Differentiable architecture search (DARTS) is a prevailing NAS solution to identify architectures. Based on the continuous relaxation of the architecture space, DARTS learns a differentiable architecture weight and largely reduces the search cost. However, its stability has been challenged for yielding deteriorating architectures as the search proceeds. We find that the precipitous validation loss landscape, which leads to a dramatic performance drop when distilling the final architecture, is an essential factor that causes instability. Based on this observation, we propose a perturbation-based regularization - SmoothDARTS (SDARTS), to smooth the loss landscape and improve the generalizability of DARTS-based methods. In particular, our new formulations stabilize DARTS-based methods by either random smoothing or adversarial attack. The search trajectory on NAS-Bench-1Shot1 demonstrates the effectiveness of our approach and due to the improved stability, we achieve performance gain across various search spaces on 4 datasets. Furthermore, we mathematically show that SDARTS implicitly regularizes the Hessian norm of the validation loss, which accounts for a smoother loss landscape and improved performance.
Neural Ordinary Differential Equation (Neural ODE) has been proposed as a continuous approximation to the ResNet architecture. Some commonly used regularization mechanisms in discrete neural networks (e.g. dropout, Gaussian noise) are missing in current Neural ODE networks. In this paper, we propose a new continuous neural network framework called Neural Stochastic Differential Equation (Neural SDE) network, which naturally incorporates various commonly used regularization mechanisms based on random noise injection. Our framework can model various types of noise injection frequently used in di…
Facebook AI Research（脸书人工智能研究院）；Georgia Tech（佐治亚理工学院）；Diffeo Labs（Diffeo实验室）
Design of reliable systems must guarantee stability against input perturbations. In machine learning, such guarantee entails preventing overfitting and ensuring robustness of models against corruption of input data. In order to maximize stability, we analyze and develop a computationally efficient implementation of Jacobian regularization that increases classification margins of neural networks. The stabilizing effect of the Jacobian regularizer leads to significant improvements in robustness, as measured against both random and adversarial input perturbations, without severely degrading gener…
Recently, differentiable search methods have made major progress in reducing the computational costs of neural architecture search. However, these approaches often report lower accuracy in evaluating the searched architecture or transferring it to another dataset. This is arguably due to the large gap between the architecture depths in search and evaluation scenarios. In this paper, we present an efficient algorithm which allows the depth of searched architectures to grow gradually during the training procedure. This brings two issues, namely, heavier computational overheads and weaker search …
Recent works imply that the channel pruning can be regarded as searching optimal sub-structure from unpruned networks. However, existing works based on this observation require training and evaluating a large number of structures, which limits their application. In this paper, we propose a novel differentiable method for channel pruning, named Differentiable Markov Channel Pruning (DMCP), to efficiently search the optimal sub-structure. Our method is differentiable and can be directly optimized by gradient descent with respect to standard task loss and budget regularization (e.g. FLOPs constra…
This research proposes to use the Moreau-Yosida envelope to stabilize the convergence behavior of bi-level Hyperparameter optimization solvers, and introduces the new algorithm called Moreau-Yosida regularized Hyperparameter Optimization (MY-HPO) algorithm. Theoretical analysis on the correctness of the MY-HPO solution and initial convergence analysis is also provided. Our empirical results show significant improvement in loss values for a fixed computation budget, compared to the state-of-art bi-level HPO solvers.
