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Siyan Lin

Publications and source records attributed to Siyan Lin.

5 recordsLinked to original sources

TACT: Taxonomy-Aligned Post-Training for Pedagogically Adaptive English Tutoring

Large language models (LLMs) are increasingly used to provide conversational practice for English-as-a-second-language (ESL) learners. Effective ESL tutoring, however, requires more than fluent response generation: a tutor must select an appropriate pedagogical action based on learner behavior and dialogue context. Human-tutoring research offers principles for adaptive support, but they are often task-specific and remain insufficiently integrated into LLM-based ESL tutor training and evaluation. We present TACT (Taxonomy-Aligned Conversational Tutor), a human-grounded framework for post-training and evaluating pedagogically adaptive ESL tutors. Drawing on established literature, we develop two complementary taxonomies: the Tutor-Strategy Taxonomy with 13 tutor response strategies and the Student-Move Taxonomy characterizing learner behavior by move type and status. Using these taxonomies, we construct TACTCorpus, which enriches 260 authentic teacher-student conversations with 32,379 annotations and quality-controlled augmented training data. We then post-train Qwen3.5-4B through supervised fine-tuning followed by taxonomy-aligned Group Relative Policy Optimization, producing TACTutor and optimizing it for scaffolding quality rather than reference imitation alone. On TACTBench, a strategy-balanced diagnostic benchmark comprising 78 authentic tutoring contexts, TACTutor improves over its backbone by 20.30% and outperforms all evaluated proprietary baselines under the same protocol, while maintaining backbone performance on established external educational benchmarks; in a blinded study with 50 learners, it also receives the highest overall mean rating among the evaluated tutors. We release the data, benchmark, and model weights, providing an open foundation for developing pedagogically adaptive ESL tutors.

cs.AI

Dynamical zero modes, boundary dependence, and numerical instability in dynamical quantum phase transitions

Boundary conditions are usually expected to cause only finite-size corrections to bulk quantities, but this expectation can fail for dynamical quantum phase transitions. In this work, we show that such boundary dependence is encoded in dynamical zero modes (DZMs) of the Loschmidt matrix, which are defined as singular vectors whose singular values vanish in the thermodynamic limit. Using the Su-Schrieffer-Heeger (SSH) and extended SSH models as examples, we find that the time interval where the Loschmidt rate functions (LRFs) under periodic and open boundary conditions differ coincides with the emergence of DZMs in the open-boundary Loschmidt matrix. These modes carry the boundary-dependent contribution: removing them from the open-boundary LRF recovers the periodic-boundary result. We further show that these DZMs lead to finite-precision numerical instability, since their finite-size singular values decay exponentially with system size and eventually become unresolved in fixed-precision arithmetic. A reliable small-size branch before this loss of precision can be used to estimate the thermodynamic LRF by linear extrapolation. Our results identify DZMs as both a diagnostic of boundary-dependent LRFs and the origin of the associated numerical instability.

quant-ph

Distribution of fidelity zeros in two-band topological models

We investigate the distribution of fidelity zeros in two-band topological models by extending the phase transition driving parameter into the complex plane. Within the biorthogonal formulation, we unveil that fidelity zeros are related to momentum modes for which the real part of the energy gap vanishes. Guided by this relation, we analyze the Kitaev chain, the Haldane model, and the Qi-Wu-Zhang (QWZ) model. In finite-size systems the zeros form discrete lines parallel to the imaginary axis, while in the thermodynamic limit they accumulate into extended regions in the complex parameter plane. For the Kitaev and Haldane models, the accessible interval of the real part of the complexified parameter is bounded by the critical points of the corresponding topological transitions. For the QWZ model, the transitions at $u = \pm2$ are identified in the same way, whereas the critical point at $u = 0$ is signaled by fidelity zeros crossing the real axis. These results extend the fidelity-zero framework to topological quantum phase transitions and clarify how critical information is encoded in complexified parameter space.

quant-ph

Loschmidt echo zeros in finite-size quantum systems with linear quench

Dynamical quantum phase transitions reveal singularities in quench dynamics, characterized by the emergence of Loschmidt echo zeros at critical times, which usually exist only in the thermodynamic limit but are absent in finite-size quantum systems. In this Letter, we propose a theoretical scheme to probe Loschmidt echo zeros in finite-size systems by applying a two-step quenching protocol, which offers an experimentally feasible approach to study Loschmidt echo zeros. Using the transverse Ising model as a test bed, we identify that the exact Loschmidt echo zeros can be always accessed by tuning the quench rate, when the quench is across the phase transition point. The associated rate function displays divergence at critical times, accompanying with the change of the dynamical topological order parameter. The critical times are influenced by the quench rate, system size, and momentum modes, embodying the interplay between finite-size effects and critical dynamics. Moreover, the generality of these observations is further confirmed in the XY and Haldane models.

quant-ph

Deflection and gravitational lensing with finite distance effect in the strong deflection limit in stationary and axisymmetric spacetimes

We study the deflection and gravitational lensing (GL) of both timelike and null signals in the equatorial plane of arbitrary stationary and axisymmetric spacetimes in the strong deflection limit. Our approach employs a perturbative method to show that both the deflection angle and the total travel time take quasi-series forms $\displaystyle \sum_{n=0}\left[ C_n\ln (1-b_c/b)+D_n\right] (1-b_c/b)^n$, with the coefficients $C_n$ and $D_n$ incorporating the signal velocity and finite distance effect of the source and detector. This new deflection angle allows us to establish an accurate GL equation from which the apparent angles of the relativistic images and their time delays are found. These results are applied to the Kerr and the rotating Kalb-Ramond (KR) spacetimes to investigate the effect of the spacetime spin in both spacetimes, and the effective charge parameter and a transition parameter in the rotating KR spacetime on various observables. Moreover, using our approach, the effect of the signal velocity and the source angular position on these variables is also studied.

gr-qc