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Variational quantum algorithms (VQAs) are the quantum analog of classical neural networks (NNs). A VQA consists of a parameterized quantum circuit (PQC) which is composed of multiple layers of ansatzes (simpler PQCs, which are an analogy of NN layers) that differ only in selections of parameters. Previous work has identified the alternating layered ansatz as potentially a new standard ansatz in near-term quantum computing. Indeed, shallow alternating layered VQAs are easy to implement and have been shown to be both trainable and expressive. In this work, we introduce a training algorithm with an exponential reduction in training cost of such VQAs. Moreover, our algorithm uses classical shadows of quantum input data, and can hence be run on a classical computer with rigorous performance guarantees. We demonstrate 2--3 orders of magnitude improvement in the training cost using our algorithm for the example problems of finding state preparation circuits and the quantum autoencoder.

AAAI 2023

Alternating Layered Variational Quantum Circuits Can Be Classically Optimized Efficiently Using Classical Shadows

quantum machine learning

machine learning

optimization

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. AAAI-23 is the Thirty-Seventh AAAI Conference on Artificial Intelligence. The theme of this conference is to create collaborative bridges within and beyond AI. Like previous AAAI conferences, AAAI-23 will feature technical paper presentations, special tracks, invited speakers, workshops, tutorials, poster sessions, senior member presentations, competitions, and exhibit programs, and two new activities: a Bridge Program and a Lab Program. Many of these activities are tailored to the theme of bridges and all are selected according to the highest standards, with additional programs for students and young researchers. 
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The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines.

poster

We provide a unifying framework where artificial neural networks and their architectures can be formally described as particular cases of a general mathematical construction---machines of finite depth. Unlike neural networks, machines have a precise definition, from which several properties follow naturally. Machines of finite depth are modular (they can be combined), efficiently computable, and differentiable. The backward pass of a machine is again a machine and can be computed without overhead using the same procedure as the forward pass. We prove this statement theoretically and practically via a unified implementation that generalizes several classical architectures---dense, convolutional, and recurrent neural networks with a rich shortcut structure---and their respective backpropagation rules.

Machines of Finite Depth: Towards a Formalization of Neural Networks

Event sequences in continuous time space are ubiquitous across applications and have been intensively studied with both classic temporal point process (TPP) and its recent deep network variants. This work is motivated by an observation that many of event data exhibit inherent clustering patterns in terms of the sparse correlation among events, while such characteristics are seldom explicitly considered in existing neural TPP models whereby the history encoders are often embodied by RNNs or Transformers. In this work, we propose a c-NTPP (Cluster-Aware Neural Temporal Point Process) model, which leverages a sequential variational autoencoder framework to infer the latent cluster each event belongs to in the sequence. Specially, a novel event-clustered attention mechanism is devised to learn each cluster and then aggregate them together to obtain the final representation for each event. Extensive experiments show that c-NTPP achieves superior performance on both real-world and synthetic datasets, and it can also uncover the underlying clustering correlations.  

c-NTPP: Learning Cluster-Aware Neural Temporal Point Process

Modeling dynamics in the form of partial differential equations (PDEs) is an effectual way to understand real-world physics processes. For complex physics systems, analytical solutions are not available and numerical solutions are widely-used. However, traditional numerical algorithms are computationally expensive and challenging in handling multiphysics systems. Recently, using neural networks to solve PDEs has made significant progress, called physics-informed neural networks (PINNs). PINNs encode physical laws into neural networks and learn the continuous solutions of PDEs. For the training of PINNs, existing methods suffer from the problems of inefficiency and unstable convergence, since the PDE residuals require calculating automatic differentiation. In this paper, we propose Dynamic Mesh-based Importance Sampling (DMIS) to tackle these problems. DMIS is a novel sampling scheme based on importance sampling, which constructs a dynamic triangular mesh to estimate sample weights efficiently. DMIS has broad applicability and can be easily integrated into existing methods. The evaluation of DMIS on three widely-used benchmarks shows that DMIS improves the convergence speed and accuracy in the meantime. Especially in solving the highly nonlinear Schrödinger Equation, compared with state-of-the-art methods, DMIS shows up to 46% smaller root mean square error and five times faster convergence speed.

