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新论文 · v1arXiv:2611.16149

HyperPage: Learned Page Layouts for Disk-Resident Graph Vector Indexes

Xinyu Zhang, Jingze Li, Baihua Zheng, Weiwei Sun

原文摘要

Disk-resident graph indexes such as DiskANN store each vector with its graph edges as one record on SSD pages. A search needs the page of every record it expands, so its page reads depend on the page layout, that is, which records share a page. Search agents trained with reinforcement learning query one such index run after run, and every graph traversal can be logged with the records it expands. We therefore use the logs of a finished run to lay out the index for a declared memory budget, so later runs read fewer pages. In contrast, existing layouts such as Starling and MARGO are computed from the graph and vectors and use no logs. Learning a layout from logs is challenging, because the logs must stay valid under every layout, the saving depends on what the budget caches, and the best layout is NP-hard to find. Our key observation is that DiskANN-style search routes on in-memory codes and the records it expands, never on their page-mates. As a result, the logged traversals price every layout by replay, and cached records add no page reads. Accordingly, we propose HyperPage, which first builds layouts for the declared budget on the logged traversals of uncached records. It then selects one layout, together with the budget split between hot records and a page cache, by replaying validation steps. In addition, a Lagrangian lower bound shows how far a layout may be from the optimum. We learn from one Search-R1 agent run and test on a later run with a different reward, over 1M and 21M passages. Across seven cache budgets, HyperPage reads 5.2% to 21.2% fewer pages than MARGO, and no compared layout reads fewer. The advantage is largest when the cache is small. For example, at 1% of the 1M index, MARGO needs nearly 3 times the budget to read as few pages. On the 21M index, HyperPage also cuts search time per step by up to 10.4%. The saving holds for a second agent model and a second corpus.

cs.DB · cs.IR

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.16148

Calibrated Early Termination with Bounded Optimality Gaps for Constrained Vector Search

Xinyu Zhang, Jingze Li, Baihua Zheng, Weiwei Sun

原文摘要

Vector search over learned embeddings is the retrieval layer of recommendation and retrieval-augmented generation, and many applications cap how many answer items one category may contribute. Graph indexes answer a query by best-first traversal, and where it stops determines its cost and whether its answer is exact. We study early termination for such constrained $k$-nearest-neighbor ($k$-NN) queries, with plain $k$-NN as a special case, and seek the cheapest stopping rule whose answer is exact with probability at least $1-\varepsilon$. Learned early-termination methods instead target average recall, which does not guarantee exact answers. Multiple testing can calibrate any parameterized stopping rule to our target, but it cannot tell how much a better rule with the same risk and observations would save. Answering this needs a lower bound on the optimum of a rule family too large to enumerate, valid for the query population. Our key idea is to declare the observations a rule may use and to consider every rule monotone in them. Risk-constrained stopping then becomes a linear program over an order polytope, whose Lagrangian minimizers form a nested chain of staircase rules computed exactly by dynamic programming. Fixed-sequence binomial tests along this chain calibrate our rule, CaST, whose failure probability is at most $\varepsilon$ with confidence $1-δ$. Lagrangian weak duality bounds the optimum of the declared class from below at all risk levels at once, without a union bound over the rules. On two datasets of one million items each, CaST replayed on logged searches costs at most 1.132 times the class optimum for risk levels from 0.03 to 0.10, at 95% joint confidence per setting. Larger savings thus need a rule outside the class. At a common risk target on held-out queries, CaST is faster than every other calibrated rule we time, which take 4.8% to 45.5% more mean time.

cs.DB · cs.IR · cs.LG

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2609.38037

Emergence in Network Systems is Bounded by Boundary-Crossing Paths

Johnny Jingze Li, Gabriel A. Silva

原文摘要

Emergence, features of a whole that no part shows alone, is central to complex systems but rarely measured so as to locate its source. Viewing a system structurally, as a network of interacting parts, we evaluate emergence as what observing the coupled whole reveals beyond, or erases from, the combined observations of the parts. For observations that build what they see route by route, we show that every emergent feature is produced by its own route across the interface between parts, a route that traces it to the components and interactions responsible. We show the number of all such boundary-crossing paths bounds the total emergence discrepancy, and equals the emergence of measures that count routes. The bound is computed locally around the interface, validated through network examples, and in a nervous system the routes show that interneurons relay most of the emergence. Our work associates emergence with path structure in the network system that can be anticipated, attributed, and engineered.

physics.soc-ph · cs.SI · nlin.AO

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arXiv ↗PDF ↗