Statistical inference for quantum singular models

Deep learning has seen substantial achievements, with numerical and theoretical evidence suggesting that singularities of statistical models are considered a contributing factor to its performance. From this remarkable success of classical statistical models, it is naturally expected that quantum singular models will play a vital role in many quantum statistical tasks. However, while the theory of quantum statistical models in regular cases has been established, theoretical understanding of quantum singular models is still limited. To investigate the statistical properties of quantum singular models, we focus on two prominent tasks in quantum statistical inference: quantum state estimation and model selection. In particular, we base our study on classical singular learning theory and seek to extend it within the framework of Bayesian quantum state estimation. To this end, we define quantum generalization and training loss functions and give their asymptotic expansions through algebraic geometrical methods. The key idea of the proof is the introduction of a quantum analog of the likelihood function using classical shadows. Consequently, we construct an asymptotically unbiased estimator of the quantum generalization loss, the quantum widely applicable information criterion (QWAIC), as a computable model selection metric from given measurement outcomes.

MambaPEFT: Exploring Parameter-Efficient Fine-Tuning for Mamba

An ecosystem of Transformer-based models has been established by building large models with extensive data. Parameter-efficient fine-tuning (PEFT) is a crucial technology for deploying these models to downstream tasks with minimal cost while achieving effective performance. Recently, Mamba, a State Space Model (SSM)-based model, has attracted attention as a potential alternative to Transformers. While many large-scale Mamba-based models have been proposed, efficiently adapting pre-trained Mamba-based models to downstream tasks remains unexplored. In this paper, we conduct an exploratory analysis of PEFT methods for Mamba. We investigate the effectiveness of existing PEFT methods for Transformers when applied to Mamba. We also modify these methods to better align with the Mamba architecture. Additionally, we propose new Mamba-specific PEFT methods that leverage the distinctive structure of Mamba. Our experiments indicate that PEFT performs more effectively for Mamba than Transformers. Lastly, we demonstrate how to effectively combine multiple PEFT methods and provide a framework that outperforms previous works. To ensure reproducibility, we will release the code after publication.