In multi-label learning, each instance can be associated with multiple and non-exclusive labels. Previous studies assume that all the labels in the learning process are fixed and static; however, they ignore the fact that the labels will emerge continuously in changing environments. In order to fill in these research gaps, we propose a novel deep neural network (DNN) based framework, Deep Streaming Label Learning (DSLL), to classify instances with newly emerged labels effectively. DSLL can explore and incorporate the knowledge from past labels and historical models to understand and develop emerging new labels. DSLL consists of three components: 1) a streaming label mapping to extract deep relationships between new labels and past labels with a novel label-correlation aware loss; 2) a streaming feature distillation propagating feature-level knowledge from the historical model to a new model; 3) a senior student network to model new labels with the help of knowledge learned from the past. Theoretically, we prove that DSLL admits tight generalization error bounds for new labels in the DNN framework. Experimentally, extensive empirical results show that the proposed method performs significantly better than the existing state-of-the-art multi-label learning methods to handle the continually emerging new labels.

Randomized smoothing, using just a simple isotropic Gaussian distribution, has been shown to produce good robustness guarantees against $\ell_2$-norm bounded adversaries. In this work, we show that extending the smoothing technique to defend against other attack models can be challenging, especially in the high-dimensional regime. In particular, for a vast class of i.i.d.~smoothing distributions, we prove that the largest $\ell_p$-radius that can be certified decreases as $O(1/d^{\frac{1}{2} - \frac{1}{p}})$ with dimension $d$ for $p > 2$. Notably, for $p \geq 2$, this dependence on $d$ is no better than that of the $\ell_p$-radius that can be certified using isotropic Gaussian smoothing, essentially putting a matching lower bound on the robustness radius. When restricted to {\it generalized} Gaussian smoothing, these two bounds can be shown to be within a constant factor of each other in an asymptotic sense, establishing that Gaussian smoothing provides the best possible results, up to a constant factor, when $p \geq 2$. We present experimental results on CIFAR to validate our theory. For other smoothing distributions, such as, a uniform distribution within an $\ell_1$ or an $\ell_\infty$-norm ball, we show upper bounds of the form $O(1 / d)$ and $O(1 / d^{1 - \frac{1}{p}})$ respectively, which have an even worse dependence on $d$.

Joint filtering is a fundamental problem in computer vision with applications in many different areas. Most existing algorithms solve this problem with a weighted averaging process to aggregate input pixels. However, the weight matrix of this process is often empirically designed and not robust to complex input. In this work, we propose to learn the weight matrix for joint image filtering. This is a challenging problem, as directly learning a large weight matrix is computationally intractable. To address this issue, we introduce the correlation of deep features to approximate the aggregation weights. However, this strategy only uses inner product for the weight matrix estimation, which limits the performance of the proposed algorithm. Therefore, we further propose to learn a nonlinear function to predict sparse residuals of the feature correlation matrix. Note that the proposed method essentially factorizes the weight matrix into a low-rank and a sparse matrix and then learn both of them simultaneously with deep neural networks. Extensive experiments show that the proposed algorithm compares favorably against the state-of-the-art approaches on a wide variety of joint filtering tasks.

Deep neural networks are known to be fragile to small adversarial perturbations, which raises serious concerns when a neural network policy is interconnected with a physical system in a closed loop. In this paper, we show how to combine recent works on static neural network certification tools with robust control theory to certify a neural network policy in a control loop. We give a sufficient condition and an algorithm to ensure that the closed loop state and control constraints are satisfied when the persistent adversarial perturbation is l-infinity norm bounded. Our method is based on finding a positively invariant set of the closed loop dynamical system, and thus we do not require the continuity of the neural network policy. Along with the verification result, we also develop an effective attack strategy for neural network control systems that outperforms exhaustive Monte-Carlo search significantly. We show that our certification algorithm works well on learned models and could achieve 5 times better result than the traditional Lipschitz-based method to certify the robustness of a neural network policy on the cart-pole balance control problem.

