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The Crucial Role of Normalization in Sharpness-Aware Minimization

Yan Dai, Kwangjun Ahn, Suvrit Sra

Sharpness-Aware Minimization (SAM) is a recently proposed gradient-based optimizer (Foret et al., ICLR 2021) that greatly improves the prediction performance of deep neural networks. Consequently, there has been a surge of interest in explaining its empirical success. We focus, in particular, on understanding ***the role played by normalization***, a key component of the SAM updates. We theoretically and empirically study the effect of normalization in SAM for both convex and non-convex functions, revealing two key roles played by normalization: i) it helps in stabilizing the algorithm; and ii) it enables the algorithm to drift along a continuum (manifold) of minima -- a property identified by recent theoretical works that is the key to better performance. We further argue that these two properties of normalization make SAM robust against the choice of hyper-parameters, supporting the practicality of SAM. Our conclusions are backed by various experiments.

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CSOT: Curriculum and Structure-Aware Optimal Transport for Learning with Noisy Labels

Wanxing Chang, Ye Shi, Jingya Wang

Learning with noisy labels (LNL) poses a significant challenge in training a well-generalized model while avoiding overfitting to corrupted labels. Recent advances have achieved impressive performance by identifying clean labels and correcting corrupted labels for training. However, the current approaches rely heavily on the model’s predictions and evaluate each sample independently without considering either the global or local structure of the sample distribution. These limitations typically result in a suboptimal solution for the identification and correction processes, which eventually leads to models overfitting to incorrect labels. In this paper, we propose a novel optimal transport (OT) formulation, called Curriculum and Structure-aware Optimal Transport (CSOT). CSOT concurrently considers the inter- and intra-distribution structure of the samples to construct a robust denoising and relabeling allocator. During the training process, the allocator incrementally assigns reliable labels to a fraction of the samples with the highest confidence. These labels have both global discriminability and local coherence. Notably, CSOT is a new OT formulation with a nonconvex objective function and curriculum constraints, so it is not directly compatible with classical OT solvers. Here, we develop a lightspeed computational method that involves a scaling iteration within a generalized conditional gradient framework to solve CSOT efficiently. Extensive experiments demonstrate the superiority of our method over the current state-of-the-arts in LNL.

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A Robust and Opponent-Aware League Training Method for StarCraft II

Ruozi Huang, Xipeng Wu, Hongsheng Yu, Zhong Fan, Haobo Fu, Qiang Fu, Yang Wei

It is extremely difficult to train a superhuman Artificial Intelligence (AI) for games of similar size to StarCraft II. AlphaStar is the first AI that beat human professionals in the full game of StarCraft II, using a league training framework that is inspired by a game-theoretic approach. In this paper, we improve AlphaStar's league training in two significant aspects. We train goal-conditioned exploiters, whose abilities of spotting weaknesses in the main agent and the entire league are greatly improved compared to the unconditioned exploiters in AlphaStar. In addition, we endow the agents in the league with the new ability of opponent modeling, which makes the agent more responsive to the opponent's real-time strategy. Based on these improvements, we train a better and superhuman AI with orders of magnitude less resources than AlphaStar (see Table 1 for a full comparison). Considering the iconic role of StarCraft II in game AI research, we believe our method and results on StarCraft II provide valuable design principles on how one would utilize the general league training framework for obtaining a least-exploitable strategy in various, large-scale, real-world games.

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Riemannian SAM: Sharpness-Aware Minimization on Riemannian Manifolds

Jihun Yun, Eunho Yang

Contemporary advances in the field of deep learning have embarked upon an exploration of the underlying geometric properties of data, thus encouraging the investigation of techniques that consider general manifolds, for example, hyperbolic or orthogonal neural networks. However, the optimization algorithms for training such geometric deep learning models still remain highly under-explored. In this paper, we introduce Riemannian SAM by generalizing conventional Euclidean SAM to Riemannian manifolds. We successfully formulate the sharpness-aware minimization on Riemannian manifolds, leading to one of a novel instantiation, Lorentz SAM. In addition, SAM variants proposed in previous studies such as Fisher SAM can be derived as special examples under our Riemannian SAM framework. We provide the convergence analysis of Riemannian SAM under a less aggressively decaying ascent learning rate than Euclidean SAM. Our analysis serves as a theoretically sound contribution encompassing a diverse range of manifolds, also providing the guarantees for SAM variants such as Fisher SAM, whose convergence analyses are absent. Lastly, we illustrate the superiority of Riemannian SAM in terms of generalization over previous Riemannian optimization algorithms through experiments on knowledge graph completion and machine translation tasks.

