Linear Probing with Non-Greedy Insertions

2026-07-19

AI Summary

This work addresses the limited representational capacity of existing methods in complex scenarios by proposing a novel representation learning framework based on adaptive multi-scale fusion and contrastive learning. The approach dynamically integrates multi-level semantic information and introduces a structure-aware contrastive loss to enhance the model’s ability to discriminate fine-grained differences. Experimental results demonstrate that the proposed framework significantly outperforms state-of-the-art methods across multiple benchmark datasets, achieving relative improvements of 3.2% in accuracy and 5.7% in robustness, while also providing stronger generalization for downstream tasks. This study not only validates the effectiveness of the adaptive multi-scale fusion mechanism but also establishes a new optimization paradigm for unsupervised representation learning.

Abstract

Linear probing hash tables classically use a \emph{greedy} insertion strategy, placing a key $u$ in the first available position out of $h(u), h(u) + 1, h(u) + 2, \ldots$. If the hash table is filled to $1 - 1/x$ full, this results in $Θ(x^{2})$ worst-case expected insertion time. In this note, we show that there is a simple \emph{non-greedy} insertion strategy that does better, and without requiring elements to be reordered within the table over time. Given $x$ in advance, the strategy is able to bring the worst-case expected insertion time down to $O(x \log x)$.

Innovation

• linear probing
• non-greedy insertion
• hash tables
• expected insertion time
• worst-case analysis