Deep generative models based on Generative Adversarial Networks (GANs) have demonstrated impressive sample quality but in order to work they require a careful choice of architecture, parameter initialization, and selection of hyper-parameters. This fragility is in part due to a dimensional mismatch or non-overlapping support between the model distribution and the data distribution, causing their density ratio and the associated f-divergence to be undefined. We overcome this fundamental limitation and propose a new regularization approach with low computational cost that yields a stable GAN tra…
University of Freiburg（弗莱堡大学）；Bosch Center for Artificial Intelligence（博世人工智能中心）
Differentiable Architecture Search (DARTS) has attracted a lot of attention due to its simplicity and small search costs achieved by a continuous relaxation and an approximation of the resulting bi-level optimization problem. However, DARTS does not work robustly for new problems: we identify a wide range of search spaces for which DARTS yields degenerate architectures with very poor test performance. We study this failure mode and show that, while DARTS successfully minimizes validation loss, the found solutions generalize poorly when they coincide with high validation loss curvature in the a…
University of Science and Technology of China（中国科学技术大学）
Generative Adversarial Networks (GANs) are the most popular image generation models that have achieved remarkable progress on various computer vision tasks. However, training instability is still one of the open problems for all GAN-based algorithms. Quite a number of methods have been proposed to stabilize the training of GANs, the focuses of which were respectively put on the loss functions, regularization and normalization technologies, training algorithms, and model architectures. Different from the above methods, in this paper, a new perspective on stabilizing GANs training is presented. …
The convolutional neural network has achieved great success in fulfilling computer vision tasks despite large computation overhead against efficient deployment. Structured (channel) pruning is usually applied to reduce the model redundancy while preserving the network structure, such that the pruned network can be easily deployed in practice. However, existing structured pruning methods require hand-crafted rules which may lead to tremendous pruning space. In this paper, we introduce Differentiable Annealing Indicator Search (DAIS) that leverages the strength of neural architecture search in t…
Poznan University of Technology（波兹南理工大学）；Institute of Computing Science（计算机科学研究所）
Overfitting & underfitting and stable training are an important challenges in machine learning. Current approaches for these issues are mixup, SamplePairing and BC learning. In our work, we state the hypothesis that mixing many images together can be more effective than just two. Batchboost pipeline has three stages: (a) pairing: method of selecting two samples. (b) mixing: how to create a new one from two samples. (c) feeding: combining mixed samples with new ones from dataset into batch (with ratio $γ$). Note that sample that appears in our batch propagates with subsequent iterations with le…
Zhejiang University（浙江大学）；EPFL（洛桑联邦理工学院）；King’s College London（伦敦国王学院）；Alibaba Group（阿里巴巴集团）
Differentiable architecture search (DARTS) has been a mainstream direction in automatic machine learning. Since the discovery that original DARTS will inevitably converge to poor architectures, recent works alleviate this by either designing rule-based architecture selection techniques or incorporating complex regularization techniques, abandoning the simplicity of the original DARTS that selects architectures based on the largest parametric value, namely $α$. Moreover, we find that all the previous attempts only rely on classification labels, hence learning only single modal information and l…
University of Chinese Academy of Sciences（中国科学院大学）；Institute of Software Chinese Academy of Sciences（中国科学院软件研究所）
Differentiable architecture search (DARTS) is widely considered to be easy to overfit the validation set which leads to performance degradation. We first employ a series of exploratory experiments to verify that neither high-strength architecture parameters regularization nor warmup training scheme can effectively solve this problem. Based on the insights from the experiments, we conjecture that the performance of DARTS does not depend on the well-trained supernet weights and argue that the architecture parameters should be trained by the gradients which are obtained in the early stage rather …
Deep equilibrium networks (DEQs) are a new class of models that eschews traditional depth in favor of finding the fixed point of a single nonlinear layer. These models have been shown to achieve performance competitive with the state-of-the-art deep networks while using significantly less memory. Yet they are also slower, brittle to architectural choices, and introduce potential instability to the model. In this paper, we propose a regularization scheme for DEQ models that explicitly regularizes the Jacobian of the fixed-point update equations to stabilize the learning of equilibrium models. W…
