search engine engineers

Abstract: Digital news outlets compete for audience attention. Search engines equipped with generative AI systems such as Google's AI overviews increasingly decide where that attention goes, as well as the revenue it represents. Yet, the lack of a consistent data collection infrastructure between national-level regulatory bodies has hindered between-country comparative analysis of media concentration, and with it any assessment of how these intermediaries reshape digital news markets. To address this issue, we compile an ownership dataset for 9,761 digital news outlets drawn from Wikipedia and Wikidata, achieving high agreement with independently compiled US and UK news directories. Using this dataset, we derive traffic-weighted concentration indices for 77 countries. We find that journalists report more owner pressure in countries with higher concentration, and that outlet-level measures understate concentration, with owner-level indices a median 1.30x higher. Applying concentration measures to AI-mediated news discovery, we find that citation distributions from major AI systems are up to 2.08x more concentrated than traffic, and that if Google AI Overviews mediated all organic search, the resulting rise in US concentration would be several times that associated with highly regulated media mergers and acquisitions. Finally, our analyses indicate that AI systems preferentially cite state-controlled media outlets when prompted in that country's native language. Together, these findings raise concerns about the effect AI systems may have on digital media. We release the dataset to enable the monitoring of digital news globally, so that the impact of disruptive technologies on digital media markets can be tracked as they emerge.

Abstract: Large language models (LLMs) have become a powerful tool for listwise relevance ranking, which can improve web search by comparing retrieved passages jointly. However, processing every candidate verbatim and generating a permutation autoregressively can make inference costly, every candidate must be serialized verbatim into the prompt and the input therefore grows linearly with both the number and the length of the passages. While sliding-window ranking handles context limits through repeated re-encoding of overlapping blocks, hard compression techniques sacrifice the fine-grained details required for accurate discriminative judgment. To better understand and mitigate this trade-off, we conduct a comprehensive study of soft compression for LLM-based listwise ranking. Our findings reveal that a vanilla gist representation is ill-suited to ranking for two reasons: strictly causal encoding weakens how thoroughly each gist token absorbs its passage, and the representation is never trained to expose the relative-preference structure that separates closely competing candidates. To this end, we propose GistRank, a three-stage training framework that equips a large language model with gist-compressed passage representations by learning faithful gist tokens under a semi-bidirectional attention scheme, instilling discriminative comparison through pairwise training, and adapting the model to the listwise objective. GistRank collapses each passage into only $K{=}4$ gist tokens, this gives 14$\times$ speedups over one-shot full-text ranking while reaching 59.17 average nDCG@10 over TREC DL19/20 and five BEIR subsets within 0.89 of the strongest full-context baseline. Overall, GistRank provides an effective means to enhance efficiency for searches in real-world environments.

Abstract: Graph-based retrieval-augmented generation (GraphRAG) answers multi-hop questions by organizing a corpus into a graph and retrieving along its structure. Existing retrieval methods face two limitations. Diffusion- and similarity-based methods expand retrieval along fixed edge weights or by similarity to the question, without resolving its implicit entity references, allowing relevance errors to accumulate across hops. In contrast, exploration-based methods let an LLM reason about the next hop, but require a separate generation at each hop, leading to high inference costs. We observe that an LLM can resolve implicit entity references from retrieved passages and a multi-hop question before generating any tokens. Further analysis identifies a small set of attention heads, termed addressing heads, that capture this capability across multiple hops in a single forward pass. Building on this finding, we propose HyperAddress, which runs Personalized PageRank on a description-labelled hypergraph, using addressing heads to determine the restart distribution and transition weights, thereby guiding multi-hop retrieval without any generation at query time. On MuSiQue, 2WikiMultiHopQA, and HotpotQA, HyperAddress outperforms the strongest baseline by 3.5 points of Recall@5 and 7.4 points of All@5 on average, with gains that grow with the number of hops. It answers more than twice as fast and builds its index at half the cost.

Abstract: Large language models incur substantial training and inference costs in personalized search and recommendation, as growing interaction histories lengthen request inputs and repeatedly expose the same item text to the model. We propose \textbf{C}omposable and \textbf{R}eusable \textbf{I}tem \textbf{M}emory (CRIM), a framework that separates item-level semantic encoding from request-level history modeling. A small set of learnable summary tokens compresses each item into compact continuous memories, while segment-level readout tokens (REC tokens) introduce predictive supervision within the interaction history. These memories are independent of users and queries and can therefore be reused across requests. At inference time, CRIM composes cached memories in interaction order and incorporates an optional query to produce a personalized retrieval representation, reducing repeated item-text encoding while retaining request-dependent contextual modeling. We further introduce a joint training mechanism that combines cached memories with sampled live re-encoding. Re-encoding only a few history items per request allows the retrieval objective to jointly optimize the item and request encoders at limited computational cost, while periodic cache refreshes maintain consistency. Extensive evaluation and cost analysis on MovieLens-1M, Qilin, and our new LazSeq dataset show that CRIM achieves state-of-the-art retrieval performance with substantially lower inference costs at the same backbone scale, while limiting item re-encoding during joint training. We will publicly release our code and dataset.

Abstract: Navigational search aims to find a single target page among hundreds of millions of web pages. Click tables work well for queries seen before but cannot generalise to new formulations, while embedding retrievers generalise across content but often rank navigational targets poorly. We introduce Octen-WebGR, a generative retrieval framework that stores web pages in the parameters of a language model: given a query, the model generates a two-token semantic identifier constrained to a table of real URLs. We develop Octen-WebGR-4B, which indexes 201 million web pages, and evaluate it on real navigational traffic from the month after training. Generative retrieval is most effective on new ways of asking for familiar pages: for unseen queries targeting pages with substantial interaction history, it ranks the correct page first 30.9% of the time, against 17.2% for a dense retriever trained on the same clicks (21.4% with a click prior). Embedding retrieval keeps an advantage on rarely visited pages, so the two approaches generalise on complementary sides, the query and the page. Over all navigational traffic, Octen-WebGR reaches 59.6% top-1 accuracy, against 46.5% for a click-enhanced dense retriever and up to 37.5% for frontier LLMs answering from memory, which cost at least 40 times as much per query. The 4B model runs on a single GPU with 10 GB of memory, compared with 412 GB for exact dense retrieval. Scaling experiments with up to 32 million URLs show that, when every query-page pair is seen equally often, the model size needed grows sublinearly with index size, and that retrieval is constrained more by page exposure than by model capacity. We release Octen-WebGR-4B and Octen-WebGR-0.6B with their identifier tables and inference code.

