Ke Sun

You Huang, Hao Yang, Ke Sun et al.

Interactive image segmentation enables annotators to efficiently perform pixel-level annotation for segmentation tasks. However, the existing interactive segmentation pipeline suffers from inefficient computations of interactive models because of the following two issues. First, annotators' later click is based on models' feedback of annotators' former click. This serial interaction is unable to utilize model's parallelism capabilities. Second, in each interaction step, the model handles the invariant image along with the sparse variable clicks, resulting in a process that's highly repetitive and redundant. For efficient computations, we propose a method named InterFormer that follows a new pipeline to address these issues. InterFormer extracts and preprocesses the computationally time-consuming part i.e. image processing from the existing process. Specifically, InterFormer employs a large vision transformer (ViT) on high-performance devices to preprocess images in parallel, and then uses a lightweight module called interactive multi-head self attention (I-MSA) for interactive segmentation. Furthermore, the I-MSA module's deployment on low-power devices extends the practical application of interactive segmentation. The I-MSA module utilizes the preprocessed features to efficiently response to the annotator inputs in real-time. The experiments on several datasets demonstrate the effectiveness of InterFormer, which outperforms previous interactive segmentation models in terms of computational efficiency and segmentation quality, achieve real-time high-quality interactive segmentation on CPU-only devices. The code is available at https://github.com/YouHuang67/InterFormer.

He Zhao, Ke Sun, Amir Dezfouli et al.

We study the problem of imputing missing values in a dataset, which has important applications in many domains. The key to missing value imputation is to capture the data distribution with incomplete samples and impute the missing values accordingly. In this paper, by leveraging the fact that any two batches of data with missing values come from the same data distribution, we propose to impute the missing values of two batches of samples by transforming them into a latent space through deep invertible functions and matching them distributionally. To learn the transformations and impute the missing values simultaneously, a simple and well-motivated algorithm is proposed. Our algorithm has fewer hyperparameters to fine-tune and generates high-quality imputations regardless of how missing values are generated. Extensive experiments over a large number of datasets and competing benchmark algorithms show that our method achieves state-of-the-art performance.

Frank Nielsen, Ke Sun

A key technique of machine learning and computer vision is to embed discrete weighted graphs into continuous spaces for further downstream processing. Embedding discrete hierarchical structures in hyperbolic geometry has proven very successful since it was shown that any weighted tree can be embedded in that geometry with arbitrary low distortion. Various optimization methods for hyperbolic embeddings based on common models of hyperbolic geometry have been studied. In this paper, we consider Hilbert geometry for the standard simplex which is isometric to a vector space equipped with the variation polytope norm. We study the representation power of this Hilbert simplex geometry by embedding distance matrices of graphs. Our findings demonstrate that Hilbert simplex geometry is competitive to alternative geometries such as the Poincaré hyperbolic ball or the Euclidean geometry for embedding tasks while being fast and numerically robust.

Ke Sun, Bei Jiang, Linglong Kong

Distributional reinforcement learning, which focuses on learning the entire return distribution instead of only its expectation in standard RL, has demonstrated remarkable success in enhancing performance. Despite these advancements, our comprehension of how the return distribution within distributional RL still remains limited. In this study, we investigate the optimization advantages of distributional RL by utilizing its extra return distribution knowledge over classical RL within the Neural Fitted Z-Iteration~(Neural FZI) framework. To begin with, we demonstrate that the distribution loss of distributional RL has desirable smoothness characteristics and hence enjoys stable gradients, which is in line with its tendency to promote optimization stability. Furthermore, the acceleration effect of distributional RL is revealed by decomposing the return distribution. It shows that distributional RL can perform favorably if the return distribution approximation is appropriate, measured by the variance of gradient estimates in each environment. Rigorous experiments validate the stable optimization behaviors of distributional RL and its acceleration effects compared to classical RL. Our research findings illuminate how the return distribution in distributional RL algorithms helps the optimization.