We investigate the combination of actor-critic reinforcement learning algorithms with a uniform large-scale experience replay and propose solutions for two ensuing challenges: (a) efficient actor-critic learning with experience replay (b) the stability of off-policy learning where agents learn from other agents behaviour. To this end we analyze the bias-variance tradeoffs in V-trace, a form of importance sampling for actor-critic methods. Based on our analysis, we then argue for mixing experience sampled from replay with on-policy experience, and propose a new trust region scheme that scales effectively to data distributions where V-trace becomes unstable. We provide extensive empirical validation of the proposed solutions on DMLab-30 and further show the benefits of this setup in two training regimes for Atari: (1) a single agent is trained up until 200M environment frames per game (2) a population of agents is trained up until 200M environment frames each and may share experience. We demonstrate state-of-the-art data efficiency among model-free agents in both regimes.

\emph{Is there a classifier that ensures optimal robustness against all adversarial attacks?} This paper tackles the question by adopting a game-theoretic point of view. We present the adversarial attacks and defenses problem as an \emph{infinite} zero-sum game where classical results (\emph{e.g.} Nash or Sion theorems) do not apply. We demonstrate the non-existence of a Nash equilibrium in our game when the classifier and the Adversary are both deterministic, hence giving a negative answer to the above question in the deterministic regime. Nonetheless, the question remains open in the randomized regime. We tackle this problem by showing that, under mild conditions on the dataset distribution, any deterministic classifier can be outperformed by a randomized one. This gives arguments for using randomization, and leads us to a simple method for building randomized classifiers that are robust to state-or-the-art adversarial attacks. Empirical results validate our theoretical analysis, and show that our defense method considerably outperforms Adversarial Training against strong adaptive attacks, by achieving 0.55 accuracy under adaptive PGD-attack on CIFAR10, compared to 0.42 for Adversarial training.

To deal with complicated constraints via locally light computation in distributed online learning, a recent study has presented a projection-free algorithm called distributed online conditional gradient (D-OCG), and achieved an $O(T^{3/4})$ regret bound, where $T$ is the number of prediction rounds. However, in each round, the local learners of D-OCG need to communicate with their neighbors to share the local gradients, which results in a high communication complexity of $O(T)$. In this paper, we first propose an improved variant of D-OCG, namely D-BOCG, which enjoys an $O(T^{3/4})$ regret bound with only $O(\sqrt{T})$ communication complexity. The key idea is to divide the total prediction rounds into $\sqrt{T}$ equally-sized blocks, and only update the local learners at the beginning of each block by performing iterative linear optimization steps. Furthermore, to handle the more challenging bandit setting, in which only the loss value is available, we incorporate the classical one-point gradient estimator into D-BOCG, and obtain similar theoretical guarantees.

In this paper, we study the problem of learning compact (low-dimensional) representations for sequential data that captures its implicit spatio-temporal cues. To maximize extraction of such informative cues from the data, we set the problem within the context of contrastive representation learning and to that end propose a novel objective via optimal transport. Specifically, our formulation seeks a low-dimensional subspace representation of the data that jointly (i) maximizes the distance of the data (embedded in this subspace) from an adversarial data distribution under the optimal transport, a.k.a. the Wasserstein distance, (ii) captures the temporal order, and (iii) minimizes the data distortion. To generate the adversarial distribution, we propose a novel framework connecting Wasserstein GANs with a classifier, allowing a principled mechanism for producing good negative distributions for contrastive learning, which is currently a challenging problem. Our full objective is cast as a subspace learning problem on the Grassmann manifold and solved via Riemannian optimization. To empirically study our formulation, we provide experiments on the task of human action recognition in video sequences. Our results demonstrate competitive performance against challenging baselines.

