We show, both theoretically and empirically, that the algorithm naturally adapts to data lowrankness and converges exponentially fast to the ground-truth principal subspace. Notably, our result suggests that despite various recent efforts to accelerate the convergence of stochastic-gradient based methods by adding a O(n)-time variance reduction step, for the k-PCA problem, a truly online SGD variant suffices to achieve exponential convergence on intrinsically low-rank data.

Continual learning entails learning a sequence of tasks and balancing their knowledge appropriately. With limited access to old training samples, much of the current work in deep neural networks has focused on overcoming catastrophic forgetting of old tasks in gradient-based optimization. However, the normalization layers provide an exception, as they are updated interdependently by the gradient and statistics of currently observed training samples, which require specialized strategies to mitigate recency bias. In this work, we focus on the most popular Batch Normalization (BN) and provide an in-depth theoretical analysis of its sub-optimality in continual learning. Our analysis demonstrates the dilemma between balance and adaptation of BN statistics for incremental tasks, which potentially affects training stability and generalization.

Bilevel Optimization has experienced significant advancements recently with the introduction of new efficient algorithms. Mirroring the success in single-level optimization, stochastic gradient-based algorithms are widely used in bilevel optimization. However, a common limitation in these algorithms is the presumption of independent sampling, which can lead to increased computational costs due to the complicated hyper-gradient formulation of bilevel problems. To address this challenge, we study the example-selection strategy for bilevel optimization in this work. More specifically, we introduce a without-replacement sampling based algorithm which achieves a faster convergence rate compared to its counterparts that rely on independent sampling. Beyond the standard bilevel optimization formulation, we extend our discussion to conditional bilevel optimization and also two special cases: minimax and compositional optimization.

Traditional temporal action detection (TAD) usually handles untrimmed videos with small number of action instances from a single label (e.g., ActivityNet, THU-MOS). However, this setting might be unrealistic as different classes of actions often co-occur in practice. In this paper, we focus on the task of multi-label temporal action detection that aims to localize all action instances from a multi-label untrimmed video. Multi-label TAD is more challenging as it requires for finegrained class discrimination within a single video and precise localization of the co-occurring instances. To mitigate this issue, we extend the sparse query-based detection paradigm from the traditional TAD and propose the multi-label TAD framework of PointTAD.

The design of Artificial Neural Network (ANN) is inspired by the working patterns of the human brain. Connections in biological neural networks are sparse, as they only exist between few neurons. Meanwhile, the sparse representation in ANNs has been shown to possess significant advantages. Activation responses of ANNs are typically expected to promote sparse representations, where key signals get activated while irrelevant/redundant signals are suppressed. It can be observed that samples of each category are only correlated with sparse and specific channels in ANNs. However, existing activation mechanisms often struggle to suppress signals from other irrelevant channels entirely, and these signals have been verified to be detrimental to the network's final decision.

Federated Learning (FL) is a distributed learning framework, in which the local data never leaves clients' devices to preserve privacy, and the server trains models on the data via accessing only the gradients of those local data. Without further privacy mechanisms such as differential privacy, this leaves the system vulnerable against an attacker who inverts those gradients to reveal clients' sensitive data. However, a gradient is often insufficient to reconstruct the user data without any prior knowledge. By exploiting a generative model pretrained on the data distribution, we demonstrate that data privacy can be easily breached. Further, when such prior knowledge is unavailable, we investigate the possibility of learning the prior from a sequence of gradients seen in the process of FL training. We experimentally show that the prior in a form of generative model is learnable from iterative interactions in FL. Our findings strongly suggest that additional mechanisms are necessary to prevent privacy leakage in FL.

Federated Learning (FL) is a distributed learning framework, in which the local data never leaves clients' devices to preserve privacy, and the server trains models on the data via accessing only the gradients of those local data. Without further privacy mechanisms such as differential privacy, this leaves the system vulnerable against an attacker who inverts those gradients to reveal clients' sensitive data. However, a gradient is often insufficient to reconstruct the user data without any prior knowledge. By exploiting a generative model pretrained on the data distribution, we demonstrate that data privacy can be easily breached. Further, when such prior knowledge is unavailable, we investigate the possibility of learning the prior from a sequence of gradients seen in the process of FL training. We experimentally show that the prior in a form of generative model is learnable from iterative interactions in FL. Our findings strongly suggest that additional mechanisms are necessary to prevent privacy leakage in FL.