Vahid Partovi Nia, Guojun Zhang, Ivan Kobyzev et al.

Deep models are dominating the artificial intelligence (AI) industry since the ImageNet challenge in 2012. The size of deep models is increasing ever since, which brings new challenges to this field with applications in cell phones, personal computers, autonomous cars, and wireless base stations. Here we list a set of problems, ranging from training, inference, generalization bound, and optimization with some formalism to communicate these challenges with mathematicians, statisticians, and theoretical computer scientists. This is a subjective view of the research questions in deep learning that benefits the tech industry in long run.

Chen Zheng, Ke Sun, Hang Wu et al.

In recent advancements in Conversational Large Language Models (LLMs), a concerning trend has emerged, showing that many new base LLMs experience a knowledge reduction in their foundational capabilities following Supervised Fine-Tuning (SFT). This process often leads to issues such as forgetting or a decrease in the base model's abilities. Moreover, fine-tuned models struggle to align with user preferences, inadvertently increasing the generation of toxic outputs when specifically prompted. To overcome these challenges, we adopted an innovative approach by completely bypassing SFT and directly implementing Harmless Reinforcement Learning from Human Feedback (RLHF). Our method not only preserves the base model's general capabilities but also significantly enhances its conversational abilities, while notably reducing the generation of toxic outputs. Our approach holds significant implications for fields that demand a nuanced understanding and generation of responses, such as customer service. We applied this methodology to Mistral, the most popular base model, thereby creating Mistral-Plus. Our validation across 11 general tasks demonstrates that Mistral-Plus outperforms similarly sized open-source base models and their corresponding instruct versions. Importantly, the conversational abilities of Mistral-Plus were significantly improved, indicating a substantial advancement over traditional SFT models in both safety and user preference alignment.

Kezhou Lin, Xiaohan Wang, Linchao Zhu et al.

In this paper, we tackle the problem of sign language translation (SLT) without gloss annotations. Although intermediate representation like gloss has been proven effective, gloss annotations are hard to acquire, especially in large quantities. This limits the domain coverage of translation datasets, thus handicapping real-world applications. To mitigate this problem, we design the Gloss-Free End-to-end sign language translation framework (GloFE). Our method improves the performance of SLT in the gloss-free setting by exploiting the shared underlying semantics of signs and the corresponding spoken translation. Common concepts are extracted from the text and used as a weak form of intermediate representation. The global embedding of these concepts is used as a query for cross-attention to find the corresponding information within the learned visual features. In a contrastive manner, we encourage the similarity of query results between samples containing such concepts and decrease those that do not. We obtained state-of-the-art results on large-scale datasets, including OpenASL and How2Sign. The code and model will be available at https://github.com/HenryLittle/GloFE.

Chen Zheng, Ke Sun, Da Tang et al.

The emergence of Large Language Models (LLMs) such as ChatGPT and LLaMA encounter limitations in domain-specific tasks, with these models often lacking depth and accuracy in specialized areas, and exhibiting a decrease in general capabilities when fine-tuned, particularly analysis ability in small sized models. To address these gaps, we introduce ICE-GRT, utilizing Reinforcement Learning from Human Feedback (RLHF) grounded in Proximal Policy Optimization (PPO), demonstrating remarkable ability in in-domain scenarios without compromising general task performance. Our exploration of ICE-GRT highlights its understanding and reasoning ability to not only generate robust answers but also to provide detailed analyses of the reasons behind the answer. This capability marks a significant progression beyond the scope of Supervised Fine-Tuning models. The success of ICE-GRT is dependent on several crucial factors, including Appropriate Data, Reward Size Scaling, KL-Control, Advantage Normalization, etc. The ICE-GRT model exhibits state-of-the-art performance in domain-specific tasks and across 12 general Language tasks against equivalent size and even larger size LLMs, highlighting the effectiveness of our approach. We provide a comprehensive analysis of the ICE-GRT, underscoring the significant advancements it brings to the field of LLM.

