Finding the optimal model complexity that minimizes the generalization error (GE) is a key issue of machine learning. For the conventional supervised learning, this task typically involves the bias-variance tradeoff: lowering the bias by making the model more complex entails an increase in the variance. Meanwhile, little has been studied about whether the same tradeoff exists for unsupervised learning. In this study, we propose that unsupervised learning generally exhibits a two-component tradeoff of the GE, namely the model error and the data error -- using a more complex model reduces the model error at the cost of the data error, with the data error playing a more significant role for a smaller training dataset. This is corroborated by training the restricted Boltzmann machine to generate the configurations of the two-dimensional Ising model at a given temperature and the totally asymmetric simple exclusion process with given entry and exit rates. Our results also indicate that the optimal model tends to be more complex when the data to be learned are more complex.

Semi-supervised learning (SSL) has become a crucial approach in deep learning as a way to address the challenge of limited labeled data. The success of deep neural networks heavily relies on the availability of large-scale high-quality labeled data. However, the process of data labeling is time-consuming and unscalable, leading to shortages in labeled data. SSL aims to tackle this problem by leveraging additional unlabeled data in the training process. One of the popular SSL algorithms, FixMatch, trains identical weight-sharing teacher and student networks simultaneously using a siamese neural network (SNN). However, it is prone to performance degradation when the pseudo labels are heavily noisy in the early training stage. We present KD-FixMatch, a novel SSL algorithm that addresses the limitations of FixMatch by incorporating knowledge distillation. The algorithm utilizes a combination of sequential and simultaneous training of SNNs to enhance performance and reduce performance degradation. Firstly, an outer SNN is trained using labeled and unlabeled data. After that, the network of the well-trained outer SNN generates pseudo labels for the unlabeled data, from which a subset of unlabeled data with trusted pseudo labels is then carefully created through high-confidence sampling and deep embedding clustering. Finally, an inner SNN is trained with the labeled data, the unlabeled data, and the subset of unlabeled data with trusted pseudo labels. Experiments on four public data sets demonstrate that KD-FixMatch outperforms FixMatch in all cases. Our results indicate that KD-FixMatch has a better training starting point that leads to improved model performance compared to FixMatch.

Despite significant advances, the performance of state-of-the-art continual learning approaches hinges on the unrealistic scenario of fully labeled data. In this paper, we tackle this challenge and propose an approach for continual semi-supervised learning--a setting where not all the data samples are labeled. A primary issue in this scenario is the model forgetting representations of unlabeled data and overfitting the labeled samples. We leverage the power of nearest-neighbor classifiers to nonlinearly partition the feature space and flexibly model the underlying data distribution thanks to its non-parametric nature. This enables the model to learn a strong representation for the current task, and distill relevant information from previous tasks. We perform a thorough experimental evaluation and show that our method outperforms all the existing approaches by large margins, setting a solid state of the art on the continual semi-supervised learning paradigm. For example, on CIFAR-100 we surpass several others even when using at least 30 times less supervision (0.8% vs. 25% of annotations). Finally, our method works well on both low and high resolution images and scales seamlessly to more complex datasets such as ImageNet-100. The code is publicly available on https://github.com/kangzhiq/NNCSL

Recent works have demonstrated the superiority of supervised Convolutional Neural Networks (CNNs) in learning hierarchical representations from time series data for successful classification. These methods require sufficiently large labeled data for stable learning, however acquiring high-quality labeled time series data can be costly and potentially infeasible. Generative Adversarial Networks (GANs) have achieved great success in enhancing unsupervised and semi-supervised learning. Nonetheless, to our best knowledge, it remains unclear how effectively GANs can serve as a general-purpose solution to learn representations for time series recognition, i.e., classification and clustering. The above considerations inspire us to introduce a Time-series Convolutional GAN (TCGAN). TCGAN learns by playing an adversarial game between two one-dimensional CNNs (i.e., a generator and a discriminator) in the absence of label information. Parts of the trained TCGAN are then reused to construct a representation encoder to empower linear recognition methods. We conducted comprehensive experiments on synthetic and real-world datasets. The results demonstrate that TCGAN is faster and more accurate than existing time-series GANs. The learned representations enable simple classification and clustering methods to achieve superior and stable performance. Furthermore, TCGAN retains high efficacy in scenarios with few-labeled and imbalanced-labeled data. Our work provides a promising path to effectively utilize abundant unlabeled time series data.

The evaluation of noisy binary classifiers on unlabeled data is treated as a streaming task: given a data sketch of the decisions by an ensemble, estimate the true prevalence of the labels as well as each classifier's accuracy on them. Two fully algebraic evaluators are constructed to do this. Both are based on the assumption that the classifiers make independent errors. The first is based on majority voting. The second, the main contribution of the paper, is guaranteed to be correct. But how do we know the classifiers are independent on any given test? This principal/agent monitoring paradox is ameliorated by exploiting the failures of the independent evaluator to return sensible estimates. A search for nearly error independent trios is empirically carried out on the \texttt{adult}, \texttt{mushroom}, and \texttt{two-norm} datasets by using the algebraic failure modes to reject evaluation ensembles as too correlated. The searches are refined by constructing a surface in evaluation space that contains the true value point. The algebra of arbitrarily correlated classifiers permits the selection of a polynomial subset free of any correlation variables. Candidate evaluation ensembles are rejected if their data sketches produce independent estimates too far from the constructed surface. The results produced by the surviving ensembles can sometimes be as good as 1\%. But handling even small amounts of correlation remains a challenge. A Taylor expansion of the estimates produced when independence is assumed but the classifiers are, in fact, slightly correlated helps clarify how the independent evaluator has algebraic `blind spots'.

