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math/0409202
Are quandles considered a specific type of set-theoretical solution to the quantum Yang-Baxter equation?
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math/0409202
What is the relationship between the algebraic structure known as quandles and solutions to the quantum Yang-Baxter equation?
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math/0410604
What is the potential for applying polynomial invariants used to distinguish phylogenetic trees to the quantum setting?
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math/0410604
I am looking for algebraic geometry methods that extend tree-distinguishing techniques from classical phylogenetics to quantum systems.
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math/0410186
I am looking for results concerning the compactness of the layer potential operator on boundaries with cylindrical ends where singularities are present.
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math/0410303
Who established that the Hilbert function associated with the Ext module of a power of an m-primary ideal becomes a polynomial of degree equal to the ring's dimension?
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math/0410604
What algebraic objects are associated with the parameter space of the general Markov model in recent literature?
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math/0412263
What are the current theoretical developments and proven results regarding minimum spanning trees in recent decades?
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math/0412263
How has the study of minimum spanning trees evolved over the last few decades, and what significant theorems have been established?
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math/0412429
How does applying kinetic theory to rarefied gases explain the universal behavior of wealth distribution and opinion formation in market economies?
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math/0412475
What are the stability conditions for a Pexiderized quadratic equation when the orthogonality relation is symmetric in a Banach space?
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math/0412475
I am looking for results on the orthogonal stability of functional equations where the underlying structure involves both a symmetric orthogonality and a Banach space setting.
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math/0412475
Who provided the general solution and proved generalized Hyers-Ulam stability for functions mapping a real vector space to a real Banach space?
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math/0412475
What are the specific contributions of Chang and Jung regarding the Pexiderized quadratic equation in the context of functional equations?
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math/0502417
What are the conditions under which Denham and Suciu proved a result regarding the homotopy Lie algebra of an arrangement?
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math/0502417
Which authors demonstrated that for hypersolvable hyperplane arrangements satisfying a specific technical constraint, the associated homotopy Lie algebra LA is well-defined?
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math/0503035
What applications have been identified for the Kantorovich metric in analyzing synthetic versus real continuous or mixed variables?
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math/0503088
What is the title of the seminal work by Raghunathan that establishes the existence of a specific nonzero ideal for every nonzero ideal in the context of the congruence subgroup problem?
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math/0503118
What is the spectral dimension of the uniform infinite planar tree, and how does comparing a random walk on a tree to this object improve known lower bounds?
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math/0503118
In the context of random walks on trees, what specific spectral value is associated with the uniform infinite planar tree that serves as a benchmark for lower bounds?
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math/0504049
Which publication by Feng Luo and Jean-Marc Schlenker demonstrates the extension of the Casson-Rivin angle structure program to closed triangulated 3-manifolds?
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math/0504049
Identify the 2007 paper that treats the Möbius tetrahedron as the geometric prototype for an angled 3-simplex within the context of volume and angle structures.
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math/0504513
What are the advantages of using a constrained heteroscedastic trimming algorithm for cluster analysis?
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Which study utilizes maximum likelihood estimation to identify outliers and then groups the remaining data points into distinct clusters?
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I am looking for a robust algorithm that handles outlier detection by applying maximum likelihood principles before performing simultaneous partitioning of the non-outlier data.
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math/0505120
Which researcher has analyzed Schrödinger operators where the associated potential class is defined in a relatively large but rather implicit manner?
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math/0505120
What work addresses the spectral theory for Schrödinger operators involving strongly singular potentials with an implicitly defined class of potentials?
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math/0505120
Who are the researchers who independently rediscovered and expanded upon spectral theory for Schrödinger operators with strongly singular potentials?
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math/0505120
Can you identify the specific pair of authors credited with reviving interest in the spectral analysis of Schrödinger operators featuring strong singularities?
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math/0505219
What condition defines a bottom tangle as boundary in terms of bounding mutually disjoint Seifert surfaces in three-dimensional space?
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math/0505334
How does the technique of algebraic shifting transform an arbitrary simplicial complex into a shifted version, and what role does this play in establishing rigidity results for doubly Cohen-Macaulay complexes?
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math/0506287
Which prior work on structure constants in the spherical Hecke algebra is cited as the predecessor to the Gaussent-Littelmann formula?
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What is the specific reference attributed by Schwer for an earlier result related to Hall-Littlewood polynomials and spherical Hecke algebra structure constants?
