterior-approximation, generalization, and teacher-noise components. On a controlled Austrian-law benchmark (5,000 queries; 84 laws; 10,762 units), KAHM attains the strongest teacher-space reconstruction…
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