非凸优化

Behavior of neural networks is irremediably determined by the specific loss and data used during training. However it is often desirable to tune the model at inference time based on external factors such as preferences of the user or dynamic characteristics of the data. This is especially important to balance the perception-distortion trade-off of ill-posed image-to-image translation tasks. In this work, we propose to optimize a parametric tunable convolutional layer, which includes a number of different kernels, using a parametric multi-loss, which includes an equal number of objectives. Our key insight is to use a shared set of parameters to dynamically interpolate both the objectives and the kernels. During training, these parameters are sampled at random to explicitly optimize all possible combinations of objectives and consequently disentangle their effect into the corresponding kernels. During inference, these parameters become interactive inputs of the model hence enabling reliable and consistent control over the model behavior. Extensive experimental results demonstrate that our tunable convolutions effectively work as a drop-in replacement for traditional convolutions in existing neural networks at virtually no extra computational cost, outperforming state-of-the-art control strategies in a wide range of applications; including image denoising, deblurring, super-resolution, and style transfer.

We propose a new approach to learned optimization where we represent the computation of an optimizer's update step using a neural network. The parameters of the optimizer are then learned by training on a set of optimization tasks with the objective to perform minimization efficiently. Our innovation is a new neural network architecture, Optimus, for the learned optimizer inspired by the classic BFGS algorithm. As in BFGS, we estimate a preconditioning matrix as a sum of rank-one updates but use a Transformer-based neural network to predict these updates jointly with the step length and direction. In contrast to several recent learned optimization-based approaches, our formulation allows for conditioning across the dimensions of the parameter space of the target problem while remaining applicable to optimization tasks of variable dimensionality without retraining. We demonstrate the advantages of our approach on a benchmark composed of objective functions traditionally used for the evaluation of optimization algorithms, as well as on the real world-task of physics-based visual reconstruction of articulated 3d human motion.

Decision forests are among the most accurate models in machine learning. This is remarkable given that the way they are trained is highly heuristic: neither the individual trees nor the overall forest optimize any well-defined loss. While diversity mechanisms such as bagging or boosting have been until now critical in the success of forests, we think that a better optimization should lead to better forests---ideally eliminating any need for an ensembling heuristic. However, unlike for most other models, such as neural networks, optimizing forests or trees is not easy, because they define a non-differentiable function. We show, for the first time, that it is possible to learn a forest by optimizing a desirable loss and regularization jointly over all its trees and parameters. Our algorithm, Forest Alternating Optimization, is based on defining a forest as a parametric model with a fixed number of trees and structure (rather than adding trees indefinitely as in bagging or boosting). It then iteratively updates each tree in alternation so that the objective function decreases monotonically. The algorithm is so effective at optimizing that it easily overfits, but this can be corrected by averaging. The result is a forest that consistently exceeds the accuracy of the state-of-the-art while using fewer, smaller trees.

Our paper seeks to transfer the hairstyle of a reference image to an input photo for virtual hair try-on. We target a variety of challenges scenarios, such as transforming a long hairstyle with bangs to a pixie cut, which requires removing the existing hair and inferring how the forehead would look, or transferring partially visible hair from a hat-wearing person in a different pose. Past solutions leverage StyleGAN for hallucinating any missing parts and producing a seamless face-hair composite through so-called GAN inversion or projection. However, there remains a challenge in controlling the hallucinations to accurately transfer hairstyle and preserve the face shape and identity of the input. To overcome this, we propose a multi-view optimization framework that uses "two different views" of reference composites to semantically guide occluded or ambiguous regions. Our optimization shares information between two poses, which allows us to produce high fidelity and realistic results from incomplete references. Our framework produces high-quality results and outperforms prior work in a user study that consists of significantly more challenging hair transfer scenarios than previously studied. Project page: https://stylegan-salon.github.io/.

Robust generalization aims to tackle the most challenging data distributions which are rare in the training set and contain severe noises, i.e., photon-limited corruptions. Common solutions such as distributionally robust optimization (DRO) focus on the worst-case empirical risk to ensure low training error on the uncommon noisy distributions. However, due to the over-parameterized model being optimized on scarce worst-case data, DRO fails to produce a smooth loss landscape, thus struggling on generalizing well to the test set. Therefore, instead of focusing on the worst-case risk minimization, we propose SharpDRO by penalizing the sharpness of the worst-case distribution, which measures the loss changes around the neighbor of learning parameters. Through worst-case sharpness minimization, the proposed method successfully produces a flat loss curve on the corrupted distributions, thus achieving robust generalization. Moreover, by considering whether the distribution annotation is available, we apply SharpDRO to two problem settings and design a worst-case selection process for robust generalization. Theoretically, we show that SharpDRO has a great convergence guarantee. Experimentally, we simulate photon-limited corruptions using CIFAR10/100 and ImageNet30 datasets and show that SharpDRO exhibits a strong generalization ability against severe corruptions and exceeds well-known baseline methods with large performance gains.