Abstract: Dense retrievers provide grounded evidence that mitigates hallucinations in outputs from Large Language Models (LLMs). Real-world queries are often verbose, ambiguously framed, or require multi-step reasoning, introducing irrelevant details that weaken semantic matching for dense retrievers. Query rewriting is a widely adopted pre-retrieval technique that leverages LLMs to reformulate queries and bridge the semantic gap between such queries and the retrieval target. Existing rewriting approaches either rely on expensive proprietary models, substantial training data, or iterative retrieval and rewriting, while largely applying a uniform rewriting strategy regardless of the retrieval corpus. We observe that effective query rewriting instructions are not universal: the optimal strategy depends on the retrieval target, rather than the model alone. We introduce SkillQR, a query rewriting framework that automatically discovers reasoning strategy sets from the retrieval target and dynamically routes a query to the appropriate rewriting strategy at inference time. Without relying on training data, SkillQR achieves competitive performance compared to fine-tuned rewriting models on the BRIGHT and R2MED benchmarks, while also providing lower inference latency than iterative rewriting approaches.

Abstract: Advances in Multimodal Large Language Models (MLLMs) have driven substantial progress in multimodal embeddings. Recent methods exploit generative capabilities by augmenting embedded inputs with self-generated reasoning to produce more informative embeddings. However, conventional retrieval supervision for training embedding models specifies pairwise relevance relations without explicitly guiding the reasoning used for input augmentation. Such reasoning is neither directly observed nor uniquely determined by the input, allowing multiple plausible traces to introduce semantic cues of varying retrieval utility. Existing approaches largely optimize reasoning conditioned on the input alone, limiting the exploration of retrieval-relevant traces. We introduce PILOT, a framework that models reasoning as a latent variable and instantiates its prior and posterior distributions as distinct reasoning modes of a shared MLLM. The prior conditions only on the input, whereas the posterior uses additional training-time relational evidence to guide reasoning exploration. To translate the posterior's broader exploration into inference-time improvements, we derive an importance-weighted variational objective and instantiate it as a prior-posterior co-evolution framework that improves both modes under a shared inference-compatible reward while selectively transferring posterior trajectories to the prior according to their utility and prior reachability. On the 78-task MMEB-V2 benchmark, PILOT outperforms the primary baseline across all 12 task groups at both 2B and 7B parameters, improving overall scores by 3.2 and 3.3 points, respectively, with the largest gains in visual-document retrieval (+6.1 and +6.4 points). Our results show that relational supervision is most valuable not as a post-hoc reward but as a signal for shaping how reasoning is explored in training reasoning-enhanced embedding models.

Abstract: In this report, we introduce pplx-embed-v2-late, a pair of 0.6B and 9B multilingual and multimodal late-interaction models. Both models achieve state-of-the-art results within their respective size classes across a range of text, image, and visual document retrieval benchmarks. On visual document retrieval tasks, pplx-embed-v2-late-0.6b is competitive with models several times larger than itself. The models are trained via representation distillation from an 18B teacher. Consequently, they share an embedding space that supports asymmetric deployment: documents can be indexed with the 9B model and queried with the low-latency 0.6B model. Both models are available at https://huggingface.co/collections/perplexity-ai/pplx-embed-v2.

Abstract: Dense retrieval has become a fundamental paradigm for modern information retrieval, supporting efficient semantic search across a wide range of applications. Its effectiveness, however, relies critically on query embeddings that adequately capture users' information needs, which can be difficult for short, ambiguous, or underspecified queries. Feedback-based query reformulation approaches like pseudo-relevance feedback (PRF) alleviate this by incorporating additional evidence from retrieved or generated content. However, existing embedding-space approaches commonly aggregate or interpolate feedback vectors, implicitly treating them as complete target representations. Such pointwise fusion can unnecessarily suppress query corrections along directions not expressed by individual feedback items, even when these directions are supported by complementary evidence. To address this limitation, we propose Directional Posterior Feedback Fusion (DIFF), a query reformulation framework that models feedback as directional evidence rather than target points. DIFF represents feedback as confidence-weighted directional evidence in the tangent space of the original query and jointly infers a controlled query update through prior-regularized posterior fusion, without retraining the underlying dense retriever. Experiments across multiple dense retrievers and different feedback sources show that DIFF achieves the best overall retrieval performance, demonstrating the effectiveness of explicitly modeling how feedback should constrain query updates.

Abstract: Generative retrieval (GR) casts search and recommendation as autoregressive generation of discrete semantic identifiers (SIDs). SID design largely determines GR quality, but its discrete, interdependent components (SID construction, collision handling, decoding, and training) cannot be optimized end-to-end with gradients and remain largely hand-designed. We introduce a framework that improves these components through LLM-driven evolutionary program search, to our knowledge the first application of this approach to GR. A locally served, open-weight 31B model mutates executable GR components, so no proprietary LLM API is used, and a 1M-parameter proxy decoder provides fast feedback in place of repeatedly training the 1B target generator. Across 21 SID programs on NQ320K, proxy and target Recall@100 show strong rank correlation (Spearman $ρ= 0.90$). Guided by this proxy, evolution improves the seed GR on NQ320K, MSMARCO300K, and a multilingual e-commerce dataset under a fixed training recipe. On NQ320K, jointly evolving SID construction and collision handling improves Recall@1 from 55.8% to 59.3% and Recall@100 from 85.8% to 90.6%. A component study shows that proxy reliability depends on what is evolved: improvements transfer reliably for the semantic index but not for the generator's training objective or the full pipeline. LLM-driven evolutionary search is thus a practical tool for GR design, provided proxy reliability is established for the chosen search space.

Abstract: Many modern language models have adopted hybrid architectures that incorporate both linear-time recurrence and softmax attention. Modern recurrence layers provide a highly expressive mixing mechanism while ensuring high throughput by compressing contextual information into a fixed-size state, but underperform softmax attention in contextual information retrieval. In this paper, we reveal a Competing Learning phenomenon where different kinds of mixers compete to learn the same function, and when any layer learns a function, it suppresses the corresponding learning signal for other layers. Layer attribution analysis reveals that under typical data distributions, modern recurrence learns retrieval functions faster than softmax attention, causing attention to fail to learn retrieval in most cases. Stopping weight updates in recurrence in the middle of training helps attention learn retrieval. Based on these results, we propose a staged training procedure for pre-training hybrid architectures on natural language. Empirical results on models up to 1B parameters show that our method results in substantial improvement in language modeling loss, common-sense reasoning, as well as a wide range of retrieval-related tasks across different context lengths.

