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1. A Deeper Look at 3D Shape Classifiers

   Su JC., Gadelha M. (January 2019, Computer Vision – ECCV 2018 Workshops. ECCV 2018. Lecture Notes in Computer Science)

   We investigate the role of representations and architectures for classifying 3D shapes in terms of their computational efficiency, generalization, and robustness to adversarial transformations. By varying the number of training examples and employing cross-modal transfer learning we study the role of initialization of existing deep architectures for 3D shape classification. Our analysis shows that multiview methods continue to offer the best generalization even without pretraining on large labeled image datasets, and even when trained on simplified inputs such as binary silhouettes. Furthermore, the performance of voxel-based 3D convolutional networks and point-based architectures can be improved via cross-modal transfer from image representations. Finally, we analyze the robustness of 3D shape classifiers to adversarial transformations and present a novel approach for generating adversarial perturbations of a 3D shape for multiview classifiers using a differentiable renderer. We find that point-based networks are more robust to point position perturbations while voxel-based and multiview networks are easily fooled with the addition of imperceptible noise to the input. 

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2. Bridging multitask representational geometry and intrinsic connectivity in the human brain

   Chakravarthula, Lakshman; Tzalavras, Alexandros; Ito, Takuya; Cole, Michael (August 2024, Cognitive Computational Neuroscience)

   Representational geometry and connectivity-based studies offer complementary insights into neural information processing, but it is unclear how representations and networks interact to generate neural information. Using a multi-task fMRI dataset, we investigate the role of intrinsic connectivity in shaping diverse representational geometries across the human cortex. Activity flow modeling, which generates neural activity based on connectivity-weighted propagation from other regions, successfully recreated similarity structure and a compression-then-expansion pattern of task representation dimensionality. We introduce a novel measure, convergence, quantifying the degree to which connectivity converges onto target regions. As hypothesized, convergence corresponded with compression of representations and helped explain the observed compression-then-expansion pattern of task representation dimensionality along the cortical hierarchy. These results underscore the generative role of intrinsic connectivity in sculpting representational geometries and suggest that structured connectivity properties, such as convergence, contribute to representational transformations. By bridging representational geometry and connectivity-based frameworks, this work offers a more unified understanding of neural information processing and the computational relevance of brain architecture. 

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3. What Can the Neural Tangent Kernel Tell Us About Adversarial Robustness?

   Tsilivis, Nikolaos; Kempe, Julia (October 2022, NeurIPS)

   The adversarial vulnerability of neural nets, and subsequent techniques to create robust models have attracted significant attention; yet we still lack a full understanding of this phenomenon. Here, we study adversarial examples of trained neural networks through analytical tools afforded by recent theory advances connecting neural networks and kernel methods, namely the Neural Tangent Kernel (NTK), following a growing body of work that leverages the NTK approximation to successfully analyze important deep learning phenomena and design algorithms for new applications. We show how NTKs allow to generate adversarial examples in a ``training-free'' fashion, and demonstrate that they transfer to fool their finite-width neural net counterparts in the ``lazy'' regime. We leverage this connection to provide an alternative view on robust and non-robust features, which have been suggested to underlie the adversarial brittleness of neural nets. Specifically, we define and study features induced by the eigendecomposition of the kernel to better understand the role of robust and non-robust features, the reliance on both for standard classification and the robustness-accuracy trade-off. We find that such features are surprisingly consistent across architectures, and that robust features tend to correspond to the largest eigenvalues of the model, and thus are learned early during training. Our framework allows us to identify and visualize non-robust yet useful features. Finally, we shed light on the robustness mechanism underlying adversarial training of neural nets used in practice: quantifying the evolution of the associated empirical NTK, we demonstrate that its dynamics falls much earlier into the ``lazy'' regime and manifests a much stronger form of the well known bias to prioritize learning features within the top eigenspaces of the kernel, compared to standard training. 

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4. Benefits of Overparameterized Convolutional Residual Networks: Function Approximation under Smoothness Constraint

   Liu, Hao; Chen, Minshuo; Er, Siawpeng; Liao, Wenjing; Zhang, Tong; Zhao, Tuo (January 2022, International Conference on Machine Learning)

   Overparameterized neural networks enjoy great representation power on complex data, and more importantly yield sufficiently smooth output, which is crucial to their generalization and robustness. Most existing function approximation theories suggest that with sufficiently many parameters, neural networks can well approximate certain classes of functions in terms of the function value. The neural network themselves, however, can be highly nonsmooth. To bridge this gap, we take convolutional residual networks (ConvResNets) as an example, and prove that large ConvResNets can not only approximate a target function in terms of function value, but also exhibit sufficient first-order smoothness. Moreover, we extend our theory to approximating functions supported on a low-dimensional manifold. Our theory partially justifies the benefits of using deep and wide networks in practice. Numerical experiments on adversarial robust image classification are provided to support our theory. 

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5. Adjoint dynamics of stable limit cycle neural networks

   Sokol, P.; Jordan, I.; Kadile, E.; Park, I. M. (October 2019, Asilomar Conference on Signals, Systems and Computers)

   Exploding and vanishing gradient are both major problems often faced when an artificial neural network is trained with gradient descent. Inspired by the ubiquity and robustness of nonlinear oscillations in biological neural systems, we investigate the properties of their artificial counterpart, the stable limit cycle neural networks. Using a continuous time dynamical system interpretation of neural networks and backpropagation, we show that stable limit cycle neural networks have non-exploding gradients, and at least one effective non-vanishing gradient dimension. We conjecture that limit cycles can support the learning of long temporal dependence in both biological and artificial neural networks. 

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