Quantum algorithms for solving a wide range of practical problems have been proposed in the last ten years, such as data search and analysis, product recommendation, and credit scoring. The concern about privacy and other ethical issues in quantum computing naturally rises up. In this paper, we define a formal framework for detecting violations of differential privacy for quantum algorithms. A detection algorithm is developed to verify whether a (noisy) quantum algorithm is differentially private and automatically generate bugging information when the violation of differential privacy is reported. The information consists of a pair of quantum states that violate the privacy, to illustrate the cause of the violation. Our algorithm is equipped with Tensor Networks, a highly efficient data structure, and executed both on TensorFlow Quantum and TorchQuantum which are the quantum extensions of famous machine learning platforms -- TensorFlow and PyTorch, respectively. The effectiveness and efficiency of our algorithm are confirmed by the experimental results of almost all types of quantum algorithms already implemented on realistic quantum computers, including quantum supremacy algorithms (beyond the capability of classical algorithms), quantum machine learning models, quantum approximate optimization algorithms, and variational quantum eigensolvers with up to 21 quantum bits.
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Obtaining the solutions of partial differential equations based on various machine learning methods has drawn more and more attention in the fields of scientific computation and engineering applications. In this work, we first propose a coupled Extreme Learning Machine (called CELM) method incorporated with the physical laws to solve a class of fourth-order biharmonic equations by reformulating it into two well-posed Poisson problems. In addition, some activation functions including tangent, gauss, sine, and trigonometric (sin+cos) functions are introduced to assess our CELM method. Notably, the sine and trigonometric functions demonstrate a remarkable ability to effectively minimize the approximation error of the CELM model. In the end, several numerical experiments are performed to study the initializing approaches for both the weights and biases of the hidden units in our CELM model and explore the required number of hidden units. Numerical results show the proposed CELM algorithm is high-precision and efficient to address the biharmonic equation in both regular and irregular domains.
We discuss a vulnerability involving a category of attribution methods used to provide explanations for the outputs of convolutional neural networks working as classifiers. It is known that this type of networks are vulnerable to adversarial attacks, in which imperceptible perturbations of the input may alter the outputs of the model. In contrast, here we focus on effects that small modifications in the model may cause on the attribution method without altering the model outputs.
Path reasoning methods over knowledge graphs have gained popularity for their potential to improve transparency in recommender systems. However, the resulting models still rely on pre-trained knowledge graph embeddings, fail to fully exploit the interdependence between entities and relations in the KG for recommendation, and may generate inaccurate explanations. In this paper, we introduce PEARLM, a novel approach that efficiently captures user behaviour and product-side knowledge through language modelling. With our approach, knowledge graph embeddings are directly learned from paths over the KG by the language model, which also unifies entities and relations in the same optimisation space. Constraints on the sequence decoding additionally guarantee path faithfulness with respect to the KG. Experiments on two datasets show the effectiveness of our approach compared to state-of-the-art baselines. Source code and datasets: AVAILABLE AFTER GETTING ACCEPTED.
The searching efficiency of the quantum approximate optimization algorithm is dependent on both the classical and quantum sides of the algorithm. Recently a quantum approximate Bayesian optimization algorithm (QABOA) that includes two mixers was developed, where surrogate-based Bayesian optimization is applied to improve the sampling efficiency of the classical optimizer. A continuous-time quantum walk mixer is used to enhance exploration, and the generalized Grover mixer is also applied to improve exploitation. In this paper, an extension of QABOA is proposed to further improve its searching efficiency. The searching efficiency is enhanced through two aspects. First, two mixers, including one for exploration and the other for exploitation, are applied in an alternating fashion. Second, uncertainty of the quantum circuit is quantified with a new quantum Mat\'ern kernel based on the kurtosis of the basis state distribution, which increases the chance of obtaining the optimum. The proposed new two-mixer QABOA$'$s with and without uncertainty quantification are compared with three single-mixer QABOA$'$s on five discrete and four mixed-integer problems. The results show that the proposed two-mixer QABOA with uncertainty quantification has the best performance in efficiency and consistency for five out of the nine tested problems. The results also show that QABOA with the generalized Grover mixer performs the best among the single-mixer algorithms, thereby demonstrating the benefit of exploitation and the importance of dynamic exploration-exploitation balance in improving searching efficiency.