Ke Sun

The high dimensional parameter space of modern deep neural networks -- the neuromanifold -- is endowed with a unique metric tensor defined by the Fisher information, estimating which is crucial for both theory and practical methods in deep learning. To analyze this tensor for classification networks, we return to a low dimensional space of probability distributions -- the core space -- and carefully analyze the spectrum of its Riemannian metric. We extend our discoveries there into deterministic bounds of the metric tensor on the neuromanifold. We introduce an unbiased random estimate of the metric tensor and its bounds based on Hutchinson's trace estimator. It can be evaluated efficiently through a single backward pass and can be used to estimate the diagonal, or block diagonal, or the full tensor. Its quality is guaranteed with a standard deviation bounded by the true value up to scaling.

Chen Zheng, Ke Sun, Xun Zhou

Despite the advances in Large Language Models (LLMs), exemplified by models like GPT-4 and Claude, smaller-scale LLMs such as Llama and Mistral often struggle with generating in-depth and coherent dialogues. This paper presents a novel two-step Coarse-to-Fine Actor model to address the inherent limitations in conversational and analytical capabilities of small-sized LLMs. Our approach begins with the Policy-based Coarse Actor, employing a technique we term "Continuous Maximization". The Coarse Actor establishes an enhanced, knowledge-rich pool adept at aligning with human preference styles in analysis and reasoning. Through the RLHF process, it employs Continuous Maximization, a strategy that dynamically and adaptively extends the output length limit, enabling the generation of more detailed and analytical content. Subsequently, the Fine Actor refines this analytical content, addressing the generation of excessively redundant information from the Coarse Actor. We introduce a "Knowledge Residue Merger" approach, refining the content from the Coarse Actor and merging it with an existing Instruction model to improve quality, correctness, and reduce redundancies. We applied our methodology to the popular Mistral model, creating Mistral-C2F, which has demonstrated exceptional performance across 11 general language tasks and the MT-Bench Dialogue task, outperforming similar-scale models and even larger models with 13B and 30B parameters. Our model has significantly improved conversational and analytical reasoning abilities.

Zhongxi Chen, Ke Sun, Xianming Lin et al.

Camouflaged Object Detection (COD) is a challenging task in computer vision due to the high similarity between camouflaged objects and their surroundings. Existing COD methods primarily employ semantic segmentation, which suffers from overconfident incorrect predictions. In this paper, we propose a new paradigm that treats COD as a conditional mask-generation task leveraging diffusion models. Our method, dubbed CamoDiffusion, employs the denoising process of diffusion models to iteratively reduce the noise of the mask. Due to the stochastic sampling process of diffusion, our model is capable of sampling multiple possible predictions from the mask distribution, avoiding the problem of overconfident point estimation. Moreover, we develop specialized learning strategies that include an innovative ensemble approach for generating robust predictions and tailored forward diffusion methods for efficient training, specifically for the COD task. Extensive experiments on three COD datasets attest the superior performance of our model compared to existing state-of-the-art methods, particularly on the most challenging COD10K dataset, where our approach achieves 0.019 in terms of MAE.

Alexander Soen, Ibrahim Alabdulmohsin, Sanmi Koyejo et al.

We introduce a new family of techniques to post-process ("wrap") a black-box classifier in order to reduce its bias. Our technique builds on the recent analysis of improper loss functions whose optimization can correct any twist in prediction, unfairness being treated as a twist. In the post-processing, we learn a wrapper function which we define as an $α$-tree, which modifies the prediction. We provide two generic boosting algorithms to learn $α$-trees. We show that our modification has appealing properties in terms of composition of $α$-trees, generalization, interpretability, and KL divergence between modified and original predictions. We exemplify the use of our technique in three fairness notions: conditional value-at-risk, equality of opportunity, and statistical parity; and provide experiments on several readily available datasets.

