Xiaotian Gao

Xinquan Huang, Wenlei Shi, Xiaotian Gao et al.

Neural operators, as a powerful approximation to the non-linear operators between infinite-dimensional function spaces, have proved to be promising in accelerating the solution of partial differential equations (PDE). However, it requires a large amount of simulated data, which can be costly to collect. This can be avoided by learning physics from the physics-constrained loss, which we refer to it as mean squared residual (MSR) loss constructed by the discretized PDE. We investigate the physical information in the MSR loss, which we called long-range entanglements, and identify the challenge that the neural network requires the capacity to model the long-range entanglements in the spatial domain of the PDE, whose patterns vary in different PDEs. To tackle the challenge, we propose LordNet, a tunable and efficient neural network for modeling various entanglements. Inspired by the traditional solvers, LordNet models the long-range entanglements with a series of matrix multiplications, which can be seen as the low-rank approximation to the general fully-connected layers and extracts the dominant pattern with reduced computational cost. The experiments on solving Poisson's equation and (2D and 3D) Navier-Stokes equation demonstrate that the long-range entanglements from the MSR loss can be well modeled by the LordNet, yielding better accuracy and generalization ability than other neural networks. The results show that the Lordnet can be $40\times$ faster than traditional PDE solvers. In addition, LordNet outperforms other modern neural network architectures in accuracy and efficiency with the smallest parameter size.

Xinquan Huang, Wenlei Shi, Qi Meng et al.

Neural networks have shown great potential in accelerating the solution of partial differential equations (PDEs). Recently, there has been a growing interest in introducing physics constraints into training neural PDE solvers to reduce the use of costly data and improve the generalization ability. However, these physics constraints, based on certain finite dimensional approximations over the function space, must resolve the smallest scaled physics to ensure the accuracy and stability of the simulation, resulting in high computational costs from large input, output, and neural networks. This paper proposes a general acceleration methodology called NeuralStagger by spatially and temporally decomposing the original learning tasks into several coarser-resolution subtasks. We define a coarse-resolution neural solver for each subtask, which requires fewer computational resources, and jointly train them with the vanilla physics-constrained loss by simply arranging their outputs to reconstruct the original solution. Due to the perfect parallelism between them, the solution is achieved as fast as a coarse-resolution neural solver. In addition, the trained solvers bring the flexibility of simulating with multiple levels of resolution. We demonstrate the successful application of NeuralStagger on 2D and 3D fluid dynamics simulations, which leads to an additional $10\sim100\times$ speed-up. Moreover, the experiment also shows that the learned model could be well used for optimal control.

Zhengyi Li, Cong Guo, Zhanda Zhu et al.

Post-training quantization attracts increasing attention due to its convenience in deploying quantized neural networks. Although rounding-to-nearest remains the prevailing method for DNN quantization, prior research has demonstrated its suboptimal nature when applied to weight quantization. They propose optimizing weight rounding schemes by leveraging output error rather than the traditional weight quantization error. Our study reveals that similar rounding challenges also extend to activation quantization. Despite the easy generalization, the challenges lie in the dynamic nature of activation. Adaptive rounding is expected for varying activations and the method is subjected to runtime overhead. To tackle this, we propose the AQuant quantization framework with a novel perspective to reduce output error by adjusting rounding schemes of activations. Instead of using the constant rounding border 0.5 of the rounding-to-nearest operation, we make the border become a function w.r.t. the activation value to change the activation rounding by the adaptive border. To deal with the runtime overhead, we use a coarse-grained version of the border function. Finally, we introduce our framework to optimize the border function. Extensive experiments show that AQuant achieves notable improvements compared to state-of-the-art works and pushes the accuracy of ResNet-18 up to 60.31% under the 2-bit weight and activation quantization.

Di He, Shanda Li, Wenlei Shi et al.

