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Junjie Liao

Publications and source records attributed to Junjie Liao.

8 recordsLinked to original sources
arXiv2026

Palindromic Length in Free Groups: Reflections, Noncrossing Matchings, and Catalan Forms

Let $F=F(X)$ be a free group of finite rank, with palindromic length taken with respect to the fixed basis $X$. We embed $F$ as the index-two subgroup of the universal Coxeter group $W=F\rtimes_θ\langle t\mid t^2=1\rangle$, where $θ(x)=x^{-1}$ for $x\in X$, and prove $\mathrm{pl}(g)=\min{\ell_T(g),\ell_T(gt)}$. Dyer's deletion theorem then identifies reflection length with the minimum number of unmatched positions in a noncrossing equal-label partial matching on a reduced Coxeter word. This gives an $O(n^3)$-time, $O(n^2)$-space algorithm for palindromic length, together with recovery of an optimal palindromic factorization. The matching model also gives a structural characterization. For every ordered full binary tree with $k$ leaves we define a literal word template whose leaves are palindromes and whose internal vertices carry arbitrary words. A reduced word $w$ represents an element of palindromic length at most $k$ if and only if $w$ is a literal instance of one of these templates. Hence the $C_{k-1}$ ordered binary-tree shapes give a complete finite family for each fixed $k$. For $k=4$ the five templates are exactly the five forms proposed by Frid, proving the completeness of that list. A companion Lean 4 development verifies the four-palindrome classification end to end for every finite rank, including the ordinary reduced-word formulation and the literal five-form conclusion.

math.GR↗
arXiv2026

MedSNIP: Building and Benchmarking Snippet-Level Granularity for Medical Fact Verification

A medical claim's correctness often depends not on the claim alone, but on the clinical structure around it. A claim may require a lab reference range, a causal or conditional link, or patient-specific details to be judged correctly, and atom-level decomposition can fragment these dependencies, leaving the verifier with clinically incomplete claims. We reformulate medical fact-checking around snippet-level verification, where clause-grouped units preserve local clinical structure. We introduce MedSNIP-Bench, a human-annotated benchmark for snippet-level medical fact verification, and MedSNIP, an automatic snippet-generation pipeline. MedSNIP-Bench covers 276 consumer-health and clinical-vignette responses, segmented into 2,524 snippets with dual in-general and in-patient-context labels and six structural pattern codes. MedSNIP is evaluated against human snippet boundaries on MedSNIP-Bench and then used to generate snippet-level units for external corpora. Across MedSNIP-Bench, HealthFC, and MedHallu, snippet-level verification preserves or improves false-class F1, with gains concentrated where answers are long enough to fragment and where the verifier is strong enough to exploit the recovered structure. The largest merge-pattern gain is on causal-conditional clinical chains. It also reduces verifier calls by 24-73%, though the saving survives end-to-end only when decomposition is cheap, which an open-weight decomposer makes possible at no loss of chunking fidelity.

cs.CL↗
arXiv2026

How do Role Models Shape Collective Morality? Exemplar-Driven Moral Learning in Multi-Agent Simulation

Do We Need Role Models? How do Role Models Shape Collective Morality? To explore the questions, we build a multi-agent simulation powered by a Large Language Model, where agents with diverse intrinsic drives, ranging from cooperative to competitive, interact and adapt through a four-stage cognitive loop (plan-act-observe-reflect). We design four experimental games (Alignment, Collapse, Conflict, and Construction) and conduct motivational ablation studies to identify the key drivers of imitation. The results indicate that identity-driven conformity can powerfully override initial dispositions. Agents consistently adapt their values to align with a perceived successful exemplar, leading to rapid value convergence.

cs.MA↗
arXiv2026

GEnSHIN: Graphical Enhanced Spatio-temporal Hierarchical Inference Network for Traffic Flow Prediction

