Sharpness-Aware Minimization (SAM) is an optimizer that takes a descent step based on the gradient at a perturbation $y_t = x_t + \rho \frac{\nabla f(x_t)}{\lVert \nabla f(x_t) \rVert}$ of the current point $x_t$. Existing studies prove convergence of SAM for smooth functions, but they do so by assuming decaying perturbation size $\rho$ and/or no gradient normalization in $y_t$, which is detached from practice. To address this gap, we study deterministic/stochastic versions of SAM with practical configurations (i.e., constant $\rho$ and gradient normalization in $y_t$) and explore their convergence properties on smooth functions with (non)convexity assumptions. Perhaps surprisingly, in many scenarios, we find out that SAM has limited capability to converge to global minima or stationary points. For smooth strongly convex functions, we show that while deterministic SAM enjoys tight global convergence rates of $\tilde \Theta(\frac{1}{T^2})$, the convergence bound of stochastic SAM suffers an inevitable additive term $O(\rho^2)$, indicating convergence only up to neighborhoods of optima. In fact, such $O(\rho^2)$ factors arise for stochastic SAM in all the settings we consider, and also for deterministic SAM in nonconvex cases; importantly, we prove by examples that such terms are unavoidable. Our results highlight vastly different characteristics of SAM with vs. without decaying perturbation size or gradient normalization, and suggest that the intuitions gained from one version may not apply to the other.
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We introduce a framework for intrinsic latent diffusion models operating directly on the surfaces of 3D shapes, with the goal of synthesizing high-quality textures. Our approach is underpinned by two contributions: field latents, a latent representation encoding textures as discrete vector fields on the mesh vertices, and field latent diffusion models, which learn to denoise a diffusion process in the learned latent space on the surface. We consider a single-textured-mesh paradigm, where our models are trained to generate variations of a given texture on a mesh. We show the synthesized textures are of superior fidelity compared those from existing single-textured-mesh generative models. Our models can also be adapted for user-controlled editing tasks such as inpainting and label-guided generation. The efficacy of our approach is due in part to the equivariance of our proposed framework under isometries, allowing our models to seamlessly reproduce details across locally similar regions and opening the door to a notion of generative texture transfer.
Over-the-Air (OtA) computation is a newly emerged concept for computing functions of data from distributed nodes by taking advantage of the wave superposition property of wireless channels. Despite its advantage in communication efficiency, OtA computation is associated with significant security and privacy concerns that have so far not been thoroughly investigated, especially in the case of active attacks. In this paper, we propose and evaluate a detection scheme against active attacks in OtA computation systems. More explicitly, we consider an active attacker which is an external node sending random or misleading data to alter the aggregated data received by the server. To detect the presence of the attacker, in every communication period, legitimate users send some dummy samples in addition to the real data. We propose a detector design that relies on the existence of a shared secret only known by the legitimate users and the server, that can be used to hide the transmitted signal in a secret subspace. After the server projects the received vector back to the original subspace, the dummy samples can be used to detect active attacks. We show that this design achieves good detection performance for a small cost in terms of channel resources.
The major advantage of reduced magnetic vector potential formulations (RMVPs) is that complicated coil structures do not need to be resolved by a computational mesh. Instead, they are modeled by thin wires, whose source field is included into the simulation model along Biot-Savart's law. Such an approach has already been successfully employed in ROXIE for the simulation of superconducting Large Hadron Collider magnets at CERN. This work presents an updated RMVP approach, which significantly outperforms the original method. The updated formulation is postulated, implemented, verified, compared to the original formulation, and applied for the simulation of a quadrupole magnet. The promising results of this work encourage further investigation towards an updated simulation framework for next-generation accelerator magnets.
Representing a polygon using a set of simple shapes has numerous applications in different use-case scenarios. We consider the problem of covering the interior of a rectilinear polygon with holes by a set of area-weighted, axis-aligned rectangles such that the total weight of the rectangles in the cover is minimized. Already the unit-weight case is known to be NP-hard and the general problem has, to the best of our knowledge, not been studied experimentally before. We show a new basic property of optimal solutions of the weighted problem. This allows us to speed up existing algorithms for the unit-weight case, obtain an improved ILP formulation for both the weighted and unweighted problem, and develop several approximation algorithms and heuristics for the weighted case. All our algorithms are evaluated in a large experimental study on 186 837 polygons combined with six cost functions, which provides evidence that our algorithms are both fast and yield close-to-optimal solutions in practice.
Macro-level modeling is still the dominant approach in many demographic applications because of its simplicity. Individual-level models, on the other hand, provide a more comprehensive understanding of observed patterns; however, their estimation using real data has remained a challenge. The approach we introduce in this article attempts to overcome this limitation. Using likelihood-free inference techniques, we show that it is possible to estimate the parameters of a simple but demographically interpretable individual-level model of the reproductive process from a set of aggregate fertility rates. By estimating individual-level quantities from widely available aggregate data, this approach can contribute to a better understanding of reproductive behavior and its driving mechanisms. It also allows for a more direct link between individual-level and population-level processes. We illustrate our approach using data from three natural fertility populations.
An approach for encoding abstract dialectical frameworks and their semantics into classical higher-order logic is presented. Important properties and semantic relationships are formally encoded and proven using the proof assistant Isabelle/HOL. This approach allows for the computer-assisted analysis of abstract dialectical frameworks using automated and interactive reasoning tools within a uniform logic environment. Exemplary applications include the formal analysis and verification of meta-theoretical properties, and the generation of interpretations and extensions under specific semantic constraints.
In LiDAR-based 3D object detection for autonomous driving, the ratio of the object size to input scene size is significantly smaller compared to 2D detection cases. Overlooking this difference, many 3D detectors directly follow the common practice of 2D detectors, which downsample the feature maps even after quantizing the point clouds. In this paper, we start by rethinking how such multi-stride stereotype affects the LiDAR-based 3D object detectors. Our experiments point out that the downsampling operations bring few advantages, and lead to inevitable information loss. To remedy this issue, we propose Single-stride Sparse Transformer (SST) to maintain the original resolution from the beginning to the end of the network. Armed with transformers, our method addresses the problem of insufficient receptive field in single-stride architectures. It also cooperates well with the sparsity of point clouds and naturally avoids expensive computation. Eventually, our SST achieves state-of-the-art results on the large scale Waymo Open Dataset. It is worth mentioning that our method can achieve exciting performance (83.8 LEVEL 1 AP on validation split) on small object (pedestrian) detection due to the characteristic of single stride. Codes will be released at //github.com/TuSimple/SST
Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.
Deep Learning (DL) is vulnerable to out-of-distribution and adversarial examples resulting in incorrect outputs. To make DL more robust, several posthoc anomaly detection techniques to detect (and discard) these anomalous samples have been proposed in the recent past. This survey tries to provide a structured and comprehensive overview of the research on anomaly detection for DL based applications. We provide a taxonomy for existing techniques based on their underlying assumptions and adopted approaches. We discuss various techniques in each of the categories and provide the relative strengths and weaknesses of the approaches. Our goal in this survey is to provide an easier yet better understanding of the techniques belonging to different categories in which research has been done on this topic. Finally, we highlight the unsolved research challenges while applying anomaly detection techniques in DL systems and present some high-impact future research directions.
Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.
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