Hao Zhu, Ke Sun, Piotr Koniusz

Graph contrastive learning attracts/disperses node representations for similar/dissimilar node pairs under some notion of similarity. It may be combined with a low-dimensional embedding of nodes to preserve intrinsic and structural properties of a graph. In this paper, we extend the celebrated Laplacian Eigenmaps with contrastive learning, and call them COntrastive Laplacian EigenmapS (COLES). Starting from a GAN-inspired contrastive formulation, we show that the Jensen-Shannon divergence underlying many contrastive graph embedding models fails under disjoint positive and negative distributions, which may naturally emerge during sampling in the contrastive setting. In contrast, we demonstrate analytically that COLES essentially minimizes a surrogate of Wasserstein distance, which is known to cope well under disjoint distributions. Moreover, we show that the loss of COLES belongs to the family of so-called block-contrastive losses, previously shown to be superior compared to pair-wise losses typically used by contrastive methods. We show on popular benchmarks/backbones that COLES offers favourable accuracy/scalability compared to DeepWalk, GCN, Graph2Gauss, DGI and GRACE baselines.

Ke Sun, Taiping Yao, Shen Chen et al.

With various facial manipulation techniques arising, face forgery detection has drawn growing attention due to security concerns. Previous works always formulate face forgery detection as a classification problem based on cross-entropy loss, which emphasizes category-level differences rather than the essential discrepancies between real and fake faces, limiting model generalization in unseen domains. To address this issue, we propose a novel face forgery detection framework, named Dual Contrastive Learning (DCL), which specially constructs positive and negative paired data and performs designed contrastive learning at different granularities to learn generalized feature representation. Concretely, combined with the hard sample selection strategy, Inter-Instance Contrastive Learning (Inter-ICL) is first proposed to promote task-related discriminative features learning by especially constructing instance pairs. Moreover, to further explore the essential discrepancies, Intra-Instance Contrastive Learning (Intra-ICL) is introduced to focus on the local content inconsistencies prevalent in the forged faces by constructing local-region pairs inside instances. Extensive experiments and visualizations on several datasets demonstrate the generalization of our method against the state-of-the-art competitors.

Ke Sun, Mingjie Li, Zhouchen Lin

Adversarial robustness, which primarily comprises sensitivity-based robustness and spatial robustness, plays an integral part in achieving robust generalization. In this paper, we endeavor to design strategies to achieve universal adversarial robustness. To achieve this, we first investigate the relatively less-explored realm of spatial robustness. Then, we integrate the existing spatial robustness methods by incorporating both local and global spatial vulnerability into a unified spatial attack and adversarial training approach. Furthermore, we present a comprehensive relationship between natural accuracy, sensitivity-based robustness, and spatial robustness, supported by strong evidence from the perspective of robust representation. Crucially, to reconcile the interplay between the mutual impacts of various robustness components into one unified framework, we incorporate the \textit{Pareto criterion} into the adversarial robustness analysis, yielding a novel strategy called Pareto Adversarial Training for achieving universal robustness. The resulting Pareto front, which delineates the set of optimal solutions, provides an optimal balance between natural accuracy and various adversarial robustness. This sheds light on solutions for achieving universal robustness in the future. To the best of our knowledge, we are the first to consider universal adversarial robustness via multi-objective optimization.

Ke Sun, Yafei Wang, Yi Liu et al.

Anderson mixing has been heuristically applied to reinforcement learning (RL) algorithms for accelerating convergence and improving the sampling efficiency of deep RL. Despite its heuristic improvement of convergence, a rigorous mathematical justification for the benefits of Anderson mixing in RL has not yet been put forward. In this paper, we provide deeper insights into a class of acceleration schemes built on Anderson mixing that improve the convergence of deep RL algorithms. Our main results establish a connection between Anderson mixing and quasi-Newton methods and prove that Anderson mixing increases the convergence radius of policy iteration schemes by an extra contraction factor. The key focus of the analysis roots in the fixed-point iteration nature of RL. We further propose a stabilization strategy by introducing a stable regularization term in Anderson mixing and a differentiable, non-expansive MellowMax operator that can allow both faster convergence and more stable behavior. Extensive experiments demonstrate that our proposed method enhances the convergence, stability, and performance of RL algorithms.

