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1. Issues in the Reproducibility of Deep Learning Results

   https://doi.org/10.1109/SPMB47826.2019.9037840  

   Jean-Paul, S. ; Elseify, T. ; Obeid, I. ; Picone, J. ( December 2019 , IEEE Signal Processing in Medicine and Biology Symposium (SPMB))

   Obeid, I. ; Selesnik, I. ; Picone, J. (Ed.)

   The Neuronix high-performance computing cluster allows us to conduct extensive machine learning experiments on big data [1]. This heterogeneous cluster uses innovative scheduling technology, Slurm [2], that manages a network of CPUs and graphics processing units (GPUs). The GPU farm consists of a variety of processors ranging from low-end consumer grade devices such as the Nvidia GTX 970 to higher-end devices such as the GeForce RTX 2080. These GPUs are essential to our research since they allow extremely compute-intensive deep learning tasks to be executed on massive data resources such as the TUH EEG Corpus [2]. We use TensorFlow [3] as the core machine learning library for our deep learning systems, and routinely employ multiple GPUs to accelerate the training process. Reproducible results are essential to machine learning research. Reproducibility in this context means the ability to replicate an existing experiment – performance metrics such as error rates should be identical and floating-point calculations should match closely. Three examples of ways we typically expect an experiment to be replicable are: (1) The same job run on the same processor should produce the same results each time it is run. (2) A job run on a CPU and GPU should produce identical results. (3) A job should produce comparable results if the data is presented in a different order. System optimization requires an ability to directly compare error rates for algorithms evaluated under comparable operating conditions. However, it is a difficult task to exactly reproduce the results for large, complex deep learning systems that often require more than a trillion calculations per experiment [5]. This is a fairly well-known issue and one we will explore in this poster. Researchers must be able to replicate results on a specific data set to establish the integrity of an implementation. They can then use that implementation as a baseline for comparison purposes. A lack of reproducibility makes it very difficult to debug algorithms and validate changes to the system. Equally important, since many results in deep learning research are dependent on the order in which the system is exposed to the data, the specific processors used, and even the order in which those processors are accessed, it becomes a challenging problem to compare two algorithms since each system must be individually optimized for a specific data set or processor. This is extremely time-consuming for algorithm research in which a single run often taxes a computing environment to its limits. Well-known techniques such as cross-validation [5,6] can be used to mitigate these effects, but this is also computationally expensive. These issues are further compounded by the fact that most deep learning algorithms are susceptible to the way computational noise propagates through the system. GPUs are particularly notorious for this because, in a clustered environment, it becomes more difficult to control which processors are used at various points in time. Another equally frustrating issue is that upgrades to the deep learning package, such as the transition from TensorFlow v1.9 to v1.13, can also result in large fluctuations in error rates when re-running the same experiment. Since TensorFlow is constantly updating functions to support GPU use, maintaining an historical archive of experimental results that can be used to calibrate algorithm research is quite a challenge. This makes it very difficult to optimize the system or select the best configurations. The overall impact of all of these issues described above is significant as error rates can fluctuate by as much as 25% due to these types of computational issues. Cross-validation is one technique used to mitigate this, but that is expensive since you need to do multiple runs over the data, which further taxes a computing infrastructure already running at max capacity. GPUs are preferred when training a large network since these systems train at least two orders of magnitude faster than CPUs [7]. Large-scale experiments are simply not feasible without using GPUs. However, there is a tradeoff to gain this performance. Since all our GPUs use the NVIDIA CUDA® Deep Neural Network library (cuDNN) [8], a GPU-accelerated library of primitives for deep neural networks, it adds an element of randomness into the experiment. When a GPU is used to train a network in TensorFlow, it automatically searches for a cuDNN implementation. NVIDIA’s cuDNN implementation provides algorithms that increase the performance and help the model train quicker, but they are non-deterministic algorithms [9,10]. Since our networks have many complex layers, there is no easy way to avoid this randomness. Instead of comparing each epoch, we compare the average performance of the experiment because it gives us a hint of how our model is performing per experiment, and if the changes we make are efficient. In this poster, we will discuss a variety of issues related to reproducibility and introduce ways we mitigate these effects. For example, TensorFlow uses a random number generator (RNG) which is not seeded by default. TensorFlow determines the initialization point and how certain functions execute using the RNG. The solution for this is seeding all the necessary components before training the model. This forces TensorFlow to use the same initialization point and sets how certain layers work (e.g., dropout layers). However, seeding all the RNGs will not guarantee a controlled experiment. Other variables can affect the outcome of the experiment such as training using GPUs, allowing multi-threading on CPUs, using certain layers, etc. To mitigate our problems with reproducibility, we first make sure that the data is processed in the same order during training. Therefore, we save the data from the last experiment and to make sure the newer experiment follows the same order. If we allow the data to be shuffled, it can affect the performance due to how the model was exposed to the data. We also specify the float data type to be 32-bit since Python defaults to 64-bit. We try to avoid using 64-bit precision because the numbers produced by a GPU can vary significantly depending on the GPU architecture [11-13]. Controlling precision somewhat reduces differences due to computational noise even though technically it increases the amount of computational noise. We are currently developing more advanced techniques for preserving the efficiency of our training process while also maintaining the ability to reproduce models. In our poster presentation we will demonstrate these issues using some novel visualization tools, present several examples of the extent to which these issues influence research results on electroencephalography (EEG) and digital pathology experiments and introduce new ways to manage such computational issues. 

