Zheng Zhang

Xinling Yu, Sean Hooten, Ziyue Liu et al.

Operator learning has become a powerful tool in machine learning for modeling complex physical systems governed by partial differential equations (PDEs). Although Deep Operator Networks (DeepONet) show promise, they require extensive data acquisition. Physics-informed DeepONets (PI-DeepONet) mitigate data scarcity but suffer from inefficient training processes. We introduce Separable Operator Networks (SepONet), a novel framework that significantly enhances the efficiency of physics-informed operator learning. SepONet uses independent trunk networks to learn basis functions separately for different coordinate axes, enabling faster and more memory-efficient training via forward-mode automatic differentiation. We provide a universal approximation theorem for SepONet proving the existence of a separable approximation to any nonlinear continuous operator. Then, we comprehensively benchmark its representational capacity and computational performance against PI-DeepONet. Our results demonstrate SepONet's superior performance across various nonlinear and inseparable PDEs, with SepONet's advantages increasing with problem complexity, dimension, and scale. For 1D time-dependent PDEs, SepONet achieves up to 112x faster training and 82x reduction in GPU memory usage compared to PI-DeepONet, while maintaining comparable accuracy. For the 2D time-dependent nonlinear diffusion equation, SepONet efficiently handles the complexity, achieving a 6.44% mean relative $\ell_{2}$ test error, while PI-DeepONet fails due to memory constraints. This work paves the way for extreme-scale learning of continuous mappings between infinite-dimensional function spaces. Open source code is available at \url{https://github.com/HewlettPackard/separable-operator-networks}.

Yequan Zhao, Xinling Yu, Zhixiong Chen et al.

Backward propagation (BP) is widely used to compute the gradients in neural network training. However, it is hard to implement BP on edge devices due to the lack of hardware and software resources to support automatic differentiation. This has tremendously increased the design complexity and time-to-market of on-device training accelerators. This paper presents a completely BP-free framework that only requires forward propagation to train realistic neural networks. Our technical contributions are three-fold. Firstly, we present a tensor-compressed variance reduction approach to greatly improve the scalability of zeroth-order (ZO) optimization, making it feasible to handle a network size that is beyond the capability of previous ZO approaches. Secondly, we present a hybrid gradient evaluation approach to improve the efficiency of ZO training. Finally, we extend our BP-free training framework to physics-informed neural networks (PINNs) by proposing a sparse-grid approach to estimate the derivatives in the loss function without using BP. Our BP-free training only loses little accuracy on the MNIST dataset compared with standard first-order training. We also demonstrate successful results in training a PINN for solving a 20-dim Hamiltonian-Jacobi-Bellman PDE. This memory-efficient and BP-free approach may serve as a foundation for the near-future on-device training on many resource-constraint platforms (e.g., FPGA, ASIC, micro-controllers, and photonic chips).

Ziyue Liu, Xinling Yu, Zheng Zhang

Physics-informed neural networks (PINNs) have been increasingly employed due to their capability of modeling complex physics systems. To achieve better expressiveness, increasingly larger network sizes are required in many problems. This has caused challenges when we need to train PINNs on edge devices with limited memory, computing and energy resources. To enable training PINNs on edge devices, this paper proposes an end-to-end compressed PINN based on Tensor-Train decomposition. In solving a Helmholtz equation, our proposed model significantly outperforms the original PINNs with few parameters and achieves satisfactory prediction with up to 15$\times$ overall parameter reduction.

Xinling Yu, José E. C. Serrallés, Ilias I. Giannakopoulos et al.

We propose Physics-Informed Fourier Networks for Electrical Properties (EP) Tomography (PIFON-EPT), a novel deep learning-based method for EP reconstruction using noisy and/or incomplete magnetic resonance (MR) measurements. Our approach leverages the Helmholtz equation to constrain two networks, responsible for the denoising and completion of the transmit fields, and the estimation of the object's EP, respectively. We embed a random Fourier features mapping into our networks to enable efficient learning of high-frequency details encoded in the transmit fields. We demonstrated the efficacy of PIFON-EPT through several simulated experiments at 3 and 7 tesla (T) MR imaging, and showed that our method can reconstruct physically consistent EP and transmit fields. Specifically, when only $20\%$ of the noisy measured fields were used as inputs, PIFON-EPT reconstructed the EP of a phantom with $\leq 5\%$ error, and denoised and completed the measurements with $\leq 1\%$ error. Additionally, we adapted PIFON-EPT to solve the generalized Helmholtz equation that accounts for gradients of EP between inhomogeneities. This yielded improved results at interfaces between different materials without explicit knowledge of boundary conditions. PIFON-EPT is the first method that can simultaneously reconstruct EP and transmit fields from incomplete noisy MR measurements, providing new opportunities for EPT research.