For many decades, experimental solid mechanics has played a crucial role in characterizing and understanding the mechanical properties of natural and novel materials. Recent advances in machine learning (ML) provide new opportunities for the field, including experimental design, data analysis, uncertainty quantification, and inverse problems. As the number of papers published in recent years in this emerging field is exploding, it is timely to conduct a comprehensive and up-to-date review of recent ML applications in experimental solid mechanics. Here, we first provide an overview of common ML algorithms and terminologies that are pertinent to this review, with emphasis placed on physics-informed and physics-based ML methods. Then, we provide thorough coverage of recent ML applications in traditional and emerging areas of experimental mechanics, including fracture mechanics, biomechanics, nano- and micro-mechanics, architected materials, and 2D material. Finally, we highlight some current challenges of applying ML to multi-modality and multi-fidelity experimental datasets and propose several future research directions. This review aims to provide valuable insights into the use of ML methods as well as a variety of examples for researchers in solid mechanics to integrate into their experiments.

Advances in Semi-Supervised Learning (SSL) have almost entirely closed the gap between SSL and Supervised Learning at a fraction of the number of labels. However, recent performance improvements have often come \textit{at the cost of significantly increased training computation}. To address this, we propose Curriculum Batch Size (CBS), \textit{an unlabeled batch size curriculum which exploits the natural training dynamics of deep neural networks.} A small unlabeled batch size is used in the beginning of training and is gradually increased to the end of training. A fixed curriculum is used regardless of dataset, model or number of epochs, and reduced training computations is demonstrated on all settings. We apply CBS, strong labeled augmentation, Curriculum Pseudo Labeling (CPL) \citep{FlexMatch} to FixMatch \citep{FixMatch} and term the new SSL algorithm Fast FixMatch. We perform an ablation study to show that strong labeled augmentation and/or CPL do not significantly reduce training computations, but, in synergy with CBS, they achieve optimal performance. Fast FixMatch also achieves substantially higher data utilization compared to previous state-of-the-art. Fast FixMatch achieves between $2.1\times$ - $3.4\times$ reduced training computations on CIFAR-10 with all but 40, 250 and 4000 labels removed, compared to vanilla FixMatch, while attaining the same cited state-of-the-art error rate \citep{FixMatch}. Similar results are achieved for CIFAR-100, SVHN and STL-10. Finally, Fast MixMatch achieves between $2.6\times$ - $3.3\times$ reduced training computations in federated SSL tasks and online/streaming learning SSL tasks, which further demonstrate the generializbility of Fast MixMatch to different scenarios and tasks.

This paper investigates the suitability of using Generative Adversarial Networks (GANs) to generate stable structures for the physics-based puzzle game Angry Birds. While previous applications of GANs for level generation have been mostly limited to tile-based representations, this paper explores their suitability for creating stable structures made from multiple smaller blocks. This includes a detailed encoding/decoding process for converting between Angry Birds level descriptions and a suitable grid-based representation, as well as utilizing state-of-the-art GAN architectures and training methods to produce new structure designs. Our results show that GANs can be successfully applied to generate a varied range of complex and stable Angry Birds structures.

Learning time-series representations when only unlabeled data or few labeled samples are available can be a challenging task. Recently, contrastive self-supervised learning has shown great improvement in extracting useful representations from unlabeled data via contrasting different augmented views of data. In this work, we propose a novel Time-Series representation learning framework via Temporal and Contextual Contrasting (TS-TCC) that learns representations from unlabeled data with contrastive learning. Specifically, we propose time-series-specific weak and strong augmentations and use their views to learn robust temporal relations in the proposed temporal contrasting module, besides learning discriminative representations by our proposed contextual contrasting module. Additionally, we conduct a systematic study of time-series data augmentation selection, which is a key part of contrastive learning. We also extend TS-TCC to the semi-supervised learning settings and propose a Class-Aware TS-TCC (CA-TCC) that benefits from the available few labeled data to further improve representations learned by TS-TCC. Specifically, we leverage the robust pseudo labels produced by TS-TCC to realize a class-aware contrastive loss. Extensive experiments show that the linear evaluation of the features learned by our proposed framework performs comparably with the fully supervised training. Additionally, our framework shows high efficiency in the few labeled data and transfer learning scenarios. The code is publicly available at \url{https://github.com/emadeldeen24/CA-TCC}.

Densely annotating LiDAR point clouds is costly, which restrains the scalability of fully-supervised learning methods. In this work, we study the underexplored semi-supervised learning (SSL) in LiDAR segmentation. Our core idea is to leverage the strong spatial cues of LiDAR point clouds to better exploit unlabeled data. We propose LaserMix to mix laser beams from different LiDAR scans, and then encourage the model to make consistent and confident predictions before and after mixing. Our framework has three appealing properties: 1) Generic: LaserMix is agnostic to LiDAR representations (e.g., range view and voxel), and hence our SSL framework can be universally applied. 2) Statistically grounded: We provide a detailed analysis to theoretically explain the applicability of the proposed framework. 3) Effective: Comprehensive experimental analysis on popular LiDAR segmentation datasets (nuScenes, SemanticKITTI, and ScribbleKITTI) demonstrates our effectiveness and superiority. Notably, we achieve competitive results over fully-supervised counterparts with 2x to 5x fewer labels and improve the supervised-only baseline significantly by 10.8% on average. We hope this concise yet high-performing framework could facilitate future research in semi-supervised LiDAR segmentation. Code is publicly available.