With the acceleration of urbanization, intelligent transportation systems have an increasing demand for accurate traffic flow prediction. This paper proposes a novel Graph Enhanced Spatio-temporal Hierarchical Inference Network (GEnSHIN) to handle the complex spatio-temporal dependencies in traffic flow prediction. The model integrates three innovative designs: 1) An attention-enhanced Graph Convolutional Recurrent Unit (GCRU), which strengthens the modeling capability for long-term temporal dependencies by introducing Transformer modules; 2) An asymmetric dual-embedding graph generation mechanism, which leverages the real road network and data-driven latent asymmetric topology to generate graph structures that better fit the characteristics of actual traffic flow; 3) A dynamic memory bank module, which utilizes learnable traffic pattern prototypes to provide personalized traffic pattern representations for each sensor node, and introduces a lightweight graph updater during the decoding phase to adapt to dynamic changes in road network states. Extensive experiments on the public dataset METR-LA show that GEnSHIN achieves or surpasses the performance of comparative models across multiple metrics such as Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE). Notably, the model demonstrates excellent prediction stability during peak morning and evening traffic hours. Ablation experiments further validate the effectiveness of each core module and its contribution to the final performance.

cs.LG↗
arXiv2025

The Eighth Power Moments of $Δ(x)$

Using Voronoi's truncated formula for $Δ(x)$ involving Bessel functions, the first author derives an asymptotic formula for the eighth-power moments with an error term of order $O\left(X^{3 - \frac{1}{254} + \varepsilon}\right)$

math.NT↗
arXiv2024

Compton Scattering on 4He with Nuclear One- and Two-Body Densities

We present the first \emph{ab initio} calculation of elastic Compton scattering from 4He. It is carried out to $\mathcal{O}(e^2 δ^3)$ [N3LO] in the $δ$ expansion of $χ$EFT. At this order and for this target, the only free parameters are the scalar-isoscalar electric and magnetic dipole polarisabilities of the nucleon. Adopting current values for these yields a parameter-free prediction. This compares favourably with the world data from HI$γ$S, Illinois and Lund for photon energies $50\;\mathrm{MeV}\lesssimω\lesssim120\;\mathrm{MeV}$ within our theoretical uncertainties of $\pm10\%$. We predict a cross section up to 7 times that for deuterium. As in 3He, this emphasises and tests the key role of meson-exchange currents between np pairs in Compton scattering on light nuclei. We assess the sensitivity of the cross section and beam asymmetry to the nucleon polarisabilities, providing clear guidance to future experiments seeking to further constrain them. The calculation becomes tractable by use of the Transition Density Method. The one- and two-body densities generated from 5 chiral potentials and the AV18$+$UIX potential are available using the python package provided at \url{https://pypi.org/project/nucdens/}.

nucl-th↗
arXiv2021

Quantum verification of NP problems with single photons and linear optics

Quantum computing is seeking to realize hardware-optimized algorithms for application-related computational tasks. NP (nondeterministic-polynomial-time) is a complexity class containing many important but intractable problems like the satisfiability of potentially conflict constraints (SAT). According to the well-founded exponential time hypothesis, verifying an SAT instance of size $n$ requires generally the complete solution in an $O(n)$-bit proof. In contrast, quantum verification algorithms, which encode the solution into quantum bits rather than classical bit strings, can perform the verification task with quadratically reduced information about the solution in $\tilde{O}(\sqrt{n})$ qubits. Here we realize the quantum verification machine of SAT with single photons and linear optics. By using tunable optical setups, we efficiently verify satisfiable and unsatisfiable SAT instances and achieve a clear completeness-soundness gap even in the presence of experimental imperfections. The protocol requires only unentangled photons, linear operations on multiple modes and at most two-photon joint measurements. These features make the protocol suitable for photonic realization and scalable to large problem sizes. Our results open an essentially new route towards quantum advantages and extend the computational capability of optical quantum computing.

quant-ph↗