One of the major concerns for neural network training is that the non-convexity of the associated loss functions may cause bad landscape. The recent success of neural networks suggests that their loss landscape is not too bad, but what specific results do we know about the landscape? In this article, we review recent findings and results on the global landscape of neural networks. First, we point out that wide neural nets may have sub-optimal local minima under certain assumptions. Second, we discuss a few rigorous results on the geometric properties of wide networks such as "no bad basin", and some modifications that eliminate sub-optimal local minima and/or decreasing paths to infinity. Third, we discuss visualization and empirical explorations of the landscape for practical neural nets. Finally, we briefly discuss some convergence results and their relation to landscape results.

Most algorithms used in neural networks(NN)-based leaning tasks are strongly affected by the choices of initialization. Good initialization can avoid sub-optimal solutions and alleviate saturation during training. However, designing improved initialization strategies is a difficult task and our understanding of good initialization is still very primitive. Here, we propose persistent neurons, a strategy that optimizes the learning trajectory using information from previous converged solutions. More precisely, we let the parameters explore new landscapes by penalizing the model from converging to the previous solutions under the same initialization. Specifically, we show that persistent neurons, under certain data distribution, is able to converge to more optimal solutions while initializations under popular framework find bad local minima. We further demonstrate that persistent neurons helps improve the model's performance under both good and poor initializations. Moreover, we evaluate full and partial persistent model and show it can be used to boost the performance on a range of NN structures, such as AlexNet and residual neural network. Saturation of activation functions during persistent training is also studied.

Mode connectivity provides novel geometric insights on analyzing loss landscapes and enables building high-accuracy pathways between well-trained neural networks. In this work, we propose to employ mode connectivity in loss landscapes to study the adversarial robustness of deep neural networks, and provide novel methods for improving this robustness. Our experiments cover various types of adversarial attacks applied to different network architectures and datasets. When network models are tampered with backdoor or error-injection attacks, our results demonstrate that the path connection learned using limited amount of bonafide data can effectively mitigate adversarial effects while maintaining the original accuracy on clean data. Therefore, mode connectivity provides users with the power to repair backdoored or error-injected models. We also use mode connectivity to investigate the loss landscapes of regular and robust models against evasion attacks. Experiments show that there exists a barrier in adversarial robustness loss on the path connecting regular and adversarially-trained models. A high correlation is observed between the adversarial robustness loss and the largest eigenvalue of the input Hessian matrix, for which theoretical justifications are provided. Our results suggest that mode connectivity offers a holistic tool and practical means for evaluating and improving adversarial robustness.

The purpose of the study is to investigate the relative effectiveness of four different sentiment analysis techniques: (1) unsupervised lexicon-based model using Sent WordNet; (2) traditional supervised machine learning model using logistic regression; (3) supervised deep learning model using Long Short-Term Memory (LSTM); and, (4) advanced supervised deep learning models using Bidirectional Encoder Representations from Transformers (BERT). We use publicly available labeled corpora of 50,000 movie reviews originally posted on internet movie database (IMDB) for analysis using Sent WordNet lexicon, logistic regression, LSTM, and BERT. The first three models were run on CPU based system whereas BERT was run on GPU based system. The sentiment classification performance was evaluated based on accuracy, precision, recall, and F1 score. The study puts forth two key insights: (1) relative efficacy of four highly advanced and widely used sentiment analysis techniques; (2) undisputed superiority of pre-trained advanced supervised deep learning BERT model in sentiment analysis from text data. This study provides professionals in analytics industry and academicians working on text analysis key insight regarding comparative classification performance evaluation of key sentiment analysis techniques, including the recently developed BERT. This is the first research endeavor to compare the advanced pre-trained supervised deep learning model of BERT vis-\`a-vis other sentiment analysis models of LSTM, logistic regression, and Sent WordNet.

Randomized controlled trials typically analyze the effectiveness of treatments with the goal of making treatment recommendations for patient subgroups. With the advance of electronic health records, a great variety of data has been collected in clinical practice, enabling the evaluation of treatments and treatment policies based on observational data. In this paper, we focus on learning individualized treatment rules (ITRs) to derive a treatment policy that is expected to generate a better outcome for an individual patient. In our framework, we cast ITRs learning as a contextual bandit problem and minimize the expected risk of the treatment policy. We conduct experiments with the proposed framework both in a simulation study and based on a real-world dataset. In the latter case, we apply our proposed method to learn the optimal ITRs for the administration of intravenous (IV) fluids and vasopressors (VP). Based on various offline evaluation methods, we could show that the policy derived in our framework demonstrates better performance compared to both the physicians and other baselines, including a simple treatment prediction approach. As a long-term goal, our derived policy might eventually lead to better clinical guidelines for the administration of IV and VP.