A fundamental problem in computational chemistry is to find a set of reactants to synthesize a target molecule, a.k.a. retrosynthesis prediction. Existing state-of-the-art methods rely on matching the target molecule with a large set of reaction templates, which are very computationally expensive and also suffer from the problem of coverage. In this paper, we propose a novel template-free approach called G2Gs by transforming a target molecular graph into a set of reactant molecular graphs. G2Gs first splits the target molecular graph into a set of synthons by identifying the reaction centers, and then translates the synthons to the final reactant graphs via a variational graph translation framework. Experimental results show that G2Gs significantly outperforms existing template-free approaches by up to 63% in terms of the top-1 accuracy and achieves a performance close to that of state-of-the-art template-based approaches, but does not require domain knowledge and is much more scalable.

Recent encoder-decoder approaches typically employ string decoders to convert images into serialized strings for image-to-markup. However, for tree-structured representational markup, string representations can hardly cope with the structural complexity. In this work, we first show via a set of toy problems that string decoders struggle to decode tree structures, especially as structural complexity increases, we then propose a tree-structured decoder that specifically aims at generating a tree-structured markup. Our decoders works sequentially, where at each step a child node and its parent node are simultaneously generated to form a sub-tree. This sub-tree is consequently used to construct the final tree structure in a recurrent manner. Key to the success of our tree decoder is twofold, (i) it strictly respects the parent-child relationship of trees, and (ii) it explicitly outputs trees as oppose to a linear string. Evaluated on both math formula recognition and chemical formula recognition, the proposed tree decoder is shown to greatly outperform strong string decoder baselines.

In many real tasks, we care about how to make decisions rather than mere predictions on an event, e.g. how to increase the revenue next month instead of merely knowing it will drop. The key is to identify the causal effects on the desired event. It is achievable with do-calculus if the causal structure is known; however, in many real tasks it is not easy to infer the whole causal structure with the observational data. Introducing external interventions is needed to achieve it. In this paper, we study the situation where only the response variable is observable under intervention. We propose a novel approach which is able to cost-effectively identify the causal effects, by an active strategy introducing limited interventions, and thus guide decision-making. Theoretical analysis and empirical studies validate the effectiveness of the proposed approach.

The Markov assumption (MA) is fundamental to the empirical validity of reinforcement learning. In this paper, we propose a novel Forward-Backward Learning procedure to test MA in sequential decision making. The proposed test does not assume any parametric form on the joint distribution of the observed data and plays an important role for identifying the optimal policy in high-order Markov decision processes (MDPs) and partially observable MDPs. Theoretically, we establish the validity of our test. Empirically, we apply our test to both synthetic datasets and a real data example from mobile health studies to illustrate its usefulness.

Overparameterized deep networks have the capacity to memorize training data with zero \emph{training error}. Even after memorization, the \emph{training loss} continues to approach zero, making the model overconfident and the test performance degraded. Since existing regularizers do not directly aim to avoid zero training loss, it is hard to tune their hyperparameters in order to maintain a fixed/preset level of training loss. We propose a direct solution called \emph{flooding} that intentionally prevents further reduction of the training loss when it reaches a reasonably small value, which we call the \emph{flood level}. Our approach makes the loss float around the flood level by doing mini-batched gradient descent as usual but gradient ascent if the training loss is below the flood level. This can be implemented with one line of code and is compatible with any stochastic optimizer and other regularizers. With flooding, the model will continue to ``random walk'' with the same non-zero training loss, and we expect it to drift into an area with a flat loss landscape that leads to better generalization. We experimentally show that flooding improves performance and, as a byproduct, induces a double descent curve of the test loss.

Modern deep neural networks require a significant amount of computing time and power to train and deploy, which limits their usage on edge devices. Inspired by the iterative weight pruning in the Lottery Ticket Hypothesis, we propose DropNet, an iterative pruning method which prunes nodes/filters to reduce network complexity. DropNet iteratively removes nodes/filters with the lowest average post-activation value across all training samples. Empirically, we show that DropNet is robust across a wide range of scenarios, including MLPs and CNNs using the MNIST and CIFAR datasets. We show that up to 90% of the nodes/filters can be removed without any significant loss of accuracy. The final pruned network performs well even with reinitialisation of the weights and biases. DropNet also achieves similar accuracy to an oracle which greedily removes nodes/filters one at a time to minimise training loss, highlighting its effectiveness.