Abstract: Answerability readouts predict whether a passage supplies an answer, but whether calibration can compensate for removing negative passages during training remains unclear. We present a controlled study of how training-negative construction affects calibrated prediction, ranking, and downstream answer retention. We compare native training, which retains negative passages, with empty training, which removes them, holding questions, labels, positive examples, and model weights fixed. Both are calibrated on the same labeled native examples. On SQuAD 2.0 and RepLiQA, native-trained logistic readouts at selected depths achieve lower Brier loss for Qwen2.5-7B-Instruct and Gemma-2-9B-it, with or without output scores. Native fusion also outperforms calibrated output alone. Post-hoc AUROC analysis shows better ranking under native training, beyond what threshold adjustment alone can explain. On the official SQuAD 2.0 development set, native readout policies improve F1 over empty policies but retain more answers to unanswerable questions. The advantage varies by estimator and depth, while RepLiQA's text shortcuts limit claims about contextual understanding. Unfinished generations prevent complete answer-level evaluation, although worst-case bounds preserve the native-empty F1 gains. Our findings show that training negatives affect ranking and downstream decisions even after common calibration, without establishing a universal advantage for native training.

Abstract: Agentic knowledge graph question answering (KGQA) requires large language models (LLMs) to solve complex questions through multi-turn interactions with a knowledge graph (KG). Outcome-supervised reinforcement learning derives verifiable outcome rewards from final answers but uniformly assigns each rollout's outcome-level advantage to all policy-generated tokens, creating a trajectory-to-operation mismatch since KG operations within a rollout can have varying effects on the search process and final answer. To address this, we propose Outcome-Anchored Credit Reallocation (OACR), which employs a training-only KG-state outcome model to estimate outcome-reward changes between adjacent KG search states and converts them into operation credit, from which token-wise weights are derived. These multiplicative weights reallocate token-level update magnitudes while preserving the sign of the outcome-level advantage at every generated token. Across three benchmarks, OACR achieves stronger overall performance than existing KGQA methods while using fewer inference-time LLM calls and tokens.

Abstract: Dense vector retrieval can miss evidence connected through intermediate entities, while direct graph retrieval requires access to the graph at query time. We compare five offline graph-based embedding transformations and strategies for using the resulting graph-modified embeddings alongside the originals, without query-time graph access. On a synthetic professional-network benchmark with complete supporting-evidence sets, direct replacement of the original embeddings reduces evidence recovery. Multi-stage strategies improve recovery by using graph-modified embeddings to guide the search while retaining the originals for semantic relevance. On questions requiring linked facts or comparisons among candidates, the strongest configuration improves recovery by up to 25.9% relative to plain vector retrieval. It also matches baseline recovery with 40% fewer returned nodes. Controls confirm that graph information contributes beyond multi-stage retrieval alone. Across the tested methods, retrieval performance depends more on how graph-modified embeddings are used than on how they are produced.

Abstract: Generative retrieval is known for its efficient end-to-end indexing and retrieval. In particular, numeric Document Identifiers (DocIDs) are generally more efficient because they are shorter and generally fixed-length sequences over a small vocabulary, requiring fewer decoding steps during beam search. However, they tend to generalize poorly to unseen documents and must be learned during indexing-stage training. In this paper, we propose a numeric DocID design for generative retrieval that enables better adaptation to unseen documents without retraining.Our DocID design inherits the language model's knowledge: each DocID is a sequence of tokens factorized into bits, and each token is scored as the sum of its bits. Unlike existing numeric DocIDs, whose tokens carry meaning only through embeddings memorized during indexing training, each bit here derives its meaning from the model's representation. Therefore, the DocIDs of unseen documents remain scorable without retraining.Experiments on three benchmarks show that our DocID design substantially improves unseen-document retrieval while maintaining comparable performance on seen documents. It achieves over 20 percentage points higher Hit@10 on unseen documents and up to 7 times lower inference latency than existing numeric DocID designs on NQ320K and TriviaQA, while performing only 3 percentage points below weight-update methods on MS MARCO without additional training. These results show that an appropriate DocID design can heavily reduce retraining costs when adapting generative retrievers to new documents.

Abstract: Under a limited context budget, a long-term agent must recall not merely memories that are individually relevant, but evidence that is collectively sufficient for the current query. Conventional memory access retrieves, scores, and truncates memories, often spending multiple context slots on redundant facts while leaving complementary evidence behind. We cast the read phase of long-term memory as query-conditioned evidence composition: each memory is valued by what it adds beyond the evidence already selected. We instantiate this operation with MemPursuit, a training-free mechanism that uses the residual of a sparse convex query reconstruction as a representation-space proxy for what the current memory set is missing. By reusing the query and candidate embeddings already available from retrieval, MemPursuit progressively composes nested evidence contexts without invoking a language model or cross-encoder to score each query--memory pair. The effectiveness of our method is verified on 3 popular benchmarks in comparison to strong baselines. In fixed-budget LoCoMo experiments, MemPursuit improves end-to-end accuracy by 7.2 percentage points at Top-10 and 5.5 percentage points at Top-20, with consistent gains across multiple memory frameworks, while achieving a 32.9$\times$ speedup in median reranking latency over fully batched BGE-v2-m3. Our implementation is available at https://github.com/FengQi-HITSZ/MemPursuit.

Abstract: Generative engines such as ChatGPT Web retrieve webpages to answer user queries, but only a subset are shown as citations. Understanding this retrieval-to-citation process is important for generative engine optimization (GEO), which aims to improve content visibility in generative-engine responses. However, prior studies mainly analyze final responses, leaving the internal execution process and its variation across model settings less understood. To this end, we conduct an observational study of four ChatGPT Web settings from ChatGPT 5.2 to 5.5, covering Instant and Thinking modes at the URL, hostname, and entity levels. We examine how ChatGPT rewrites queries, retrieves candidate webpages, and selects references. The Instant settings remain mostly single-round, while GPT-5.4 Thinking frequently performs multiple retrieval rounds. Across repeated runs, candidates retrieved more often are also more likely to be cited. We then evaluate Google Search and the OpenAI Responses API as external proxies. Responses API candidates provide broader coverage, while its citations more closely match sources cited by ChatGPT Web. Both proxies match ChatGPT Web better at the hostname and entity levels than at the exact-URL level. Even when combined, they recover only about one quarter of cited URLs. We further test whether these external signals remain predictive when combined. Within the external candidate set, a supervised model combining them reaches AUCs above 0.74 for GPT-5.3 and GPT-5.5 at all three levels. These findings suggest that GEO should distinguish retrieval visibility from citation visibility, account for rewritten queries and run-to-run variation, and consider hostname- and entity-level presence in addition to exact URLs. Differences across settings also suggest that GEO strategies should be re-evaluated when the deployed setting or serving environment changes.

