Decomposing User-APP Graph into Subgraphs for Effective APP and User Embedding Learning

APP-installation information is helpful to describe the user's characteristics. The users with similar APPs installed might share several common interests and behave similarly in some scenarios. In this work, we learn a user embedding vector based on each user's APP-installation information. Since the user APP-installation embedding is learnable without dependency on the historical intra-APP behavioral data of the user, it complements the intra-APP embedding learned within each specific APP. Thus, they considerably help improve the effectiveness of the personalized advertising in each APP, and they are particularly beneficial for the cold start of the new users in the APP. In this paper, we formulate the APP-installation user embedding learning into a bipartite graph embedding problem. The main challenge in learning an effective APP-installation user embedding is the imbalanced data distribution. In this case, graph learning tends to be dominated by the popular APPs, which billions of users have installed. In other words, some niche/specialized APPs might have a marginal influence on graph learning. To effectively exploit the valuable information from the niche APPs, we decompose the APP-installation graph into a set of subgraphs. Each subgraph contains only one APP node and the users who install the APP. For each mini-batch, we only sample the users from the same subgraph in the training process. Thus, each APP can be involved in the training process in a more balanced manner. After integrating the learned APP-installation user embedding into our online personal advertising platform, we obtained a considerable boost in CTR, CVR, and revenue.

DIGAT: Modeling News Recommendation with Dual-Graph Interaction

News recommendation (NR) is essential for online news services. Existing NR methods typically adopt a news-user representation learning framework, facing two potential limitations. First, in news encoder, single candidate news encoding suffers from an insufficient semantic information problem. Second, existing graph-based NR methods are promising but lack effective news-user feature interaction, rendering the graph-based recommendation suboptimal. To overcome these limitations, we propose dual-interactive graph attention networks (DIGAT) consisting of news- and user-graph channels. In the news-graph channel, we enrich the semantics of single candidate news by incorporating the semantically relevant news information with a semantic-augmented graph (SAG). In the user-graph channel, multi-level user interests are represented with a news-topic graph. Most notably, we design a dual-graph interaction process to perform effective feature interaction between the news and user graphs, which facilitates accurate news-user representation matching. Experiment results on the benchmark dataset MIND show that DIGAT outperforms existing news recommendation methods. Further ablation studies and analyses validate the effectiveness of (1) semantic-augmented news graph modeling and (2) dual-graph interaction.

Leap-frog neural network for learning the symplectic evolution from partitioned data

For the Hamiltonian system, this work considers the learning and prediction of the position (q) and momentum (p) variables generated by a symplectic evolution map. Similar to Chen & Tao (2021), the symplectic map is represented by the generating function. In addition, we develop a new learning scheme by splitting the time series (q_i, p_i) into several partitions, and then train a leap-frog neural network (LFNN) to approximate the generating function between the first (i.e. initial condition) and one of the rest partitions. For predicting the system evolution in a short timescale, the LFNN could effectively avoid the issue of accumulative error. Then the LFNN is applied to learn the behavior of the 2:3 resonant Kuiper belt objects, in a much longer time period, and there are two significant improvements on the neural network constructed in our previous work (Li et al. 2022): (1) conservation of the Jacobi integral ; (2) highly accurate prediction of the orbital evolution. We propose that the LFNN may be useful to make the prediction of the long time evolution of the Hamiltonian system.

Simple and Optimal Stochastic Gradient Methods for Nonsmooth Nonconvex Optimization