Jinming Lu, Jiayi Tian, Hai Li et al.

The increasing demand for on-device training of deep neural networks (DNNs) aims to leverage personal data for high-performance applications while addressing privacy concerns and reducing communication latency. However, resource-constrained platforms face significant challenges due to the intensive computational and memory demands of DNN training. Tensor decomposition emerges as a promising approach to compress model size without sacrificing accuracy. Nevertheless, training tensorized neural networks (TNNs) incurs non-trivial overhead and severe performance degradation on conventional accelerators due to complex tensor shaping requirements. To address these challenges, we propose FETTA, an algorithm and hardware co-optimization framework for efficient TNN training. On the algorithm side, we develop a contraction sequence search engine (CSSE) to identify the optimal contraction sequence with the minimal computational overhead. On the hardware side, FETTA features a flexible and efficient architecture equipped with a reconfigurable contraction engine (CE) array to support diverse dataflows. Furthermore, butterfly-based distribution and reduction networks are implemented to perform flexible tensor shaping operations during computation. Evaluation results demonstrate that FETTA achieves reductions of 20.5x/100.9x, 567.5x/45.03x, and 11609.7x/4544.8x in terms of processing latency, energy, and energy-delay product (EDP) over GPU and TPU, respectively. Moreover, working on the tensorized training, FETTA outperforms prior accelerators with a speedup of 3.87~14.63x, and an energy efficiency improvement of 1.41~2.73x on average.

Ryan Solgi, Zichang He, William Jiahua Liang et al.

Various tensor decomposition methods have been proposed for data compression. In real world applications of the tensor decomposition, selecting the tensor shape for the given data poses a challenge and the shape of the tensor may affect the error and the compression ratio. In this work, we study the effect of the tensor shape on the tensor decomposition and propose an optimization model to find an optimum shape for the tensor train (TT) decomposition. The proposed optimization model maximizes the compression ratio of the TT decomposition given an error bound. We implement a genetic algorithm (GA) linked with the TT-SVD algorithm to solve the optimization model. We apply the proposed method for the compression of RGB images. The results demonstrate the effectiveness of the proposed evolutionary tensor shape search for the TT decomposition.

Chunfeng Cui, Zheng Zhang

Stochastic spectral methods have achieved great success in the uncertainty quantification of many engineering problems, including electronic and photonic integrated circuits influenced by fabrication process variations. Existing techniques employ a generalized polynomial-chaos expansion, and they almost always assume that all random parameters are mutually independent or Gaussian correlated. However, this assumption is rarely true in real applications. How to handle non-Gaussian correlated random parameters is a long-standing and fundamental challenge. A main bottleneck is the lack of theory and computational methods to perform a projection step in a correlated uncertain parameter space. This paper presents an optimization-based approach to automatically determinate the quadrature nodes and weights required in a projection step, and develops an efficient stochastic collocation algorithm for systems with non-Gaussian correlated parameters. We also provide some theoretical proofs for the complexity and error bound of our proposed method. Numerical experiments on synthetic, electronic and photonic integrated circuit examples show the nearly exponential convergence rate and excellent efficiency of our proposed approach. Many other challenging uncertainty-related problems can be further solved based on this work.