Abstract: Jev's documented interface evaluates typed questions independently against shared evidence. We audit request independence in seven open Jev-style checkpoints on 276 constructed three-passage states from 92 TREC retrieval queries. Paired interventions separately change requested questions, displayed evidence, and candidate eligibility. Request expansion induces strict binary flips in 9.1%/8.0% of Nimble's judgments and changes 21.4%/18.9% of selection-or-abstention actions in TREC DL2019/2020 under a threshold of 0.5 fixed before inference. Correct-action rates change by 0.0/+8.2 percentage points, respectively, with 95% query-bootstrap intervals of [-6.0,6.0] and [3.8,12.6]. Field masking traces all 70 request-set flips to the schema fields serialized into each scoring prompt. In Von, fixing a shared separator's position eliminates two eligibility-induced preference flips in selected diagnostic states. Laya-typed's default CUDA path produces five passage swaps without strict binary flips, and both yearly action-change intervals include zero; in an FP32 rerun, its probability movement vanishes at the model's four-decimal reporting resolution.

Abstract: Late-interaction (multi-vector) models represent documents using a set of token-level vectors, providing a middle ground between cross-encoders and dense encoders in terms of quality and cost of embedding. However, compared to the latter, the indices are costly to store and score. Pooling and pruning based compression techniques are deployed widely but deteriorate in quality noticeably with aggressive compression. We investigate whether a lightweight change to the scoring function can recover retrieval quality after document-vector compression. For each combination of encoder, compressor, and vector budget, we learn a global linear correction by distilling the uncompressed model's score distributions over candidate documents. The encoder and compressor remain frozen, and the correction can be applied to each query at search time or once, offline, to the stored vectors. We evaluate the method with ColBERTv2 and Jina v4 on MS MARCO and BEIR, and with ColPali2 on the ViDoRe v3 visual document retrieval benchmark. Experiments cover four training-free compression methods, multiple vector budgets, in-domain adaptation, and transfer from MS MARCO to BEIR. In the in-domain setting, the correction improves over baseline compression in 154 of 160 BEIR settings, while transfer from MS MARCO is more variable across models and datasets. We also find that matrices trained with synthetic queries can improve over baseline compression on ViDoRe v3. These results show that a small learned correction can recover some of the quality lost to compression without retraining the encoder or recompressing the documents.

Abstract: System One models output constrained decisions and probability distributions rather than free-form text generation. While prevailing paradigms rely on structured schema objects to encode state, intent, and candidate choices, we revisit a fully natural language-based System One interface. In this framework, both the user request and each candidate option are expressed in natural language, supported by multimodal (image and video) auxiliary inputs. We introduce MetaEncoder, which fine-tunes a pre-trained Muse-Glimmer 30B decoder into an instruction-following decision-making encoder. To scale effectively across both small closed-set (< 256) and massive open-set (millions) candidate spaces, MetaEncoder employs a bi-encoder architecture trained via unidirectional contrastive learning for request-candidate alignment. We conduct extensive evaluations across 11 benchmark suites and 190 tasks spanning multimodal decision-making, understanding (closed-set) and retrieval (open-set), highlighting where MetaEncoder beats SOTA multimodal encoders, as well as its current limits on reasoning-intensive tasks.

Abstract: Cross-modal vector retrieval is widely used in multimodal systems, such as search engines and vector databases. It typically operates in out-of-distribution (OOD) settings, where query vectors follow a distribution that differs from that of the vectors stored in the database. In such cases, conventional indexes suffer significant performance degradation, and even methods specially designed for OOD remain limited by inefficient use of query modal characteristics, restricted GPU parallelism, and inadequate support for dynamic updates. We present CORAL, a novel GPU-accelerated graph-based vector index for scalable cross-modal retrieval, featuring hierarchical memory management that spans GPU, CPU, and disk. Specifically, CORAL incrementally incorporates the characteristics of query modality and terminates index construction timely. Crucially, it introduces coverage-aware adaptive pruning to address the imbalanced coverage of the query vector's neighbors. Moreover, CORAL presents a fully neighborhood-aware projection approach to efficiently utilize GPUs for highly parallel index construction, and a targeted connectivity enhancement method to refine the index structure. Besides, CORAL also supports modal-semantics-based vector insertion and topology-repairing deletion that restore node connectivity. Experimental results demonstrate that CORAL outperforms existing methods with up to 1.6 times the throughput at matched recall while reducing construction time by up to 56%. Furthermore, it exhibits remarkable resilience under dynamic updates and remains effective at the billion scale.

Abstract: Conversational Query Rewriting (CQR) turns a context dependent user turn into a standalone query for a retriever, and most methods do this in a single step from the dialogue history before retrieving once. The rewrite is therefore fixed before any corpus evidence is available to correct its reference resolution or its vocabulary. We recast CQR as a sequential retrieval problem: an agent rewrites the current turn, retrieves, and conditions its next rewrite on the returned passages. The agent acts in a typed space of three rewriting operations, resolving conversational intent into a standalone query, generating lexical reformulations, or synthesizing pseudo-documents for document-to-document matching, together with a stop action that ends the episode. We train the policy with supervised fine-tuning followed by reinforcement learning against a single retrieval-quality reward, using no human rewrite annotations. Across TopiOCQA and QReCC, the agent outperforms several retrieval-aligned baselines, while remaining effective across retrieval backends and generalizing to the CAsT benchmarks without additional training. Further analysis shows that, through retrieval-reward optimization alone, the learned policy develops a behavior of grounding pseudo-documents in passages retrieved by earlier steps, substantially improving retrieval.