We study the problem of constructing black-box adversarial attacks, where no model information is revealed except for the feedback knowledge of the given inputs. To obtain sufficient knowledge for crafting adversarial examples, previous methods query the target model with inputs that are perturbed with different searching directions. However, these methods suffer from poor query efficiency since the employed searching directions are sampled randomly. To mitigate this issue, we formulate the goal of mounting efficient attacks as an optimization problem in which the adversary tries to fool the target model with a limited number of queries. Under such settings, the adversary has to select appropriate searching directions to reduce the number of model queries. By solving the efficient-attack problem, we find that we need to distill the knowledge in both the path of the adversarial examples and the path of the searching directions. Therefore, we propose a novel framework, dual-path distillation, that utilizes the feedback knowledge not only to craft adversarial examples but also to alter the searching directions to achieve efficient attacks. Experimental results suggest that our framework can significantly increase the query efficiency.

We propose a new algorithmic framework for learning autoencoders of data distributions. In this framework, we minimize the discrepancy between the model distribution and the target one, with relational regularization on learnable latent prior. This regularization penalizes the fused Gromov-Wasserstein (FGW) distance between the latent prior and its corresponding posterior, which allows us to learn a structured prior distribution associated with the generative model in a flexible way. Moreover, it helps us co-train multiple autoencoders even if they are with heterogeneous architectures and incomparable latent spaces. We implement the framework with two scalable algorithms, making it applicable for both probabilistic and deterministic autoencoders. Our relational regularized autoencoder (RAE) outperforms existing methods, e.g., variational autoencoder, Wasserstein autoencoder, and their variants, on generating images. Additionally, our relational co-training strategy of autoencoders achieves encouraging results in both synthesis and real-world multi-view learning tasks.

We provide theoretical investigations into off-policy evaluation in reinforcement learning using function approximators for (marginalized) importance weights and value functions. Our contributions include: (1) A new estimator, MWL, that directly estimates importance ratios over the state-action distributions, removing the reliance on knowledge of the behavior policy as in prior work (Liu et.al, 2018), (2) Another new estimator, MQL, obtained by swapping the roles of importance weights and value-functions in MWL. MQL has an intuitive interpretation of minimizing average Bellman errors and can be combined with MWL in a doubly robust manner, (3) Several additional results that offer further insights, including the sample complexities of MWL and MQL, their asymptotic optimality in the tabular setting, how the learned importance weights depend the choice of the discriminator class, and how our methods provide a unified view of some old and new algorithms in RL.

Researches using margin based comparison loss demonstrate the effectiveness of penalizing the distance between face feature and their corresponding class centers. Despite their popularity and excellent performance, they do not explicitly encourage the generic embedding learning for an open set recognition problem. In this paper, we analyse margin based softmax loss in probability view. With this perspective, we propose two general principles: 1) monotonically decreasing and 2) margin probability penalty, for designing new margin loss functions. Unlike methods optimized with single comparison metric, we provide a new perspective to treat open set face recognition as a problem of information transmission. And the generalization capability for face embedding is gained with more clean information. An auto-encoder architecture called Linear-Auto-TS-Encoder(LATSE) is proposed to corroborate this finding. Extensive experiments on several benchmarks demonstrate that LATSE help face embedding to gain more generalization capability and it boost the single model performance with open training dataset to more than 99% on MegaFace test.

We study multinomial logit bandit with limited adaptivity, where the algorithms change their exploration actions as infrequently as possible when achieving almost optimal minimax regret. We propose two measures of adaptivity: the assortment switching cost and the more fine-grained item switching cost. We present an anytime algorithm (AT-DUCB) with $O(N \log T)$ assortment switches, almost matching the lower bound $\Omega(\frac{N \log T}{ \log \log T})$. In the fixed-horizon setting, our algorithm FH-DUCB incurs $O(N \log \log T)$ assortment switches, matching the asymptotic lower bound. We also present the ESUCB algorithm with item switching cost $O(N \log^2 T)$.