Chunfeng Cui, Zheng Zhang

Since the invention of generalized polynomial chaos in 2002, uncertainty quantification has impacted many engineering fields, including variation-aware design automation of integrated circuits and integrated photonics. Due to the fast convergence rate, the generalized polynomial chaos expansion has achieved orders-of-magnitude speedup than Monte Carlo in many applications. However, almost all existing generalized polynomial chaos methods have a strong assumption: the uncertain parameters are mutually independent or Gaussian correlated. This assumption rarely holds in many realistic applications, and it has been a long-standing challenge for both theorists and practitioners. This paper propose a rigorous and efficient solution to address the challenge of non-Gaussian correlation. We first extend generalized polynomial chaos, and propose a class of smooth basis functions to efficiently handle non-Gaussian correlations. Then, we consider high-dimensional parameters, and develop a scalable tensor method to compute the proposed basis functions. Finally, we develop a sparse solver with adaptive sample selections to solve high-dimensional uncertainty quantification problems. We validate our theory and algorithm by electronic and photonic ICs with 19 to 57 non-Gaussian correlated variation parameters. The results show that our approach outperforms Monte Carlo by $2500\times$ to $3000\times$ in terms of efficiency. Moreover, our method can accurately predict the output density functions with multiple peaks caused by non-Gaussian correlations, which is hard to handle by existing methods. Based on the results in this paper, many novel uncertainty quantification algorithms can be developed and can be further applied to a broad range of engineering domains.

Zheng Zhang, Tsui-Wei Weng, Luca Daniel

Fabrication process variations are a major source of yield degradation in the nano-scale design of integrated circuits (IC), microelectromechanical systems (MEMS) and photonic circuits. Stochastic spectral methods are a promising technique to quantify the uncertainties caused by process variations. Despite their superior efficiency over Monte Carlo for many design cases, these algorithms suffer from the curse of dimensionality; i.e., their computational cost grows very fast as the number of random parameters increases. In order to solve this challenging problem, this paper presents a high-dimensional uncertainty quantification algorithm from a big-data perspective. Specifically, we show that the huge number of (e.g., $1.5 \times 10^{27}$) simulation samples in standard stochastic collocation can be reduced to a very small one (e.g., $500$) by exploiting some hidden structures of a high-dimensional data array. This idea is formulated as a tensor recovery problem with sparse and low-rank constraints; and it is solved with an alternating minimization approach. Numerical results show that our approach can simulate efficiently some ICs, as well as MEMS and photonic problems with over 50 independent random parameters, whereas the traditional algorithm can only handle several random parameters.

Zheng Zhang, Hossein Amiri, Dazhou Yu et al.

Semantic trajectories, which enrich spatial-temporal data with textual information such as trip purposes or location activities, are key for identifying outlier behaviors critical to healthcare, social security, and urban planning. Traditional outlier detection relies on heuristic rules, which requires domain knowledge and limits its ability to identify unseen outliers. Besides, there lacks a comprehensive approach that can jointly consider multi-modal data across spatial, temporal, and textual dimensions. Addressing the need for a domain-agnostic model, we propose the Transferable Outlier Detection for Human Semantic Trajectories (TOD4Traj) framework.TOD4Traj first introduces a modality feature unification module to align diverse data feature representations, enabling the integration of multi-modal information and enhancing transferability across different datasets. A contrastive learning module is further pro-posed for identifying regular mobility patterns both temporally and across populations, allowing for a joint detection of outliers based on individual consistency and group majority patterns. Our experimental results have shown TOD4Traj's superior performance over existing models, demonstrating its effectiveness and adaptability in detecting human trajectory outliers across various datasets.

Chunfeng Cui, Zheng Zhang

This paper generalizes stochastic collocation methods to handle correlated non-Gaussian random parameters. The key challenge is to perform a multivariate numerical integration in a correlated parameter space when computing the coefficient of each basis function via a projection step. We propose an optimization model and a block coordinate descent solver to compute the required quadrature samples. Our method is verified with a CMOS ring oscillator and an optical ring resonator, showing 3000x speedup over Monte Carlo.

Zi Yang, Ziyue Liu, Samridhi Choudhary et al.

Training large AI models such as LLMs and DLRMs costs massive GPUs and computing time. The high training cost has become only affordable to big tech companies, meanwhile also causing increasing concerns about the environmental impact. This paper presents CoMERA, a Computing- and Memory-Efficient training method via Rank-Adaptive tensor optimization. CoMERA achieves rank-adaptive tensor-compressed (pre)-training via a multi-objective optimization formulation and improves the training to provide both a high compression ratio and excellent accuracy in the training process. Our optimized numerical computation (e.g., optimized tensorized embedding and tensor-network contractions) and GPU implementation eliminate part of the run-time overhead in the tensorized training on GPU. This leads to, for the first time, $2-3\times$ speedup per training epoch compared with standard training. CoMERA also outperforms the recent GaLore in terms of both memory and computing efficiency. Specifically, CoMERA is $2\times$ faster per training epoch and $9\times$ more memory-efficient than GaLore on a tested six-encoder transformer with single-batch training. Our method also shows $\sim 2\times$ speedup than standard pre-training on a BERT-like code-generation LLM while achieving $4.23\times$ compression ratio in pre-training. With further HPC optimization, CoMERA may reduce the pre-training cost of many other LLMs. An implementation of CoMERA is available at https://github.com/ziyangjoy/CoMERA.