CT-Guided Spatially-varying Regularization for Voxel-Wise Deformable Whole-Body PET Registration
Institute of Medical Technology, Peking University Health Science Center（北京大学医学部医学技术研究所）；Ren Ji Hospital, Shanghai Jiao Tong University（上海交通大学仁济医院）；University of Oxford（牛津大学）
Transferrable neural architecture search can be viewed as a binary optimization problem where a single optimal path should be selected among candidate paths in each edge within the repeated cell block of the directed a cyclic graph form. Recently, the field of differentiable architecture search attempts to relax the search problem continuously using a one-shot network that combines all the candidate paths in search space. However, when the one-shot network is pruned to the model in the discrete architecture space by the derivation algorithm, performance is significantly degraded to an almost r…
Scaling up and Stabilizing Differentiable Planning with Implicit Differentiation
Khoury College of Computer Sciences, Northeastern University（东北大学Khoury计算机科学学院）；Institute for Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院）；Shanghai Qi Zhi Institute（上海期智研究院）
IRIT, University of Toulouse（图卢兹大学 IRIT 研究所）；IRT Saint-Exupery（圣埃克苏佩里技术研究所）；ISAE-SUPAERO, University of Toulouse（图卢兹大学 ISAE-SUPAERO 高等航空与航天学院）
Differentiable Architecture Search (DARTS) is a recent neural architecture search (NAS) method based on a differentiable relaxation. Due to its success, numerous variants analyzing and improving parts of the DARTS framework have recently been proposed. By considering the problem as a constrained bilevel optimization, we present and analyze DARTS-PRIME, a variant including improvements to architectural weight update scheduling and regularization towards discretization. We propose a dynamic schedule based on per-minibatch network information to make architecture updates more informed, as well as…
Stabilizing PINNs: A regularization scheme for PINN training to avoid unstable fixed points of dynamical systems
Know Center Research GmbH；Christian Doppler Laboratory for Physics-driven Machine Learning in Industrial Applications；Institute of Thermodynamics and Sustainable Propulsion Systems（热力学与可持续推进系统研究所）；Signal Processing and Speech Communication Laboratory（信号处理与语音通信实验室）
This paper proposes a differentiable linear quadratic Model Predictive Control (MPC) framework for safe imitation learning. The infinite-horizon cost is enforced using a terminal cost function obtained from the discrete-time algebraic Riccati equation (DARE), so that the learned controller can be proven to be stabilizing in closed-loop. A central contribution is the derivation of the analytical derivative of the solution of the DARE, thereby allowing the use of differentiation-based learning methods. A further contribution is the structure of the MPC optimization problem: an augmented Lagrangi…
University of Maryland（马里兰大学）；Aunalytics；Hillsdale College（希尔斯代尔学院）；Potomac Research LLC（波托马克研究有限责任公司）
Recent work has shown that machine learning (ML) models can be trained to accurately forecast the dynamics of unknown chaotic dynamical systems. Short-term predictions of the state evolution and long-term predictions of the statistical patterns of the dynamics (``climate'') can be produced by employing a feedback loop, whereby the model is trained to predict forward one time step, then the model output is used as input for multiple time steps. In the absence of mitigating techniques, however, this technique can result in artificially rapid error growth. In this article, we systematically exami…
Fudan University（复旦大学）；Shanghai AI Laboratory（上海人工智能实验室）；Oracle（甲骨文公司）
Neural Architecture Search has attracted increasing attention in recent years. Among them, differential NAS approaches such as DARTS, have gained popularity for the search efficiency. However, they still suffer from three main issues, that are, the weak stability due to the performance collapse, the poor generalization ability of the searched architectures, and the inferior robustness to different kinds of proxies. To solve the stability and generalization problems, a simple-but-effective regularization method, termed as Beta-Decay, is proposed to regularize the DARTS-based NAS searching proce…
Fudan University（复旦大学）；BAIDU USA LLC（百度美国有限责任公司）；Shanghai AI Laboratory（上海人工智能实验室）；The University of Sydney（悉尼大学）
Neural Architecture Search~(NAS) has attracted increasingly more attention in recent years because of its capability to design deep neural networks automatically. Among them, differential NAS approaches such as DARTS, have gained popularity for the search efficiency. However, they suffer from two main issues, the weak robustness to the performance collapse and the poor generalization ability of the searched architectures. To solve these two problems, a simple-but-efficient regularization method, termed as Beta-Decay, is proposed to regularize the DARTS-based NAS searching process. Specifically…