We propose and analyze several stochastic gradient algorithms for finding stationary points or local minimum in nonconvex, possibly with nonsmooth regularizer, finite-sum and online optimization problems. First, we propose a simple proximal stochastic gradient algorithm based on variance reduction called ProxSVRG+. We provide a clean and tight analysis of ProxSVRG+, which shows that it outperforms the deterministic proximal gradient descent (ProxGD) for a wide range of minibatch sizes, hence solves an open problem proposed in Reddi et al. (2016b). Also, ProxSVRG+ uses much less proximal oracle calls than ProxSVRG (Reddi et al., 2016b) and extends to the online setting by avoiding full gradient computations. Then, we further propose an optimal algorithm, called SSRGD, based on SARAH (Nguyen et al., 2017) and show that SSRGD further improves the gradient complexity of ProxSVRG+ and achieves the optimal upper bound, matching the known lower bound of (Fang et al., 2018; Li et al., 2021). Moreover, we show that both ProxSVRG+ and SSRGD enjoy automatic adaptation with local structure of the objective function such as the Polyak-\L{}ojasiewicz (PL) condition for nonconvex functions in the finite-sum case, i.e., we prove that both of them can automatically switch to faster global linear convergence without any restart performed in prior work ProxSVRG (Reddi et al., 2016b). Finally, we focus on the more challenging problem of finding an $(\epsilon, \delta)$-local minimum instead of just finding an $\epsilon$-approximate (first-order) stationary point (which may be some bad unstable saddle points). We show that SSRGD can find an $(\epsilon, \delta)$-local minimum by simply adding some random perturbations. Our algorithm is almost as simple as its counterpart for finding stationary points, and achieves similar optimal rates.

Waveform Design for Mutual Interference Mitigation in Automotive Radar

The mutual interference between similar radar systems can result in reduced radar sensitivity and increased false alarm rates. To address the synchronous and asynchronous interference mitigation problems in similar radar systems, we first propose herein two slow-time coding schemes to modulate the pulses within a coherent processing interval (CPI) for a single-input-single-output (SISO) scenario. Specifically, the first coding scheme relies on Doppler shifting and the second one is devised based on an optimization approach. We further extend our discussion to the more general case of multiple-input-multiple-output (MIMO) radars and propose an efficient algorithm to design waveforms to mitigate mutual interference in such systems. The proposed coding schemes are computationally efficient in practice and the incorporation of the coding schemes requires only a slight modification of the existing systems. Our numerical examples indicate that the proposed coding schemes can reduce the interference power level in a desired area of the cross-ambiguity function significantly.

Efficient Algorithms for Sparse Moment Problems without Separation

We consider the sparse moment problem of learning a $k$-spike mixture in high dimensional space from its noisy moment information in any dimension. We measure the accuracy of the learned mixtures using transportation distance. Previous algorithms either assume certain separation assumptions, use more recovery moments, or run in (super) exponential time. Our algorithm for the 1-dimension problem (also called the sparse Hausdorff moment problem) is a robust version of the classic Prony's method, and our contribution mainly lies in the analysis. We adopt a global and much tighter analysis than previous work (which analyzes the perturbation of the intermediate results of Prony's method). A useful technical ingredient is a connection between the linear system defined by the Vandermonde matrix and the Schur polynomial, which allows us to provide tight perturbation bound independent of the separation and may be useful in other contexts. To tackle the high dimensional problem, we first solve the 2-dimensional problem by extending the 1-dimension algorithm and analysis to complex numbers. Our algorithm for the high dimensional case determines the coordinates of each spike by aligning a 1-d projection of the mixture to a random vector and a set of 2d-projections of the mixture. Our results have applications to learning topic models and Gaussian mixtures, implying improved sample complexity results or running time over prior work.

Analyzing Sharpness along GD Trajectory: Progressive Sharpening and Edge of Stability

Recent findings (e.g., arXiv:2103.00065) demonstrate that modern neural networks trained by full-batch gradient descent typically enter a regime called Edge of Stability (EOS). In this regime, the sharpness, i.e., the maximum Hessian eigenvalue, first increases to the value 2/(step size) (the progressive sharpening phase) and then oscillates around this value (the EOS phase). This paper aims to analyze the GD dynamics and the sharpness along the optimization trajectory. Our analysis naturally divides the GD trajectory into four phases depending on the change of the sharpness. We empirically identify the norm of output layer weight as an interesting indicator of sharpness dynamics. Based on this empirical observation, we attempt to theoretically and empirically explain the dynamics of various key quantities that lead to the change of sharpness in each phase of EOS. Moreover, based on certain assumptions, we provide a theoretical proof of the sharpness behavior in EOS regime in two-layer fully-connected linear neural networks. We also discuss some other empirical findings and the limitation of our theoretical results.

