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In this paper, we present a stochastic gradient algorithm for minimizing a smooth objective function that is an expectation over noisy cost samples, and only the latter are observed for any given parameter. Our algorithm employs a gradient estimation scheme with random perturbations, which are formed using the truncated Cauchy distribution from the delta sphere. We analyze the bias and variance of the proposed gradient estimator. Our algorithm is found to be particularly useful in the case when the objective function is non-convex, and the parameter dimension is high. From an asymptotic convergence analysis, we establish that our algorithm converges almost surely to the set of stationary points of the objective function and obtains the asymptotic convergence rate. We also show that our algorithm avoids unstable equilibria, implying convergence to local minima. Further, we perform a non-asymptotic convergence analysis of our algorithm. In particular, we establish here a non-asymptotic bound for finding an epsilon-stationary point of the non-convex objective function. Finally, we demonstrate numerically through simulations that the performance of our algorithm outperforms GSF, SPSA, and RDSA by a significant margin over a few non-convex settings and further validate its performance over convex (noisy) objectives.

Ongoing advances in force field and computer hardware development enable the use of molecular dynamics (MD) to simulate increasingly complex systems with the ultimate goal of reaching cellular complexity. At the same time, rational design by high-throughput (HT) simulations is another forefront of MD. In these areas, the Martini coarse-grained force field, especially the latest version (i.e. v3), is being actively explored because it offers enhanced spatial-temporal resolution. However, the automation tools for preparing simulations with the Martini force field, accompanying the previous version, were not designed for HT simulations or studies of complex cellular systems. Therefore, they become a major limiting factor. To address these shortcomings, we present the open-source Vermouth python library. Vermouth is designed to become the unified framework for developing programs, which prepare, run, and analyze Martini simulations of complex systems. To demonstrate the power of the Vermouth library, the Martinize2 program is showcased as a generalization of the martinize script, originally aimed to set up simulations of proteins. In contrast to the previous version, Martinize2 automatically handles protonation states in proteins and post-translation modifications, offers more options to fine-tune structural biases such as the elastic network, and can convert non-protein molecules such as ligands. Finally, Martinize2 is used in two high-complexity benchmarks. The entire I-TASSER protein template database as well as a subset of 200,000 structures from the AlphaFold Protein Structure Database are converted to CG resolution and we illustrate how the checks on input structure quality can safeguard high-throughput applications.

The vulnerability of deep neural network models to adversarial example attacks is a practical challenge in many artificial intelligence applications. A recent line of work shows that the use of randomization in adversarial training is the key to find optimal strategies against adversarial example attacks. However, in a fully randomized setting where both the defender and the attacker can use randomized strategies, there are no efficient algorithm for finding such an optimal strategy. To fill the gap, we propose the first algorithm of its kind, called FRAT, which models the problem with a new infinite-dimensional continuous-time flow on probability distribution spaces. FRAT maintains a lightweight mixture of models for the defender, with flexibility to efficiently update mixing weights and model parameters at each iteration. Furthermore, FRAT utilizes lightweight sampling subroutines to construct a random strategy for the attacker. We prove that the continuous-time limit of FRAT converges to a mixed Nash equilibria in a zero-sum game formed by a defender and an attacker. Experimental results also demonstrate the efficiency of FRAT on CIFAR-10 and CIFAR-100 datasets.

We investigate the problem of joint statistical estimation of several parameters for a stochastic differential equations driven by an additive fractional Brownian motion. Based on discrete-time observations of the model, we construct an estimator of the Hurst parameter, the diffusion parameter and the drift, which lies in a parametrised family of coercive drift coefficients. Our procedure is based on the assumption that the stationary distribution of the SDE and of its increments permits to identify the parameters of the model. Under this assumption, we prove consistency results and derive a rate of convergence for the estimator. Finally, we show that the identifiability assumption is satisfied in the case of a family of fractional Ornstein-Uhlenbeck processes and illustrate our results with some numerical experiments.