Shuo Lu, Yanyin Chen, Wei Feng et al.

Layout generation plays a crucial role in enhancing both user experience and design efficiency. However, current approaches suffer from task-specific generation capabilities and perceptually misaligned evaluation metrics, leading to limited applicability and ineffective measurement. In this paper, we propose \textit{Uni-Layout}, a novel framework that achieves unified generation, human-mimicking evaluation and alignment between the two. For universal generation, we incorporate various layout tasks into a single taxonomy and develop a unified generator that handles background or element contents constrained tasks via natural language prompts. To introduce human feedback for the effective evaluation of layouts, we build \textit{Layout-HF100k}, the first large-scale human feedback dataset with 100,000 expertly annotated layouts. Based on \textit{Layout-HF100k}, we introduce a human-mimicking evaluator that integrates visual and geometric information, employing a Chain-of-Thought mechanism to conduct qualitative assessments alongside a confidence estimation module to yield quantitative measurements. For better alignment between the generator and the evaluator, we integrate them into a cohesive system by adopting Dynamic-Margin Preference Optimization (DMPO), which dynamically adjusts margins based on preference strength to better align with human judgments. Extensive experiments show that \textit{Uni-Layout} significantly outperforms both task-specific and general-purpose methods. Our code is publicly available at https://github.com/JD-GenX/Uni-Layout.

Xinling Yu, Ziyue Liu, Hai Li et al.

Thermal analysis is crucial in 3D-IC design due to increased power density and complex heat dissipation paths. Although operator learning frameworks such as DeepOHeat~\cite{liu2023deepoheat} have demonstrated promising preliminary results in accelerating thermal simulation, they face critical limitations in prediction capability for multi-scale thermal patterns, training efficiency, and trustworthiness of results during design optimization. This paper presents DeepOHeat-v1, an enhanced physics-informed operator learning framework that addresses these challenges through three key innovations. First, we integrate Kolmogorov-Arnold Networks with learnable activation functions as trunk networks, enabling an adaptive representation of multi-scale thermal patterns. This approach achieves a 1.25x and 6.29x reduction in error in two representative test cases. Second, we introduce a separable training method that decomposes the basis function along the coordinate axes, achieving 62x training speedup and 31x GPU memory reduction in our baseline case, and enabling thermal analysis at resolutions previously infeasible due to GPU memory constraints. Third, we propose a confidence score to evaluate the trustworthiness of the predicted results, and further develop a hybrid optimization workflow that combines operator learning with finite difference (FD) using Generalized Minimal Residual (GMRES) method for incremental solution refinement, enabling efficient and trustworthy thermal optimization. Experimental results demonstrate that DeepOHeat-v1 achieves accuracy comparable to optimization using high-fidelity finite difference solvers, while speeding up the entire optimization process by $70.6\times$ in our test cases, effectively minimizing the peak temperature through optimal placement of heat-generating components. Open source code is available at https://github.com/xlyu0127/DeepOHeat-v1.

Cole Hawkins, Alec Koppel, Zheng Zhang

A fundamental challenge in Bayesian inference is efficient representation of a target distribution. Many non-parametric approaches do so by sampling a large number of points using variants of Markov Chain Monte Carlo (MCMC). We propose an MCMC variant that retains only those posterior samples which exceed a KSD threshold, which we call KSD Thinning. We establish the convergence and complexity tradeoffs for several settings of KSD Thinning as a function of the KSD threshold parameter, sample size, and other problem parameters. Finally, we provide experimental comparisons against other online nonparametric Bayesian methods that generate low-complexity posterior representations, and observe superior consistency/complexity tradeoffs. Code is available at github.com/colehawkins/KSD-Thinning.

Zheng Zhang, Wenbo Hu, Yixing Lao et al.

