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1. Robust Models Are More Interpretable Because Attributions Look Normal

   Wang, Zifan ; Fredrikson, Matt ; Datta, Anupam ( July 2022 , Proceedings of Machine Learning Research)

   Chaudhuri, Kamalika ; Jegelka, Stefanie ; Song, Le ; Szepesvari, Csaba ; Niu, Gang ; Sabato, Sivan (Ed.)

   Recent work has found that adversarially-robust deep networks used for image classification are more interpretable: their feature attributions tend to be sharper, and are more concentrated on the objects associated with the image’s ground- truth class. We show that smooth decision boundaries play an important role in this enhanced interpretability, as the model’s input gradients around data points will more closely align with boundaries’ normal vectors when they are smooth. Thus, because robust models have smoother boundaries, the results of gradient- based attribution methods, like Integrated Gradients and DeepLift, will capture more accurate information about nearby decision boundaries. This understanding of robust interpretability leads to our second contribution: boundary attributions, which aggregate information about the normal vectors of local decision bound- aries to explain a classification outcome. We show that by leveraging the key fac- tors underpinning robust interpretability, boundary attributions produce sharper, more concentrated visual explanations{—}even on non-robust models. 

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2. A framework for machine learning of model error in dynamical systems

   https://doi.org/10.1090/cams/10  

   Levine, Matthew ; Stuart, Andrew ( October 2022 , Communications of the American Mathematical Society)

   The development of data-informed predictive models for dynamical systems is of widespread interest in many disciplines. We present a unifying framework for blending mechanistic and machine-learning approaches to identify dynamical systems from noisily and partially observed data. We compare pure data-driven learning with hybrid models which incorporate imperfect domain knowledge, referring to the discrepancy between an assumed truth model and the imperfect mechanistic model as model error. Our formulation is agnostic to the chosen machine learning model, is presented in both continuous- and discrete-time settings, and is compatible both with model errors that exhibit substantial memory and errors that are memoryless. First, we study memoryless linear (w.r.t. parametric-dependence) model error from a learning theory perspective, defining excess risk and generalization error. For ergodic continuous-time systems, we prove that both excess risk and generalization error are bounded above by terms that diminish with the square-root of T T , the time-interval over which training data is specified. Secondly, we study scenarios that benefit from modeling with memory, proving universal approximation theorems for two classes of continuous-time recurrent neural networks (RNNs): both can learn memory-dependent model error, assuming that it is governed by a finite-dimensional hidden variable and that, together, the observed and hidden variables form a continuous-time Markovian system. In addition, we connect one class of RNNs to reservoir computing, thereby relating learning of memory-dependent error to recent work on supervised learning between Banach spaces using random features. Numerical results are presented (Lorenz ’63, Lorenz ’96 Multiscale systems) to compare purely data-driven and hybrid approaches, finding hybrid methods less datahungry and more parametrically efficient. We also find that, while a continuous-time framing allows for robustness to irregular sampling and desirable domain- interpretability, a discrete-time framing can provide similar or better predictive performance, especially when data are undersampled and the vector field defining the true dynamics cannot be identified. Finally, we demonstrate numerically how data assimilation can be leveraged to learn hidden dynamics from noisy, partially-observed data, and illustrate challenges in representing memory by this approach, and in the training of such models. 

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3. Robust Attribution Regularization

   Chen, Jiefeng ; Wu, Xi ; Rastogi, Vaibhav ; Liang, Yingyu ; Jha, Somesh ( December 2019 , Conference on Neural Information Processing Systems)

   An emerging problem in trustworthy machine learning is to train models that pro- duce robust interpretations for their predictions. We take a step towards solving this problem through the lens of axiomatic attribution of neural networks. Our theory is grounded in the recent work, Integrated Gradients (IG) [STY17], in axiomatically attributing a neural network’s output change to its input change. We propose training objectives in classic robust optimization models to achieve robust IG attributions. Our objectives give principled generalizations of previous objectives designed for robust predictions, and they naturally degenerate to classic soft-margin training for one-layer neural networks. We also generalize previous theory and prove that the objectives for different robust optimization models are closely related. Experiments demonstrate the effectiveness of our method, and also point to intriguing problems which hint at the need for better optimization techniques or better neural network architectures for robust attribution training. 

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4. Model-assisted deep learning of rare extreme events from partial observations

   https://doi.org/10.1063/5.0077646  

   Asch, Anna ; J. Brady, Ethan ; Gallardo, Hugo ; Hood, John ; Chu, Bryan ; Farazmand, Mohammad ( April 2022 , Chaos: An Interdisciplinary Journal of Nonlinear Science)

   To predict rare extreme events using deep neural networks, one encounters the so-called small data problem because even long-term observations often contain few extreme events. Here, we investigate a model-assisted framework where the training data are obtained from numerical simulations, as opposed to observations, with adequate samples from extreme events. However, to ensure the trained networks are applicable in practice, the training is not performed on the full simulation data; instead, we only use a small subset of observable quantities, which can be measured in practice. We investigate the feasibility of this model-assisted framework on three different dynamical systems (Rössler attractor, FitzHugh–Nagumo model, and a turbulent fluid flow) and three different deep neural network architectures (feedforward, long short-term memory, and reservoir computing). In each case, we study the prediction accuracy, robustness to noise, reproducibility under repeated training, and sensitivity to the type of input data. In particular, we find long short-term memory networks to be most robust to noise and to yield relatively accurate predictions, while requiring minimal fine-tuning of the hyperparameters.

    

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5. Machine learning for parameter auto-tuning in molecular dynamics simulations: Efficient dynamics of ions near polarizable nanoparticles

   https://doi.org/10.1177/1094342019899457  

   Kadupitiya, JCS ; Fox, Geoffrey C ; Jadhao, Vikram ( May 2020 , The International Journal of High Performance Computing Applications)

   Simulating the dynamics of ions near polarizable nanoparticles (NPs) using coarse-grained models is extremely challenging due to the need to solve the Poisson equation at every simulation timestep. Recently, a molecular dynamics (MD) method based on a dynamical optimization framework bypassed this obstacle by representing the polarization charge density as virtual dynamic variables and evolving them in parallel with the physical dynamics of ions. We highlight the computational gains accessible with the integration of machine learning (ML) methods for parameter prediction in MD simulations by demonstrating how they were realized in MD simulations of ions near polarizable NPs. An artificial neural network–based regression model was integrated with MD simulation and predicted the optimal simulation timestep and optimization parameters characterizing the virtual system with 94.3% success. The ML-enabled auto-tuning of parameters generated accurate dynamics of ions for ≈ 10 million steps while improving the stability of the simulation by over an order of magnitude. The integration of ML-enhanced framework with hybrid Open Multi-Processing / Message Passing Interface (OpenMP/MPI) parallelization techniques reduced the computational time of simulating systems with thousands of ions and induced charges from thousands of hours to tens of hours, yielding a maximum speedup of ≈ 3 from ML-only acceleration and a maximum speedup of ≈ 600 from the combination of ML and parallel computing methods. Extraction of ionic structure in concentrated electrolytes near oil–water emulsions demonstrates the success of the method. The approach can be generalized to select optimal parameters in other MD applications and energy minimization problems. 

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