Modern neural network architectures typically have many millions of parameters and can be pruned significantly without substantial loss in effectiveness which demonstrates they are over-parameterized. The contribution of this work is two-fold. The first is a method for approximating a multivariate Bernoulli random variable by means of a deterministic and differentiable transformation of any real-valued multivariate random variable. The second is a method for model selection by element-wise multiplication of parameters with approximate binary gates that may be computed deterministically or stoc…
Differentiable Entropy Regularization: A Complexity-Aware Approach for Neural Optimization
Department of Computer Science Iowa State University（计算机科学系爱荷华州立大学）；Department of Civil, Construction and Environmental Engineering Iowa State University（土木、建设与环境工程系爱荷华州立大学）
Despite the success of Lipschitz regularization in stabilizing GAN training, the exact reason of its effectiveness remains poorly understood. The direct effect of $K$-Lipschitz regularization is to restrict the $L2$-norm of the neural network gradient to be smaller than a threshold $K$ (e.g., $K=1$) such that $\|\nabla f\| \leq K$. In this work, we uncover an even more important effect of Lipschitz regularization by examining its impact on the loss function: It degenerates GAN loss functions to almost linear ones by restricting their domain and interval of attainable gradient values. Our analy…
Ecole Polytechnique（巴黎综合理工学院）；Université Paris Dauphine-PSL（巴黎第九大学-巴黎文理研究大学）
Deep Learning (DL) is considered the state-of-the-art in computer vision, speech recognition and natural language processing. Until recently, it was also widely accepted that DL is irrelevant for learning tasks on tabular data, especially in the small sample regime where ensemble methods are acknowledged as the gold standard. We present a new end-to-end differentiable method to train a standard FFNN. Our method, \textbf{Muddling labels for Regularization} (\texttt{MLR}), penalizes memorization through the generation of uninformative labels and the application of a differentiable close-form reg…
RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）
This work studies the entropic regularization formulation of the 2-Wasserstein distance on an infinite-dimensional Hilbert space, in particular for the Gaussian setting. We first present the Minimum Mutual Information property, namely the joint measures of two Gaussian measures on Hilbert space with the smallest mutual information are joint Gaussian measures. This is the infinite-dimensional generalization of the Maximum Entropy property of Gaussian densities on Euclidean space. We then give closed form formulas for the optimal entropic transport plan, entropic 2-Wasserstein distance, and Sink…
Bhargava Cube--Inspired Quadratic Regularization for Structured Neural Embeddings
Department of Computer Science；Engineering (AI \& ML), PES University, Bangalore 560 085, India Department of Electronics；Communication Engineering, PES University, Bangalore 560 085, India
University of California San Francisco（加州大学旧金山分校）；University of San Francisco（旧金山大学）；Stanford University（斯坦福大学）
Many regression and classification procedures fit a parameterized function $f(x;w)$ of predictor variables $x$ to data $\{x_{i},y_{i}\}_1^N$ based on some loss criterion $L(y,f)$. Often, regularization is applied to improve accuracy by placing a constraint $P(w)\leq t$ on the values of the parameters $w$. Although efficient methods exist for finding solutions to these constrained optimization problems for all values of $t\geq0$ in the special case when $f$ is a linear function, none are available when $f$ is non-linear (e.g. Neural Networks). Here we present a fast algorithm that provides all …
In this work we introduce a differentiable version of the Compositional Pattern Producing Network, called the DPPN. Unlike a standard CPPN, the topology of a DPPN is evolved but the weights are learned. A Lamarckian algorithm, that combines evolution and learning, produces DPPNs to reconstruct an image. Our main result is that DPPNs can be evolved/trained to compress the weights of a denoising autoencoder from 157684 to roughly 200 parameters, while achieving a reconstruction accuracy comparable to a fully connected network with more than two orders of magnitude more parameters. The regulariza…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
A family of regularization functionals is said to admit a linear representer theorem if every member of the family admits minimizers that lie in a fixed finite dimensional subspace. A recent characterization states that a general class of regularization functionals with differentiable regularizer admits a linear representer theorem if and only if the regularization term is a non-decreasing function of the norm. In this report, we improve over such result by replacing the differentiability assumption with lower semi-continuity and deriving a proof that is independent of the dimensionality of th…