Ke Sun, Yingnan Zhao, Enze Shi et al.

The remarkable empirical performance of distributional reinforcement learning (RL) has garnered increasing attention to understanding its theoretical advantages over classical RL. By decomposing the categorical distributional loss commonly employed in distributional RL, we find that the potential superiority of distributional RL can be attributed to a derived distribution-matching entropy regularization. This less-studied entropy regularization aims to capture additional knowledge of return distribution beyond only its expectation, contributing to an augmented reward signal in policy optimization. In contrast to the vanilla entropy regularization in MaxEnt RL, which explicitly encourages exploration by promoting diverse actions, the novel entropy regularization derived from categorical distributional loss implicitly updates policies to align the learned policy with (estimated) environmental uncertainty. Finally, extensive experiments verify the significance of this uncertainty-aware regularization from distributional RL on the empirical benefits over classical RL. Our study offers an innovative exploration perspective to explain the intrinsic benefits of distributional learning in RL.

Hongming Zhang, Ke Sun, Bo Xu et al.

In deep reinforcement learning (RL) systems, abnormal states pose significant risks by potentially triggering unpredictable behaviors and unsafe actions, thus impeding the deployment of RL systems in real-world scenarios. It is crucial for reliable decision-making systems to have the capability to cast an alert whenever they encounter unfamiliar observations that they are not equipped to handle. In this paper, we propose a novel Mahalanobis distance-based (MD) anomaly detection framework, called \textit{MDX}, for deep RL algorithms. MDX simultaneously addresses random, adversarial, and out-of-distribution (OOD) state outliers in both offline and online settings. It utilizes Mahalanobis distance within class-conditional distributions for each action and operates within a statistical hypothesis testing framework under the Gaussian assumption. We further extend it to robust and distribution-free versions by incorporating Robust MD and conformal inference techniques. Through extensive experiments on classical control environments, Atari games, and autonomous driving scenarios, we demonstrate the effectiveness of our MD-based detection framework. MDX offers a simple, unified, and practical anomaly detection tool for enhancing the safety and reliability of RL systems in real-world applications.

Ke Sun, Yingnan Zhao, Shangling Jui et al.

In real scenarios, state observations that an agent observes may contain measurement errors or adversarial noises, misleading the agent to take suboptimal actions or even collapse while training. In this paper, we study the training robustness of distributional Reinforcement Learning (RL), a class of state-of-the-art methods that estimate the whole distribution, as opposed to only the expectation, of the total return. Firstly, we validate the contraction of distributional Bellman operators in the State-Noisy Markov Decision Process (SN-MDP), a typical tabular case that incorporates both random and adversarial state observation noises. In the noisy setting with function approximation, we then analyze the vulnerability of least squared loss in expectation-based RL with either linear or nonlinear function approximation. By contrast, we theoretically characterize the bounded gradient norm of distributional RL loss based on the categorical parameterization equipped with the KL divergence. The resulting stable gradients while the optimization in distributional RL accounts for its better training robustness against state observation noises. Finally, extensive experiments on the suite of environments verified that distributional RL is less vulnerable against both random and adversarial noisy state observations compared with its expectation-based counterpart.

Alexander Soen, Ke Sun

In the realm of deep learning, the Fisher information matrix (FIM) gives novel insights and useful tools to characterize the loss landscape, perform second-order optimization, and build geometric learning theories. The exact FIM is either unavailable in closed form or too expensive to compute. In practice, it is almost always estimated based on empirical samples. We investigate two such estimators based on two equivalent representations of the FIM -- both unbiased and consistent. Their estimation quality is naturally gauged by their variance given in closed form. We analyze how the parametric structure of a deep neural network can affect the variance. The meaning of this variance measure and its upper bounds are then discussed in the context of deep learning.