DMIS: Dynamic Mesh-based Importance Sampling for Training Physics-Informed Neural Networks

Camera and radar sensors have significant advantages in cost, reliability, and maintenance compared to LiDAR. Existing fusion methods often fuse the outputs of single modalities at the result-level, called the late fusion strategy. This can benefit from using off-the-shelf single sensor detection algorithms, but late fusion cannot fully exploit the complementary properties of sensors, thus having limited performance despite the huge potential of camera-radar fusion. Here we propose a novel proposal-level early fusion approach that effectively exploits both spatial and contextual properties of camera and radar for 3D object detection. Our fusion framework first associates image proposal with radar points in the polar coordinate system to efficiently handle the discrepancy between the coordinate system and spatial properties. Using this as a first stage, following consecutive cross-attention based feature fusion layers adaptively exchange spatio-contextual information between camera and radar, leading to a robust and attentive fusion. Our camera-radar fusion approach achieves the state-of-the-art 41.1% mAP and 52.3% NDS on the nuScenes test set, which is 8.7 and 10.8 points higher than the camera-only baseline, as well as yielding competitive performance on the LiDAR method.

CRAFT: Camera-Radar 3D Object Detection with Spatio-Contextual Fusion Transformer

Federated learning is a contemporary machine learning paradigm where locally trained models are distilled into a global model. Due to the intrinsic permutation invariance of neural networks, Probabilistic Federated Neural Matching (PFNM) employs a Bayesian nonparametric framework in the generation process of local neurons, and then creates a linear sum assignment formulation in each alternative optimization iteration. But according to our theoretical analysis, the optimization iteration in PFNM omits global information from existing. In this study, we propose a novel approach that overcomes this flaw by introducing a Kullback-Leibler  divergence penalty at each iteration.
The effectiveness of our approach is demonstrated by experiments on both image classification and semantic segmentation tasks.

Bayesian Federated Neural Matching that Completes Full Information

Universal domain adaptation (UniDA) aims to transfer knowledge from a labeled source domain to an unlabeled target domain without requiring the same label sets of both domains. The existence of domain and category shift makes the task challenging and requires us to distinguish “known” samples (i.e., samples whose labels exist in both domains) and “unknown” samples (i.e., samples whose labels exist in only one domain) in both domains before reducing the domain gap. In this paper, we consider the problem from the point of view of distribution matching which we only need to align two distributions partially. A novel approach, dubbed mini-batch Prototypical Partial Optimal Transport (m-PPOT), is proposed to conduct partial distribution alignment for UniDA. In training phase, besides minimizing m-PPOT, we also leverage the transport plan of m-PPOT to reweight source prototypes and target samples, and design reweighted entropy loss and reweighted cross-entropy loss to distinguish “known” and “unknown” samples. Experiments on four benchmarks show that our method outperforms the previous state-of-the-art UniDA methods.

Prototypical Partial Optimal Transport for Universal Domain Adaptation

Recently, webly supervised learning (WSL) has been studied to leverage numerous and accessible data from the Internet. Most existing methods focus on learning noise-robust models from web images while neglecting the performance drop caused by the differences between web domain and real-world domain. However, only by tackling the performance gap above can we fully exploit the practical value of web datasets. To this end, we propose a Few-shot guided Prototypical (FoPro) representation learning method, which only needs a few labeled examples from reality and can significantly improve the performance in the real-world domain. Specifically, we initialize each class center with few-shot real-world data as the ``realistic" prototype. Then, the intra-class distance between web instances and ``realistic" prototypes is narrowed by contrastive learning. Finally, we measure image-prototype distance with a learnable metric. Prototypes are polished by adjacent high-quality web images and involved in removing distant out-of-distribution samples. In experiments, FoPro is trained on web datasets with a few real-world examples guided and evaluated on real-world datasets. Our method achieves the state-of-the-art performance on three fine-grained datasets and two large-scale datasets. Compared with existing WSL methods under the same few-shot settings, FoPro still excels in real-world generalization. Code is available at https://github.com/yuleiqin/fopro.