This paper studies an entropy-based multi-objective Bayesian optimization (MBO). Existing entropy-based MBO methods need complicated approximations to evaluate entropy or employ over-simplification that ignores trade-off among objectives. We propose a novel entropy-based MBO called Pareto-frontier entropy search (PFES), which is based on the information gain of Pareto-frontier. We show that our entropy evaluation can be reduced to a closed form whose computation is quite simple while capturing the trade-off relation in Pareto-frontier. We further propose an extension for the ``decoupled'' setting, in which each objective function can be observed separately, and show that the PFES-based approach derives a natural extension of the original acquisition function which can also be evaluated simply. Our numerical experiments show effectiveness of PFES through several benchmark datasets, and real-word datasets from materials science.

State-of-the-art neural machine translation models generate a translation from left to right and every step is conditioned on the previously generated tokens. The sequential nature of this generation process causes fundamental latency in inference since we cannot generate multiple tokens in each sentence in parallel. We propose an attention-masking based model, called Disentangled Context (DisCo) transformer, that simultaneously generates all tokens given different contexts. The DisCo transformer is trained to predict every output token given an arbitrary subset of the other reference tokens. We also develop the parallel easy-first inference algorithm, which iteratively refines every token in parallel and reduces the number of required iterations. Our extensive experiments on 7 translation directions with varying data sizes demonstrate that our model achieves competitive, if not better, performance compared to the state of the art in non-autoregressive machine translation while significantly reducing decoding time on average.

We consider the product of determinantal point processes (DPPs), a point process whose probability mass is proportional to the product of principal minors of multiple matrices as a natural, promising generalization of DPPs. We study the computational complexity of computing its normalizing constant, which is among the most essential probabilistic inference tasks. Our complexity-theoretic results (almost) rule out the existence of efficient algorithms for this task, unless input matrices are forced to have favorable structures. In particular, we prove the following: (1) Computing $\sum_{S} \det(\mat{A}_{S,S})^p$ exactly for every (fixed) positive even integer $p$ is UP-hard and Mod3P-hard, which gives a negative answer to an open question posed by Kulesza and Taskar (2012). (2) $\sum_{S} \det(\mat{A}_{S,S}) \det(\mat{B}_{S,S}) \det(\mat{C}_{S,S})$ is NP-hard to approximate within a factor of $ 2^{O(|I|^{1-\epsilon})} $ for any $\epsilon > 0$, where $|I|$ is the input size. This result is stronger than #P-hardness for the case of two matrices by Gillenwater (2014). (3) There exists a $ k^{O(k)} |I|^{O(1)} $-time algorithm for computing $\sum_{S} \det(\mat{A}_{S,S}) \det(\mat{B}_{S,S})$, where $k$ is ``the maximum rank of $\mat{A}$ and $\mat{B}$'' or ``the treewidth of the graph formed by nonzero entries of $\mat{A}$ and $\mat{B}$.'' Such parameterized algorithms are said to be fixed-parameter tractable.

The goal of compressed sensing is to learn a structured signal $x$ from a limited number of noisy linear measurements $y \approx Ax$. In traditional compressed sensing, ``structure'' is represented by sparsity in some known basis. Inspired by the success of deep learning in modeling images, recent work starting with Bora-Jalal-Price-Dimakis'17 has instead considered structure to come from a generative model $G: \mathbb{R}^k \to \mathbb{R}^n$. We present two results establishing the difficulty and strength of this latter task, showing that existing bounds are tight: First, we provide a lower bound matching the Bora et.al upper bound for compressed sensing with $L$-Lipschitz generative models $G$ which holds even for the more relaxed goal of \emph{non-uniform} recovery. Second, we show that generative models generalize sparsity as a representation of structure by constructing a ReLU-based neural network with $2$ hidden layers and $O(n)$ activations per layer whose range is precisely the set of all $k$-sparse vectors.