Abstract: Retrieval diversification is widely available in retrieval-augmented generation (RAG) frameworks, yet prior studies disagree on whether it improves retrieval and answer quality. We show that its effectiveness varies primarily with candidate-pool redundancy, in a pattern consistent with the number of distinct evidence pieces a query requires. Using controlled near-duplicate injection and production-style overlapping chunking, we find that diversification harms relevance, evidence coverage and answer quality on clean pools, but becomes beneficial on multi-evidence tasks when redundancy causes nearest-neighbor retrieval to select repeated passages. We therefore introduce a query-adaptive rule that diversifies only when the effective number of distinct documents in the nearest-neighbor top-$k$ selection falls below the query's evidence requirement. Computed from existing embeddings, the rule captures most of the achievable gain, transfers across datasets and encoders and automatically reduces to nearest-neighbor retrieval for single-evidence queries. We also introduce RNG-Score, a geometric reranker with an exact nearest-neighbor fallback whose margin indicates duplicate structure. Overall, we conclude that diversification should be used selectively, based on observable redundancy and evidence requirements.

Abstract: Generative retrieval trains a language model to generate the identifier of a relevant document. Recent work replaces the autoregressive decoder with diffusion, but changes identifiers, training recipe and decoding at once, so differences cannot be credited to the paradigm. On NQ320K and MS300K, we train autoregressive, masked-diffusion and block-diffusion models with residual-quantised, product-quantised and random identifiers. With identifier length and training budget fixed, we decode each model in several ways. Decoding alone moves a diffusion model's Hit@1 by 6.6 to 13.7 points. Our reference diffusion decoding, generate-and-match, generates an identifier, then retrieves the closest corpus identifiers. The generated identifier is right for 14-21% of NQ320K queries. We test one-pass scoring to decode diffusion retrievers: the model reads a fully masked identifier once, and each document is scored by its codes' probabilities. It matches or beats generate-and-match in 11 of 12 settings. Autoregressive models still lead in Hit@1; on NQ320K, the lead comes from the model, not beam search. Starting from one sampled identifier, one-pass scoring removes 46-83% of masked diffusion's deficit to beam search; from generate-and-match, at most a quarter. On NQ320K, every paradigm largely memorises which identifier answers which query: random identifiers keep 83-90% of the Hit@1 of residual-quantised ones. There, product-quantised identifiers lead residual-quantised ones by 3.4 points in the autoregressive model and by -0.7 to +3.6 in diffusion models; across decodings, AR's gap exceeds diffusion's by 1.5-2.3 points, around our 2-point threshold. Paradigm comparisons must report each paradigm at its own recipe and best decoding.

Abstract: Sequential test-time training adapts a memory network through successive updates, each computing an inner-loop gradient based on the network's previous state. Intuitively, this state dependence should allow each update to account for what the memory has already learned and better incorporate new information. However, we find that this expected advantage does not consistently materialize in nonlinear memories: a fixed-base parallel TTT baseline outperforms its serial counterpart. Our exploratory experiments point to a key underlying difficulty: nonlinear memories can be harder to optimize than linear ones within a single pass over the sequence. To alleviate this optimization difficulty, we introduce DeltaTTT, which replaces joint inner-loop optimization of a two-layer memory network with layerwise learning. Each layer is assigned a local prediction target and updated through a state-dependent delta rule. This formulation retains a nonlinear readout while enabling chunkwise parallel computation. Experiments on DeltaNet and LaCT backbones show improvements in language modeling and retrieval over their recurrent baselines.

Abstract: A search tool never says no: it returns its top-k passages even when the index holds no answer, so the agent sees irrelevant text instead of a miss signal. We ask what frozen search agents do when the tool refuses instead. On an index-hole testbed (257 NQ and 300 HotpotQA questions run with and without their gold passages in a 21M-passage BM25 index), seven agents receive one of five refusal wordings. An un-announced one-sentence refusal raises abstention on unanswerable questions from 23% to 97% on average for Qwen3-8B/32B and from 28% to 57% for Claude Haiku 4.5, cutting wrong answers almost one-for-one and beating a system-prompt instruction by 51 points on average. Search-R1 ignores the refusal and fabricates retrievals; Claude Sonnet 5.5 and Opus 5.5 answer from memory (abstention +2 points) and obey a system-prompt directive instead (+16). We also found that wording matters: an explanation beats a bare token; a directive inside the observation is decisive for Haiku; a soft warning is useless. Realistic triggers, from a lightweight score-based predictor to an LLM grounding judge, fall well short of the oracle, and all land on a benefit-versus-signal-quality curve that prices any trigger by its recall at a fixed false-refusal budget: for compliant agents the bottleneck is the detector inside the tool, not the agent, and the curve tells future detector work what each point of recall is worth.

Abstract: We introduce HyperBrowseComp, a multilingual and multimodal browsing benchmark comprising 423 manually authored and human-validated questions across 13 languages, written by native or highly proficient speakers. Questions are designed to be extremely challenging. Each question targets a concise, publicly verifiable answer whose discovery requires locating obscure evidence, following multi-step clue chains, or inspecting heterogeneous sources such as videos, scanned documents, images, or maps. Easier questions are filtered out by evaluating them with models without internet access to reduce the likelihood that they can be answered with parametric knowledge alone. We evaluate several models using provider-native search and a shared external retrieval harness under a common agent protocol. To contextualize model performance and effort, we also conduct a human evaluation on a sample of the questions. HyperBrowseComp provides a challenging testbed for persistent information seeking across languages and evidence modalities, with difficulty arising from discovering and connecting evidence on the open web.

Abstract: Multilingual encoders can exhibit reduced retrieval effectiveness when queries and relevant documents differ in language, despite strong same-language performance. We investigate whether Finnish and Swedish cross-lingual retrieval can improve while preserving an encoder's existing same-language performance and document index. We combine a query-only low-rank adapter, trained against frozen document embeddings, with deterministic routing based on query and index languages. Cross-language queries use the adapter, while same-language queries use the original encoder. SampoTron, our fine-tuned low-rank (LoRA) adapter alongwith the Nemotron-3-Embed-1B model, improves average retrieval quality across six English, Finnish, and Swedish directions from 0.241 to 0.291 in normalized discounted cumulative gain (nDCG) at rank ten, a 20.9% relative gain on a sampled financial benchmark. All six cross-lingual directions improve, and routing preserves the original same-language performance, including two full-corpus Finnish evaluations. The approach enables selective cross-language specialization with reusable document embedding vectors.

Abstract: Recent work on neural sparse retrieval has demonstrated strong relevance by leveraging Large Language Models (LLMs) for semantic term expansion. However, learned models paired with previous sparsification techniques still yield overly long document and query vectors partly due to a large LLM vocabulary, imposing a serious challenge to retrieval time and space efficiency. This paper proposes a scheme for optimizing model sparsity through a synergy of adaptive strategies, including learnable soft top-K, per-term thresholding, and FLOPs regularization to increase the sparsity of query and document vectors. Experimental results with Lion-SP model on the MS MARCO and BEIR datasets demonstrate that the proposed scheme can outperform the baselines by significantly reducing the average query and document lengths. Our scheme can achieve much shorter retrieval latency and lower storage cost while maintaining highly competitive relevance.

