Stability and Generalization for Distributed SGDA

Minimax optimization is gaining increasing attention in modern machine learning applications. Driven by large-scale models and massive volumes of data collected from edge devices, as well as the concern to preserve client privacy, communication-efficient distributed minimax optimization algorithms become popular, such as Local Stochastic Gradient Descent Ascent (Local-SGDA), and Local Decentralized SGDA (Local-DSGDA). While most existing research on distributed minimax algorithms focuses on convergence rates, computation complexity, and communication efficiency, the generalization performance remains underdeveloped, whereas generalization ability is a pivotal indicator for evaluating the holistic performance of a model when fed with unknown data. In this paper, we propose the stability-based generalization analytical framework for Distributed-SGDA, which unifies two popular distributed minimax algorithms including Local-SGDA and Local-DSGDA, and conduct a comprehensive analysis of stability error, generalization gap, and population risk across different metrics under various settings, e.g., (S)C-(S)C, PL-SC, and NC-NC cases. Our theoretical results reveal the trade-off between the generalization gap and optimization error and suggest hyperparameters choice to obtain the optimal population risk. Numerical experiments for Local-SGDA and Local-DSGDA validate the theoretical results.

Magnitude Pruning of Large Pretrained Transformer Models with a Mixture Gaussian Prior

Large pretrained transformer models have revolutionized modern AI applications with their state-of-the-art performance in natural language processing (NLP). However, their substantial parameter count poses challenges for real-world deployment. To address this, researchers often reduce model size by pruning parameters based on their magnitude or sensitivity. Previous research has demonstrated the limitations of magnitude pruning, especially in the context of transfer learning for modern NLP tasks. In this paper, we introduce a new magnitude-based pruning algorithm called mixture Gaussian prior pruning (MGPP), which employs a mixture Gaussian prior for regularization. MGPP prunes non-expressive weights under the guidance of the mixture Gaussian prior, aiming to retain the model's expressive capability. Extensive evaluations across various NLP tasks, including natural language understanding, question answering, and natural language generation, demonstrate the superiority of MGPP over existing pruning methods, particularly in high sparsity settings. Additionally, we provide a theoretical justification for the consistency of the sparse transformer, shedding light on the effectiveness of the proposed pruning method.

WaveRoRA: Wavelet Rotary Route Attention for Multivariate Time Series Forecasting

In recent years, Transformer-based models (Transformers) have achieved significant success in multivariate time series forecasting (MTSF). However, previous works focus on extracting features either from the time domain or the frequency domain, which inadequately captures the trends and periodic characteristics. To address this issue, we propose a wavelet learning framework to model complex temporal dependencies of the time series data. The wavelet domain integrates both time and frequency information, allowing for the analysis of local characteristics of signals at different scales. Additionally, the Softmax self-attention mechanism used by Transformers has quadratic complexity, which leads to excessive computational costs when capturing long-term dependencies. Therefore, we propose a novel attention mechanism: Rotary Route Attention (RoRA). Unlike Softmax attention, RoRA utilizes rotary position embeddings to inject relative positional information to sequence tokens and introduces a small number of routing tokens $r$ to aggregate information from the $KV$ matrices and redistribute it to the $Q$ matrix, offering linear complexity. We further propose WaveRoRA, which leverages RoRA to capture inter-series dependencies in the wavelet domain. We conduct extensive experiments on eight real-world datasets. The results indicate that WaveRoRA outperforms existing state-of-the-art models while maintaining lower computational costs.

Autoregressive Moving-average Attention Mechanism for Time Series Forecasting

We propose an Autoregressive (AR) Moving-average (MA) attention structure that can adapt to various linear attention mechanisms, enhancing their ability to capture long-range and local temporal patterns in time series. In this paper, we first demonstrate that, for the time series forecasting (TSF) task, the previously overlooked decoder-only autoregressive Transformer model can achieve results comparable to the best baselines when appropriate tokenization and training methods are applied. Moreover, inspired by the ARMA model from statistics and recent advances in linear attention, we introduce the full ARMA structure into existing autoregressive attention mechanisms. By using an indirect MA weight generation method, we incorporate the MA term while maintaining the time complexity and parameter size of the underlying efficient attention models. We further explore how indirect parameter generation can produce implicit MA weights that align with the modeling requirements for local temporal impacts. Experimental results show that incorporating the ARMA structure consistently improves the performance of various AR attentions on TSF tasks, achieving state-of-the-art results.

A-FedPD: Aligning Dual-Drift is All Federated Primal-Dual Learning Needs

As a popular paradigm for juggling data privacy and collaborative training, federated learning (FL) is flourishing to distributively process the large scale of heterogeneous datasets on edged clients. Due to bandwidth limitations and security considerations, it ingeniously splits the original problem into multiple subproblems to be solved in parallel, which empowers primal dual solutions to great application values in FL. In this paper, we review the recent development of classical federated primal dual methods and point out a serious common defect of such methods in non-convex scenarios, which we say is a "dual drift" caused by dual hysteresis of those longstanding inactive clients under partial participation training. To further address this problem, we propose a novel Aligned Federated Primal Dual (A-FedPD) method, which constructs virtual dual updates to align global consensus and local dual variables for those protracted unparticipated local clients. Meanwhile, we provide a comprehensive analysis of the optimization and generalization efficiency for the A-FedPD method on smooth non-convex objectives, which confirms its high efficiency and practicality. Extensive experiments are conducted on several classical FL setups to validate the effectiveness of our proposed method.