Deep neural networks are typically initialized with random weights, with variances chosen to facilitate signal propagation and stable gradients. It is also believed that diversity of features is an important property of these initializations. We construct a deep convolutional network with identical features by initializing almost all the weights to $0$. The architecture also enables perfect signal propagation and stable gradients, and achieves high accuracy on standard benchmarks. This indicates that random, diverse initializations are \textit{not} necessary for training neural networks. An essential element in training this network is a mechanism of symmetry breaking; we study this phenomenon and find that standard GPU operations, which are non-deterministic, can serve as a sufficient source of symmetry breaking to enable training.

Deep Neural Networks were first developed decades ago, but it was not until recently that they started being extensively used, due to their computing power requirements. Since then, they are increasingly being applied to many fields and have undergone far-reaching advancements. More importantly, they have been utilized for critical matters, such as making decisions in healthcare procedures or autonomous driving, where risk management is crucial. Any mistakes in the diagnostics or decision-making in these fields could entail grave accidents, and even death. This is preoccupying, because it has been repeatedly reported that it is straightforward to attack this type of models. Thus, these attacks must be studied to be able to assess their risk, and defenses need to be developed to make models more robust. For this work, the most widely known attack was selected (adversarial attack) and several defenses were implemented against it (i.e. adversarial training, dimensionality reduc tion and prediction similarity). The obtained outcomes make the model more robust while keeping a similar accuracy. The idea was developed using a breast cancer dataset and a VGG16 and dense neural network model, but the solutions could be applied to datasets from other areas and different convolutional and dense deep neural network models.

Transformers have become widely used for language modeling and sequence learning tasks, and are one of the most important machine learning workloads today. Training one is a very compute-intensive task, often taking days or weeks, and significant attention has been given to optimizing transformers. Despite this, existing implementations do not efficiently utilize GPUs. We find that data movement is the key bottleneck when training. Due to Amdahl's Law and massive improvements in compute performance, training has now become memory-bound. Further, existing frameworks use suboptimal data layouts. Using these insights, we present a recipe for globally optimizing data movement in transformers. We reduce data movement by up to 22.91% and overall achieve a 1.30x performance improvement over state-of-the-art frameworks when training BERT. Our approach is applicable more broadly to optimizing deep neural networks, and offers insight into how to tackle emerging performance bottlenecks.

Sparse neural networks are shown to give accurate predictions competitive to denser versions, while also minimizing the number of arithmetic operations performed. However current hardware like GPU's can only exploit structured sparsity patterns for better efficiency. Hence the run time of a sparse neural network may not correspond to the arithmetic operations required. In this work, we propose RBGP( Ramanujan Bipartite Graph Product) framework for generating structured multi level block sparse neural networks by using the theory of Graph products. We also propose to use products of Ramanujan graphs which gives the best connectivity for a given level of sparsity. This essentially ensures that the i.) the networks has the structured block sparsity for which runtime efficient algorithms exists ii.) the model gives high prediction accuracy, due to the better expressive power derived from the connectivity of the graph iii.) the graph data structure has a succinct representation that can be stored efficiently in memory. We use our framework to design a specific connectivity pattern called RBGP4 which makes efficient use of the memory hierarchy available on GPU. We benchmark our approach by experimenting on image classification task over CIFAR dataset using VGG19 and WideResnet-40-4 networks and achieve 5-9x and 2-5x runtime gains over unstructured and block sparsity patterns respectively, while achieving the same level of accuracy.

While second order optimizers such as natural gradient descent (NGD) often speed up optimization, their effect on generalization remains controversial. For instance, it has been pointed out that gradient descent (GD), in contrast to many preconditioned updates, converges to small Euclidean norm solutions in overparameterized models, leading to favorable generalization properties. This work presents a more nuanced view on the comparison of generalization between first- and second-order methods. We provide an asymptotic bias-variance decomposition of the generalization error of overparameterized ridgeless regression under a general class of preconditioner $\boldsymbol{P}$, and consider the inverse population Fisher information matrix (used in NGD) as a particular example. We determine the optimal $\boldsymbol{P}$ for both the bias and variance, and find that the relative generalization performance of different optimizers depends on the label noise and the "shape" of the signal (true parameters): when the labels are noisy, the model is misspecified, or the signal is misaligned with the features, NGD can achieve lower risk; conversely, GD generalizes better than NGD under clean labels, a well-specified model, or aligned signal. Based on this analysis, we discuss several approaches to manage the bias-variance tradeoff, and the potential benefit of interpolating between GD and NGD. We then extend our analysis to regression in the reproducing kernel Hilbert space and demonstrate that preconditioned GD can decrease the population risk faster than GD. Lastly, we empirically compare the generalization performance of first- and second-order optimizers in neural network experiments, and observe robust trends matching our theoretical analysis.