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Gradient methods have become mainstream techniques for Bi-Level Optimization (BLO) in learning fields. The validity of existing works heavily rely on either a restrictive Lower-Level Strong Convexity (LLSC) condition or on solving a series of approximation subproblems with high accuracy or both. In this work, by averaging the upper and lower level objectives, we propose a single loop Bi-level Averaged Method of Multipliers (sl-BAMM) for BLO that is simple yet efficient for large-scale BLO and gets rid of the limited LLSC restriction. We further provide non-asymptotic convergence analysis of sl-BAMM towards KKT stationary points, and the comparative advantage of our analysis lies in the absence of strong gradient boundedness assumption, which is always required by others. Thus our theory safely captures a wider variety of applications in deep learning, especially where the upper-level objective is quadratic w.r.t. the lower-level variable. Experimental results demonstrate the superiority of our method.

Owing to their remarkable learning capabilities and performance in real-world applications, the use of machine learning systems based on Neural Networks (NNs) has been continuously increasing. However, various case studies and empirical findings in the literature suggest that slight variations to NN inputs can lead to erroneous and undesirable NN behavior. This has led to considerable interest in their formal analysis, aiming to provide guarantees regarding a given NN's behavior. Existing frameworks provide robustness and/or safety guarantees for the trained NNs, using satisfiability solving and linear programming. We proposed FANNet, the first model checking-based framework for analyzing a broader range of NN properties. However, the state-space explosion associated with model checking entails a scalability problem, making the FANNet applicable only to small NNs. This work develops state-space reduction and input segmentation approaches, to improve the scalability and timing efficiency of formal NN analysis. Compared to the state-of-the-art FANNet, this enables our new model checking-based framework to reduce the verification's timing overhead by a factor of up to 8000, making the framework applicable to NNs even with approximately $80$ times more network parameters. This in turn allows the analysis of NN safety properties using the new framework, in addition to all the NN properties already included with FANNet. The framework is shown to be efficiently able to analyze properties of NNs trained on healthcare datasets as well as the well--acknowledged ACAS Xu NNs.

Regularization is a set of techniques that are used to improve the generalization ability of deep neural networks. In this paper, we introduce weight compander (WC), a novel effective method to improve generalization by reparameterizing each weight in deep neural networks using a nonlinear function. It is a general, intuitive, cheap and easy to implement method, which can be combined with various other regularization techniques. Large weights in deep neural networks are a sign of a more complex network that is overfitted to the training data. Moreover, regularized networks tend to have a greater range of weights around zero with fewer weights centered at zero. We introduce a weight reparameterization function which is applied to each weight and implicitly reduces overfitting by restricting the magnitude of the weights while forcing them away from zero at the same time. This leads to a more democratic decision-making in the network. Firstly, individual weights cannot have too much influence in the prediction process due to the restriction of their magnitude. Secondly, more weights are used in the prediction process, since they are forced away from zero during the training. This promotes the extraction of more features from the input data and increases the level of weight redundancy, which makes the network less sensitive to statistical differences between training and test data. We extend our method to learn the hyperparameters of the introduced weight reparameterization function. This avoids hyperparameter search and gives the network the opportunity to align the weight reparameterization with the training progress. We show experimentally that using weight compander in addition to standard regularization methods improves the performance of neural networks.

Artificial intelligence represents a new frontier in human medicine that could save more lives and reduce the costs, thereby increasing accessibility. As a consequence, the rate of advancement of AI in cancer medical imaging and more particularly tissue pathology has exploded, opening it to ethical and technical questions that could impede its adoption into existing systems. In order to chart the path of AI in its application to cancer tissue imaging, we review current work and identify how it can improve cancer pathology diagnostics and research. In this review, we identify 5 core tasks that models are developed for, including regression, classification, segmentation, generation, and compression tasks. We address the benefits and challenges that such methods face, and how they can be adapted for use in cancer prevention and treatment. The studies looked at in this paper represent the beginning of this field and future experiments will build on the foundations that we highlight.

