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arxivcs.LGcs.AI2026-07-01

Scaling Laws for Grid-Based Approximate Nearest Neighbor Search in High Dimensions

Matthew J Liu, Wei Hang Zheng, Vidhan Purohit, Siqi Xie, Chieh-En Li, Jerry Li, Noah Flynn

Grid-based approaches to approximate nearest neighbor (ANN) search have been absent from modern scaling analyses. We present a systematic characterization of a multiprobe grid algorithm with respect to dataset size $N$ and dimensionality $d$. Our experiments reveal a previously unreported $d$-scaling crossover on the GloVe embedding family, in which multiprobe grid search maintains an approximately constant dimensional scaling exponent while other graph-, tree-, and partitioning-based methods exhibit degrading throughput. The advantage comes with near-linear query scaling in $N$, but also with lower indexing cost than competing ANN methods. Our results suggest that grid-based methods such as multiprobe grid may be competitive in rebuild-heavy or high-dimensional settings where indexing cost and dimensional robustness dictate performance. More broadly, recent work has formalized self-attention as an ANN operation. Thus, the $N$- and $d$-scaling properties of ANN algorithms may guide cost analysis of efficient transformer architectures. Code is available at: https://github.com/weiz345/MultiProbeANN.

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arxivcs.LGcs.AI2026-07-01

Staleness-Learning Rate Scaling Laws for Asynchronous RLHF

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High-throughput RLHF systems often decouple rollout generation from policy optimization, leading to the use of stale rollouts during learner updates. In this work, we study the effect of such staleness in asynchronous GRPO. We make the behavior policy explicit in the GRPO surroga…

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arxivcs.LGcond-mat.dis-nncs.AIstat.ML2026-06-26

How Width and Data Shape Generalization Scaling Laws in Quadratic Neural Networks

Julius Girardin, Emanuele Troiani, Yizhou Xu, Vittorio Erba, Florent Krzakala, Lenka Zdeborová

Understanding how performance scales jointly with model size and data is a central problem in modern machine learning. Existing theoretical works on scaling laws typically describe generalization as a function of data or compute, often in fixed-feature or infinite-width regimes a…

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arxivstat.MLcs.AIcs.LG2026-06-29

A Stochastic--Geometric Theory of Scaling Laws in Grokking

Róisín Luo, Christian Gagné, Jonas Ngnawé, Ihsan Ullah, Karyn Morrissey

Delayed generalization (\ie~grokking) refers to the phenomenon in which a neural network fits its training data early in training but only begins to generalize after a prolonged delay, often through an abrupt transition. Despite extensive empirical study, its underlying mechanism…

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arxivcs.LGcs.AImath.PRstat.ML2026-06-29

A Stationary-Distribution Theory for Triplet-Based Plateau Search in Random Forest Ensemble-Size Selection

Andrey A. Dukhovny, Andrey M. Lange

The number of trees is a central computational parameter in Random Forests: increasing it reduces finite-ensemble variability but increases training and prediction cost. Plateau-based tuning adapts this parameter through local comparisons of out-of-bag scores at a geometric tripl…

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arxivcs.LGcs.AIcs.DCcs.PF2026-07-16

An Auto-Scaling Approach for Serverless Environments Based on a Multi-Expert Consensus Mechanism

Mobina Kashaniyan, Mehrdad Ashtiani, Amirhossein Ghassemi

Serverless computing provides automatic resource management and pay-per-use execution, but effective autoscaling remains challenging because of dynamic workloads, cold-start latency, and dependencies among functions. We present a dependency-aware autoscaling framework that integr…

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