arXiv:2609. 02143v1 Announce Type: cross Abstract: Most vector databases rely on graph-based indexes, notably HNSW and Vamana, for approximate nearest neighbor search.
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arXiv:2606. 11780v1 Announce Type: cross Abstract: We establish conditions for embedding a corpus of $N$ documents as $d$-dimensional vectors such that every $k$-subset $S \subseteq [N]$ is realizable as a result of top-$k$ retrieval by some query vector.
The paper introduces a new closed‑form scaling law that extends Chinchilla’s original formula to handle data‑constrained regimes. It decomposes loss into undercapacity, undertraining, and overfitting components, saturating between an irreducible loss and an uninformed baseline. The authors validate the model on diverse architectures and domains, achieving state‑of‑the‑art RMSE across multiple LLM scaling‑law grids and enabling cost‑aware training allocations.
arXiv:2605. 05189v2 Announce Type: replace-cross Abstract: How many key-value associations can a $d\times d$ linear memory store?
arXiv:2606. 30473v1 Announce Type: cross Abstract: We study retrieval over catalogs of structured metadata, where each record is a small schema whose fields answer different kinds of query.
arXiv:2609.20276v2 Announce Type: replace-cross Abstract: Memoizing an expensive function of a sorted score vector is a data-structure problem before it is a numerical one: at a billion gridpoints, a...
The paper investigates how much learned memory is required to leverage additional data in autoregressive prediction models. It introduces a predictive‑energy spectrum that jointly governs data and memory scaling, proving a minimax law that links the number of prediction blocks and the size of the learned state to this spectrum. The authors demonstrate that optimal bit allocation and masked query‑key attention mechanisms realize this law, and they provide experimental evidence across multiple pretrained‑model scales.