3D Gaussian Splatting (3DGS) has demonstrated impressive novel view synthesis results while advancing real-time rendering performance. However, it relies heavily on the quality of the initial point cloud, resulting in blurring and needle-like artifacts in areas with insufficient initializing points. This is mainly attributed to the point cloud growth condition in 3DGS that only considers the average gradient magnitude of points from observable views, thereby failing to grow for large Gaussians that are observable for many viewpoints while many of them are only covered in the boundaries. To this end, we propose a novel method, named Pixel-GS, to take into account the number of pixels covered by the Gaussian in each view during the computation of the growth condition. We regard the covered pixel numbers as the weights to dynamically average the gradients from different views, such that the growth of large Gaussians can be prompted. As a result, points within the areas with insufficient initializing points can be grown more effectively, leading to a more accurate and detailed reconstruction. In addition, we propose a simple yet effective strategy to scale the gradient field according to the distance to the camera, to suppress the growth of floaters near the camera. Extensive experiments both qualitatively and quantitatively demonstrate that our method achieves state-of-the-art rendering quality while maintaining real-time rendering speed, on the challenging Mip-NeRF 360 and Tanks & Temples datasets.

Jinming Lu, Jiayi Tian, Yequan Zhao et al.

Physics-Informed Neural Networks (PINNs) have emerged as a promising paradigm for solving partial differential equations (PDEs) by embedding physical laws into neural network training objectives. However, their deployment on resource-constrained platforms is hindered by substantial computational and memory overhead, primarily stemming from higher-order automatic differentiation, intensive tensor operations, and reliance on full-precision arithmetic. To address these challenges, we present a framework that enables scalable and energy-efficient PINN training on edge devices. This framework integrates fully quantized training, Stein's estimator (SE)-based residual loss computation, and tensor-train (TT) decomposition for weight compression. It contributes three key innovations: (1) a mixed-precision training method that use a square-block MX (SMX) format to eliminate data duplication during backpropagation; (2) a difference-based quantization scheme for the Stein's estimator that mitigates underflow; and (3) a partial-reconstruction scheme (PRS) for TT-Layers that reduces quantization-error accumulation. We further design PINTA, a precision-scalable hardware accelerator, to fully exploit the performance of the framework. Experiments on the 2-D Poisson, 20-D Hamilton-Jacobi-Bellman (HJB), and 100-D Heat equations demonstrate that the proposed framework achieves accuracy comparable to or better than full-precision, uncompressed baselines while delivering 5.5x to 83.5x speedups and 159.6x to 2324.1x energy savings. This work enables real-time PDE solving on edge devices and paves the way for energy-efficient scientific computing at scale.

Ryan Solgi, Parsa Madinei, Jiayi Tian et al.

Large language models (LLM) and vision-language models (VLM) have achieved state-of-the-art performance, but they impose significant memory and computing challenges in deployment. We present a novel low-rank compression framework to address this challenge. First, we upper bound the change of network loss via layer-wise activation-based compression errors, filling a theoretical gap in the literature. We then formulate low-rank model compression as a bi-objective optimization and prove that a single uniform tolerance yields surrogate Pareto-optimal heterogeneous ranks. Based on our theoretical insights, we propose Pareto-Guided Singular Value Decomposition (PGSVD), a zero-shot pipeline that improves activation-aware compression via Pareto-guided rank selection and alternating least-squares implementation. We apply PGSVD to both LLM and VLM, showing better accuracy at the same compression levels and inference speedup.

Ryan Solgi, Kai Zhen, Rupak Vignesh Swaminathan et al.

The efficient implementation of large language models (LLMs) is crucial for deployment on resource-constrained devices. Low-rank tensor compression techniques, such as tensor-train (TT) networks, have been widely studied for over-parameterized neural networks. However, their applications to compress pre-trained large language models (LLMs) for downstream tasks (post-training) remains challenging due to the high-rank nature of pre-trained LLMs and the lack of access to pretraining data. In this study, we investigate low-rank tensorized LLMs during fine-tuning and propose sparse augmented tensor networks (Saten) to enhance their performance. The proposed Saten framework enables full model compression. Experimental results demonstrate that Saten enhances both accuracy and compression efficiency in tensorized language models, achieving state-of-the-art performance.

Yao Chen, Cole Hawkins, Kaiqi Zhang et al.