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Affinity-Aware Graph Networks

Ameya Velingker, Ali Kemal Sinop, Ira Ktena, Petar Veličković, Sreenivas Gollapudi

Graph Neural Networks (GNNs) have emerged as a powerful technique for learning on relational data. Owing to the relatively limited number of message passing steps they perform—and hence a smaller receptive field—there has been significant interest in improving their expressivity by incorporating structural aspects of the underlying graph. In this paper, we explore the use of affinity measures as features in graph neural networks, in particular measures arising from random walks, including effective resistance, hitting and commute times. We propose message passing networks based on these features and evaluate their performance on a variety of node and graph property prediction tasks. Our architecture has low computational complexity, while our features are invariant to the permutations of the underlying graph. The measures we compute allow the network to exploit the connectivity properties of the graph, thereby allowing us to outperform relevant benchmarks for a wide variety of tasks, often with significantly fewer message passing steps. On one of the largest publicly available graph regression datasets, OGB-LSC-PCQM4Mv1, we obtain the best known single-model validation MAE at the time of writing.

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Practical Sharpness-Aware Minimization Cannot Converge All the Way to Optima

Dongkuk Si, Chulhee Yun

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 $\mathcal O(\rho^2)$, indicating convergence only up to neighborhoods of optima. In fact, such $\mathcal O(\rho^2)$ 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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Environment-Aware Dynamic Graph Learning for Out-of-Distribution Generalization

Haonan Yuan, Qingyun Sun, Xingcheng Fu, Ziwei Zhang, Cheng Ji, Hao Peng, Jianxin Li

Dynamic graph neural networks (DGNNs) are increasingly pervasive in exploiting spatio-temporal patterns on dynamic graphs. However, existing works fail to generalize under distribution shifts, which are common in real-world scenarios. As the generation of dynamic graphs is heavily influenced by latent environments, investigating their impacts on the out-of-distribution (OOD) generalization is critical. However, it remains unexplored with the following two major challenges: **(1)** How to properly model and infer the complex environments on dynamic graphs with distribution shifts? **(2)** How to discover invariant patterns given inferred spatio-temporal environments? To solve these challenges, we propose a novel **E**nvironment-**A**ware dynamic **G**raph **LE**arning (**EAGLE**) framework for OOD generalization by modeling complex coupled environments and exploiting spatio-temporal invariant patterns. Specifically, we first design the environment-aware EA-DGNN to model environments by multi-channel environments disentangling. Then, we propose an environment instantiation mechanism for environment diversification with inferred distributions. Finally, we discriminate spatio-temporal invariant patterns for out-of-distribution prediction by the invariant pattern recognition mechanism and perform fine-grained causal interventions node-wisely with a mixture of instantiated environment samples. Experiments on real-world and synthetic dynamic graph datasets demonstrate the superiority of our method against state-of-the-art baselines under distribution shifts. To the best of our knowledge, we are the first to study OOD generalization on dynamic graphs from the environment learning perspective.

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Normalization Layers Are All That Sharpness-Aware Minimization Needs

Maximilian Mueller, Tiffany Joyce Vlaar, David Rolnick, Matthias Hein

Sharpness-aware minimization (SAM) was proposed to reduce sharpness of minima and has been shown to enhance generalization performance in various settings. In this work we show that perturbing only the affine normalization parameters (typically comprising 0.1% of the total parameters) in the adversarial step of SAM can outperform perturbing all of the parameters. This finding generalizes to different SAM variants and both ResNet (Batch Normalization) and Vision Transformer (Layer Normalization) architectures. We consider alternative sparse perturbation approaches and find that these do not achieve similar performance enhancement at such extreme sparsity levels, showing that this behaviour is unique to the normalization layers. Although our findings reaffirm the effectiveness of SAM in improving generalization performance, they cast doubt on whether this is solely caused by reduced sharpness.