While deep neural networks achieve great performance on fitting the training distribution, the learned networks are prone to overfitting and are susceptible to adversarial attacks. In this regard, a number of mixup based augmentation methods have been recently proposed. However, these approaches mainly focus on creating previously unseen virtual examples and can sometimes provide misleading supervisory signal to the network. To this end, we propose Puzzle Mix, a mixup method for explicitly utilizing the saliency information and the underlying statistics of the natural examples. This leads to an interesting optimization problem alternating between the multi-label objective for optimal mixing mask and saliency discounted optimal transport objective. Our experiments show Puzzle Mix achieves the state of the art generalization and the adversarial robustness results compared to other mixup methods on CIFAR-100, Tiny-ImageNet, and ImageNet datasets, and the source code is available at https://github.com/snu-mllab/PuzzleMix.

The goal of standard 1-bit compressive sensing is to accurately recover an unknown sparse vector from binary-valued measurements, each indicating the sign of a linear function of the vector. Motivated by recent advances in compressive sensing with generative models, where a generative modeling assumption replaces the usual sparsity assumption, we study the problem of 1-bit compressive sensing with generative models. We first consider noiseless 1-bit measurements, and provide sample complexity bounds for approximate recovery under i.i.d.~Gaussian measurements and a Lipschitz continuous generative prior, as well as a near-matching algorithm-independent lower bound. Moreover, we demonstrate that the Binary $\epsilon$-Stable Embedding property, which characterizes the robustness of the reconstruction to measurement errors and noise, also holds for 1-bit compressive sensing with Lipschitz continuous generative models with sufficiently many Gaussian measurements. In addition, we apply our results to neural network generative models, and provide a proof-of-concept numerical experiment demonstrating significant improvements over sparsity-based approaches.

Heretofore, neural networks with external memory are restricted to single memory with lossy representations of memory interactions. A rich representation of relationships between memory pieces urges a high-order and segregated relational memory. In this paper, we propose to separate the storage of individual experiences (item memory) and their occurring relationships (relational memory). The idea is implemented through a novel Self-attentive Associative Memory (SAM) operator. Found upon outer product, SAM forms a set of associative memories that represent the hypothetical high-order relationships between arbitrary pairs of memory elements, through which a relational memory is constructed from an item memory. The two memories are wired into a single sequential model capable of both memorization and relational reasoning. We achieve competitive results with our proposed two-memory model in a diversity of machine learning tasks, from challenging synthetic problems to practical testbeds such as geometry, graph, reinforcement learning, and question answering.

In this paper, we provide an explicit theoretical connection between Sparse subspace clustering (SSC) and spectral clustering (SC) from the perspective of learning a data similarity matrix. We show that spectral clustering with Gaussian kernel can be viewed as sparse subspace clustering with entropy-norm (SSC+E). Compared to SSC, SSC+E can obtain an analytical, symmetrical, nonnegative and nonlinearly-representational similarity matrix. Besides, SSC+E makes use of Gaussian kernel to compute the sparse similarity matrix of objects, which can avoid the complex computation of the sparse optimization program of SSC. Finally, we provide the experimental analysis to compare the efficiency and effectiveness of sparse subspace clustering and spectral clustering on ten benchmark data sets. The theoretical and experimental analysis can well help users for the selection of high-dimensional data clustering algorithms.

Modern data acquisition routinely produce massive amounts of event sequence data in various domains, such as social media, healthcare, and financial markets. These data often exhibit complicated short-term and long-term temporal dependencies. However, most of the existing recurrent neural network based point process models fail to capture such dependencies, and yield unreliable prediction performance. To address this issue, we propose a Transformer Hawkes Process (THP) model, which leverages the self-attention mechanism to capture long-term dependencies and meanwhile enjoys computational efficiency. Numerical experiments on various datasets show that THP outperforms existing models in terms of both likelihood and event prediction accuracy by a notable margin. Moreover, THP is quite general and can incorporate additional structural knowledge. We provide a concrete example, where THP achieves improved prediction performance for learning multiple point processes when incorporating their relational information.