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math/0505457
Who demonstrated that solutions to the cubic NLS and DNLS are locally well-posed in L^p for 1 < p < infinity with global existence extending to 5/3 < p < 2?
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math/0506591
Which study demonstrates that the Neuhauser-Pacala model converges to super-Brownian motion with a non-trivial drift upon appropriate scaling?
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math/0507536
How can one mathematically characterize a sequence of bounded variation to ensure it has a unique representation within its associated group structure?
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What is the name of the mathematical framework that extends classical analysis to handle paths of bounded variation and defines a reduced path group?
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math/0507536
Which paper establishes the uniqueness of the signature for paths with bounded variation within the context of rough paths theory?
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math/0508058
How does the concept of gauging in integrable systems transform the Calogero system into a generalized Euler top with gyrostat momentum?
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math/0509262
Could you explain the specific lower bound on the parameter alpha that Tao proved is required for the Lp boundedness of the multilinear restriction operator in dimension d?
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How did the development of multilinear analysis and the polynomial method contribute to solving problems related to the Kakeya conjecture and multilinear restriction estimates?
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math/0510529
What are the algebraic properties of the quotient ring formed by a two-sided ladder ideal within the associated polynomial ring?
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Is it possible for determinantal varieties derived from mixed ladder configurations to possess the Cohen-Macaulay property in their defining quotient structures?
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I am looking for a reference that resolves the local Donaldson-Thomas theory for curves on toric manifolds via explicit computation.
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I am looking for the paper discussing local Donaldson-Thomas theory where it is shown that certain conjectures extend to specific geometric boundaries and underpin degeneration arguments.
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What is the mechanism for defining composition in the context of coloured operads and homotopy algebras?
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What is the correspondence between the elements of the colored operad Delta and the fundamental components defining a category's structure?
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Who is the mathematician credited with pioneering noncommutative geometry in the 1980s, and what are some recent developments in this field?
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How does Dyson's partition rank concept extend to overpartitions, specifically regarding the definition of the D-rank in terms of the largest part and number of parts?
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What is the explicit formula for the D-rank of an overpartition, defined as the difference between the largest part and the count of parts?
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How can a specific ordered sequence of alpha and beta steps be reinterpreted as a lattice path starting from a prescribed initial position to study Rogers-Ramanujan identities?
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How are lattice paths encoded using a binary word and an initial vertical position to characterize overpartitions in the context of Rogers-Ramanujan identities?
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What is the relationship between the structure of fully characterized lattice paths defined by a binary sequence and their connection to Rogers-Ramanujan identities?
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Which paper establishes that stationary viscous Hamilton-Jacobi equations admit a unique solution in L1 with an L1 gradient?
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I am looking for results on the uniqueness of unbounded solutions for stationary viscous Hamilton-Jacobi equations where both the function and its gradient are integrable.
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Under what conditions on the gradient and function space can one establish uniqueness for stationary viscous Hamilton-Jacobi equations with unbounded solutions?
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Which paper demonstrates that a solution to a stationary viscous Hamilton-Jacobi equation exists uniquely within the class of functions in L-infinity where the gradient is also in L-infinity?
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What is known about the uniqueness of unbounded solutions for stationary viscous Hamilton-Jacobi equations?
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I am looking for research on minimal entropy and geometric decompositions specifically applied to four-dimensional manifolds with Seifert fibrations or geodesic circle foliations.
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What are the main results regarding deformation rings and Hecke algebras established in a manuscript circulated by Fujiwara over totally real fields?
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What is the established lower bound for A2(D) in U-type designs that serves as a benchmark for design evaluation?
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Which study provided a useful lower bound on the A2(D) criterion specifically for U-type designs to assist in evaluating their quality?
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How do existing measures of supersaturated designs relate to each other in the context of Xu and Wu's work?
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What specific connection did Xu and Wu demonstrate between the standard criteria used for evaluating supersaturated designs?
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How are specific lattice Boltzmann method limiters constructed by decomposing the distribution function into its quasiequilibrium component and a nonequilibrium part?
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What is the standard mathematical representation of the nonequilibrium contribution in LBM limiters, expressed as a product of a norm and another term?
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0704.0159
What is the primary alternative explanation proposed for the formation of the commensurate 2x2x2 state in 1T-TiSe$_{2}$?