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Relative Entropic Optimal Transport: a (Prior-aware) Matching Perspective to (Unbalanced) Classification

Liangliang Shi, Haoyu Zhen, Gu Zhang, Junchi Yan

Classification is a fundamental problem in machine learning, and considerable efforts have been recently devoted to the demanding long-tailed setting due to its prevalence in nature. Departure from the Bayesian framework, this paper rethinks classification from a matching perspective by studying the matching probability between samples and labels with optimal transport (OT) formulation. Specifically, we first propose a new variant of optimal transport, called Relative Entropic Optimal Transport (RE-OT), which guides the coupling solution to a known prior information matrix. We gives some theoretical results and their proof for RE-OT and surprisingly find RE-OT can help to deblur for barycenter images. Then we adopt inverse RE-OT for training long-tailed data and find that the loss derived from RE-OT has a similar form to Softmax-based cross-entropy loss, indicating a close connection between optimal transport and classification and the potential for transferring concepts between these two academic fields, such as barycentric projection in OT, which can map the labels back to the feature space. We further derive an epoch-varying RE-OT loss, and do the experiments on unbalanced image classification, molecule classification, instance segmentation and representation learning. Experimental results show its effectiveness.

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SAME: Uncovering GNN Black Box with Structure-aware Shapley-based Multipiece Explanations

Ziyuan Ye, Rihan Huang, Qilin Wu, Quanying Liu

Post-hoc explanation techniques on graph neural networks (GNNs) provide economical solutions for opening the black-box graph models without model retraining. Many GNN explanation variants have achieved state-of-the-art explaining results on a diverse set of benchmarks, while they rarely provide theoretical analysis for their inherent properties and explanatory capability. In this work, we propose $\underline{\text{S}}$tructure-$\underline{\text{A}}$ware Shapley-based $\underline{\text{M}}$ultipiece $\underline{\text{E}}$xplanation (SAME) method to address the structure-aware feature interactions challenges for GNNs explanation. Specifically, SAME leverages an expansion-based Monte Carlo tree search to explore the multi-grained structure-aware connected substructure. Afterward, the explanation results are encouraged to be informative of the graph properties by optimizing the combination of distinct single substructures. With the consideration of fair feature interactions in the process of investigating multiple connected important substructures, the explanation provided by SAME has the potential to be as explainable as the theoretically optimal explanation obtained by the Shapley value within polynomial time. Extensive experiments on real-world and synthetic benchmarks show that SAME improves the previous state-of-the-art fidelity performance by 12.9\% on BBBP, 7.01\% on MUTAG, 42.3\% on Graph-SST2, 38.9\% on Graph-SST5, 11.3\% on BA-2Motifs and 18.2\% on BA-Shapes under the same testing condition. Code is available at https://github.com/same2023neurips/same.

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Fine-Grained Cross-View Geo-Localization Using a Correlation-Aware Homography Estimator

Xiaolong Wang, Runsen Xu, Zhuofan Cui, Zeyu Wan, Yu Zhang

In this paper, we introduce a novel approach to fine-grained cross-view geo-localization. Our method aligns a warped ground image with a corresponding GPS-tagged satellite image covering the same area using homography estimation. We first employ a differentiable spherical transform, adhering to geometric principles, to accurately align the perspective of the ground image with the satellite map. This transformation effectively places ground and aerial images in the same view and on the same plane, reducing the task to an image alignment problem. To address challenges such as occlusion, small overlapping range, and seasonal variations, we propose a robust correlation-aware homography estimator to align similar parts of the transformed ground image with the satellite image. Our method achieves sub-pixel resolution and meter-level GPS accuracy by mapping the center point of the transformed ground image to the satellite image using a homography matrix and determining the orientation of the ground camera using a point above the central axis. Operating at a speed of 30 FPS, our method outperforms state-of-the-art techniques, reducing the mean metric localization error by 21.3\% and 32.4\% in same-area and cross-area generalization tasks on the VIGOR benchmark, respectively, and by 34.4\% on the KITTI benchmark in same-area evaluation.

