Figure S2: Number of iterations at each grid point for the Newton and gradient descent methods applying to the ℓ2-regularized logistic regression over simulated data generated in Example 2. We summarize the results in Figure S1-S3. Figure S1 presents the results for ridge regression. In this case, the number of iterations by gradient method first increases and then stays flat as tk grows. Newton method, however, only takes one 1.51.5 iteration at each grid point. Moreover, the level of approximation (i.e., ϵ) seems to have no impact onthe number of iterations at each grid point, which is highly desirable.

Multi-task and multi-domain learning methods seek to learn multiple tasks/domains, jointly or one after another, using a single unified network. The key challenge and opportunity is to exploit shared information across tasks and domains to improve the efficiency of the unified network. The efficiency can be in terms of accuracy, storage cost, computation, or sample complexity. In this paper, we propose a factorized tensor network (FTN) that can achieve accuracy comparable to independent single-task/domain networks with a small number of additional parameters. FTN uses a frozen backbone network from a source model and incrementally adds task/domain-specific low-rank tensor factors to the shared frozen network. This approach can adapt to a large number of target domains and tasks without catastrophic forgetting. Furthermore, FTN requires a significantly smaller number of task-specific parameters compared to existing methods. We performed experiments on widely used multi-domain and multi-task datasets. We show the experiments on convolutional-based architecture with different backbones and on transformer-based architecture. We observed that FTN achieves similar accuracy as single-task/domain methods while using only a fraction of additional parameters per task.

Faster-than-Nyquist (FTN) signaling can improve the spectral efficiency (SE); however, at the expense of high computational complexity to remove the introduced intersymbol interference (ISI). Motivated by the recent success of ML in physical layer (PHY) problems, in this paper we investigate the use of ML in reducing the detection complexity of FTN signaling. In particular, we view the FTN signaling detection problem as a classification task, where the received signal is considered as an unlabeled class sample that belongs to a set of all possible classes samples. If we use an off-shelf classifier, then the set of all possible classes samples belongs to an $N$-dimensional space, where $N$ is the transmission block length, which has a huge computational complexity. We propose a low-complexity classifier (LCC) that exploits the ISI structure of FTN signaling to perform the classification task in $N_p \ll N$-dimension space. The proposed LCC consists of two stages: 1) offline pre-classification that constructs the labeled classes samples in the $N_p$-dimensional space and 2) online classification where the detection of the received samples occurs. The proposed LCC is extended to produce soft-outputs as well. Simulation results show the effectiveness of the proposed LCC in balancing performance and complexity.

Deep learning-based segmentation methods are vulnerable to unforeseen data distribution shifts during deployment, e.g. change of image appearances or contrasts caused by different scanners, unexpected imaging artifacts etc. In this paper, we present a cooperative framework for training image segmentation models and a latent space augmentation method for generating hard examples. Both contributions improve model generalization and robustness with limited data. The cooperative training framework consists of a fast-thinking network (FTN) and a slow-thinking network (STN). The FTN learns decoupled image features and shape features for image reconstruction and segmentation tasks. The STN learns shape priors for segmentation correction and refinement. The two networks are trained in a cooperative manner. The latent space augmentation generates challenging examples for training by masking the decoupled latent space in both channel-wise and spatial-wise manners. We performed extensive experiments on public cardiac imaging datasets. Using only 10 subjects from a single site for training, we demonstrated improved cross-site segmentation performance and increased robustness against various unforeseen imaging artifacts compared to strong baseline methods. Particularly, cooperative training with latent space data augmentation yields 15% improvement in terms of average Dice score when compared to a standard training method.