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Disentangling Locality and Entropy in Ranking Distillation

Andrew Parry, Debasis Ganguly, Sean MacAvaney

TL;DR

The paper addresses why modern ranking distillation systems gain effectiveness and whether complex hard-negative pipelines are necessary. It develops a theoretical framework that separates locality (geometric proximity of relevant items) from target entropy (information content of teacher signals) and proves a generalisation bound dependent on the essential diameter $\Delta_Q$ and teacher entropy $H(g)$. Empirically, it shows that many elaborate sampling pipelines offer limited advantages under distillation, whereas balancing entropy and locality can yield stable in-domain gains, with risks of overfitting when entropy is too high or domain shifts occur. The findings advocate simpler, geometry-aware training protocols that reduce computational cost while preserving performance, enhancing reproducibility and real-world applicability in semantic ranking tasks.

Abstract

The training process of ranking models involves two key data selection decisions: a sampling strategy, and a labeling strategy. Modern ranking systems, especially those for performing semantic search, typically use a ``hard negative'' sampling strategy to identify challenging items using heuristics and a distillation labeling strategy to transfer ranking "knowledge" from a more capable model. In practice, these approaches have grown increasingly expensive and complex, for instance, popular pretrained rankers from SentenceTransformers involve 12 models in an ensemble with data provenance hampering reproducibility. Despite their complexity, modern sampling and labeling strategies have not been fully ablated, leaving the underlying source of effectiveness gains unclear. Thus, to better understand why models improve and potentially reduce the expense of training effective models, we conduct a broad ablation of sampling and distillation processes in neural ranking. We frame and theoretically derive the orthogonal nature of model geometry affected by example selection and the effect of teacher ranking entropy on ranking model optimization, establishing conditions in which data augmentation can effectively improve bias in a ranking model. Empirically, our investigation on established benchmarks and common architectures shows that sampling processes that were once highly effective in contrastive objectives may be spurious or harmful under distillation. We further investigate how data augmentation, in terms of inputs and targets, can affect effectiveness and the intrinsic behavior of models in ranking. Through this work, we aim to encourage more computationally efficient approaches that reduce focus on contrastive pairs and instead directly understand training dynamics under rankings, which better represent real-world settings.

Disentangling Locality and Entropy in Ranking Distillation

TL;DR

The paper addresses why modern ranking distillation systems gain effectiveness and whether complex hard-negative pipelines are necessary. It develops a theoretical framework that separates locality (geometric proximity of relevant items) from target entropy (information content of teacher signals) and proves a generalisation bound dependent on the essential diameter and teacher entropy . Empirically, it shows that many elaborate sampling pipelines offer limited advantages under distillation, whereas balancing entropy and locality can yield stable in-domain gains, with risks of overfitting when entropy is too high or domain shifts occur. The findings advocate simpler, geometry-aware training protocols that reduce computational cost while preserving performance, enhancing reproducibility and real-world applicability in semantic ranking tasks.

Abstract

The training process of ranking models involves two key data selection decisions: a sampling strategy, and a labeling strategy. Modern ranking systems, especially those for performing semantic search, typically use a ``hard negative'' sampling strategy to identify challenging items using heuristics and a distillation labeling strategy to transfer ranking "knowledge" from a more capable model. In practice, these approaches have grown increasingly expensive and complex, for instance, popular pretrained rankers from SentenceTransformers involve 12 models in an ensemble with data provenance hampering reproducibility. Despite their complexity, modern sampling and labeling strategies have not been fully ablated, leaving the underlying source of effectiveness gains unclear. Thus, to better understand why models improve and potentially reduce the expense of training effective models, we conduct a broad ablation of sampling and distillation processes in neural ranking. We frame and theoretically derive the orthogonal nature of model geometry affected by example selection and the effect of teacher ranking entropy on ranking model optimization, establishing conditions in which data augmentation can effectively improve bias in a ranking model. Empirically, our investigation on established benchmarks and common architectures shows that sampling processes that were once highly effective in contrastive objectives may be spurious or harmful under distillation. We further investigate how data augmentation, in terms of inputs and targets, can affect effectiveness and the intrinsic behavior of models in ranking. Through this work, we aim to encourage more computationally efficient approaches that reduce focus on contrastive pairs and instead directly understand training dynamics under rankings, which better represent real-world settings.

Paper Structure

This paper contains 25 sections, 8 theorems, 65 equations, 4 figures, 6 tables.

Key Result

Theorem 2.1

Let $(\mathcal{X},d, \mu_Q)$ be a metric-measure space for $Q$ and let $\mathcal{H}$ be a hypothesis class of VC dimension $d$ such that every $h\in\mathcal{H}$ is $L$-Lipschitz. Let $f^{\star}=\arg\min_{h\in\mathcal{H}}\mathcal{R}(h)$ and let $\widehat{f}$ minimise an empirical semi-supervised Breg where $\zeta$ depends only on divergence potential $\phi$, and $C>0$ is an absolute universal const

Figures (4)

  • Figure 1: The existing SentenceTransformers reimers:2019 pipeline for hard negatives. Even naive sampling pipelines can often have three stages of prior sampling song:2023wang:2024. This practise reduces our ability to attribute effectiveness gain to a particular source and more broadly replicate this process due to cross-mining of examples from different stages in the pipeline.
  • Figure 2: Score versus rank ratio comparing the teacher (LCE) and two RankNet-trained students with different sampling distributions evaluated on TREC DL'19. Note the log-log scale and alignment with power laws plotted in grey.
  • Figure 3: Training loss in the form of the KL divergence (left) and gradient norm of the student $f$(right). Note the log scale of loss values. Observe the reduced variance in gradient under locality but otherwise minimal difference between sampling domains, we observe that loss converges marginally higher inversely with density ratio $\kappa_Q$.
  • Figure 4: log-log plots of average score at each document rank on MS MARCO passage (TREC DL 2019 judged) for each loss function (rows) and domain (columns) when training a cross-encoder.

Theorems & Definitions (23)

  • Definition 2.1: Pair-wise Risk
  • Definition 2.2: Bregman Distillation Loss
  • Definition 2.3: Query Entropy
  • Definition 2.4: Misordering-Probability under Entropy (Proof in Appendix \ref{['app:pinsker-entropy']})
  • Theorem 2.1: Ranking Distillation Generalisation Bound (Proof in Appendix \ref{['app:risk']})
  • Corollary 2.1: Fixed-miner density–ratio bound (Proof in Appendix \ref{['app:biased']})
  • Definition A.1: Bregman divergence
  • Definition A.2: Polish metric space
  • Definition A.3: Lipschitz continuity weaver:1999
  • Definition A.4: Pair-wise Risk
  • ...and 13 more