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Does the transition to a specific commensurate structure in 1T-TiSe$_{2}$ result from exciton condensation or some other mechanism?
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Which material is identified in recent literature as a primary candidate for hosting an excitonic insulator phase, specifically linked to the observation of a charge-density wave instability near 200 K?
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I am looking for research discussing the proposal that a specific transition metal dichalcogenide, characterized by a low-temperature charge-density wave transition, could be the host for an excitonic insulator state.
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How does the ADCR method contribute to the holistic characterization required in quantum circuit layout generation?
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How do researchers automate the generation of layout and control parameters for quantum circuits?
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What is the process for deriving a complete quantum circuit from a tile-based layout by computing qubit movement from storage?
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0704.0737
What is the status of deriving the proposed structure for soft terms when generalized to Calabi-Yau models?
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Are there existing derivations that explain how soft term structures apply in large volume compactifications within Calabi-Yau geometry?
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What are the two key observations used to conjecture the specific form of soft terms arising from large volume compactifications in string theory?
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0704.0802
How does a random access protocol function within a distributed multiple-relay-single-destination architecture in hybrid automatic repeat request systems?
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0704.0802
What are the characteristics of a scheme where multiple relay nodes and a single sink node operate using distributed hybrid ARQ with opportunistic selection?
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0704.1249
Identify the literature describing maximal Cohen-Macaulay modules for isolated complete local commutative Gorenstein singularities as instances of exact stably 2-Calabi-Yau categories.
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How are square and triangular involutions classified for grid polygons derived from permutations using the kernel method, specifically regarding their maximum number of faces?
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What are the specific examples of stably 2-Calabi-Yau categories arising from isolated hypersurface singularities and preprojective algebras associated with Dynkin quivers?
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Which paper provides concrete instances of stably 2-CY categories, such as Cohen-Macaulay modules over isolated hypersurface singularities or representations of preprojective algebras for Dynkin types?
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I am looking for research that establishes upper bounds on the effectiveness of layout-preserving quantum circuit optimizations alongside practical automation methods for these transformations.
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How do one-loop open string corrections and alpha-prime effects influence the resulting FI models in string theory compactification scenarios?
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What is the stable category of maximal Cohen–Macaulay modules for one-dimensional hypersurface singularities?
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What do existing research findings indicate about human motivation and capability to sustain personal digital archives across local and cloud storage environments?
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What historical limitation in stellar occultation analysis of Titan's atmosphere prevented the study of nitrogen cross sections prior to recent years?
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Why were measurements limited to hydrocarbon components during the earlier phase of stellar occultation studies on Titan?
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What is the primary methodological distinction between ISS observations and UVIS measurements regarding how they derive extinction coefficients in Titan's upper atmosphere?
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What are the proposed strategies for enhancing search efficiency in network navigation, specifically regarding multi-source random walks and route information integration?
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How can network search efficiency be improved by incorporating route information or employing random-walk strategies from multiple starting points?
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What specific modifications to navigation on networks involve using routes and multi-source random walks to enhance search performance?
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What are the common behaviors of individuals regarding the long-term preservation of their digital assets when they depend on internet service providers?
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What is the electrical behavior of the original topological insulator state near the Dirac point, specifically regarding how conductance scales?
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I am looking for experimental evidence of one-parameter scaling laws that apply to the electronic properties of graphene at its charge neutrality point.
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What are the key parallels between curating internet-based personal data and managing local digital assets?
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How does the theta term influence the flow of a system with small conductivity toward fixed points in graphene models?
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How does a transverse magnetic field gradient influence the refractive index profile of an Electromagnetically Induced Transparency medium to steer a light beam?
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What mechanism causes optical beam deflection in EIT media when the magnetic susceptibility becomes spatially inhomogeneous due to field gradients?
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I need a model that improves accuracy over earlier approaches when estimating the frequency trajectory of a beneficial allele in regions with large recombination rates.
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End of preview. Expand in Data Studio