Convergent Differential Privacy Analysis for General Federated Learning: the f-DP Perspective

Federated learning (FL) is an efficient collaborative training paradigm extensively developed with a focus on local privacy protection, and differential privacy (DP) is a classical approach to capture and ensure the reliability of local privacy. The powerful cooperation of FL and DP provides a promising learning framework for large-scale private clients, juggling both privacy securing and trustworthy learning. As the predominant algorithm of DP, the noisy perturbation has been widely studied and incorporated into various federated algorithms, theoretically proven to offer significant privacy protections. However, existing analyses in noisy FL-DP mostly rely on the composition theorem and cannot tightly quantify the privacy leakage challenges, which is nearly tight for small numbers of communication rounds but yields an arbitrarily loose and divergent bound under the large communication rounds. This implies a counterintuitive judgment, suggesting that FL may not provide adequate privacy protection during long-term training. To further investigate the convergent privacy and reliability of the FL-DP framework, in this paper, we comprehensively evaluate the worst privacy of two classical methods under the non-convex and smooth objectives based on the f-DP analysis, i.e. Noisy-FedAvg and Noisy-FedProx methods. With the aid of the shifted-interpolation technique, we successfully prove that the worst privacy of the Noisy-FedAvg method achieves a tight convergent lower bound. Moreover, in the Noisy-FedProx method, with the regularization of the proxy term, the worst privacy has a stable constant lower bound. Our analysis further provides a solid theoretical foundation for the reliability of privacy protection in FL-DP. Meanwhile, our conclusions can also be losslessly converted to other classical DP analytical frameworks, e.g. $(\epsilon,\delta)$-DP and R$\acute{\text{e}}$nyi-DP (RDP).

A Confidence Interval for the $\ell_2$ Expected Calibration Error

Recent advances in machine learning have significantly improved prediction accuracy in various applications. However, ensuring the calibration of probabilistic predictions remains a significant challenge. Despite efforts to enhance model calibration, the rigorous statistical evaluation of model calibration remains less explored. In this work, we develop confidence intervals the $\ell_2$ Expected Calibration Error (ECE). We consider top-1-to-$k$ calibration, which includes both the popular notion of confidence calibration as well as full calibration. For a debiased estimator of the ECE, we show asymptotic normality, but with different convergence rates and asymptotic variances for calibrated and miscalibrated models. We develop methods to construct asymptotically valid confidence intervals for the ECE, accounting for this behavior as well as non-negativity. Our theoretical findings are supported through extensive experiments, showing that our methods produce valid confidence intervals with shorter lengths compared to those obtained by resampling-based methods.

Coherent FDA Radar: Transmitter and Receiver Design and Analysis

The combination of frequency diverse array (FDA) radar technology with the multiple input multiple output (MIMO) radar architecture and waveform diversity techniques potentially promises a high integration gain with respect to conventional phased array (PA) radars. In this paper, we propose an approach to the design of the transmitter and the receiver of a coherent FDA (C-FDA) radar, that enables it to perform the demodulation with spectral overlapping, due to the small frequency offset. To this purpose, we derive the generalized space-time-range signal model and we prove that the proposed C-FDA radar has a higher coherent array gain than a PA radar, and at the same time, it effectively resolves the secondary range-ambiguous (SRA) problem of FDA-MIMO radar, allowing for mainlobe interference suppression and range-ambiguous clutter suppression. Numerical analysis results prove the effectiveness of the proposed C-FDA radar in terms on anti-interference and anti-clutter capabilities over conventional radars.

FDA Jamming Against Airborne Phased-MIMO Radar-Part II: Jamming STAP Performance Analysis

The first part of this series introduced the effectiveness of frequency diverse array (FDA) jamming through direct wave propagation in countering airborne phased multiple-input multiple-output (Phased-MIMO) radar. This part focuses on the effectiveness of FDA scattered wave (FDA-SW) jamming on the space-time adaptive processing (STAP) for airborne phased-MIMO radar. Distinguished from the clutter signals, the ground equidistant scatterers of FDA-SW jamming constitute an elliptical ring, whose trajectory equations are mathematically derived to further determine the spatial frequency and Doppler frequency. For the phased-MIMO radar with different transmitting partitions, the effects of jamming frequency offset of FDA-SW on the clutter rank and STAP performance are discussed. Theoretical analysis provides the variation interval of clutter rank and the relationship between the jamming frequency offset and the improvement factor (IF) notch of phased-MIMO-STAP. Importantly, the requirements of jamming frequency offset for both two-part applications are discussed in this part. Numerical results verify these mathematical findings and validate the effectiveness of the proposed FDA jamming in countering the phased-MIMO radar.

MPT-PAR:Mix-Parameters Transformer for Panoramic Activity Recognition

The objective of the panoramic activity recognition task is to identify behaviors at various granularities within crowded and complex environments, encompassing individual actions, social group activities, and global activities. Existing methods generally use either parameter-independent modules to capture task-specific features or parameter-sharing modules to obtain common features across all tasks. However, there is often a strong interrelatedness and complementary effect between tasks of different granularities that previous methods have yet to notice. In this paper, we propose a model called MPT-PAR that considers both the unique characteristics of each task and the synergies between different tasks simultaneously, thereby maximizing the utilization of features across multi-granularity activity recognition. Furthermore, we emphasize the significance of temporal and spatial information by introducing a spatio-temporal relation-enhanced module and a scene representation learning module, which integrate the the spatio-temporal context of action and global scene into the feature map of each granularity. Our method achieved an overall F1 score of 47.5\% on the JRDB-PAR dataset, significantly outperforming all the state-of-the-art methods.