theory->optimization

By integrating certain optimization solvers with deep neural networks, deep unfolding network (DUN) with good interpretability and high performance has attracted growing attention in compressive sensing (CS). However, existing DUNs often improve the visual quality at the price of a large number of parameters and have the problem of feature information loss during iteration. In this paper, we propose an Optimization-inspired Cross-attention Transformer (OCT) module as an iterative process, leading to a lightweight OCT-based Unfolding Framework (OCTUF) for image CS. Specifically, we design a novel Dual Cross Attention (Dual-CA) sub-module, which consists of an Inertia-Supplied Cross Attention (ISCA) block and a Projection-Guided Cross Attention (PGCA) block. ISCA block introduces multi-channel inertia forces and increases the memory effect by a cross attention mechanism between adjacent iterations. And, PGCA block achieves an enhanced information interaction, which introduces the inertia force into the gradient descent step through a cross attention block. Extensive CS experiments manifest that our OCTUF achieves superior performance compared to state-of-the-art methods while training lower complexity. Codes are available at https://github.com/songjiechong/OCTUF.

In theory, vector quantization (VQ) is always better than scalar quantization (SQ) in terms of rate-distortion (R-D) performance. Recent state-of-the-art methods for neural image compression are mainly based on nonlinear transform coding (NTC) with uniform scalar quantization, overlooking the benefits of VQ due to its exponentially increased complexity. In this paper, we first investigate on some toy sources, demonstrating that even if modern neural networks considerably enhance the compression performance of SQ with nonlinear transform, there is still an insurmountable chasm between SQ and VQ. Therefore, revolving around VQ, we propose a novel framework for neural image compression named Nonlinear Vector Transform Coding (NVTC). NVTC solves the critical complexity issue of VQ through (1) a multi-stage quantization strategy and (2) nonlinear vector transforms. In addition, we apply entropy-constrained VQ in latent space to adaptively determine the quantization boundaries for joint rate-distortion optimization, which improves the performance both theoretically and experimentally. Compared to previous NTC approaches, NVTC demonstrates superior rate-distortion performance, faster decoding speed, and smaller model size. Our code is available at https://github.com/USTC-IMCL/NVTC.

Federated learning enables the privacy-preserving training of neural network models using real-world data across distributed clients. FedAvg has become the preferred optimizer for federated learning because of its simplicity and effectiveness. FedAvg uses naive aggregation to update the server model, interpolating client models based on the number of instances used in their training. However, naive aggregation suffers from client-drift when the data is heterogenous (non-IID), leading to unstable and slow convergence. In this work, we propose a novel aggregation approach, elastic aggregation, to overcome these issues. Elastic aggregation interpolates client models adaptively according to parameter sensitivity, which is measured by computing how much the overall prediction function output changes when each parameter is changed. This measurement is performed in an unsupervised and online manner. Elastic aggregation reduces the magnitudes of updates to the more sensitive parameters so as to prevent the server model from drifting to any one client distribution, and conversely boosts updates to the less sensitive parameters to better explore different client distributions. Empirical results on real and synthetic data as well as analytical results show that elastic aggregation leads to efficient training in both convex and non-convex settings, while being fully agnostic to client heterogeneity and robust to large numbers of clients, partial participation, and imbalanced data. Finally, elastic aggregation works well with other federated optimizers and achieves significant improvements across the board.

Deep hashing is an appealing approach for large-scale image retrieval. Most existing supervised deep hashing methods learn hash functions using pairwise or triple image similarities in randomly sampled mini-batches. They suffer from low training efficiency, insufficient coverage of data distribution, and pair imbalance problems. Recently, central similarity quantization (CSQ) attacks the above problems by using "hash centers" as a global similarity metric, which encourages the hash codes of similar images to approach their common hash center and distance themselves from other hash centers. Although achieving SOTA retrieval performance, CSQ falls short of a worst-case guarantee on the minimal distance between its constructed hash centers, i.e. the hash centers can be arbitrarily close. This paper presents an optimization method that finds hash centers with a constraint on the minimal distance between any pair of hash centers, which is non-trivial due to the non-convex nature of the problem. More importantly, we adopt the Gilbert-Varshamov bound from coding theory, which helps us to obtain a large minimal distance while ensuring the empirical feasibility of our optimization approach. With these clearly-separated hash centers, each is assigned to one image class, we propose several effective loss functions to train deep hashing networks. Extensive experiments on three datasets for image retrieval demonstrate that the proposed method achieves superior retrieval performance over the state-of-the-art deep hashing methods.