The rapid advancement of quantum computing has led to an extensive demand for effective techniques to extract classical information from quantum systems, particularly in fields like quantum machine learning and quantum chemistry. However, quantum systems are inherently susceptible to noises, which adversely corrupt the information encoded in quantum systems. In this work, we introduce an efficient algorithm that can recover information from quantum states under Pauli noise. The core idea is to learn the necessary information of the unknown Pauli channel by post-processing the classical shadows of the channel. For a local and bounded-degree observable, only partial knowledge of the channel is required rather than its complete classical description to recover the ideal information, resulting in a polynomial-time algorithm. This contrasts with conventional methods such as probabilistic error cancellation, which requires the full information of the channel and exhibits exponential scaling with the number of qubits. We also prove that this scalable method is optimal on the sample complexity and generalise the algorithm to the weight contracting channel. Furthermore, we demonstrate the validity of the algorithm on the 1D anisotropic Heisenberg-type model via numerical simulations. As a notable application, our method can be severed as a sample-efficient error mitigation scheme for Clifford circuits.
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Gaussianization is a simple generative model that can be trained without backpropagation. It has shown compelling performance on low dimensional data. As the dimension increases, however, it has been observed that the convergence speed slows down. We show analytically that the number of required layers scales linearly with the dimension for Gaussian input. We argue that this is because the model is unable to capture dependencies between dimensions. Empirically, we find the same linear increase in cost for arbitrary input $p(x)$, but observe favorable scaling for some distributions. We explore potential speed-ups and formulate challenges for further research.
Reinforcement learning often needs to deal with the exponential growth of states and actions when exploring optimal control in high-dimensional spaces (often known as the curse of dimensionality). In this work, we address this issue by learning the inherent structure of action-wise similar MDP to appropriately balance the performance degradation versus sample/computational complexity. In particular, we partition the action spaces into multiple groups based on the similarity in transition distribution and reward function, and build a linear decomposition model to capture the difference between the intra-group transition kernel and the intra-group rewards. Both our theoretical analysis and experiments reveal a \emph{surprising and counter-intuitive result}: while a more refined grouping strategy can reduce the approximation error caused by treating actions in the same group as identical, it also leads to increased estimation error when the size of samples or the computation resources is limited. This finding highlights the grouping strategy as a new degree of freedom that can be optimized to minimize the overall performance loss. To address this issue, we formulate a general optimization problem for determining the optimal grouping strategy, which strikes a balance between performance loss and sample/computational complexity. We further propose a computationally efficient method for selecting a nearly-optimal grouping strategy, which maintains its computational complexity independent of the size of the action space.
We propose a method for in-hand 3D scanning of an unknown object with a monocular camera. Our method relies on a neural implicit surface representation that captures both the geometry and the appearance of the object, however, by contrast with most NeRF-based methods, we do not assume that the camera-object relative poses are known. Instead, we simultaneously optimize both the object shape and the pose trajectory. As direct optimization over all shape and pose parameters is prone to fail without coarse-level initialization, we propose an incremental approach that starts by splitting the sequence into carefully selected overlapping segments within which the optimization is likely to succeed. We reconstruct the object shape and track its poses independently within each segment, then merge all the segments before performing a global optimization. We show that our method is able to reconstruct the shape and color of both textured and challenging texture-less objects, outperforms classical methods that rely only on appearance features, and that its performance is close to recent methods that assume known camera poses.
Quantum image computing draws a lot of attention due to storing and processing image data faster than classical. With increasing the image size, the number of connections also increases, leading to the circuit complex. Therefore, efficient quantum image representation and compression issues are still challenging. The encoding of images for representation and compression in quantum systems is different from classical ones. In quantum, encoding of position is more concerned which is the major difference from the classical. In this paper, a novel zero-discarded state connection novel enhance quantum representation (ZSCNEQR) approach is introduced to reduce complexity further by discarding '0' in the location representation information. In the control operational gate, only input '1' contribute to its output thus, discarding zero makes the proposed ZSCNEQR circuit more efficient. The proposed ZSCNEQR approach significantly reduced the required bit for both representation and compression. The proposed method requires 11.76\% less qubits compared to the recent existing method. The results show that the proposed approach is highly effective for representing and compressing images compared to the two relevant existing methods in terms of rate-distortion performance.
We propose a quantum soft-covering problem for a given general quantum channel and one of its output states, which consists in finding the minimum rank of an input state needed to approximate the given channel output. We then prove a one-shot quantum covering lemma in terms of smooth min-entropies by leveraging decoupling techniques from quantum Shannon theory. This covering result is shown to be equivalent to a coding theorem for rate distortion under a posterior (reverse) channel distortion criterion [Atif, Sohail, Pradhan, arXiv:2302.00625]. Both one-shot results directly yield corollaries about the i.i.d. asymptotics, in terms of the coherent information of the channel. The power of our quantum covering lemma is demonstrated by two additional applications: first, we formulate a quantum channel resolvability problem, and provide one-shot as well as asymptotic upper and lower bounds. Secondly, we provide new upper bounds on the unrestricted and simultaneous identification capacities of quantum channels, in particular separating for the first time the simultaneous identification capacity from the unrestricted one, proving a long-standing conjecture of the last author.