We study few-shot supervised domain adaptation (DA) for regression problems, where only a few labeled target domain data and many labeled source domain data are available. Many of the current DA methods base their transfer assumptions on either parametrized distribution shift or apparent distribution similarities, e.g., identical conditionals or small distributional discrepancies. However, these assumptions may preclude the possibility of adaptation from intricately shifted and apparently very different distributions. To overcome this problem, we propose mechanism transfer, a meta-distributional scenario in which a data generating mechanism is invariant among domains. This transfer assumption can accommodate nonparametric shifts resulting in apparently different distributions while providing a solid statistical basis for DA. We take the structural equations in causal modeling as an example and propose a novel DA method, which is shown to be useful both theoretically and experimentally. Our method can be seen as the first attempt to fully leverage the invariance of structural causal models for DA.

We consider the problem of the limited-bandwidth communication for multi-agent reinforcement learning, where agents cooperate with the assistance of a communication protocol and a scheduler. The protocol and scheduler jointly determine which agent is communicating what message and to whom. Under the limited bandwidth constraint, a communication protocol is required to generate informative messages. Meanwhile, an unnecessary communication connection should not be established because it occupies limited resources in vain. In this paper, we develop an Informative Multi-Agent Communication (IMAC) method to learn efficient communication protocols as well as scheduling. First, from the perspective of communication theory, we prove that the limited bandwidth constraint requires low-entropy messages throughout the transmission. Then inspired by the information bottleneck principle, we learn a valuable and compact communication protocol and a weight-based scheduler. To demonstrate the efficiency of our method, we conduct extensive experiments in various cooperative and competitive multi-agent tasks with different numbers of agents and different bandwidths. We show that IMAC converges faster and leads to efficient communication among agents under the limited bandwidth as compared to many baseline methods.

The Transformer is widely used in natural language processing tasks. To train a Transformer however, one usually needs a carefully designed learning rate warm-up stage, which is shown to be crucial to the final performance but will slow down the optimization and bring more hyper-parameter tunings. In this paper, we first study theoretically why the learning rate warm-up stage is essential and show that the location of layer normalization matters. Specifically, we prove with mean field theory that at initialization, for the original-designed Post-LN Transformer, which places the layer normalization between the residual blocks, the expected gradients of the parameters near the output layer are large. Therefore, using a large learning rate on those gradients makes the training unstable. The warm-up stage is practically helpful for avoiding this problem. On the other hand, our theory also shows that if the layer normalization is put inside the residual blocks (recently proposed as Pre-LN Transformer), the gradients are well-behaved at initialization. This motivates us to remove the warm-up stage for the training of Pre-LN Transformers. We show in our experiments that Pre-LN Transformers without the warm-up stage can reach comparable results with baselines while requiring significantly less training time and hyper-parameter tuning on a wide range of applications.

Many real-world applications have to tackle the Positive-Unlabeled (PU) learning problem, i.e., learning binary classifiers from a large amount of unlabeled data and a few labeled positive examples. While current state-of-the-art methods employ importance reweighting to design various biased or unbiased risk estimators, they completely ignored the learning capability of the model itself, which could provide reliable supervision. This motivates us to propose a novel Self-PU learning framework, which seamlessly integrates PU learning and self-training. Self-PU highlights three ``self''-oriented building blocks: a self-paced training algorithm that adaptively discovers and augments confident positive/negative examples as the training proceeds; a self-reweighted, instance-aware loss; and a self-distillation scheme that introduces teacher-students learning as an effective regularization for PU learning. We demonstrate the state-of-the-art performance of Self-PU on common PU learning benchmarks (MNIST and CIFAR10), which compare favorably against the latest competitors. Moreover, we study a real-world application of PU learning, i.e., classifying brain images of Alzheimer's Disease. Self-PU obtains significantly improved results on the renowned Alzheimer's Disease Neuroimaging Initiative (ADNI) database over existing methods.