发表机构
Texas A&M University（德克萨斯农工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出NS-RIS算法学习隐量子马尔可夫模型，使其在非量子生成序列数据上优于经典HMM，在多基准任务中提升性能并降低运行时间，推动HQMM成为实用序列数据模型。
AI 中文摘要
隐马尔可夫模型（Hidden Markov models, HMMs）是广泛应用于离散序列数据的概率模型，但在隐动态复杂时存在局限性。隐量子马尔可夫模型（Hidden quantum Markov models, HQMMs）通过将概率向量替换为密度矩阵、随机转移替换为量子操作对HMM进行泛化，能够实现更丰富的隐表示。然而，现有HQMM学习方法在非量子过程生成的数据上始终未优于经期望最大化（Expectation--Maximization, EM）训练的HMM，限制了其实际应用。我们提出NS-RIS（Newton--Schulz Retraction-based Inference on the Stiefel manifold），这是一种用于学习保迹HQMM的可扩展算法。NS-RIS利用Newton--Schulz正交化计算极因子搜索方向，同时保持Stiefel流形的可行性，避免了代价高昂的矩阵分解。我们还在平滑性、随机梯度和有限Newton--Schulz精度的标准假设下，建立了有限时间平稳性保证。实验表明，NS-RIS提供了首个基准证据，证明HQMM可在非量子模型生成的数据上显著优于经EM训练的HMM：在合成HMM生成的基准上，NS-RIS的评估指标较EM和现有最优HQMM方法COSM分别平均提升38.5%、最高提升50.6%；在合成HQMM基准上，其测试指标较COSM提升18.9%，同时运行时间减少12.0%；在真实世界的剪接分类（Splice classification）基准上，NS-RIS在高维隐状态场景下也优于EM和COSM，隐维度为6时较COSM降低平均分类误差17.9%，隐维度为8时降低14.9%。这些结果使HQMM超越了HMM的理论泛化，确立其为适用于科学序列数据的实用且表达力强的模型。
英文摘要
Hidden Markov models (HMMs) are widely used probabilistic models for discrete sequential data but can be limited when hidden dynamics are complex. Hidden quantum Markov models (HQMMs) generalize HMMs by replacing probability vectors with density matrices and stochastic transitions with quantum operations, enabling richer latent representations. However, existing HQMM learning methods have not consistently outperformed Expectation--Maximization (EM)-trained HMMs on data not generated by quantum processes, limiting their practical applicability. We introduce NS-RIS, Newton--Schulz Retraction-based Inference on the Stiefel manifold, a scalable algorithm for learning trace-preserving HQMMs. NS-RIS uses Newton--Schulz orthogonalization to compute a polar-factor search direction while preserving Stiefel-manifold feasibility, avoiding costly matrix decompositions. We further establish a finite-time stationarity guarantee under standard assumptions on smoothness, stochastic gradients, and finite Newton--Schulz accuracy. Empirically, NS-RIS provides the first benchmark evidence that an HQMM can significantly outperform an EM-trained HMM on data not generated by a quantum model. On synthetic HMM-generated benchmarks, NS-RIS outperforms both EM and the state-of-the-art HQMM method COSM, improving the evaluation metric by an average of 38.5% and by up to 50.6%. On a synthetic HQMM benchmark, it improves the test metric over COSM by 18.9% while reducing runtime by 12.0%. On the real-world Splice classification benchmark, NS-RIS also surpasses both EM and COSM in higher-dimensional latent regimes, reducing mean classification error by 17.9% for latent dimension 6 and 14.9% for latent dimension 8 relative to COSM. These results move HQMMs beyond a theoretical generalization of HMMs and establish them as practical and expressive models for scientific sequence data.