sci_index_train

A high-quality semi-synthetic training set for embedding models for searching scientific literature. It consists of 142,478 training and 7,516 dev queries over arXiv, with 631,611 query-paper positive pairs and mined hard negatives.

We create this dataset to model how users actually pose queries for literature search. We mostly target descriptive information needs ("recent advances in formal verification of stochastic dynamical systems") instead of titles or keywords. Many of these queries have several relevant papers, not one. These are the cases where general-purpose embedding models do worst.

We employ this dataset to fine-tune granite-embedding-small-english-r2 in our scientific_granite model. On the held-out benchmark sci_index_bench it improves ndcg@10 from 0.756 to 0.800, with +0.082 on exploratory queries, showing the value of this dataset for fine-tuning embedding models for literature search. The gains also generalize to other benchmarks with gains in ndgc@10 of +0.057 on LitSearch over the base model.

Dataset composition

We synthetically sample different types of input queries.

category rows row % positive pairs pair % pos/row neg/row median words of which jargon variants
nl_question 48,864 34.3% 48,864 7.7% 1.0 14.5 13 6,477
exploratory 39,103 27.4% 389,344 61.6% 10.0 90.5 12 7,056
problem 27,172 19.1% 27,172 4.3% 1.0 14.3 8 2,759
cit_rewrite 15,579 10.9% 154,471 24.5% 9.9 89.2 21 105
known_item 5,994 4.2% 5,994 0.9% 1.0 14.7 12 966
keyword 5,766 4.0% 5,766 0.9% 1.0 8.3 5 1,640
train total 142,478 631,611 19,003

dev: 7,516 queries in the same proportions (nl_question 2,606 · exploratory 2,074 · problem 1,442 · cit_rewrite 751 · known_item 330 · keyword 313).

These categories simulate the following:

category what it simulates example
exploratory a survey-style topic need with several relevant papers current limitations and scaling challenges in high-density associative memory architectures
cit_rewrite a specific research question, phrased the way other papers describe the cited work How do latent diffusion models utilize a gradual spreading of data distribution to perform short-term rainfall prediction?
nl_question a natural-language question about one paper's finding Can federated learning match centralized training on generalizing to unseen mammographic data?
problem a terse, search-engine-style description of a problem or method domain expert annotated dataset for medical summarization
keyword keyword fragments improved sugama collision
known_item a half-remembered paper: partial or garbled title, often with an author a paper by Antamanova, something about Anode current saturation of
  • Jargon variants (13.3% of rows, generator starting with jargon_) are copies of another query in the same category with a technical term swapped for its acronym, its expansion or a synonym. They are paired with the original query and share its labels, which teaches invariance to how a concept is named. Either a curated acronym lexicon (jargon_lexicon) or an LLM (jargon_llm) made the substitution.
  • cit_rewrite queries are LLM paraphrases, written as questions, of sentences in which other arXiv papers cite the target paper. The sentences were retrieved via the Semantic Scholar API. No citation sentence is included verbatim.

Schema

column type notes
query_id string content hash of the query
category string query type (table above)
generator string specific generator; jargon_* marks a jargon variant
model_tier string model (or algorithmic) that produced q
register string question · brief · keyword · statement · recollection
specificity string broad · specific
paper_id string arXiv ID of the paper the query was generated from
q string the query text
positives list[string] arXiv IDs of relevant papers, sorted by positive_scores (descending)
positive_scores list[float] cross-encoder relevance in [0, 1], aligned to positives
hard_negatives list[string] arXiv IDs of mined non-relevant papers
no_in_batch_negatives bool true for multi-positive rows. Mask their positives from each other
dev_hard bool dev only: the lowest-lexical-overlap tercile (2,929 rows)

Single- vs multi-positive rows. For the four single-positive categories, positives == [paper_id]. For exploratory and cit_rewrite, positives is the top 10 candidates by cross-encoder score, whether or not they include the source paper. The source paper is in the set for 40% (exploratory) and 67% (cit_rewrite) of rows, because another paper often answers the query better. Treat positive_scores as soft labels. The lowest-ranked positives can score close to 0, so a hard 0/1 reading over-trusts the tail.

Positives and negatives are arXiv identifiers, not text. A script that rebuilds the paper text from the public arXiv metadata snapshot ships with the dataset (Getting the paper text).