Abstract: Large Language Models (LLMs) are increasingly used to enrich user queries in information retrieval (IR) so that a standard retriever such as BM25 can bridge vocabulary gaps with the target corpus. Any single LLM, however, is limited by its training data and architectural biases, and its enrichment behavior depends on hand-crafted prompts that must be re-engineered for each new model -- an expensive and poorly scalable process. We present MERGE (Multi-LLM Ensemble for Retrieval via Generative Enrichment), a two-stage framework: three heterogeneous 7-8B open-source LLMs independently produce candidate expansions, and a larger LLM generatively synthesizes them into a single query. To make prompt engineering scalable across the ensemble, we integrate a task-grounded Automatic Prompt Optimization (APO) loop into both stages. Unlike APO methods that judge candidates with an LLM evaluator, our loop scores each candidate by its downstream retrieval performance and runs a small tournament between the current champion prompt and optimizer-proposed drafts, terminating once the champion survives two consecutive rounds; a history-augmented variant additionally feeds the recent tournament trajectory back to the optimizer. MERGE is retriever-agnostic and issues a single BM25 pass with no rank fusion, no supervised document expansion, and no re-indexing. On five BEIR benchmarks (NQ, SciFact, FiQA, Touche-2020, DBPedia), MERGE improves BM25 nDCG@10 over the original queries by +2.1 to +14.9 points and matches or outperforms strong LLM-based query-expansion baselines despite using only compact open-source models. Ablations confirm that the Stage-2 ensemble beats any single Stage-1 LLM, and that task-grounded APO converts large seed-prompt regressions into consistent gains without hand-tuning.

Abstract: We often learn from multiple sources that convey information in different ways. How informative is it to know the source of a signal, and how is this informativeness shaped by the distribution of sources? We extend the standard (binary-state, binary-signal) Blackwell experiment model by introducing a commonly known distribution over signaling schemes, representing the distribution of information sources. We compare learning under two information models: source-aware, where decision makers observe a signaling scheme and its realization (e.g., raw reviews, search results), and source-blind, where only the signal realization is observed (e.g., aggregate ratings, LLM-generated summaries). We show that a mean-preserving spread in the distribution of signaling schemes translates into Blackwell dominance for source-aware decision makers, implying they are "risk-loving" in information sources. In contrast, it has no impact on source-blind decision makers. When learning from repeated draws of signaling schemes, source-blind decision makers learn more slowly. However, as long as the average signaling scheme is $\varepsilon$ away from being completely uninformative, source-blind learning can match source-aware learning by using at most $O(1/\varepsilon)$ times more data.

Abstract: Passage reranking plays a crucial role in information retrieval by refining the ordering of candidate passages to better reflect relevance. Existing listwise LLM rerankers with Chain-of-Thought (CoT) reasoning can handle complex queries effectively, but they suffer from substantial redundancy and high latency due to sliding-window strategies, which repeatedly generate highly similar CoTs. To address this, we propose QReason, a decoupled framework that separates query-focused reasoning from window-specific passage relevance assessment. Specifically, QReason introduces a dedicated rewriter that generates a ranking-oriented reasoning query once, capturing the query's core intent while avoiding redundant reasoning, and then reuses it across all windows with a non-reasoning reranker. The rewriter is trained via a two-stage process that first uses supervised fine-tuning with relevant-passage guidance through semantic evidence to produce deeply grounded, query-focused CoTs. It then applies reinforcement learning to align CoT generation with both the inference-time setting and the reranking objective, optimizing listwise metrics and passage-level discrimination to produce reusable reasoning chains for reranking. Experiments on the BRIGHT benchmark demonstrate that QReason significantly reduces redundant reasoning, achieves ranking performance comparable to or better than strong reasoning-based rerankers, and outperforms existing query rewriting models.

Abstract: Document retrieval is a crucial component of many modern AI systems, directly influencing their effectiveness, robustness, and fairness in downstream tasks. While recent years have seen a growing number of retrievers, comparative studies in the literature are typically limited in scope or focused on singular benchmarks, domains, or model families. This fragmentation makes it difficult to draw reliable conclusions about the relative strengths, weaknesses, and trade-offs of document retrievers. To address this gap, we conduct a large-scale empirical evaluation of document retrievers, covering three families (sparse, dense, and expansion-based) and evaluating 33 retrievers across seven IR datasets, analyzing retrieval quality, runtime, and failure points. Rather than tuning each model individually, we evaluate every retriever off the shelf, under the configuration reconstructable from its public documentation and a uniform compute budget. Our results show that NV-Embed-v2 achieves the strongest performance on four of the seven datasets, albeit at the cost of substantial query latencies. Among sparse retrievers, we find that SPLADE-v3 rivals the top-performing approach despite much lower latency, and even achieves top scores on MS MARCO. On instruction-following datasets, GritLM delivers the best performance. Finally, an analysis of the retrievers' failure points reveals contrasts between models and families that indicate potential for unrealized gains in retrieval performance.

Abstract: Retrieval-augmented generation (RAG) is hard to monitor in production: exhaustive relevance labels do not exist for non-stationary multi-million-passage corpora that re-index in real time. As a result, retrieval quality is generally understudied and often deprioritised in favour of generation-oriented metrics. In this work, we propose auditing retrieval coverage by probing for evidence of missing documents rather than enumerating every relevant one. Our method Re:CAP (REtrieval Coverage Audit by iterative Probing) is a reference-free audit loop applied to a deployed RAG pipeline's initial answer and retrieved context: it identifies the topics already covered, generates probing questions for plausibly missing topics, retrieves candidate documents, and applies an LLM-as-judge to retain only those that introduce previously-unretrieved information. On four public benchmarks, Re:CAP recovers 9-29% of gold labels that flat BM25 top-500 cannot reach, rising to 48% on TREC-COVID. On MuSiQue Re:CAP beats flat hybrid top-500 by +12.9 pp on recall at less than half the document budget. An ensemble BM25, dense, and hybrid baseline (top-500 each) still leaves out 21.2% of gold docs on TREC-COVID that Re:CAP recovers; human annotators judge that 78.9% of those structurally distinct documents add new information to the baseline answer (Fleiss $κ$ = 0.79, n = 123), and 73.9% on live production traffic (n = 180). End-to-end recall is reproducible to within $\pm$1% across three independent runs, making Re:CAP a stable instrument for periodic retrieval audits.