Marcel Keller, Ke Sun

We implement training of neural networks in secure multi-party computation (MPC) using quantization commonly used in said setting. We are the first to present an MNIST classifier purely trained in MPC that comes within 0.2 percent of the accuracy of the same convolutional neural network trained via plaintext computation. More concretely, we have trained a network with two convolutional and two dense layers to 99.2% accuracy in 3.5 hours (under one hour for 99% accuracy). We have also implemented AlexNet for CIFAR-10, which converges in a few hours. We develop novel protocols for exponentiation and inverse square root. Finally, we present experiments in a range of MPC security models for up to ten parties, both with honest and dishonest majority as well as semi-honest and malicious security.

Shunxin Xu, Ke Sun, Dong Liu et al.

The capability of image semantic segmentation may be deteriorated due to noisy input image, where image denoising prior to segmentation helps. Both image denoising and semantic segmentation have been developed significantly with the advance of deep learning. Thus, we are interested in the synergy between them by using a holistic deep model. We observe that not only denoising helps combat the drop of segmentation accuracy due to noise, but also pixel-wise semantic information boosts the capability of denoising. We then propose a boosting network to perform denoising and segmentation alternately. The proposed network is composed of multiple segmentation and denoising blocks (SDBs), each of which estimates semantic map then uses the map to regularize denoising. Experimental results show that the denoised image quality is improved substantially and the segmentation accuracy is improved to close to that of clean images. Our code and models will be made publicly available.

Marcel Keller, Ke Sun

Softmax is widely used in deep learning to map some representation to a probability distribution. As it is based on exp/log functions that are relatively expensive in multi-party computation, Mohassel and Zhang (2017) proposed a simpler replacement based on ReLU to be used in secure computation. However, we could not reproduce the accuracy they reported for training on MNIST with three fully connected layers. Later works (e.g., Wagh et al., 2019 and 2021) used the softmax replacement not for computing the output probability distribution but for approximating the gradient in back-propagation. In this work, we analyze the two uses of the replacement and compare them to softmax, both in terms of accuracy and cost in multi-party computation. We found that the replacement only provides a significant speed-up for a one-layer network while it always reduces accuracy, sometimes significantly. Thus we conclude that its usefulness is limited and one should use the original softmax function instead.

Ke Sun, Frank Nielsen

This letter introduces an abstract learning problem called the "set embedding": The objective is to map sets into probability distributions so as to lose less information. We relate set union and intersection operations with corresponding interpolations of probability distributions. We also demonstrate a preliminary solution with experimental results on toy set embedding examples.

Ke Sun, Bing Yu, Zhouchen Lin et al.

Regularization plays a crucial role in machine learning models, especially for deep neural networks. The existing regularization techniques mainly rely on the i.i.d. assumption and only consider the knowledge from the current sample, without the leverage of the neighboring relationship between samples. In this work, we propose a general regularizer called \textbf{Patch-level Neighborhood Interpolation~(Pani)} that conducts a non-local representation in the computation of networks. Our proposal explicitly constructs patch-level graphs in different layers and then linearly interpolates neighborhood patch features, serving as a general and effective regularization strategy. Further, we customize our approach into two kinds of popular regularization methods, namely Virtual Adversarial Training (VAT) and MixUp as well as its variants. The first derived \textbf{Pani VAT} presents a novel way to construct non-local adversarial smoothness by employing patch-level interpolated perturbations. The second derived \textbf{Pani MixUp} method extends the MixUp, and achieves superiority over MixUp and competitive performance over state-of-the-art variants of MixUp method with a significant advantage in computational efficiency. Extensive experiments have verified the effectiveness of our Pani approach in both supervised and semi-supervised settings.

Marcel Keller, Ke Sun

iDASH is a competition soliciting implementations of cryptographic schemes of interest in the context of biology. In 2019, one track asked for multi-party computation implementations of training of a machine learning model suitable for two datasets from cancer research. In this note, we describe our solution submitted to the competition. We found that the training can be run on three AWS c5.9xlarge instances in less then one minute using MPC tolerating one semi-honest corruption, and less than ten seconds at a slightly lower accuracy.