Physics-Informed Neural Network (PINN) has become a commonly used machine learning approach to solve partial differential equations (PDE). But, facing high-dimensional secondorder PDE problems, PINN will suffer from severe scalability issues since its loss includes second-order derivatives, the computational cost of which will grow along with the dimension during stacked back-propagation. In this work, we develop a novel approach that can significantly accelerate the training of Physics-Informed Neural Networks. In particular, we parameterize the PDE solution by the Gaussian smoothed model and show that, derived from Stein's Identity, the second-order derivatives can be efficiently calculated without back-propagation. We further discuss the model capacity and provide variance reduction methods to address key limitations in the derivative estimation. Experimental results show that our proposed method can achieve competitive error compared to standard PINN training but is significantly faster. Our code is released at https://github.com/LithiumDA/PINN-without-Stacked-BP.

Cong Guo, Yuxian Qiu, Jingwen Leng et al.

Quantization of deep neural networks (DNN) has been proven effective for compressing and accelerating DNN models. Data-free quantization (DFQ) is a promising approach without the original datasets under privacy-sensitive and confidential scenarios. However, current DFQ solutions degrade accuracy, need synthetic data to calibrate networks, and are time-consuming and costly. This paper proposes an on-the-fly DFQ framework with sub-second quantization time, called SQuant, which can quantize networks on inference-only devices with low computation and memory requirements. With the theoretical analysis of the second-order information of DNN task loss, we decompose and approximate the Hessian-based optimization objective into three diagonal sub-items, which have different areas corresponding to three dimensions of weight tensor: element-wise, kernel-wise, and output channel-wise. Then, we progressively compose sub-items and propose a novel data-free optimization objective in the discrete domain, minimizing Constrained Absolute Sum of Error (or CASE in short), which surprisingly does not need any dataset and is even not aware of network architecture. We also design an efficient algorithm without back-propagation to further reduce the computation complexity of the objective solver. Finally, without fine-tuning and synthetic datasets, SQuant accelerates the data-free quantization process to a sub-second level with >30% accuracy improvement over the existing data-free post-training quantization works, with the evaluated models under 4-bit quantization. We have open-sourced the SQuant framework at https://github.com/clevercool/SQuant.

Yuge Zhang, Quanlu Zhang, Li Lyna Zhang et al.

One of the key challenges in Neural Architecture Search (NAS) is to efficiently rank the performances of architectures. The mainstream assessment of performance rankers uses ranking correlations (e.g., Kendall's tau), which pay equal attention to the whole space. However, the optimization goal of NAS is identifying top architectures while paying less attention on other architectures in the search space. In this paper, we show both empirically and theoretically that Normalized Discounted Cumulative Gain (NDCG) is a better metric for rankers. Subsequently, we propose a new algorithm, AceNAS, which directly optimizes NDCG with LambdaRank. It also leverages weak labels produced by weight-sharing NAS to pre-train the ranker, so as to further reduce search cost. Extensive experiments on 12 NAS benchmarks and a large-scale search space demonstrate that our approach consistently outperforms SOTA NAS methods, with up to 3.67% accuracy improvement and 8x reduction on search cost.

Xiaotian Gao, Cui Wei, Lintao Zhang et al.

Training and inference efficiency of deep neural networks highly rely on the performance of tensor operators on hardware platforms. Manually optimizing tensor operators has limitations in terms of supporting new operators or hardware platforms. Therefore, automatically optimizing device code configurations of tensor operators is getting increasingly attractive. However, current methods for tensor operator optimization usually suffer from poor sample-efficiency due to the combinatorial search space. In this work, we propose a novel evolutionary method, OpEvo, which efficiently explores the search spaces of tensor operators by introducing a topology-aware mutation operation based on q-random walk to leverage the topological structures over the search spaces. Our comprehensive experiment results show that compared with state-of-the-art (SOTA) methods OpEvo can find the best configuration with the lowest variance and least efforts in the number of trials and wall-clock time. All code of this work is available online.