Abstract: Questions scraped from the web are used across academia and industry as a proxy for what people want to know. Across QA training data, retrieval benchmarks, and content strategy, questions on a page are assumed to reflect human intent. We test this assumption at scale by extracting 13.4B question occurrences across 110 FineWeb snapshots (2013-2025), and report three findings. First, you can tell who is asking: provenance (the host/page of questions) leaves a signal in question form, and a logistic model can separate genuine user questions from templated/manufactured ones at AUC 0.725 via length and surrounding context rather than question type, though only 0.554 against commerce FAQ writing. Second, question frequency does not measure demand: the most-frequent questions are boilerplate/templated (over 70% of the top thousand), so occurrence counts measure how often a string was published and not how often it was asked. Third, over twelve years the genuine share of occurrences fell by 79% (42-56% after controlling for crawl composition), with question length and context decreasing. We present the first diachronic, occurrence-level measurement of web question provenance, and find the crawlable web's questions have shifted from being asked by humans toward manufactured for machines to read.

Abstract: Approximate nearest neighbor search (ANNS) underpins large-scale vector retrieval in search, recommendation, and retrieval-augmented generation. Graph-based indexes have demonstrated state-of-the-art search performance for ANNS. They connect each corpus vector to a small set of nearby or navigationally useful vertices and answer queries by traversing the resulting graph. Because these edges are selected using construction-time distances, the graph index is tied to the embedding model. Re-encoding a corpus with a new model may change distances and neighborhoods of the vectors. Reconstructing the graph for the new embedding vectors incurs substantial construction cost and delays deployment. When the embedding model changes, we observe a phenomenon in the old graph index that we call residual reachability. Specifically, although derived from different models, the vectors describe the same underlying objects and often retain part of their similarity structure. These shared relations are reflected in the connectivity of the old graph index, leaving many exact new-model neighbors reachable within a few hops in the old graph index. Motivated by this observation, we develop an index-migration approach that utilize the residual reachability in the old graph index to faster construct the new graph index for the new embedding vectors. Our method, Drift-Guided Migration (DGM), provides two migration paths. DGM-Local performs parallel shallow expansion over the inherited graph index and screens second-hop candidates with packed position sign codes before exact evaluation. DGM-Search uses hop-bounded beam traversal to explore beyond shallow expansion. Across eight text and image migrations, our DGM methods can achieve up to 17.43 times speedup on constructing the new graph index than the fastest degree-matched reconstruction method while keeping competitive recalls.

Abstract: Recent work asks whether generative-engine visibility can be approximated with deterministic, engine-free page scores. We separate two stages such scores can conflate: exposure to a live engine and citation selection conditional on exposure. In an observational audit of ChatGPT, Microsoft Copilot, Google, and Perplexity, 15 fixed commercial prompts produced 589 citation observations on 6 June 2026, corresponding to 528 unique URLs and 356 domains. Same-prompt cross-engine URL overlap was extremely small: mean pairwise Jaccard similarity was 0.0079, the median was zero, and 84.9% of engine pairs shared no cited URL. On the ten prompts observed on all four engines, mean exact-URL Jaccard was 0.0072. A matched-size hypergeometric baseline preserving each prompt's four-engine URL universe and each engine's list length predicts 0.1272, so observed overlap was only 5.7% of that baseline; zero URL overlap occurred in 86.7% of comparisons versus 12.3% expected. Top-five exact-URL overlap was zero in all 60 pairwise comparisons. A single engine captured only 11.4%-42.6% of the four-engine URL union, and 96.4% of observed URLs appeared in only one engine. A separate 5-to-6 June same-engine comparison found 67.0% mean URL-set turnover. These results do not invalidate engine-free page scoring; they identify its estimand. A score computed without a live engine can estimate page quality or query-page fit, while end-to-end visibility additionally depends on engine-specific exposure and selection. We therefore argue for reporting page fit, observed exposure, conditional selection, and final visibility as distinct quantities.

Abstract: Multi-hop retrieval failures are not uniformly distributed across queries: they cluster in structurally predictable subpopulations. We prove two results formalizing this structure. First (CWAR Reducibility): confident-failure reduction is achievable if and only if retrieval features carry mutual information about success, a condition satisfied by LLM-judge pipelines but substantially weaker in dense-only settings, explaining the AUC-AC gap between regimes. Second (Feature Regime Complementarity): no single ANN score feature achieves best predictive performance across all failure regimes; the dominant feature differs between datasets (query length on MuSiQue, hop-1 concentration on HoVer), and a constructive witness pair shows each is necessary in one regime and non-contributory in the other. We instantiate these principles in RegimeAbstain, which computes a Retrieval Confidence Score (RCS), a logistic function of up to nine query-ANN structural features, all available without any additional LLM call, and uses it to implement a calibrated abstention policy. We define the Confident-Wrong-Answer Rate (CWAR) metric and evaluate across three multi-hop benchmarks (MuSiQue, 2WikiMultiHopQA, HoVer) and two retrieval architectures (LLM-judge and dense-only), covering five failure regimes with CWAR from 14.5% to 62.1%. RCS achieves best or co-best AUC-AC in all five conditions against eight confidence baselines. On MuSiQue (LLM-judge), RCS reduces CWAR from 39.5% to 20.6% at 50% coverage (47.8% relative reduction), with ECE=0.035. A model trained on MuSiQue transfers to 2WikiMultiHopQA with only -0.5pp AUC loss, confirming the domain-agnostic structure of regime features.