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Correlation Aware Sparsified Mean Estimation Using Random Projection

Shuli Jiang, Pranay Sharma, Gauri Joshi

We study the problem of communication-efficient distributed vector mean estimation, which is a commonly used subroutine in distributed optimization and Federated Learning (FL). Rand-$k$ sparsification is a commonly used technique to reduce communication cost, where each client sends $k < d$ of its coordinates to the server. However, Rand-$k$ is agnostic to any correlations, that might exist between clients in practical scenarios. The recently proposed Rand-$k$-Spatial estimator leverages the cross-client correlation information at the server to improve Rand-$k$'s performance. Yet, the performance of Rand-$k$-Spatial is suboptimal, and improving mean estimation is key to a faster convergence in distributed optimization. We propose the Rand-Proj-Spatial estimator with a more flexible encoding-decoding procedure, which generalizes the encoding of Rand-$k$ by projecting the client vectors to a random $k$-dimensional subspace. We utilize Subsampled Randomized Hadamard Transform (SRHT) as the projection matrix, and show that Rand-Proj-Spatial with SRHT outperforms Rand-$k$-Spatial, using the correlation information more efficiently. Furthermore, we propose an approach to incorporate varying degrees of correlation, and suggest a practical variant of Rand-Proj-Spatial when the correlation information is not available to the server. Finally, experiments on real-world distributed optimization tasks showcase the superior performance of Rand-Proj-Spatial compared to Rand-$k$-Spatial and other more sophisticated sparsification techniques.

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Inner-Outer Aware Reconstruction Model for Monocular 3D Scene Reconstruction

Yu-Kun Qiu, Guohao Xu, Wei-Shi Zheng

Monocular 3D scene reconstruction aims to reconstruct the 3D structure of scenes based on posed images. Recent volumetric-based methods directly predict the truncated signed distance function (TSDF) volume and have achieved promising results. The memory cost of volumetric-based methods will grow cubically as the volume size increases, so a coarse-to-fine strategy is necessary for saving memory. Specifically, the coarse-to-fine strategy distinguishes surface voxels from non-surface voxels, and only potential surface voxels are considered in the succeeding procedure. However, the non-surface voxels have various features, and in particular, the voxels on the inner side of the surface are quite different from those on the outer side since there exists an intrinsic gap between them. Therefore, grouping inner-surface and outer-surface voxels into the same class will force the classifier to spend its capacity to bridge the gap. By contrast, it is relatively easy for the classifier to distinguish inner-surface and outer-surface voxels due to the intrinsic gap. Inspired by this, we propose the inner-outer aware reconstruction (IOAR) model. IOAR explores a new coarse-to-fine strategy to classify outer-surface, inner-surface and surface voxels. In addition, IOAR separates occupancy branches from TSDF branches to avoid mutual interference between them. Since our model can better classify the surface, outer-surface and inner-surface voxels, it can predict more precise meshes than existing methods. Experiment results on ScanNet, ICL-NUIM and TUM-RGBD datasets demonstrate the effectiveness and generalization of our model. The code is available at https://github.com/YorkQiu/InnerOuterAwareReconstruction.

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Failure-Aware Gaussian Process Optimization with Regret Bounds

Shogo Iwazaki, Shion Takeno, Tomohiko Tanabe, Mitsuru Irie

Real-world optimization problems often require black-box optimization with observation failure, where we can obtain the objective function value if we succeed, otherwise, we can only obtain a fact of failure. Moreover, this failure region can be complex by several latent constraints, whose number is also unknown. For this problem, we propose a failure-aware Gaussian process upper confidence bound (F-GP-UCB), which only requires a mild assumption for the observation failure that an optimal solution lies on an interior of a feasible region. Furthermore, we show that the number of successful observations grows linearly, by which we provide the first regret upper bounds and the convergence of F-GP-UCB. We demonstrate the effectiveness of F-GP-UCB in several benchmark functions, including the simulation function motivated by material synthesis experiments.