The deep neural network (DNN) based AI applications on the edge require both low-cost computing platforms and high-quality services. However, the limited memory, computing resources, and power budget of the edge devices constrain the effectiveness of the DNN algorithms. Developing edge-oriented AI algorithms and implementations (e.g., accelerators) is challenging. In this paper, we summarize our recent efforts for efficient on-device AI development from three aspects, including both training and inference. First, we present on-device training with ultra-low memory usage. We propose a novel rank-adaptive tensor-based tensorized neural network model, which offers orders-of-magnitude memory reduction during training. Second, we introduce an ultra-low bitwidth quantization method for DNN model compression, achieving the state-of-the-art accuracy under the same compression ratio. Third, we introduce an ultra-low latency DNN accelerator design, practicing the software/hardware co-design methodology. This paper emphasizes the importance and efficacy of training, quantization and accelerator design, and calls for more research breakthroughs in the area for AI on the edge.

Zichang He, Zheng Zhang

Fabrication process variations can significantly influence the performance and yield of nano-scale electronic and photonic circuits. Stochastic spectral methods have achieved great success in quantifying the impact of process variations, but they suffer from the curse of dimensionality. Recently, low-rank tensor methods have been developed to mitigate this issue, but two fundamental challenges remain open: how to automatically determine the tensor rank and how to adaptively pick the informative simulation samples. This paper proposes a novel tensor regression method to address these two challenges. We use a $\ell_{q}/ \ell_{2}$ group-sparsity regularization to determine the tensor rank. The resulting optimization problem can be efficiently solved via an alternating minimization solver. We also propose a two-stage adaptive sampling method to reduce the simulation cost. Our method considers both exploration and exploitation via the estimated Voronoi cell volume and nonlinearity measurement respectively. The proposed model is verified with synthetic and some realistic circuit benchmarks, on which our method can well capture the uncertainty caused by 19 to 100 random variables with only 100 to 600 simulation samples.

Zichang He, Bo Zhao, Zheng Zhang

Magnetic resonance imaging (MRI) is a powerful imaging modality that revolutionizes medicine and biology. The imaging speed of high-dimensional MRI is often limited, which constrains its practical utility. Recently, low-rank tensor models have been exploited to enable fast MR imaging with sparse sampling. Most existing methods use some pre-defined sampling design, and active sensing has not been explored for low-rank tensor imaging. In this paper, we introduce an active low-rank tensor model for fast MR imaging. We propose an active sampling method based on a Query-by-Committee model, making use of the benefits of low-rank tensor structure. Numerical experiments on a 3-D MRI data set demonstrate the effectiveness of the proposed method.

Cole Hawkins, Xing Liu, Zheng Zhang

While post-training model compression can greatly reduce the inference cost of a deep neural network, uncompressed training still consumes a huge amount of hardware resources, run-time and energy. It is highly desirable to directly train a compact neural network from scratch with low memory and low computational cost. Low-rank tensor decomposition is one of the most effective approaches to reduce the memory and computing requirements of large-size neural networks. However, directly training a low-rank tensorized neural network is a very challenging task because it is hard to determine a proper tensor rank {\it a priori}, which controls the model complexity and compression ratio in the training process. This paper presents a novel end-to-end framework for low-rank tensorized training of neural networks. We first develop a flexible Bayesian model that can handle various low-rank tensor formats (e.g., CP, Tucker, tensor train and tensor-train matrix) that compress neural network parameters in training. This model can automatically determine the tensor ranks inside a nonlinear forward model, which is beyond the capability of existing Bayesian tensor methods. We further develop a scalable stochastic variational inference solver to estimate the posterior density of large-scale problems in training. Our work provides the first general-purpose rank-adaptive framework for end-to-end tensorized training. Our numerical results on various neural network architectures show orders-of-magnitude parameter reduction and little accuracy loss (or even better accuracy) in the training process. Specifically, on a very large deep learning recommendation system with over $4.2\times 10^9$ model parameters, our method can reduce the variables to only $1.6\times 10^5$ automatically in the training process (i.e., by $2.6\times 10^4$ times) while achieving almost the same accuracy.