In the scenario of class-incremental learning (CIL), deep neural networks have to adapt their model parameters to non-stationary data distributions, e.g., the emergence of new classes over time. However, CIL models are challenged by the well-known catastrophic forgetting phenomenon. Typical methods such as rehearsal-based ones rely on storing exemplars of old classes to mitigate catastrophic forgetting, which limits real-world applications considering memory resources and privacy issues. In this paper, we propose a novel rehearsal-free CIL approach that learns continually via the synergy between two Complementary Learning Subnetworks. Our approach involves jointly optimizing a plastic CNN feature extractor and an analytical feed-forward classifier. The inaccessibility of historical data is tackled by holistically controlling the parameters of a well-trained model, ensuring that the decision boundary learned fits new classes while retaining recognition of previously learned classes. Specifically, the trainable CNN feature extractor provides task-dependent knowledge separately without interference; and the final classifier integrates task-specific knowledge incrementally for decision-making without forgetting. In each CIL session, it accommodates new tasks by attaching a tiny set of declarative parameters to its backbone, in which only one matrix per task or one vector per class is kept for knowledge retention. Extensive experiments on a variety of task sequences show that our method achieves competitive results against state-of-the-art methods, especially in accuracy gain, memory cost, training efficiency, and task-order robustness. Furthermore, to make the non-growing backbone (i.e., a model with limited network capacity) suffice to train on more incoming tasks, a graceful forgetting implementation on previously learned trivial tasks is empirically investigated.
We consider the problem of discovering $K$ related Gaussian directed acyclic graphs (DAGs), where the involved graph structures share a consistent causal order and sparse unions of supports. Under the multi-task learning setting, we propose a $l_1/l_2$-regularized maximum likelihood estimator (MLE) for learning $K$ linear structural equation models. We theoretically show that the joint estimator, by leveraging data across related tasks, can achieve a better sample complexity for recovering the causal order (or topological order) than separate estimations. Moreover, the joint estimator is able to recover non-identifiable DAGs, by estimating them together with some identifiable DAGs. Lastly, our analysis also shows the consistency of union support recovery of the structures. To allow practical implementation, we design a continuous optimization problem whose optimizer is the same as the joint estimator and can be approximated efficiently by an iterative algorithm. We validate the theoretical analysis and the effectiveness of the joint estimator in experiments.
As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.
Conventionally, spatiotemporal modeling network and its complexity are the two most concentrated research topics in video action recognition. Existing state-of-the-art methods have achieved excellent accuracy regardless of the complexity meanwhile efficient spatiotemporal modeling solutions are slightly inferior in performance. In this paper, we attempt to acquire both efficiency and effectiveness simultaneously. First of all, besides traditionally treating H x W x T video frames as space-time signal (viewing from the Height-Width spatial plane), we propose to also model video from the other two Height-Time and Width-Time planes, to capture the dynamics of video thoroughly. Secondly, our model is designed based on 2D CNN backbones and model complexity is well kept in mind by design. Specifically, we introduce a novel multi-view fusion (MVF) module to exploit video dynamics using separable convolution for efficiency. It is a plug-and-play module and can be inserted into off-the-shelf 2D CNNs to form a simple yet effective model called MVFNet. Moreover, MVFNet can be thought of as a generalized video modeling framework and it can specialize to be existing methods such as C2D, SlowOnly, and TSM under different settings. Extensive experiments are conducted on popular benchmarks (i.e., Something-Something V1 & V2, Kinetics, UCF-101, and HMDB-51) to show its superiority. The proposed MVFNet can achieve state-of-the-art performance with 2D CNN's complexity.
We consider the problem of zero-shot recognition: learning a visual classifier for a category with zero training examples, just using the word embedding of the category and its relationship to other categories, which visual data are provided. The key to dealing with the unfamiliar or novel category is to transfer knowledge obtained from familiar classes to describe the unfamiliar class. In this paper, we build upon the recently introduced Graph Convolutional Network (GCN) and propose an approach that uses both semantic embeddings and the categorical relationships to predict the classifiers. Given a learned knowledge graph (KG), our approach takes as input semantic embeddings for each node (representing visual category). After a series of graph convolutions, we predict the visual classifier for each category. During training, the visual classifiers for a few categories are given to learn the GCN parameters. At test time, these filters are used to predict the visual classifiers of unseen categories. We show that our approach is robust to noise in the KG. More importantly, our approach provides significant improvement in performance compared to the current state-of-the-art results (from 2 ~ 3% on some metrics to whopping 20% on a few).
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