Ke Sun, Frank Nielsen

Why do deep neural networks (DNNs) benefit from very high dimensional parameter spaces? Their huge parameter complexities vs stunning performance in practice is all the more intriguing and not explainable using the standard theory of model selection for regular models. In this work, we propose a geometrically flavored information-theoretic approach to study this phenomenon. With the belief that simplicity is linked to better generalization, as grounded in the theory of minimum description length, the objective of our analysis is to examine and bound the complexity of DNNs. We introduce the locally varying dimensionality of the parameter space of neural network models by considering the number of significant dimensions of the Fisher information matrix, and model the parameter space as a manifold using the framework of singular semi-Riemannian geometry. We derive model complexity measures which yield short description lengths for deep neural network models based on their singularity analysis thus explaining the good performance of DNNs despite their large number of parameters.

Ke Sun, Piotr Koniusz, Zhen Wang

In a graph convolutional network, we assume that the graph $G$ is generated wrt some observation noise. During learning, we make small random perturbations $ΔG$ of the graph and try to improve generalization. Based on quantum information geometry, $ΔG$ can be characterized by the eigendecomposition of the graph Laplacian matrix. We try to minimize the loss wrt the perturbed $G+Δ{G}$ while making $Δ{G}$ to be effective in terms of the Fisher information of the neural network. Our proposed model can consistently improve graph convolutional networks on semi-supervised node classification tasks with reasonable computational overhead. We present three different geometries on the manifold of graphs: the intrinsic geometry measures the information theoretic dynamics of a graph; the extrinsic geometry characterizes how such dynamics can affect externally a graph neural network; the embedding geometry is for measuring node embeddings. These new analytical tools are useful in developing a good understanding of graph neural networks and fostering new techniques.

Ke Sun, Zhanxing Zhu, Zhouchen Lin

Deep neural networks have been widely deployed in various machine learning tasks. However, recent works have demonstrated that they are vulnerable to adversarial examples: carefully crafted small perturbations to cause misclassification by the network. In this work, we propose a novel defense mechanism called Boundary Conditional GAN to enhance the robustness of deep neural networks against adversarial examples. Boundary Conditional GAN, a modified version of Conditional GAN, can generate boundary samples with true labels near the decision boundary of a pre-trained classifier. These boundary samples are fed to the pre-trained classifier as data augmentation to make the decision boundary more robust. We empirically show that the model improved by our approach consistently defenses against various types of adversarial attacks successfully. Further quantitative investigations about the improvement of robustness and visualization of decision boundaries are also provided to justify the effectiveness of our strategy. This new defense mechanism that uses boundary samples to enhance the robustness of networks opens up a new way to defense adversarial attacks consistently.

Ke Sun, Zhanxing Zhu, Zhouchen Lin

Most previous works usually explained adversarial examples from several specific perspectives, lacking relatively integral comprehension about this problem. In this paper, we present a systematic study on adversarial examples from three aspects: the amount of training data, task-dependent and model-specific factors. Particularly, we show that adversarial generalization (i.e. test accuracy on adversarial examples) for standard training requires more data than standard generalization (i.e. test accuracy on clean examples); and uncover the global relationship between generalization and robustness with respect to the data size especially when data is augmented by generative models. This reveals the trade-off correlation between standard generalization and robustness in limited training data regime and their consistency when data size is large enough. Furthermore, we explore how different task-dependent and model-specific factors influence the vulnerability of deep neural networks by extensive empirical analysis. Relevant recommendations on defense against adversarial attacks are provided as well. Our results outline a potential path towards the luminous and systematic understanding of adversarial examples.

