Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2109.08655

Semantic Preserving Bijective Mappings of Mathematical Formulae between Document Preparation Systems and Computer Algebra Systems

Howard S. Cohl·Moritz Schubotz·Abdou Youssef·André Greiner-Petter·Jürgen Gerhard·Bonita V. Saunders·Marjorie A. ~McClain
View original source ↗Read source document ↗Export metadata ↓

Abstract

Document preparation systems like LaTeX offer the ability to render mathematical expressions as one would write these on paper. Using LaTeX, LaTeXML, and tools generated for use in the National Institute of Standards (NIST) Digital Library of Mathematical Functions, semantically enhanced mathematical LaTeX markup (semantic LaTeX) is achieved by using a semantic macro set. Computer algebra systems (CAS) such as Maple and Mathematica use alternative markup to represent mathematical expressions. By taking advantage of Youssef's Part-of-Math tagger and CAS internal representations, we develop algorithms to translate mathematical expressions represented in semantic LaTeX to corresponding CAS representations and vice versa. We have also developed tools for translating the entire Wolfram Encoding Continued Fraction Knowledge and University of Antwerp Continued Fractions for Special Functions datasets, for use in the NIST Digital Repository of Mathematical Formulae. The overall goal of these efforts is to provide semantically enriched standard conforming MathML representations to the public for formulae in digital mathematics libraries. These representations include presentation MathML, content MathML, generic LaTeX, semantic LaTeX, and now CAS representations as well.

Explore related subjects

cs.IRcs.DL

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Howard S. Cohl, Moritz Schubotz, Abdou Youssef, André Greiner-Petter, Jürgen Gerhard, Bonita V. Saunders, Marjorie A. ~McClain. 2021-09-17. Semantic Preserving Bijective Mappings of Mathematical Formulae between Document Preparation Systems and Computer Algebra Systems. https://doi.org/10.1007/978-3-319-62075-6_9

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

UniRec: Cross-stage Multi-Task Fusion with Preference Alignment for Cascaded Recommender Systems

Industrial recommender systems use cascaded stages with different objectives, feature spaces, and latency constraints. Optimizing pre-ranking and ranking separately can create cross-stage inconsistency: upstream models may filter out items preferred by downstream rankers, and independently tuned downstream fusion can offset upstream improvements. Existing multi-task fusion methods focus on multi-objective fusion within the ranking stage, and cross-stage methods typically only add a downstream score factor to upstream ranking. Joint optimization of fusion modules across both stages remains largely unexplored. We propose UniRec, a Unified Cross-stage Recommendation Fusion model. First, the two fusion agents partially share input embeddings and are trained in a single computation graph, so gradients from either stage propagate through the shared representation and influence the other. Second, we introduce a dual-axis preference alignment objective: a vertical cross-stage consistency term transfers downstream pairwise preferences to the upstream fusion score, and a horizontal compact aggregation term reorganizes dozens of pairwise objectives over heterogeneous prior signals into bidirectional preference evidence. Third, we find that unconstrained end-to-end fusion optimization can exploit imbalances in item attribute distributions, over-concentrating on high-reward regions at the cost of other objectives. We therefore add an attribute group-relative regularization that computes advantages within attribute groups and normalizes the policy over the same groups, so uniformly promoting an entire high-reward group yields no optimization gain. Offline, UniRec consistently outperforms single-stage fusion and cross-stage coordination baselines. Online A/B tests show a 0.616\% gain in app usage duration. UniRec is fully deployed on the Kuaishou platform.

cs.IR↗
arXiv2026

VikingRAG: Accurate and Token-efficient Retrieval-augmented Generation over Structured Documents

State-of-the-art retrieval-augmented generation (RAG) methods exploit document structures to acquire sufficient evidence, but often incur substantial token costs. To reduce structural-context tokens without compromising high RAG accuracy, we present {\sf VikingRAG}, a directory-aware semantic data management system that tightly integrates semantic and structural access to support structural-context-efficient, evidence-gap-driven multi-round retrieval. To further reduce token overhead of multi-round interaction, we materialize agentic multi-round retrieval traces as experience edges, and reuse these edges for similar queries, avoiding repeated multi-round exploration. To additionally reduce token costs when agentic multi-round retrieval is unnecessary, we introduce an adaptive escalation strategy that answers from one-round experience-augmented retrieval when the evidence is sufficient, and invokes agentic multi-round retrieval only otherwise. Experiments on real datasets show that the base system {\sf VikingRAG} matches high accuracy of state-of-the-art methods while consuming only 11.6\%--51.9\% of their tokens. With retrieval-trace reuse and adaptive escalation, token costs drop to 5.1\%--32.5\% while maintaining competitive accuracy and practical document-storage performance, showing the utility of this work for emerging AI knowledge bases.

cs.IR↗
arXiv2026

TimelyRAG: Semantic-Temporal Hybrid Retrieval for Time-Critical Question Answering in Overlapping-Evolving Documents

Although large language models (LLMs) and retrieval-augmented generation (RAG) have advanced open-domain question answering (QA), they remain unreliable when documents evolve through amendments. Existing time-sensitive retrieval methods address only the disjoint-evolving environment, where each update is an independent snapshot. However, laws, policies, and regulations often operate in overlapping-evolving environments, where amendments override earlier clauses while preserving most content, creating strong semantic overlap across versions. We propose TimelyRAG, a retriever-agnostic framework that incorporates temporal distance into ranking to align queries with version-appropriate documents. We also introduce TimelyQABench, the first benchmark for regulation-heavy domains with overlapping-evolving challenges. Experiments show consistent gains, up to +28.6% in nDCG@10, highlighting the importance of temporal reasoning for reliable QA over evolving documents. All resources are available at https://github.com/kaist-dmlab/TimelyRAG.

cs.IR↗