We evaluate embedding retrieval where surface form and meaning are pulled apart on purpose: retrieving items that share underlying structure but not wording, in two unrelated domains under one protocol, competition mathematics (MathNet-Retrieve; 500 queries, 117,088-item corpus) and embodied-agent trajectories (ALFWorld-derived; 118 queries, 336 trajectories). In mathematics the failure is complete: strict Hit@1 at the heaviest disguise tier is 0.0% for both production embedders (bootstrap 95% CI [0.0, 0.0]) while the correct item sits in the top 10 nearly always, and in 95.2 to 99.8% of misses the winner is more lexically similar to the query than the correct answer. In trajectories, where surface variation is incidental, the same models land at or near hypergeometric chance when gold must involve a different object, and below chance for all three embedders once gold must differ in object and receptacle: retrieval anchors on literal tokens, not task structure. A lexical reranker control hurts in mathematics and helps in trajectories (closing 26 to 36% of the gap, CIs excluding zero); its sign reveals whether a benchmark's surface variation is adversarial or incidental. An LLM reranker recovers 5 to 63% of the gap in mathematics and 43 to 76% in trajectories; direction replicates across three judges (all 21 cells positive), but effect sizes, tier profiles, and the outlier judge change with domain (paired differences excluding zero everywhere). Mathematics gains concentrate on well-known competitions (+19.8 points, CI [+6.7, +33.2], one of six cells), so part of the recovery is memorization. In a paired downstream experiment (210 queries, graders at 96 to 99% agreement), oracle retrieval was indistinguishable from adversarially bad retrieval (McNemar p = 0.678); the solver's 69.5% zero-shot accuracy is largely a truncation proxy (97 to 100% on finished answers), leaving no headroom.
Nikolay Georgiev, Maria Drencheva, Kseniia Ibragimova +3cs.IR cs.AI cs.CL cs.LG
As agentic AI systems tackle more complex mathematical tasks, they increasingly rely on information retrieval (IR) to search problem databases, theorem libraries, and educational resources. However, choosing the right retriever remains difficult, as it is infeasible to directly isolate its effect on downstream performance. On the other hand, existing retrieval-specific benchmarks often fail to capture fine-grained mathematical relevance, penalizing relevant documents. We address this gap by introducing SABER-Math, the first fully automated benchmark for evaluating mathematical IR without expert annotation. Starting from 283K high-school-level math problems with solutions, SABER-Math builds challenging reranking tasks in three steps: (i) first, LLMs extract concise solution summaries and mathematical topics for each problem; (ii) then, per-query relevant documents are discovered using ontology topic-based and lexical solutions-summary-based similarities, and (iii) finally, a Swiss-style LLM preference tournament produces fine-grained relevance ratings for the documents. We evaluate lexical retrievers, specialized mathematical retrieval systems, and recent embedding models. We find that while modern embedding models substantially outperform classical and math-specific baselines, even the strongest systems struggle in symbol-heavy domains like Algebra and Calculus. Importantly, we show that general-purpose IR benchmarks such as MTEB do not reliably predict mathematical performance, especially for recent embedding models, highlighting the need for math-specific retrieval benchmarks.