Less Is More: Fast Multivariate Time Series Forecasting with Light Sampling-oriented MLP Structures

Multivariate time series forecasting has seen widely ranging applications in various domains, including finance, traffic, energy, and healthcare. To capture the sophisticated temporal patterns, plenty of research studies designed complex neural network architectures based on many variants of RNNs, GNNs, and Transformers. However, complex models are often computationally expensive and thus face a severe challenge in training and inference efficiency when applied to large-scale real-world datasets. In this paper, we introduce LightTS, a light deep learning architecture merely based on simple MLP-based structures. The key idea of LightTS is to apply an MLP-based structure on top of two delicate down-sampling strategies, including interval sampling and continuous sampling, inspired by a crucial fact that down-sampling time series often preserves the majority of its information. We conduct extensive experiments on eight widely used benchmark datasets. Compared with the existing state-of-the-art methods, LightTS demonstrates better performance on five of them and comparable performance on the rest. Moreover, LightTS is highly efficient. It uses less than 5% FLOPS compared with previous SOTA methods on the largest benchmark dataset. In addition, LightTS is robust and has a much smaller variance in forecasting accuracy than previous SOTA methods in long sequence forecasting tasks.

Learning to Break the Loop: Analyzing and Mitigating Repetitions for Neural Text Generation

While large-scale neural language models, such as GPT2 and BART, have achieved impressive results on various text generation tasks, they tend to get stuck in undesirable sentence-level loops with maximization-based decoding algorithms (\textit{e.g.}, greedy search). This phenomenon is counter-intuitive since there are few consecutive sentence-level repetitions in human corpora (e.g., 0.02\% in Wikitext-103). To investigate the underlying reasons for generating consecutive sentence-level repetitions, we study the relationship between the probabilities of the repetitive tokens and their previous repetitions in the context. Through our quantitative experiments, we find that 1) Language models have a preference to repeat the previous sentence; 2) The sentence-level repetitions have a \textit{self-reinforcement effect}: the more times a sentence is repeated in the context, the higher the probability of continuing to generate that sentence; 3) The sentences with higher initial probabilities usually have a stronger self-reinforcement effect. Motivated by our findings, we propose a simple and effective training method \textbf{DITTO} (Pseu\underline{D}o-Repet\underline{IT}ion Penaliza\underline{T}i\underline{O}n), where the model learns to penalize probabilities of sentence-level repetitions from pseudo repetitive data. Although our method is motivated by mitigating repetitions, experiments show that DITTO not only mitigates the repetition issue without sacrificing perplexity, but also achieves better generation quality. Extensive experiments on open-ended text generation (Wikitext-103) and text summarization (CNN/DailyMail) demonstrate the generality and effectiveness of our method.

Generalization Bounds for Gradient Methods via Discrete and Continuous Prior

Proving algorithm-dependent generalization error bounds for gradient-type optimization methods has attracted significant attention recently in learning theory. However, most existing trajectory-based analyses require either restrictive assumptions on the learning rate (e.g., fast decreasing learning rate), or continuous injected noise (such as the Gaussian noise in Langevin dynamics). In this paper, we introduce a new discrete data-dependent prior to the PAC-Bayesian framework, and prove a high probability generalization bound of order $O(\frac{1}{n}\cdot \sum_{t=1}^T(\gamma_t/\varepsilon_t)^2\left\|{\mathbf{g}_t}\right\|^2)$ for Floored GD (i.e. a version of gradient descent with precision level $\varepsilon_t$), where $n$ is the number of training samples, $\gamma_t$ is the learning rate at step $t$, $\mathbf{g}_t$ is roughly the difference of the gradient computed using all samples and that using only prior samples. $\left\|{\mathbf{g}_t}\right\|$ is upper bounded by and and typical much smaller than the gradient norm $\left\|{\nabla f(W_t)}\right\|$. We remark that our bound holds for nonconvex and nonsmooth scenarios. Moreover, our theoretical results provide numerically favorable upper bounds of testing errors (e.g., $0.037$ on MNIST). Using a similar technique, we can also obtain new generalization bounds for certain variants of SGD. Furthermore, we study the generalization bounds for gradient Langevin Dynamics (GLD). Using the same framework with a carefully constructed continuous prior, we show a new high probability generalization bound of order $O(\frac{1}{n} + \frac{L^2}{n^2}\sum_{t=1}^T(\gamma_t/\sigma_t)^2)$ for GLD. The new $1/n^2$ rate is due to the concentration of the difference between the gradient of training samples and that of the prior.