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Xuehuai He

/ɕye'hwaɪ/, they/them

Email: xuehuai [dot] he [at] yale [dot] edu

Last updated on May 10, 2026.

Academic interests​

  • Syntax: voice, case, and person; argument structures; Uralic languages; differential object marking
  • Semantics: numerals; the mathematical structure of plurals and partitives
  • Others: programming languages theory; geometry, topology, algebra, and related math topics

Recent updates​

Manuscripts​

Accepted​

Approximation on Numerals: Insights from the Grammar of Approximating Number Pairs (ANPs) in Mandarin Chinese

Xuehuai He

NACCL36

  • Under review for the Proceedings of the 36th North American Conference on Chinese Linguistics, the Ohio State University, 2024.
  • Abstract: Approximating number pairs (ANPs), like in ‘twenty or thirty people’, appear cross-linguistically and usually indicate an approximate range rather than a precise disjunction of either twenty or thirty. This paper explores the syntax and semantics of well-formed ANPs in Mandarin Chinese, proposing generalizations in semantic types and scopes of approximation across various approximative numeral expressions in Mandarin Chinese. I propose that approximative expressions on numerals are independent of the specific numerals chosen and the only variable parameter in the construction would be the range specific to the concrete approximative expression used.
  • [PDF for current version]

Talks and posters​

2026​

Approximating number pairs

Xuehuai He

WCCFL44

You can view my poster here and abstract here.

2025​

Unfolding Search Synthesis

Qihong Chen, Xuehuai He, Eli Pregerson, Lucas Bang

Haskell 2025

G[8,4][8,2][8,4]->[8,2][8,6][8,4]->[8,6][8,1][8,2]->[8,1][8,3][8,2]->[8,3][8,5][8,6]->[8,5][8,7][8,6]->[8,7][4,1][8,1]->[4,1][4,2][8,1]->[4,2][4,3][8,3]->[4,3][4,4][8,3]->[4,4][2,1][4,1]->[2,1][6,1][4,1]->[6,1][2,2][4,2]->[2,2][6,2][4,2]->[6,2][1,1][2,1]->[1,1][3,1][2,1]->[3,1][5,1][6,1]->[5,1][7,1][6,1]->[7,1][1,2][2,2]->[1,2][3,2][2,2]->[3,2][5,2][6,2]->[5,2][7,2][6,2]->[7,2][2,3][4,3]->[2,3][6,3][4,3]->[6,3][2,4][4,4]->[2,4][6,4][4,4]->[6,4][1,3][2,3]->[1,3][3,3][2,3]->[3,3][5,3][6,3]->[5,3][7,3][6,3]->[7,3][1,4][2,4]->[1,4][3,4][2,4]->[3,4][5,4][6,4]->[5,4][7,4][6,4]->[7,4][4,5][8,5]->[4,5][4,6][8,5]->[4,6][4,7][8,7]->[4,7][4,8][8,7]->[4,8][2,5][4,5]->[2,5][6,5][4,5]->[6,5][2,6][4,6]->[2,6][6,6][4,6]->[6,6][1,5][2,5]->[1,5][3,5][2,5]->[3,5][5,5][6,5]->[5,5][7,5][6,5]->[7,5][1,6][2,6]->[1,6][3,6][2,6]->[3,6][5,6][6,6]->[5,6][7,6][6,6]->[7,6][2,7][4,7]->[2,7][6,7][4,7]->[6,7][2,8][4,8]->[2,8][6,8][4,8]->[6,8][1,7][2,7]->[1,7][3,7][2,7]->[3,7][5,7][6,7]->[5,7][7,7][6,7]->[7,7][1,8][2,8]->[1,8][3,8][2,8]->[3,8][5,8][6,8]->[5,8][7,8][6,8]->[7,8][8,4][8,2][8,4]->[8,2][8,6][8,4]->[8,6][8,1][8,2]->[8,1][8,3][8,2]->[8,3][8,5][8,6]->[8,5][8,7][8,6]->[8,7][4,1][8,1]->[4,1][4,2][8,1]->[4,2][4,3][8,3]->[4,3][4,4][8,3]->[4,4][2,1][4,1]->[2,1][6,1][4,1]->[6,1][2,2][4,2]->[2,2][6,2][4,2]->[6,2][1,1][2,1]->[1,1][3,1][2,1]->[3,1][5,1][6,1]->[5,1][7,1][6,1]->[7,1][1,2][2,2]->[1,2][3,2][2,2]->[3,2][5,2][6,2]->[5,2][7,2][6,2]->[7,2][2,3][4,3]->[2,3][6,3][4,3]->[6,3][2,4][4,4]->[2,4][6,4][4,4]->[6,4][1,3][2,3]->[1,3][3,3][2,3]->[3,3][5,3][6,3]->[5,3][7,3][6,3]->[7,3][1,4][2,4]->[1,4][3,4][2,4]->[3,4][5,4][6,4]->[5,4][7,4][6,4]->[7,4][4,5][8,5]->[4,5][4,6][8,5]->[4,6][4,7][8,7]->[4,7][4,8][8,7]->[4,8][2,5][4,5]->[2,5][6,5][4,5]->[6,5][2,6][4,6]->[2,6][6,6][4,6]->[6,6][1,5][2,5]->[1,5][3,5][2,5]->[3,5][5,5][6,5]->[5,5][7,5][6,5]->[7,5][1,6][2,6]->[1,6][3,6][2,6]->[3,6][5,6][6,6]->[5,6][7,6][6,6]->[7,6][2,7][4,7]->[2,7][6,7][4,7]->[6,7][2,8][4,8]->[2,8][6,8][4,8]->[6,8][1,7][2,7]->[1,7][3,7][2,7]->[3,7][5,7][6,7]->[5,7][7,7][6,7]->[7,7][1,8][2,8]->[1,8][3,8][2,8]->[3,8][5,8][6,8]->[5,8][7,8][6,8]->[7,8]

