Qingyu Meng

Qingyu Meng, Yangshuai Wang

Variational quantum circuits are increasingly studied as continuous-function approximators, but quantum regression remains difficult to train when global losses, finite-shot stochasticity, and circuit-depth growth combine to produce weak or ill-conditioned gradient signals. We study this trainability problem in a controlled hybrid quantum--classical regression design. The central ingredient is a capacity-controlled classical embedding that acts as a learnable geometric preconditioner: it reshapes the input distribution seen by a data-reuploading variational circuit while preserving a low-dimensional quantum bottleneck. We pair this representation design with a curriculum protocol that grows circuit depth progressively and switches from SPSA-based stochastic exploration to Adam-based analytic-gradient fine-tuning. We formalize the mechanism through a local quantum-tangent contraction statement: in the linearized quantum-parameter dynamics, the embedding changes the empirical Gram matrix that controls residual contraction and one-step loss decrease. Across finite-size statevector audits on PDE-informed regression benchmarks and small-data tabular tasks, the Hybrid QNN lowers error relative to Pure QNN baselines under matched quantum-model budgets. Strong classical references remain competitive, and in several cases are better in absolute error; the evidence therefore supports a trainability claim for the hybrid QNN design rather than a claim of classical or hardware quantum advantage.

Yifan Mo, Xiao Fu, Yue Su et al.

This work investigates the ability of large language models (LLMs) to generate mathematical equations from scientific texts. Prior work faces challenges in unstructured grounding, multi-equation dependency, and humanaligned evaluation. To this end, we construct a dataset of AI research papers, pairing contextual passages with ground-truth equations and variable descriptions. We develop an explainable equation generation workflow and evaluate it across diverse open- and closed-source LLM backbones. We introduce an evaluation protocol combining automatic metrics, LLM-based rubrics, and human judgments to assess accuracy, explainability, and human-LLM alignment. Results indicate that LLMs perform moderately on lexical- and syntactic-based similarity, while struggling with semantic accuracy. Comparisons between LLM-based evaluations and human judgments reveal limited alignment, highlighting challenges in using LLMs to assess equation quality. These findings offer insights for improving equation generation models and developing more reliable evaluation methods for scientific text. We provide code and data for reproducibility.