Abstract: Multi-hop retrieval-augmented generation (RAG) requires evidence that remains relevant to a query while introducing enough novelty to bridge semantic gaps. Dense retrieval tends to concentrate on semantically similar documents, whereas graph-based alternatives often depend on costly Large Language Model (LLM) entity extraction and may propagate through noisy connections. We introduce Geometric Gain Graph RAG (G$^3$RAG), a document-only framework whose offline graph construction uses no LLM calls or generated tokens. G$^3$RAG assigns each edge a geometric gain score, $\cosθ\cdot \sinθ$, that jointly captures directional consistency and orthogonality between document representations. A density-aware topological penalty suppresses highly connected hubs, while single-step controlled diffusion expands from filtered query seeds toward complementary evidence. We evaluate G$^3$RAG on MusiQue, 2WikiMultiHopQA, and HotpotQA using Nv-embed-v2 and Qwen3-8B-embed. G$^3$RAG obtains the best average F1 and answer-document hit rate among the evaluated graph-based baselines in both embedding settings, with gains of up to 4.26 F1 points in average performance and 5.76 points on MusiQue. It also removes the graph-construction token cost incurred by entity-based graph methods. These results show that geometric structure can support efficient multi-hop evidence discovery without LLM-based graph construction. Code is available at https://anonymous.4open.science/r/G3RAG-99D9/

Abstract: Traditional retrieval systems typically use multi-stage cascading architectures (MCA), where each module is optimized independently, leading to inconsistent objectives and the premature elimination of high-potential candidates. Recent LLM-based generation methods offer end-to-end solutions but use discrete semantic identifiers (SIDs) to retrieve ads, which are not learned by the base LLM and require memorization of numerous SID-to-ad mappings during SFT, suffering from limited generalization to unseen ads, high maintenance and update costs. The one-to-one mapping between SIDs and advertisements leads to inefficient decoding. Moreover, these methods rely on a small reward model (e.g. pctr) for relevance and ranking, limiting the LLM's ability to fully assess ads' commercial value. To address these challenges, we propose A uNified Generation-discriminative-ranking reaL-time rEtrieval (ANGLE) framework. ANGLE uses LLM-generated hierarchical textual representations, which consist of commercial intent that provide high-level overviews and ad abstract that deliver fine-grained details. Additionally, ANGLE integrates retrieval, relevance, and ranking directly within a single LLM, enabling precise and efficient ranking of ads by leveraging the full capabilities of the LLM. We applied ANGLE to the real-world search scenarios, achieving a 1.81% increase in consumption and a 2.16% increase in gross merchandise volume (GMV). We also conducted offline evaluations of ANGLE and seven baselines, with ANGLE outperforming all across key metrics such as HR and ACR.

Abstract: Local PageRank algorithms seek sparse approximations with work independent of graph size. We give a deterministic algorithm for regularized personalized PageRank with additive objective accuracy $ε$ in $\widetilde{\mathcal{O}}(1/(ρ\sqrtα))$ local work, where $α$ is the lazy teleportation parameter and $ρ$ is the regularizer. Accuracy enters only polylogarithmically. The bound charges discovery, repeated neighborhood scans, numerical updates, certification, and output, without graph-wide preprocessing or a supplied solution support. The algorithm combines regularization continuation with accelerated corrections constrained by a degree-scaled box and a mass cap. Two energies for the same recurrence control objective convergence and the response that activates coordinates. A selected-flow argument bounds cumulative scanned volume, and a sparse threshold reporter realizes the bound. We also specify a bounded-arithmetic implementation for rational inputs. A second, randomized algorithm uses support-safe threshold batches. A block-Cholesky and Chebyshev argument bounds their depth, and certified SDD solves give expected work $\widetilde{\mathcal{O}}(V_*\min\{k_*,α^{-1/2}\})$, where $k_*$ and $V_*$ are the optimal support's cardinality and degree volume. Both methods imply the corresponding accelerated degree-normalized PPR approximation. The concurrent September 2026 preprint of Cui, Wei, and Yang also attains the randomized work scale. Our principal distinction is deterministic local acceleration with only polylogarithmic overhead and no SDD oracle.

Abstract: TF-IDF and BM25 are two of the most widely used methods for scoring query-document relevance, yet neither has a standard probabilistic derivation that justifies it as a statistical method within a unified framework. We address this gap by showing that both scoring methods admit an exact interpretation as Kullback-Leibler divergences between two probability models. We treat the BM25 variant that includes the plus 1 correction in the IDF term, which is the one used in practice, and also discuss the original BM25 formulation without that correction. The resulting framework provides a common theoretical basis for TF-IDF and BM25, clarifies what they measure, and allows them to be compared theoretically with other information retrieval methods rather than only experimentally.

Abstract: Approximate Nearest Neighbor (ANN) algorithms achieve high efficiency through interdependent phases across index construction and query execution. This coupling allows upstream performance loss to propagate downstream, affecting execution behavior and measurable outputs. Existing component-level analyses mainly compare isolated design choices, while end-to-end benchmarks report aggregate metrics; neither traces loss propagation across dependent phases, hindering root-cause attribution and automated redesign. We present SmartANN, a framework based on the object causal model (OCM) for ANN bottleneck attribution and automated redesign. SmartANN represents an ANN workflow as eight ordered, replaceable objects and diagnoses them with a sequential diagnose-and-replace loop. At each iteration, it identifies the first object deviating from expected behavior or output as a bottleneck. Because an upstream bottleneck can obscure downstream ones, SmartANN replaces it with a test oracle when available, or with an implementation producing a better outcome, then continues downstream diagnosis. From the diagnosed bottlenecks and failure causes, SmartANN composes compatible actions from a pluggable action library to generate an optimized end-to-end ANN design. We instantiate SmartANN for IVF-PQ and HNSW, covering partition-and-quantization and graph-based ANN families. Experiments on eight real-world datasets show that SmartANN improves Recall by 0.24--74.20%, and increases QPS by 28.8--256.5% at comparable Recall, with low diagnosis and auto-design overhead. The code is available at https://github.com/zhouyutong20/SmartANN.

Abstract: Late-interaction models such as ColBERT achieve strong effectiveness by representing each document with many token-level vectors, but this expressivity leads to large indexing cost, storage footprints and expensive MaxSim scoring. We show that late-interaction representations exhibit an intrinsic low-rank structure: document token embeddings concentrate in a low-dimensional subspace that preserves most of the retrieval signal. Leveraging this observation, we introduce EigenLI, a spectral approximation framework that compresses late-interaction representations via document-specific low-dimensional subspaces. Unlike clustering or pooling methods, EigenLI identifies the dominant eigendirections of each document and uses them to construct reduced interaction representations. Empirically, $k$-EigenLI with $k \le 32$ outperforms k-means and Ward clustering based pooling methods on ColBERTv2 and AnswerAI-ColBERT-small; GTE-ModernColBERT exhibits a different tradeoff at $k=32$, where clustering methods perform better. The same spectral construction also yields EigenLI-SV, an ANN-compatible single-vector representation derived from the second-order summary of the reduced structure. Across multiple datasets and all three text models, EigenLI-SV consistently outperforms comparable single-vector surrogates such as MUVERA.