NIR: Approximate Neural Instance Retrieval for ALCIQ

Dense retrieval models are typically trained with contrastive objectives that learn effective representations but do not directly optimize retrieval metrics or downstream task performance. To address this problem, we introduce RELER (REinforcement LEarning for Retrieval), a reinforcement learning framework that enables existing embedding models to learn to retrieve directly in embedding space and align to task-specific rewards. We train RELER by sampling unit-length query and document embedding actions from von Mises-Fisher (vMF) distributions centered on normalized encoder outputs, scoring the resulting retrieval or downstream outcomes as rewards, and updating the encoder with REINFORCE using a leave-one-out baseline (RLOO). As exploration in the high-dimensional embedding space is prone to sampling noise, we further propose conditional-mean projection (CMP), which projects each sampled embedding onto the low-dimensional subspace spanned by its encoder output and the candidate embeddings it is compared against, reducing noise in the policy gradient while preserving its expectation. We evaluate RELER on BRIGHT, a benchmark with reasoning-intensive queries that remain challenging for existing embedding models. RELER consistently outperforms InfoNCE and LambdaLoss in average nDCG@10 when post-training BGE-M3 and Qwen3-Embedding backbones. We further evaluate downstream utility through retrieval-augmented generation (RAG), where we adapt only the query encoder while keeping the document index and generator fixed. Across seven QA datasets, jointly optimizing retrieval and answer rewards improves both average retrieval performance and answer quality in RAG.

Complex information needs may involve set-compositional queries using conjunction, disjunction, and exclusion, yet it remains unclear whether current retrieval paradigms genuinely satisfy such constraints or exploit `semantic shortcuts'. We conduct a reproducibility study to benchmark major retrieval families and reasoning-targeted methods on QUEST and QUEST+Variants, and introduce LIMIT+, a controlled benchmark where relevance depends on arbitrary attribute predicates and constraint satisfaction, and less on pretrained knowledge. Our findings show that (i) on QUEST, the best neural retrievers achieve an effectiveness that is more than double what can be achieved with BM25 (Recall@100 ${>}$0.41 vs.\ 0.20), but reasoning-targeted methods like ReasonIR and Search-R1 do not outperform general-purpose retrievers uniformly; (ii) on LIMIT+, gains fail to transfer, where the strongest QUEST method collapses from Recall@100${\approx}$0.42 to below 0.02, while classic lexical retrieval gains to ${\sim}$0.96. Lastly, (iii) stratifying by compositional depth reveals a consistent degradation across all methods, where algebraic sparse and lexical methods show more stable performance while dense approaches collapse. We release code and LIMIT+ data generation scripts to support future reproducibility and controlled evaluation.

Efficient vector retrieval requires both a corpus geometry that supports retrieving the right documents through vector similarity, and a query encoder that can embed queries near their desired documents in the embedding space. Recent work has studied geometric capacity through the lens of the minimum embedding dimension needed to realize all top-$k$ answer sets of $n$ documents. We study a different notion of geometric capacity--the maximum recall achievable for a frozen document index--and explore whether learned query encoders can reach this ceiling. On several real-world retrieval benchmarks, we show that retrieval quality of single-vector query encoders often lies far below what the document indices can support. Motivated by this observation, we give theoretical evidence that learning query encoders can be computationally hard. In particular, we construct a retrieval task that (1) admits a query encoder with perfect recall which is representable by a small one-hidden-layer ReLU network, but (2) any statistical-query learner (a class capturing learners that access training data through aggregate statistics) provably requires exponentially many statistical queries to achieve non-trivial recall advantage over the random baseline $k/n$. Taken together, our results suggest substantial unrealized geometric capacity in retrieval benchmarks and establish query encoder learnability as a possible barrier in embedding-based retrieval.