Usage

We only include the arXiv identifiers with this dataset since not all papers on arXiv come with sufficiently permissive licenses. To use the dataset, one thus has to re-recreate the corpus from the kaggle snapshot of arXiv metadata. Download this snapshot, then you can use the rebuild_corpus.py script to recreate the required corpus:

pip install pyarrow

python rebuild_corpus.py --snapshot arxiv-metadata-oai-snapshot.json \
    --ids . --verify doc_checksums.parquet --out corpus.parquet

⚠️ Important Notes

  1. Row share is not signal share. exploratory and cit_rewrite rows carry ~10 graded positives and ~90 hard negatives each. The other four categories carry one positive and at most 15 negatives. exploratory is 27% of rows but 62% of positive pairs. If you flatten rows to (query, positive) pairs, the mix you train on is not the mix in the row counts.
  2. Mask positives out of in-batch negatives. Rows with no_in_batch_negatives = true (all exploratory and cit_rewrite rows) have several genuine positives. If two of a query's positives land in the same batch, standard MNRL will push them apart.
  3. Don't tune on dev and then report sci_index_bench. All 6,825 benchmark queries come from this dataset's dev split. Use the benchmark's selection split for checkpoint selection and report its test split. dev here suits in-training monitoring.

How the dataset was built

  1. Corpus. All arXiv papers in the July 2026 Kaggle metadata snapshot with a title and an abstract of at least 200 characters, deduplicated by normalised title: 3,040,442 papers.
  2. Source papers. A stratified sample of source papers. Papers from the evaluation benchmarks below were excluded from the sample.
  3. Query generation. Per category, LLM or algorithmic (tables above). The LLM prompts (shared by every LLM category, including the Gemini one) ask for a search need rather than a summary of the paper. They forbid naming the paper or its authors, never reuse the title as a phrase, and copy at most 4 consecutive words from the title or abstract.
  4. Quality control. Schema validation, exact-normalised deduplication across all categories, fastText language ID, and a check that no keyword / known_item query is simply the paper's title. All categories except exploratory also pass a round-trip filter, which keeps a query only if a frozen granite-embedding-311m-multilingual-r2 ranks its source paper in the top 100 of the full corpus.
  5. Hard-negative mining. Candidates are the union of BM25 and dense retrieval (top 100 each) over the full corpus.
    • Single-positive rows: NV-Retriever TopK-PercPos drops any candidate scoring ≥ 95% of the positive. A BAAI/bge-reranker-v2-m3 cross-encoder then drops any negative scoring within 0.05 of the positive. At most 15 negatives are kept.
    • Multi-positive rows: the cross-encoder scores every candidate. The top 10 become graded positives, candidates below the median score become negatives, and the ambiguous middle band is discarded.
  6. Packaging. Rows left with no negatives are dropped. For categories over quota, the 5% tails of the positive–negative cross-encoder margin are trimmed before random downsampling. exploratory has no single positive to take a margin against, so it is only downsampled. The train/dev split is by source paper (5% dev).
  7. Evaluation-set decontamination. Every paper in the LitSearch and DORIS-MAE corpora that could be matched to arXiv (by ID for DORIS-MAE, by normalised title for LitSearch) is removed from every role: source papers, positives and hard negatives. That is 20,898 papers in total, and it removed 3,005 positives and 46,218 negatives from training rows. Six rows were left with no negatives and dropped. The released data references none of the 20,898 papers (verified).

Limitations

  • Synthetic queries. All queries are LLM-generated or algorithmically constructed, not sampled from search logs. They are designed to resemble literature-search queries and are not evidence of what people actually ask. The LitSearch and DORIS-MAE results are evidence that training carries over to human-written queries but we expect possible gains from actual human logs.
  • Uneven query-shape coverage. keyword + known_item are 8.2% of rows, and title-as-query is absent. Models trained on this data regress on title lookup and keyword-style benchmarks.
  • Uneven negative depth. Multi-positive rows average ~90 negatives. The rest are capped at 15, and keyword averages 8.3 (37.5% of keyword rows have fewer than 5).
  • The train/dev split is by source paper only. A paper can still appear as a positive on both sides: 32.7% of papers that are dev positives are also train positives. No query text or source paper is shared. sci_index_bench removes this overlap from its relevance labels.
  • Labels come from models. Multi-positive sets and negative filtering rely on a cross-encoder. There are no human relevance judgements.
  • Deduplication is exact-normalised only. There is no near-duplicate pass. Jargon variants are near-duplicates by design.
  • English and arXiv only. Physics, mathematics and computer science are well covered. Biomedicine, chemistry and the social sciences are thin.
  • No test split. Report on sci_index_bench test or an external benchmark.

Licence

MIT. The dataset contains generated query text and arXiv identifiers. No paper titles, abstracts or full texts are redistributed. The arXiv metadata compilation it refers to is CC0.

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