This document discusses using natural language processing (NLP) tools for mathematics. It describes work done at various companies on NLP, including developing a conversational assistant for home appliances. It also discusses a PhD thesis on developing a hybrid NLI engine and explainability tools for mathematical text, as well as challenges in building a knowledge graph for mathematics terms and concepts. The document concludes that knowledge representation for mathematics is an underdeveloped area with high potential payoff.

1. 1/13
Introduction
NLP and Transformers
Networked Mathematics
Networked Mathematics™
NLP tools for Better Science
Valeria de Paiva
Topos Institute
April 2022
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2. 2/13
Introduction
NLP and Transformers
Networked Mathematics
Thanks, Fabio and Davide!
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3. 3/13
Introduction
NLP and Transformers
Networked Mathematics
NLP research?
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4. 4/13
Introduction
NLP and Transformers
Networked Mathematics
Semantics & Language
Samsung SRA (2019): Dialogue and Knowledge
Representation Lab,
project: systems to make Bixby (voice personal assistant)
communicate well with home appliances at SmartHome
Nuance Comms (2012-2018): AI to make sounds into
knowledge, health systems, automotive, law, CRM, banks,
insurance, etc
projects: personal assistant for Living Room (TV 2nd screen),
PA for automotive companies
Rearden Commerce (2011-2012): a white-labelling shop for
travel and expenses/procurement systems. air travel tickets,
hotels, shows & sports, restaurants, parking, etc
project: a Groupon-like app, ontologies, discover what hotel
reviewers really valued
Cuil (2008-2010) search analysis, PARC Forum: Adventures in
Searchland
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5. 5/13
Introduction
NLP and Transformers
Networked Mathematics
How to think about language understanding?
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6. 6/13
Introduction
NLP and Transformers
Networked Mathematics
How to think about language understanding?
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7. 7/13
Introduction
NLP and Transformers
Networked Mathematics
Conversational UI applications
AI Summit 2018, Luxembourg
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8. 8/13
Introduction
NLP and Transformers
Networked Mathematics
Conversational Reasoning Engines
AI Summit 2018, Luxembourg
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9. 9/13
Introduction
NLP and Transformers
Networked Mathematics
Can we read Math texts?
Work of almost nine years at PARC was out of reach when I
left in 2008
Pleased to report that almost all of it is now available
open-source, redone from scratch, using new techniques.
work of Katerina Kalouli, PhD thesis 2021
Hy-NLI: a hybrid NLI engine, computes inference in a hybrid
way by employing the symbolic system GKR4NLI and the deep
learning model BERT;
XplaiNLI: explainability of the Hy-NLI system and sketches of
explanations for the decisions made by each component of
Hy-NLI;
GKR4NLI a symbolic NLI engine that computes the inference
relation between a pair of sentences
GKR parser transforms a given sentence into a layered
semantic graph, its symbolic representation
Demos for all components!
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10. 10/13
Introduction
NLP and Transformers
Networked Mathematics
Knowledge Graph for Maths?
Doing semantics is expensive, we can get much information
with less than full semantics
But we need the specific vocabulary. How do we get it?
Term extractors: Open Tapioca, TextRank, DyGIE++,
Parmenides (our NIST collaborators) the ones we tried
No one is specific for mathematics, but DyGIE++ is about
scientific text
Bottleneck is always evaluation: difficult and not super fun
Human annotation in this domain is expensive and difficult to
obtain
Can we use ‘silver datasets’ instead?
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11. 11/13
Introduction
NLP and Transformers
Networked Mathematics
Knowledge Graph for Maths
Author keywords are ‘guaranteed’ sound keywords, but won’t
be all the story
Need to add ‘trivial’ keywords for experts – these are
extractive, e.g. ‘category’ in a journal about Category Theory
there are many expressions that are keyword-like, e.g. ”Future
work”, that do not correspond to concepts
So ‘linguistic concepts’ are broader than mathematical
concepts
Can training on guaranteed keywords be enough to obtain
concepts and only concepts?
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12. 12/13
Introduction
NLP and Transformers
Networked Mathematics
Conversational UI applications
AI Summit 2018, Luxembourg
eventually Hy-NLI!
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13. 13/13
Introduction
NLP and Transformers
Networked Mathematics
Conclusions
Knowledge representation for Mathematics is fun, interesting,
useful. and underdeveloped!
Payoff is incredibly high, see our blog post ‘Introducing the
MathFoldr Project’ https://topos.site/blog/2021/07/
introducing-the-mathfoldr-project/
NLP tools are becoming better every week, need to make use
of this productivity
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