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2. Robustness Certificates for Implicit Neural Networks: A Mixed Monotone Contractive Approach

   Jafarpour, S ; Abate, M. ; Davydov A. ; Bullo, F. ; Coogan S. ( May 2022 , Proceedings of The 4th Annual Learning for Dynamics and Control Conference, PMLR)

   Implicit neural networks are a general class of learning models that replace the layers in traditional feedforward models with implicit algebraic equations. Compared to traditional learning models, implicit networks offer competitive performance and reduced memory consumption. However, they can remain brittle with respect to input adversarial perturbations. This paper proposes a theoretical and computational framework for robustness verification of implicit neural networks; our framework blends together mixed monotone systems theory and contraction theory. First, given an implicit neural network, we introduce a related embedded network and show that, given an infinity-norm box constraint on the input, the embedded network provides an infinity-norm box overapproximation for the output of the original network. Second, using infinity-matrix measures, we propose sufficient conditions for well-posedness of both the original and embedded system and design an iterative algorithm to compute the infinity-norm box robustness margins for reachability and classification problems. Third, of independent value, we show that employing a suitable relative classifier variable in our analysis will lead to tighter bounds on the certified adversarial robustness in classification problems. Finally, we perform numerical simulations on a Non-Euclidean Monotone Operator Network (NEMON) trained on the MNIST dataset. In these simulations, we compare the accuracy and run time of our mixed monotone contractive approach with the existing robustness verification approaches in the literature for estimating the certified adversarial robustness. 

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3. Understanding Dynamics of Nonlinear Representation Learning and Its Application

   https://doi.org/10.1162/neco_a_01483  

   Kawaguchi, Kenji ; Zhang, Linjun ; Deng, Zhun ( March 2022 , Neural Computation)