Adaptive search (posing queries, observing outcomes, and refining knowledge) is a common pattern in security testing, logical deduction, and preference learning, yet typical implementations are ad-hoc and problem-specific. This talk presents a Haskell framework that expresses adaptive search purely as a recursion scheme, showing how the familiar trio of anamorphism, catamorphism, and their composition as a hylomorphism can express a generic solution to a wide range of adaptive search problems.

Starting from an imperative specification of how queries interact with an unknown target, written in a DSL, we perform symbolic execution to derive logical constraints on search parameters, perform model counting to compute probabilities of search outcomes, and generate search steps by maximizing expected Shannon information gain.

The resulting adaptive strategy is an online hylomorphism: an anamorphism lazily unfolds an optimal search tree while a catamorphism simultaneously drives the concrete interaction with an instantiated search problem, so only the explored path is ever materialized.

We will describe our Haskell implementation for adaptive search synthesis making use of functor algebras, and a few combinators, composed with model counting and information theory, unifying a wide range of problems.

Because we separates strategy synthesis (tree construction) from strategy execution, alternatives for critical components (model counters or information optimization algorithms) can be swapped in and out.

The talk will emphasize lessons for the broader Haskell community: - how recursion-scheme abstractions give a reusable template for search and inference, - how laziness enables demand-driven synthesis, and - how symbolic execution can be expressed functionally.

The work is ongoing: we are experimenting with larger search problem spaces and improved model counting. But the key ideas and approach are ready to share. We hope attendees will leave with a compact, idiomatic pattern for recognizing when a problem can be framed as an adaptive search and easily solved.

  • Contact me for more details about this paper.

2024​

The Grammar of Approximating Number Pairs in Mandarin ChineseXuehuai He

JLAO37NACCL36

2023​

Adinkras as Origami

An 4-dimensional Adinkra graph (a Hamming tesseract) embedded on a torus.An 4-dimensional Adinkra graph (a Hamming tesseract) embedded on a torus. Arsh Chhabra, Xuehuai He, Elena O'Grady, Melinda Yang, Cameron Thomas, Edray Goins

MathFest2023

Abstract: Around 20 years ago, physicists Michael Faux and Jim Gates invented Adinkras as a way to better understand Supersymmetry. These are bipartite graphs whose vertices represent bosons and fermions, and whose edges represent operators which relate the particles. Recently, Doran et al. determined that Adinkras are a type of Dessin d'Enfant by explicitly exhibiting a Belyi map as a composition $\beta: S \to \mathbb P^1(\mathbb C) \to \mathbb P^1(\mathbb C)$. We are interested in exhibiting the same Belyi map as a different composition $\beta: S \to E(\mathbb C) \to \mathbb P^1(\mathbb C)$.

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