Hypencoder Revisited: Reproducibility and Analysis of Non-Linear Scoring for First-Stage Retrieval

Transformer-based semantic encoders are effective for retrieval, but in many deployments the recurring bottleneck is online query encoding rather than offline corpus indexing. This paper studies whether, once a strong teacher representation space and corpus index are fixed, repeated neural query encoding can be replaced by a substantially lighter and analytically explicit estimator. We formulate fixed-teacher lexical-to-semantic encoding as a conditional-mean estimation problem in which the target semantic vector is represented as a noisy mixture of semantic prototypes weighted by posterior cluster probabilities. Kernel Affine Hull Machine (KAHM) geometry is used to estimate these posterior weights from inexpensive lexical features in an explicitly identified RKHS hypothesis space, and the semantic prototypes are refined by normalized least-mean-squares updates from noisy teacher embeddings. This yields a backpropagation-free query-side encoder together with an end-to-end error decomposition into posterior-approximation, finite-sample/generalization, and teacher-noise terms. We instantiate the approach on a controlled Austrian-law retrieval benchmark with 5,000 test queries, 84 candidate laws, and 10,762 aligned retrieval units, using law-specific encoders into a frozen Mixedbread embedding space. Among evaluation-matched learned adapters, KAHM achieves the strongest teacher-space reconstruction and the best rank-sensitive retrieval performance at all evaluated cutoffs. At k=20, it obtains MRR@20 = 0.504, Hit@20 = 0.694, and Top-1 Accuracy = 0.411, while reducing online per-query time by 8.53 relative to direct transformer query encoding in the reported CPU setting. The results support KAHMs as compute-efficient encoders for supervised fixed-representation deployment regimes.

Embedding-based code retrieval often suffers when encoders overfit to surface syntax. Prior work mitigates this by using LLMs to rephrase queries and corpora into a normalized style, but leaves two questions open: how much representational shift helps, and when is the per-query LLM call justified? We study a hierarchy of three rewriting strategies: stylistic rephrasing, NL-enriched PseudoCode, and full Natural-Language transcription, under joint query-corpus (QC, online) and corpus-only (C, offline) augmentation, across six CoIR benchmarks, five encoders, and three rewriters spanning independent model families (Qwen, DeepSeek, Mistral). We are the first to evaluate NL-enriched PseudoCode and snippet-level Natural Language as direct retrieval representations, rather than as transient intermediates. Full NL rewriting with QC yields the largest gains (+0.51 absolute NDCG@10 on CT-Contest for MoSE-18), while corpus-only rewriting degrades retrieval in 56 of 90 configurations, about 62%. We introduce two diagnostics, Delta H, token entropy, and Delta s, embedding cosine, and show that Delta H predicts retrieval gain under QC across all three rewriter families: pooled Spearman rho = +0.436, p < 0.001 on DeepSeek+Codestral; rho = +0.593 on Codestral alone; rho = +0.356 on Qwen. This establishes Delta H as a cheap, rewriter-agnostic proxy for deciding when rewriting pays off before running retrieval. Our analysis reframes LLM rewriting as a cost-benefit decision: it is most effective as a remediation layer for lightweight encoders on code-dominant queries, with diminishing returns for strong encoders or NL-heavy queries.

In the competitive landscape of sponsored search, balancing retrieval quality with production latency is a critical challenge. While large retrieval models based on Small Language Models (SLMs) such as Qwen3-Embedding-4B/8B set strong upper bounds on public benchmarks, their deployment in high-throughput, latency-sensitive environments remains impractical. In this paper, we present HARNESS-LM (HLM), a three-phase training framework for transferring the capabilities of large-scale retrievers into compact, cost-efficient models. The approach comprises: (1) training a high-performance reference ("teacher") retriever by fine-tuning a billion-parameter-scale SLM; (2) aligning query representations via an L2 objective to distill knowledge into a sub-600M parameter student encoder; and (3) applying a final contrastive refinement stage to optimize the student for retrieval performance. We also present a comprehensive empirical study of key design choices, including alignment objectives, embedding dimensionality, model scale, architecture, and optimization strategies, to identify configurations that are most effective in production settings. On a real-world Bing Ads evaluation benchmark, HLM recovers over 98% of the reference retriever's precision across multiple settings, while delivering up to 27x lower online query-encoder latency and 20x higher throughput on NVIDIA A100 GPUs. Online A/B testing on Bing Ads further shows a +1% Revenue, +0.6% Impression, and +0.4% Click uplift over the current ensemble of retrievers running in production with the deployed 190M parameter model, clearly highlighting the practical efficacy of the HLM recipe in a real-world sponsored search setting.