Fine-tuning large-scale pre-trained language models has been demonstrated effective for various natural language processing (NLP) tasks. Previous studies have established that incorporating adversarial training during the fine-tuning stage can significantly enhance model generalization and robustness. However, from the perspective of game theory, such utilizations of adversarial training correspond to pure-strategy games, which are inherently limited in terms of the scope of their strategies, thereby still having room for improvement. In order to push the performance boundaries, we propose a novel Mixed-strategy Adversarial Training algorithm (MAT). Methodologically, we derive the Nash equilibrium of a mixed-strategy game for adversarial training using Entropy Mirror Descent to establish MAT by sampling method. To verify the effectiveness of MAT, we conducted extensive benchmark experiments on large-scale pre-trained models, such as BERT and RoBERTa. MAT significantly outperforms the state-of-the-art methods on both the GLUE and ANLI benchmarks in terms of generalization and robustness.

Detecting adversarial samples that are carefully crafted to fool the model is a critical step to socially-secure applications. However, existing adversarial detection methods require access to sufficient training data, which brings noteworthy concerns regarding privacy leakage and generalizability. In this work, we validate that the adversarial sample generated by attack algorithms is strongly related to a specific vector in the high-dimensional inputs. Such vectors, namely UAPs (Universal Adversarial Perturbations), can be calculated without original training data. Based on this discovery, we propose a data-agnostic adversarial detection framework, which induces different responses between normal and adversarial samples to UAPs. Experimental results show that our method achieves competitive detection performance on various text classification tasks, and maintains an equivalent time consumption to normal inference.

The real-world data tends to be heavily imbalanced and severely skew the data-driven deep neural networks, which makes Long-Tailed Recognition (LTR) a massive challenging task. Existing LTR methods seldom train Vision Transformers (ViTs) with Long-Tailed (LT) data, while the off-the-shelf pretrain weight of ViTs always leads to unfair comparisons. In this paper, we systematically investigate the ViTs' performance in LTR and propose LiVT to train ViTs from scratch only with LT data. With the observation that ViTs suffer more severe LTR problems, we conduct Masked Generative Pretraining (MGP) to learn generalized features. With ample and solid evidence, we show that MGP is more robust than supervised manners. In addition, Binary Cross Entropy (BCE) loss, which shows conspicuous performance with ViTs, encounters predicaments in LTR. We further propose the balanced BCE to ameliorate it with strong theoretical groundings. Specially, we derive the unbiased extension of Sigmoid and compensate extra logit margins to deploy it. Our Bal-BCE contributes to the quick convergence of ViTs in just a few epochs. Extensive experiments demonstrate that with MGP and Bal-BCE, LiVT successfully trains ViTs well without any additional data and outperforms comparable state-of-the-art methods significantly, e.g., our ViT-B achieves 81.0% Top-1 accuracy in iNaturalist 2018 without bells and whistles. Code is available at //github.com/XuZhengzhuo/LiVT.

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.

We introduce an effective model to overcome the problem of mode collapse when training Generative Adversarial Networks (GAN). Firstly, we propose a new generator objective that finds it better to tackle mode collapse. And, we apply an independent Autoencoders (AE) to constrain the generator and consider its reconstructed samples as "real" samples to slow down the convergence of discriminator that enables to reduce the gradient vanishing problem and stabilize the model. Secondly, from mappings between latent and data spaces provided by AE, we further regularize AE by the relative distance between the latent and data samples to explicitly prevent the generator falling into mode collapse setting. This idea comes when we find a new way to visualize the mode collapse on MNIST dataset. To the best of our knowledge, our method is the first to propose and apply successfully the relative distance of latent and data samples for stabilizing GAN. Thirdly, our proposed model, namely Generative Adversarial Autoencoder Networks (GAAN), is stable and has suffered from neither gradient vanishing nor mode collapse issues, as empirically demonstrated on synthetic, MNIST, MNIST-1K, CelebA and CIFAR-10 datasets. Experimental results show that our method can approximate well multi-modal distribution and achieve better results than state-of-the-art methods on these benchmark datasets. Our model implementation is published here: //github.com/tntrung/gaan

High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.