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1. Adversarial Robustness of Flow-Based Generative Models

   Pope, Phillip ; Balaji, Yogesh ; Feizi, Soheil ( January 2020 , International Conference on Artificial Intelligence and Statistics (AISTATS))

   null (Ed.)

   Flow-based generative models leverage invertible generator functions to fit a distribution to the training data using maximum likelihood. Despite their use in several application domains, robustness of these models to adversarial attacks has hardly been explored. In this paper, we study adversarial robustness of flow-based generative models both theoretically (for some simple models) and empirically (for more complex ones). First, we consider a linear flow-based generative model and compute optimal sample-specific and universal adversarial perturbations that maximally decrease the likelihood scores. Using this result, we study the robustness of the well-known adversarial training procedure, where we characterize the fundamental trade-off between model robustness and accuracy. Next, we empirically study the robustness of two prominent deep, non-linear, flow-based generative models, namely GLOW and RealNVP. We design two types of adversarial attacks; one that minimizes the likelihood scores of in-distribution samples, while the other that maximizes the likelihood scores of out-of-distribution ones. We find that GLOW and RealNVP are extremely sensitive to both types of attacks. Finally, using a hybrid adversarial training procedure, we significantly boost the robustness of these generative models. 

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2. FlexCNN: An End-to-End Framework for Composing CNN Accelerators on FPGA

   https://doi.org/10.1145/3570928  

   Basalama, Suhail ; Sohrabizadeh, Atefeh ; Wang, Jie ; Guo, Licheng ; Cong, Jason ( December 2022 , ACM Transactions on Reconfigurable Technology and Systems)

   With reduced data reuse and parallelism, recent convolutional neural networks (CNNs) create new challenges for FPGA acceleration. Systolic arrays (SAs) are efficient, scalable architectures for convolutional layers, but without proper optimizations, their efficiency drops dramatically for reasons: 1) the different dimensions within same-type layers, 2) the different convolution layers especially transposed and dilated convolutions, and 3) CNN’s complex dataflow graph. Furthermore, significant overheads arise when integrating FPGAs into machine learning frameworks. Therefore, we present a flexible, composable architecture called FlexCNN, which delivers high computation efficiency by employing dynamic tiling, layer fusion, and data layout optimizations. Additionally, we implement a novel versatile SA to process normal, transposed, and dilated convolutions efficiently. FlexCNN also uses a fully-pipelined software-hardware integration that alleviates the software overheads. Moreover, with an automated compilation flow, FlexCNN takes a CNN in the ONNX representation, performs a design space exploration, and generates an FPGA accelerator. The framework is tested using three complex CNNs: OpenPose, U-Net, and E-Net. The architecture optimizations achieve 2.3 × performance improvement. Compared to a standard SA, the versatile SA achieves close-to-ideal speedups, with up to 15.98 × and 13.42 × for transposed and dilated convolutions, with a 6% average area overhead. The pipelined integration leads to a 5 × speedup for OpenPose. 

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3. Tree convolution for probability distributions with unbounded support

   Davis, Ethan ; Jekel, David ; Wang, Zhichao ( January 2021 , Alea)

   We develop the complex-analytic viewpoint on the tree convolutions studied by the second author and Weihua Liu in Jekel and Liu (2020), which generalize the free, boolean, monotone, and orthogonal convolutions. In particular, for each rooted subtree T of the N-regular tree (with vertices labeled by alternating strings), we define the convolution \boxplus_T (µ1, . . . , µN) for arbitrary probability measures µ1, . . . , µN on R using a certain fixed-point equation for the Cauchy transforms. The convolution operations respect the operad structure of the tree operad from Jekel and Liu (2020). We prove a general limit theorem for iterated T -free convolution similar to Bercovici and Pata’s results in the free case (Bercovici and Pata 1999), and we deduce limit theorems for measures in the domain of attraction of each of the classical stable laws. 

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4. Translation and rotation equivariant normalizing flow (TRENF) for optimal cosmological analysis

   https://doi.org/10.1093/mnras/stac2010  

   Dai, Biwei ; Seljak, Uroš ( July 2022 , Monthly Notices of the Royal Astronomical Society)

   Our Universe is homogeneous and isotropic, and its perturbations obey translation and rotation symmetry. In this work, we develop translation and rotation equivariant normalizing flow (TRENF), a generative normalizing flow (NF) model which explicitly incorporates these symmetries, defining the data likelihood via a sequence of Fourier space-based convolutions and pixel-wise non-linear transforms. TRENF gives direct access to the high dimensional data likelihood p(x|y) as a function of the labels y, such as cosmological parameters. In contrast to traditional analyses based on summary statistics, the NF approach has no loss of information since it preserves the full dimensionality of the data. On Gaussian random fields, the TRENF likelihood agrees well with the analytical expression and saturates the Fisher information content in the labels y. On non-linear cosmological overdensity fields from N-body simulations, TRENF leads to significant improvements in constraining power over the standard power spectrum summary statistic. TRENF is also a generative model of the data, and we show that TRENF samples agree well with the N-body simulations it trained on, and that the inverse mapping of the data agrees well with a Gaussian white noise both visually and on various summary statistics: when this is perfectly achieved the resulting p(x|y) likelihood analysis becomes optimal. Finally, we develop a generalization of this model that can handle effects that break the symmetry of the data, such as the survey mask, which enables likelihood analysis on data without periodic boundaries.

    

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5. Branes and symmetries for N=3 S-folds

   https://doi.org/10.1007/JHEP09(2023)005  

   Etheredge, Muldrow ; Etxebarria, Iñaki García ; Heidenreich, Ben ; Rauch, Sebastian ( September 2023 , Journal of High Energy Physics)

   We describe the higher-form and non-invertible symmetries of 4d N=3 S-folds using the brane dynamics of their holographic duals. In cases with enhancement to N=4 supersymmetry, our analysis reproduces the known field theory results of Aharony, Seiberg and Tachikawa, and is compatible with the effective action recently given by Bergman and Hirano. Likewise, for two specific N=3 theories for which Zafrir has conjectured N=1 Lagrangians our results agree with those implied by the Lagrangian description. In all other cases, our results imply novel predictions about the symmetries of the corresponding N=3 field theories. 

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