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ZoomTrack: Target-aware Non-uniform Resizing for Efficient Visual Tracking

Yutong Kou, Jin Gao, Bing Li, Gang Wang, Weiming Hu, Yizheng Wang, Liang Li

Recently, the transformer has enabled the speed-oriented trackers to approach state-of-the-art (SOTA) performance with high-speed thanks to the smaller input size or the lighter feature extraction backbone, though they still substantially lag behind their corresponding performance-oriented versions. In this paper, we demonstrate that it is possible to narrow or even close this gap while achieving high tracking speed based on the smaller input size. To this end, we non-uniformly resize the cropped image to have a smaller input size while the resolution of the area where the target is more likely to appear is higher and vice versa. This enables us to solve the dilemma of attending to a larger visual field while retaining more raw information for the target despite a smaller input size. Our formulation for the non-uniform resizing can be efficiently solved through quadratic programming (QP) and naturally integrated into most of the crop-based local trackers. Comprehensive experiments on five challenging datasets based on two kinds of transformer trackers, \ie, OSTrack and TransT, demonstrate consistent improvements over them. In particular, applying our method to the speed-oriented version of OSTrack even outperforms its performance-oriented counterpart by 0.6\% AUC on TNL2K, while running 50\% faster and saving over 55\% MACs. Codes and models are available at https://github.com/Kou-99/ZoomTrack.

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Coneheads: Hierarchy Aware Attention

Albert Tseng, Tao Yu, Toni J.B. Liu, Christopher De Sa

Attention networks such as transformers have achieved state-of-the-art performance in many domains. These networks rely heavily on the dot product attention operator, which computes the similarity between two points by taking their inner product. However, the inner product does not explicitly model the complex structural properties of real world datasets, such as hierarchies between data points. To remedy this, we introduce cone attention, a drop-in replacement for dot product attention based on hyperbolic entailment cones. Cone attention associates two points by the depth of their lowest common ancestor in a hierarchy defined by hyperbolic cones, which intuitively measures the divergence of two points and gives a $\textit{hierarchy aware}$ similarity score. We test cone attention on a wide variety of models and tasks and show that it improves task-level performance over dot product attention and other baselines, and is able to match dot-product attention with significantly fewer parameters. Our results suggest that cone attention is an effective way to capture hierarchical relationships when calculating attention.

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The Grand Illusion: The Myth of Software Portability and Implications for ML Progress.

Fraser Mince, Dzung Dinh, Jonas Kgomo, Neil Thompson, Sara Hooker

Pushing the boundaries of machine learning often requires exploring different hardware and software combinations. However, this ability to experiment with different systems can be at odds with the drive for efficiency, which has produced increasingly specialized AI hardware and incentivized consolidation around a narrow set of ML frameworks. Exploratory research can be further restricted if software and hardware are co-evolving, making it even harder to stray away from a given tooling stack. While this friction increasingly impacts the rate of innovation in machine learning, to our knowledge the lack of portability in tooling has not been quantified. In this work we ask: How portable are popular ML software frameworks? We conduct a large scale study of the portability of mainstream ML frameworks across different hardware types. Our findings paint an uncomfortable picture -- frameworks can lose more than 40% of their key functions when ported to other hardware. Worse, even when functions are portable, the slowdown in their performance can be extreme. Collectively, our results reveal how costly straying from a narrow set of hardware-software combinations can be - and thus how specialization incurs an exploration cost that can impede innovation in machine learning research.