Frank Nielsen, Ke Sun

We define a novel class of distances between statistical multivariate distributions by modeling an optimal transport problem on their marginals with respect to a ground distance defined on their conditionals. These new distances are metrics whenever the ground distance between the marginals is a metric, generalize both the Wasserstein distances between discrete measures and a recently introduced metric distance between statistical mixtures, and provide an upper bound for jointly convex distances between statistical mixtures. By entropic regularization of the optimal transport, we obtain a fast differentiable Sinkhorn-type distance. We experimentally evaluate our new family of distances by quantifying the upper bounds of several jointly convex distances between statistical mixtures, and by proposing a novel efficient method to learn Gaussian mixture models (GMMs) by simplifying kernel density estimators with respect to our distance. Our GMM learning technique experimentally improves significantly over the EM implementation of {\tt sklearn} on the {\tt MNIST} and {\tt Fashion MNIST} datasets.

Ke Sun

A basic problem in machine learning is to find a mapping $f$ from a low dimensional latent space $\mathcal{Y}$ to a high dimensional observation space $\mathcal{X}$. Modern tools such as deep neural networks are capable to represent general non-linear mappings. A learner can easily find a mapping which perfectly fits all the observations. However, such a mapping is often not considered as good, because it is not simple enough and can overfit. How to define simplicity? We try to make a formal definition on the amount of information imposed by a non-linear mapping $f$. Intuitively, we measure the local discrepancy between the pullback geometry and the intrinsic geometry of the latent space. Our definition is based on information geometry and is independent of the empirical observations, nor specific parameterizations. We prove its basic properties and discuss relationships with related machine learning methods.

Frank Nielsen, Ke Sun

The total variation distance is a core statistical distance between probability measures that satisfies the metric axioms, with value always falling in $[0,1]$. This distance plays a fundamental role in machine learning and signal processing: It is a member of the broader class of $f$-divergences, and it is related to the probability of error in Bayesian hypothesis testing. Since the total variation distance does not admit closed-form expressions for statistical mixtures (like Gaussian mixture models), one often has to rely in practice on costly numerical integrations or on fast Monte Carlo approximations that however do not guarantee deterministic lower and upper bounds. In this work, we consider two methods for bounding the total variation of univariate mixture models: The first method is based on the information monotonicity property of the total variation to design guaranteed nested deterministic lower bounds. The second method relies on computing the geometric lower and upper envelopes of weighted mixture components to derive deterministic bounds based on density ratio. We demonstrate the tightness of our bounds in a series of experiments on Gaussian, Gamma and Rayleigh mixture models.

Frank Nielsen, Ke Sun

We propose a new generic type of stochastic neurons, called $q$-neurons, that considers activation functions based on Jackson's $q$-derivatives with stochastic parameters $q$. Our generalization of neural network architectures with $q$-neurons is shown to be both scalable and very easy to implement. We demonstrate experimentally consistently improved performances over state-of-the-art standard activation functions, both on training and testing loss functions.

Ke Sun, Xiangliang Zhang

Variational autoencoders (VAE) often use Gaussian or category distribution to model the inference process. This puts a limit on variational learning because this simplified assumption does not match the true posterior distribution, which is usually much more sophisticated. To break this limitation and apply arbitrary parametric distribution during inference, this paper derives a \emph{semi-continuous} latent representation, which approximates a continuous density up to a prescribed precision, and is much easier to analyze than its continuous counterpart because it is fundamentally discrete. We showcase the proposition by applying polynomial exponential family distributions as the posterior, which are universal probability density function generators. Our experimental results show consistent improvements over commonly used VAE models.

Jun Wang, Ke Sun, Fei Sha et al.

In this paper, we present a novel two-stage metric learning algorithm. We first map each learning instance to a probability distribution by computing its similarities to a set of fixed anchor points. Then, we define the distance in the input data space as the Fisher information distance on the associated statistical manifold. This induces in the input data space a new family of distance metric with unique properties. Unlike kernelized metric learning, we do not require the similarity measure to be positive semi-definite. Moreover, it can also be interpreted as a local metric learning algorithm with well defined distance approximation. We evaluate its performance on a number of datasets. It outperforms significantly other metric learning methods and SVM.