Creating large-scale and well-annotated datasets to train AI algorithms is crucial for automated tumor detection and localization. However, with limited resources, it is challenging to determine the best type of annotations when annotating massive amounts of unlabeled data. To address this issue, we focus on polyps in colonoscopy videos and pancreatic tumors in abdominal CT scans; both applications require significant effort and time for pixel-wise annotation due to the high dimensional nature of the data, involving either temporary or spatial dimensions. In this paper, we develop a new annotation strategy, termed Drag&Drop, which simplifies the annotation process to drag and drop. This annotation strategy is more efficient, particularly for temporal and volumetric imaging, than other types of weak annotations, such as per-pixel, bounding boxes, scribbles, ellipses, and points. Furthermore, to exploit our Drag&Drop annotations, we develop a novel weakly supervised learning method based on the watershed algorithm. Experimental results show that our method achieves better detection and localization performance than alternative weak annotations and, more importantly, achieves similar performance to that trained on detailed per-pixel annotations. Interestingly, we find that, with limited resources, allocating weak annotations from a diverse patient population can foster models more robust to unseen images than allocating per-pixel annotations for a small set of images. In summary, this research proposes an efficient annotation strategy for tumor detection and localization that is less accurate than per-pixel annotations but useful for creating large-scale datasets for screening tumors in various medical modalities.
Mixture-of-experts (MoE) model incorporates the power of multiple submodels via gating functions to achieve greater performance in numerous regression and classification applications. From a theoretical perspective, while there have been previous attempts to comprehend the behavior of that model under the regression settings through the convergence analysis of maximum likelihood estimation in the Gaussian MoE model, such analysis under the setting of a classification problem has remained missing in the literature. We close this gap by establishing the convergence rates of density estimation and parameter estimation in the softmax gating multinomial logistic MoE model. Notably, when part of the expert parameters vanish, these rates are shown to be slower than polynomial rates owing to an inherent interaction between the softmax gating and expert functions via partial differential equations. To address this issue, we propose using a novel class of modified softmax gating functions which transform the input value before delivering them to the gating functions. As a result, the previous interaction disappears and the parameter estimation rates are significantly improved.
Maximum subarray is a classical problem in computer science that given an array of numbers aims to find a contiguous subarray with the largest sum. We focus on its use for a noisy statistical problem of localizing an interval with a mean different from background. While a naive application of maximum subarray fails at this task, both a penalized and a constrained version can succeed. We show that the penalized version can be derived for common exponential family distributions, in a manner similar to the change-point detection literature, and we interpret the resulting optimal penalty value. The failure of the naive formulation is then explained by an analysis of the estimated interval boundaries. Experiments further quantify the effect of deviating from the optimal penalty. We also relate the penalized and constrained formulations and show that the solutions to the former lie on the convex hull of the solutions to the latter.
With the emergence of powerful representations of continuous data in the form of neural fields, there is a need for discretization invariant learning: an approach for learning maps between functions on continuous domains without being sensitive to how the function is sampled. We present a new framework for understanding and designing discretization invariant neural networks (DI-Nets), which generalizes many discrete networks such as convolutional neural networks as well as continuous networks such as neural operators. Our analysis establishes upper bounds on the deviation in model outputs under different finite discretizations, and highlights the central role of point set discrepancy in characterizing such bounds. This insight leads to the design of a family of neural networks driven by numerical integration via quasi-Monte Carlo sampling with discretizations of low discrepancy. We prove by construction that DI-Nets universally approximate a large class of maps between integrable function spaces, and show that discretization invariance also describes backpropagation through such models. Applied to neural fields, convolutional DI-Nets can learn to classify and segment visual data under various discretizations, and sometimes generalize to new types of discretizations at test time. Code: //github.com/clintonjwang/DI-net.
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.
Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.
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