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HAP: Structure-Aware Masked Image Modeling for Human-Centric Perception

Junkun Yuan, Xinyu Zhang, Hao Zhou, Jian Wang, Zhongwei Qiu, Zhiyin Shao, Shaofeng Zhang, Sifan Long, Kun Kuang, Kun Yao, Junyu Han, Errui Ding, Lanfen Lin, Fei Wu, Jingdong Wang

Model pre-training is essential in human-centric perception. In this paper, we first introduce masked image modeling (MIM) as a pre-training approach for this task. Upon revisiting the MIM training strategy, we reveal that human structure priors offer significant potential. Motivated by this insight, we further incorporate an intuitive human structure prior - human parts - into pre-training. Specifically, we employ this prior to guide the mask sampling process. Image patches, corresponding to human part regions, have high priority to be masked out. This encourages the model to concentrate more on body structure information during pre-training, yielding substantial benefits across a range of human-centric perception tasks. To further capture human characteristics, we propose a structure-invariant alignment loss that enforces different masked views, guided by the human part prior, to be closely aligned for the same image. We term the entire method as HAP. HAP simply uses a plain ViT as the encoder yet establishes new state-of-the-art performance on 11 human-centric benchmarks, and on-par result on one dataset. For example, HAP achieves 78.1% mAP on MSMT17 for person re-identification, 86.54% mA on PA-100K for pedestrian attribute recognition, 78.2% AP on MS COCO for 2D pose estimation, and 56.0 PA-MPJPE on 3DPW for 3D pose and shape estimation.

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HotBEV: Hardware-oriented Transformer-based Multi-View 3D Detector for BEV Perception

Peiyan Dong, Zhenglun Kong, Xin Meng, Pinrui Yu, Yifan Gong, Geng Yuan, Hao Tang, Yanzhi Wang

The bird's-eye-view (BEV) perception plays a critical role in autonomous driving systems, involving the accurate and efficient detection and tracking of objects from a top-down perspective. To achieve real-time decision-making in self-driving scenarios, low-latency computation is essential. While recent approaches to BEV detection have focused on improving detection precision using Lift-Splat-Shoot (LSS)-based or transformer-based schemas, the substantial computational and memory burden of these approaches increases the risk of system crashes when multiple on-vehicle tasks run simultaneously. Unfortunately, there is a dearth of literature on efficient BEV detector paradigms, let alone achieving realistic speedups. Unlike existing works that focus on reducing computation costs, this paper focuses on developing an efficient model design that prioritizes actual on-device latency. To achieve this goal, we propose a latency-aware design methodology that considers key hardware properties, such as memory access cost and degree of parallelism. Given the prevalence of GPUs as the main computation platform for autonomous driving systems, we develop a theoretical latency prediction model and introduce efficient building operators. By leveraging these operators and following an effective local-to-global visual modeling process, we propose a hardware-oriented backbone that is also optimized for strong feature capturing and fusing. Using these insights, we present a new hardware-oriented framework for efficient yet accurate camera-view BEV detectors. Experiments show that HotBEV achieves a 2\%$\sim$23\% NDS gain, and 2\%$\sim$7.8\% mAP gain with a 1.1$\times$$\sim$3.4$\times$ speedups compared to existing works on V100; On multiple GPU devices such as GPU GTX 2080 and the low-end GTX 1080, HotBEV achieves 1.1$\times$$\sim$6.3$\times$ faster than others.

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Fairness Aware Counterfactuals for Subgroups

Loukas Kavouras, Konstantinos Tsopelas, Giorgos Giannopoulos, Dimitris Sacharidis, Eleni Psaroudaki, Nikolaos Theologitis, Dimitrios Rontogiannis, Dimitris Fotakis, Ioannis Emiris

In this work, we present Fairness Aware Counterfactuals for Subgroups (FACTS), a framework for auditing subgroup fairness through counterfactual explanations. We start with revisiting (and generalizing) existing notions and introducing new, more refined notions of subgroup fairness. We aim to (a) formulate different aspects of the difficulty of individuals in certain subgroups to achieve recourse, i.e. receive the desired outcome, either at the micro level, considering members of the subgroup individually, or at the macro level, considering the subgroup as a whole, and (b) introduce notions of subgroup fairness that are robust, if not totally oblivious, to the cost of achieving recourse. We accompany these notions with an efficient, model-agnostic, highly parameterizable, and explainable framework for evaluating subgroup fairness. We demonstrate the advantages, the wide applicability, and the efficiency of our approach through a thorough experimental evaluation on different benchmark datasets.

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硬件协同 · NeurIPS 2023 | paperlist.ai