The vulnerability of deep neural network models to adversarial example attacks is a practical challenge in many artificial intelligence applications. A recent line of work shows that the use of randomization in adversarial training is the key to find optimal strategies against adversarial example attacks. However, in a fully randomized setting where both the defender and the attacker can use randomized strategies, there are no efficient algorithm for finding such an optimal strategy. To fill the gap, we propose the first algorithm of its kind, called FRAT, which models the problem with a new infinite-dimensional continuous-time flow on probability distribution spaces. FRAT maintains a lightweight mixture of models for the defender, with flexibility to efficiently update mixing weights and model parameters at each iteration. Furthermore, FRAT utilizes lightweight sampling subroutines to construct a random strategy for the attacker. We prove that the continuous-time limit of FRAT converges to a mixed Nash equilibria in a zero-sum game formed by a defender and an attacker. Experimental results also demonstrate the efficiency of FRAT on CIFAR-10 and CIFAR-100 datasets.

We present DiffXPBD, a novel and efficient analytical formulation for the differentiable position-based simulation of compliant constrained dynamics (XPBD). Our proposed method allows computation of gradients of numerous parameters with respect to a goal function simultaneously leveraging a performant simulation model. The method is efficient, thus enabling differentiable simulations of high resolution geometries and degrees of freedom (DoFs). Collisions are naturally included in the framework. Our differentiable model allows a user to easily add additional optimization variables. Every control variable gradient requires the computation of only a few partial derivatives which can be computed using automatic differentiation code. We demonstrate the efficacy of the method with examples such as elastic material parameter estimation, initial value optimization, optimizing for underlying body shape and pose by only observing the clothing, and optimizing a time-varying external force sequence to match sparse keyframe shapes at specific times. Our approach demonstrates excellent efficiency and we demonstrate this on high resolution meshes with optimizations involving over 26 million degrees of freedom. Making an existing solver differentiable requires only a few modifications and the model is compatible with both modern CPU and GPU multi-core hardware.

Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.

The growing energy and performance costs of deep learning have driven the community to reduce the size of neural networks by selectively pruning components. Similarly to their biological counterparts, sparse networks generalize just as well, if not better than, the original dense networks. Sparsity can reduce the memory footprint of regular networks to fit mobile devices, as well as shorten training time for ever growing networks. In this paper, we survey prior work on sparsity in deep learning and provide an extensive tutorial of sparsification for both inference and training. We describe approaches to remove and add elements of neural networks, different training strategies to achieve model sparsity, and mechanisms to exploit sparsity in practice. Our work distills ideas from more than 300 research papers and provides guidance to practitioners who wish to utilize sparsity today, as well as to researchers whose goal is to push the frontier forward. We include the necessary background on mathematical methods in sparsification, describe phenomena such as early structure adaptation, the intricate relations between sparsity and the training process, and show techniques for achieving acceleration on real hardware. We also define a metric of pruned parameter efficiency that could serve as a baseline for comparison of different sparse networks. We close by speculating on how sparsity can improve future workloads and outline major open problems in the field.

Since hardware resources are limited, the objective of training deep learning models is typically to maximize accuracy subject to the time and memory constraints of training and inference. We study the impact of model size in this setting, focusing on Transformer models for NLP tasks that are limited by compute: self-supervised pretraining and high-resource machine translation. We first show that even though smaller Transformer models execute faster per iteration, wider and deeper models converge in significantly fewer steps. Moreover, this acceleration in convergence typically outpaces the additional computational overhead of using larger models. Therefore, the most compute-efficient training strategy is to counterintuitively train extremely large models but stop after a small number of iterations. This leads to an apparent trade-off between the training efficiency of large Transformer models and the inference efficiency of small Transformer models. However, we show that large models are more robust to compression techniques such as quantization and pruning than small models. Consequently, one can get the best of both worlds: heavily compressed, large models achieve higher accuracy than lightly compressed, small models.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.