Ziming Liu, Zheng Zhang

Hamiltonian Monte Carlo (HMC) is an efficient Bayesian sampling method that can make distant proposals in the parameter space by simulating a Hamiltonian dynamical system. Despite its popularity in machine learning and data science, HMC is inefficient to sample from spiky and multimodal distributions. Motivated by the energy-time uncertainty relation from quantum mechanics, we propose a Quantum-Inspired Hamiltonian Monte Carlo algorithm (QHMC). This algorithm allows a particle to have a random mass matrix with a probability distribution rather than a fixed mass. We prove the convergence property of QHMC and further show why such a random mass can improve the performance when we sample a broad class of distributions. In order to handle the big training data sets in large-scale machine learning, we develop a stochastic gradient version of QHMC using Nos{é}-Hoover thermostat called QSGNHT, and we also provide theoretical justifications about its steady-state distributions. Finally in the experiments, we demonstrate the effectiveness of QHMC and QSGNHT on synthetic examples, bridge regression, image denoising and neural network pruning. The proposed QHMC and QSGNHT can indeed achieve much more stable and accurate sampling results on the test cases.

Zijian Wang, Zheng Zhang, Yadan Luo et al.

Existing deep hashing approaches fail to fully explore semantic correlations and neglect the effect of linguistic context on visual attention learning, leading to inferior performance. This paper proposes a dual-stream learning framework, dubbed Deep Collaborative Discrete Hashing (DCDH), which constructs a discriminative common discrete space by collaboratively incorporating the shared and individual semantics deduced from visual features and semantic labels. Specifically, the context-aware representations are generated by employing the outer product of visual embeddings and semantic encodings. Moreover, we reconstruct the labels and introduce the focal loss to take advantage of frequent and rare concepts. The common binary code space is built on the joint learning of the visual representations attended by language, the semantic-invariant structure construction and the label distribution correction. Extensive experiments demonstrate the superiority of our method.

Cole Hawkins, Zheng Zhang

Tensor decomposition is an effective approach to compress over-parameterized neural networks and to enable their deployment on resource-constrained hardware platforms. However, directly applying tensor compression in the training process is a challenging task due to the difficulty of choosing a proper tensor rank. In order to achieve this goal, this paper proposes a Bayesian tensorized neural network. Our Bayesian method performs automatic model compression via an adaptive tensor rank determination. We also present approaches for posterior density calculation and maximum a posteriori (MAP) estimation for the end-to-end training of our tensorized neural network. We provide experimental validation on a fully connected neural network, a CNN and a residual neural network where our work produces $7.4\times$ to $137\times$ more compact neural networks directly from the training.

Jiali Luan, Zheng Zhang

This paper presents a multi-dimensional computational method to predict the spatial variation data inside and across multiple dies of a wafer. This technique is based on tensor computation. A tensor is a high-dimensional generalization of a matrix or a vector. By exploiting the hidden low-rank property of a high-dimensional data array, the large amount of unknown variation testing data may be predicted from a few random measurement samples. The tensor rank, which decides the complexity of a tensor representation, is decided by an available variational Bayesian approach. Our approach is validated by a practical chip testing data set, and it can be easily generalized to characterize the process variations of multiple wafers. Our approach is more efficient than the previous virtual probe techniques in terms of memory and computational cost when handling high-dimensional chip testing data.

Cole Hawkins, Zheng Zhang

Streaming tensor factorization is a powerful tool for processing high-volume and multi-way temporal data in Internet networks, recommender systems and image/video data analysis. Existing streaming tensor factorization algorithms rely on least-squares data fitting and they do not possess a mechanism for tensor rank determination. This leaves them susceptible to outliers and vulnerable to over-fitting. This paper presents a Bayesian robust streaming tensor factorization model to identify sparse outliers, automatically determine the underlying tensor rank and accurately fit low-rank structure. We implement our model in Matlab and compare it with existing algorithms on tensor datasets generated from dynamic MRI and Internet traffic.

Tianqi Chen, Mu Li, Yutian Li et al.

MXNet is a multi-language machine learning (ML) library to ease the development of ML algorithms, especially for deep neural networks. Embedded in the host language, it blends declarative symbolic expression with imperative tensor computation. It offers auto differentiation to derive gradients. MXNet is computation and memory efficient and runs on various heterogeneous systems, ranging from mobile devices to distributed GPU clusters. This paper describes both the API design and the system implementation of MXNet, and explains how embedding of both symbolic expression and tensor operation is handled in a unified fashion. Our preliminary experiments reveal promising results on large scale deep neural network applications using multiple GPU machines.