Matrix models, as quantum mechanical systems without explicit spatial dependence, provide valuable insights into higher-dimensional gauge and gravitational theories, especially within the framework of string theory, where they can describe quantum black holes via the holographic principle. Simulating these models allows for exploration of their kinematic and dynamic properties, particularly in parameter regimes that are analytically intractable. In this study, we examine the potential of tensor network techniques for such simulations. Specifically, we construct ground states as matrix product states and analyse features such as their entanglement structure.

We introduce a hybrid quantum-classical framework for efficiently implementing approximate unitary dilations of non-unitary operators with enhanced noise resilience. The method embeds a target non-unitary operator into a subblock of a unitary matrix generated by a parameterized quantum circuit with universal expressivity, while a classical optimizer adjusts circuit parameters under the global unitary constraint. As a representative application, we consider the non-unitary propagator of a Lindbladian superoperator acting on the vectorized density matrix, which is relevant for simulating open quantum systems. We further validate the approach experimentally on superconducting devices in the Quafu quantum cloud computing cluster. Compared with standard dilation protocols, our method significantly reduces quantum resource requirements and improves robustness against device noise, achieving high-fidelity simulation. Its generality also enables compatibility with non-Markovian dynamics and Kraus-operator-based evolutions, providing a practical pathway for the noise-resilient simulation of non-unitary processes on near-term quantum hardware.

The Mixture of Experts (MoE) architecture reduces the training and inference cost significantly compared to a dense model of equivalent capacity. Upcycling is an approach that initializes and trains an MoE model using a pre-trained dense model. While upcycling leads to initial performance gains, the training progresses slower than when trained from scratch, leading to suboptimal performance in the long term. We propose Drop-Upcycling - a method that effectively addresses this problem. Drop-Upcycling combines two seemingly contradictory approaches: utilizing the knowledge of pre-trained dense models while statistically re-initializing some parts of the weights. This approach strategically promotes expert specialization, significantly enhancing the MoE model's efficiency in knowledge acquisition. Extensive large-scale experiments demonstrate that Drop-Upcycling significantly outperforms previous MoE construction methods in the long term, specifically when training on hundreds of billions of tokens or more. As a result, our MoE model with 5.9B active parameters achieves comparable performance to a 13B dense model in the same model family, while requiring approximately 1/4 of the training FLOPs. All experimental resources, including source code, training data, model checkpoints and logs, are publicly available to promote reproducibility and future research on MoE.

Simulating response properties of molecules is crucial for interpreting experimental spectroscopies and accelerating materials design. However, it remains a long-standing computational challenge for electronic structure methods on classical computers. While quantum computers hold the promise to solve this problem more efficiently in the long run, existing quantum algorithms requiring deep quantum circuits are infeasible for near-term noisy quantum processors. Here, we introduce a pragmatic variational quantum response (VQR) algorithm for response properties, which circumvents the need for deep quantum circuits. Using this algorithm, we report the first simulation of linear response properties of molecules including dynamic polarizabilities and absorption spectra on a superconducting quantum processor. Our results indicate that a large class of important dynamical properties such as Green's functions are within the reach of near-term quantum hardware using this algorithm in combination with suitable error mitigation techniques.

In-context Learning (ICL) is an emerging few-shot learning paradigm based on modern Language Models (LMs), yet its inner mechanism remains unclear. In this paper, we investigate the mechanism through a novel perspective of information removal. Specifically, we demonstrate that in the zero-shot scenario, LMs encode queries into non-selective representations in hidden states containing information for all possible tasks, leading to arbitrary outputs without focusing on the intended task, resulting in near-zero accuracy. Meanwhile, we find that selectively removing specific information from hidden states by a low-rank filter effectively steers LMs toward the intended task. Building on these findings, by measuring the hidden states on carefully designed metrics, we observe that few-shot ICL effectively simulates such task-oriented information removal processes, selectively removing the redundant information from entangled non-selective representations, and improving the output based on the demonstrations, which constitutes a key mechanism underlying ICL. Moreover, we identify essential attention heads inducing the removal operation, termed Denoising Heads, which enables the ablation experiments blocking the information removal operation from the inference, where the ICL accuracy significantly degrades, especially when the correct label is absent from the few-shot demonstrations, confirming both the critical role of the information removal mechanism and denoising heads.

Why and when is deep better than shallow? We answer this question in a framework that is agnostic to network implementation. We formulate a deep model as an abstract state-transition semigroup acting on a general metric space, and separate the implementation (e.g., ReLU nets, transformers, and chain-of-thought) from the abstract state transition. We prove a bias-variance decomposition in which the variance depends only on the abstract depth-$k$ network and not on the implementation (Theorem 1). We further split the bounds into output and hidden parts to tie the depth dependence of the variance to the metric entropy of the state-transition semigroup (Theorem 2). We then investigate implementation-free conditions under which the variance grow polynomially or logarithmically with depth (Section 4). Combining these with exponential or polynomial bias decay identifies four canonical bias-variance trade-off regimes (EL/EP/PL/PP) and produces explicit optimal depths $k^\ast$. Across regimes, $k^\ast>1$ typically holds, giving a rigorous form of depth supremacy. The lowest generalization error bound is achieved under the EL regime (exp-decay bias + log-growth variance), explaining why and when deep is better, especially for iterative or hierarchical concept classes such as neural ODEs, diffusion/score models, and chain-of-thought reasoning.

Dilated convolution, which expands the receptive field by inserting gaps between its consecutive elements, is widely employed in computer vision. In this study, we propose three strategies to improve individual phases of dilated convolution from the view of spectrum analysis. Departing from the conventional practice of fixing a global dilation rate as a hyperparameter, we introduce Frequency-Adaptive Dilated Convolution (FADC), which dynamically adjusts dilation rates spatially based on local frequency components. Subsequently, we design two plug-in modules to directly enhance effective bandwidth and receptive field size. The Adaptive Kernel (AdaKern) module decomposes convolution weights into low-frequency and high-frequency components, dynamically adjusting the ratio between these components on a per-channel basis. By increasing the high-frequency part of convolution weights, AdaKern captures more high-frequency components, thereby improving effective bandwidth. The Frequency Selection (FreqSelect) module optimally balances high- and low-frequency components in feature representations through spatially variant reweighting. It suppresses high frequencies in the background to encourage FADC to learn a larger dilation, thereby increasing the receptive field for an expanded scope. Extensive experiments on segmentation and object detection consistently validate the efficacy of our approach. The code is publicly available at this https URL