   Abstract Representations of the world environment play a crucial role in artificial intelligence. It is often inefficient to conduct reasoning and inference directly in the space of raw sensory representations, such as pixel values of images. Representation learning allows us to automatically discover suitable representations from raw sensory data. For example, given raw sensory data, a deep neural network learns nonlinear representations at its hidden layers, which are subsequently used for classification (or regression) at its output layer. This happens implicitly during training through minimizing a supervised or unsupervised loss. In this letter, we study the dynamics of such implicit nonlinear representation learning. We identify a pair of a new assumption and a novel condition, called the on-model structure assumption and the data architecture alignment condition. Under the on-model structure assumption, the data architecture alignment condition is shown to be sufficient for the global convergence and necessary for global optimality. Moreover, our theory explains how and when increasing network size does and does not improve the training behaviors in the practical regime. Our results provide practical guidance for designing a model structure; for example, the on-model structure assumption can be used as a justification for using a particular model structure instead of others. As an application, we then derive a new training framework, which satisfies the data architecture alignment condition without assuming it by automatically modifying any given training algorithm dependent on data and architecture. Given a standard training algorithm, the framework running its modified version is empirically shown to maintain competitive (practical) test performances while providing global convergence guarantees for deep residual neural networks with convolutions, skip connections, and batch normalization with standard benchmark data sets, including MNIST, CIFAR-10, CIFAR-100, Semeion, KMNIST, and SVHN. 

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4. Interpretable Deep Learning for Spatial Analysis of Severe Hailstorms

   https://doi.org/10.1175/MWR-D-18-0316.1  

   Gagne II, David John ; Haupt, Sue Ellen ; Nychka, Douglas W. ; Thompson, Gregory ( July 2019 , Monthly Weather Review)

   Deep learning models, such as convolutional neural networks, utilize multiple specialized layers to encode spatial patterns at different scales. In this study, deep learning models are compared with standard machine learning approaches on the task of predicting the probability of severe hail based on upper-air dynamic and thermodynamic fields from a convection-allowing numerical weather prediction model. The data for this study come from patches surrounding storms identified in NCAR convection-allowing ensemble runs from 3 May to 3 June 2016. The machine learning models are trained to predict whether the simulated surface hail size from the Thompson hail size diagnostic exceeds 25 mm over the hour following storm detection. A convolutional neural network is compared with logistic regressions using input variables derived from either the spatial means of each field or principal component analysis. The convolutional neural network statistically significantly outperforms all other methods in terms of Brier skill score and area under the receiver operator characteristic curve. Interpretation of the convolutional neural network through feature importance and feature optimization reveals that the network synthesized information about the environment and storm morphology that is consistent with our understanding of hail growth, including large lapse rates and a wind shear profile that favors wide updrafts. Different neurons in the network also record different storm modes, and the magnitude of the output of those neurons is used to analyze the spatiotemporal distributions of different storm modes in the NCAR ensemble.

    

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5. NON-LINEAR OPERATOR APPROXIMATIONS FOR INITIAL VALUE PROBLEMS

   Gupta, Gaurav ; Xiao, Xiongye ; Balan, Radu ; Bogdan, Paul ( April 2022 , International Conference on Learning Representations (ICLR))

   Time-evolution of partial differential equations is fundamental for modeling several complex dynamical processes and events forecasting, but the operators associated with such problems are non-linear. We propose a Pad´e approximation based exponential neural operator scheme for efficiently learning the map between a given initial condition and the activities at a later time. The multiwavelets bases are used for space discretization. By explicitly embedding the exponential operators in the model, we reduce the training parameters and make it more data-efficient which is essential in dealing with scarce and noisy real-world datasets. The Pad´e exponential operator uses a recurrent structure with shared parameters to model the non-linearity compared to recent neural operators that rely on using multiple linear operator layers in succession. We show theoretically that the gradients associated with the recurrent Pad´e network are bounded across the recurrent horizon. We perform experiments on non-linear systems such as Korteweg-de Vries (KdV) and Kuramoto–Sivashinsky (KS) equations to show that the proposed approach achieves the best performance and at the same time is data-efficient. We also show that urgent real-world problems like epidemic forecasting (for example, COVID- 19) can be formulated as a 2D time-varying operator problem. The proposed Pad´e exponential operators yield better prediction results (53% (52%) better MAE than best neural operator (non-neural operator deep learning model)) compared to state-of-the-art forecasting models. 

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