FoPro: Few-Shot Guided Robust Webly-Supervised Prototypical Learning

The matrix-based R\'enyi's entropy allows us to directly quantify information measures from given data, without explicit estimation of the underlying probability distribution. This intriguing property makes it widely applied in statistical inference and machine learning tasks. However, this information theoretical quantity is not robust against noise in the data, and is computationally prohibitive in large-scale applications. To address these issues, we propose a novel measure of information, termed low-rank matrix-based R\'enyi's entropy, based on low-rank representations of infinitely divisible kernel matrices. The proposed entropy functional inherits the specialty of of the original definition to directly quantify information from data, but enjoys additional advantages including robustness and effective calculation. Specifically, our low-rank variant is more sensitive to informative perturbations induced by changes in underlying distributions, while being insensitive to uninformative ones caused by noises. Moreover, low-rank R\'enyi's entropy can be efficiently approximated by random projection and Lanczos iteration techniques, reducing the overall complexity from $\mathcal{O}(n^3)$ to $\mathcal{O}(n^2 s)$ or even $\mathcal{O}(ns^2)$, where $n$ is the number of data samples and $s \ll n$. We conduct large-scale experiments to evaluate the effectiveness of this new information measure, demonstrating superior results compared to matrix-based R\'enyi's entropy in terms of both performance and computational efficiency.

Robust and Fast Measure of Information via Low-rank Representation

In party-approval multiwinner elections the goal is to allocate the seats of a fixed-size committee to parties based on the approval ballots of the voters over the parties. In particular, each voter can approve multiple parties and each party can be assigned multiple seats. Two central requirements in this setting are proportional representation and strategyproofness. Intuitively, proportional representation requires that every sufficiently large group of voters with similar preferences is represented in the committee. Strategyproofness demands that no voter can benefit by misreporting her true preferences. We show that these two axioms are incompatible for anonymous party-approval multiwinner voting rules, thus proving a far-reaching impossibility theorem. The proof of this result is obtained by formulating the problem in propositional logic and then letting a SAT solver show that the formula is unsatisfiable. Additionally, we demonstrate how to circumvent this impossibility by considering a weakening of strategyproofness which requires that only voters who do not approve any elected party cannot manipulate. While most common voting rules fail even this weak notion of strategyproofness, we characterize Chamberlin-Courant approval voting within the class of Thiele rules based on this strategyproofness notion.

Strategyproofness and Proportionality in Party-Approval Multiwinner Elections

Modeling an unknown dynamical system is crucial in order to predict the future behavior of the system. A standard approach is training recurrent models on measurement data. While these models typically provide exact short-term predictions, accumulating errors yield deteriorated long-term behavior. In contrast, models with reliable long-term predictions can often be obtained, either by training a robust but less detailed model, or by leveraging physics-based simulations. In both cases, inaccuracies in the models yield a lack of short-time details. Thus, different models with contrastive properties on different time horizons are available. This observation immediately raises the question: Can we obtain predictions that combine the best of both worlds? Inspired by sensor fusion tasks, we interpret the problem in the frequency domain and leverage classical methods from signal processing, in particular complementary filters. This filtering technique combines two signals by applying a high-pass filter to one signal, and low-pass filtering the other. Essentially, the high-pass filter extracts high-frequencies, whereas the low-pass filter extracts low frequencies. Applying this concept to dynamics model learning enables the construction of models that yield accurate long- and short-term predictions. Here, we propose two methods, one being purely learning-based and the other one being a hybrid model that requires an additional physics-based simulator.

Alternating Layered Variational Quantum Circuits Can Be Classically Optimized Efficiently Using Classical Shadows

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