Deep learning has had remarkable success in robotic perception, but its data-centric nature suffers when it comes to generalizing to ever-changing environments. By contrast, physics-based optimization generalizes better, but it does not perform as well in complicated tasks due to the lack of high-level semantic information and reliance on manual parametric tuning. To take advantage of these two complementary worlds, we present PyPose: a robotics-oriented, PyTorch-based library that combines deep perceptual models with physics-based optimization. PyPose's architecture is tidy and well-organized, it has an imperative style interface and is efficient and user-friendly, making it easy to integrate into real-world robotic applications. Besides, it supports parallel computing of any order gradients of Lie groups and Lie algebras and 2nd-order optimizers, such as trust region methods. Experiments show that PyPose achieves more than 10x speedup in computation compared to the state-of-the-art libraries. To boost future research, we provide concrete examples for several fields of robot learning, including SLAM, planning, control, and inertial navigation.

By integrating certain optimization solvers with deep neural networks, deep unfolding network (DUN) with good interpretability and high performance has attracted growing attention in compressive sensing (CS). However, existing DUNs often improve the visual quality at the price of a large number of parameters and have the problem of feature information loss during iteration. In this paper, we propose an Optimization-inspired Cross-attention Transformer (OCT) module as an iterative process, leading to a lightweight OCT-based Unfolding Framework (OCTUF) for image CS. Specifically, we design a novel Dual Cross Attention (Dual-CA) sub-module, which consists of an Inertia-Supplied Cross Attention (ISCA) block and a Projection-Guided Cross Attention (PGCA) block. ISCA block introduces multi-channel inertia forces and increases the memory effect by a cross attention mechanism between adjacent iterations. And, PGCA block achieves an enhanced information interaction, which introduces the inertia force into the gradient descent step through a cross attention block. Extensive CS experiments manifest that our OCTUF achieves superior performance compared to state-of-the-art methods while training lower complexity. Codes are available at https://github.com/songjiechong/OCTUF.

LiDAR has become a cornerstone sensing modality for 3D vision. LiDAR systems emit pulses of light into the scene, take measurements of the returned signal, and rely on hardware digital signal processing (DSP) pipelines to construct 3D point clouds from these measurements. The resulting point clouds output by these DSPs are input to downstream 3D vision models -- both, in the form of training datasets or as input at inference time. Existing LiDAR DSPs are composed of cascades of parameterized operations; modifying configuration parameters results in significant changes in the point clouds and consequently the output of downstream methods. Existing methods treat LiDAR systems as fixed black boxes and construct downstream task networks more robust with respect to measurement fluctuations. Departing from this approach, the proposed method directly optimizes LiDAR sensing and DSP parameters for downstream tasks. To investigate the optimization of LiDAR system parameters, we devise a realistic LiDAR simulation method that generates raw waveforms as input to a LiDAR DSP pipeline. We optimize LiDAR parameters for both 3D object detection IoU losses and depth error metrics by solving a nonlinear multi-objective optimization problem with a 0th-order stochastic algorithm. For automotive 3D object detection models, the proposed method outperforms manual expert tuning by 39.5% mean Average Precision (mAP).

We present a high-fidelity 3D generative adversarial network (GAN) inversion framework that can synthesize photo-realistic novel views while preserving specific details of the input image. High-fidelity 3D GAN inversion is inherently challenging due to the geometry-texture trade-off, where overfitting to a single view input image often damages the estimated geometry during the latent optimization. To solve this challenge, we propose a novel pipeline that builds on the pseudo-multi-view estimation with visibility analysis. We keep the original textures for the visible parts and utilize generative priors for the occluded parts. Extensive experiments show that our approach achieves advantageous reconstruction and novel view synthesis quality over prior work, even for images with out-of-distribution textures. The proposed pipeline also enables image attribute editing with the inverted latent code and 3D-aware texture modification. Our approach enables high-fidelity 3D rendering from a single image, which is promising for various applications of AI-generated 3D content. The source code is at https://github.com/jiaxinxie97/HFGI3D/.

We present an approach to learning regular spatial transformations between image pairs in the context of medical image registration. Contrary to optimization-based registration techniques and many modern learning-based methods, we do not directly penalize transformation irregularities but instead promote transformation regularity via an inverse consistency penalty. We use a neural network to predict a map between a source and a target image as well as the map when swapping the source and target images. Different from existing approaches, we compose these two resulting maps and regularize deviations of the Jacobian of this composition from the identity matrix. This regularizer -- GradICON -- results in much better convergence when training registration models compared to promoting inverse consistency of the composition of maps directly while retaining the desirable implicit regularization effects of the latter. We achieve state-of-the-art registration performance on a variety of real-world medical image datasets using a single set of hyperparameters and a single non-dataset-specific training protocol. The code is available at https://github.com/uncbiag/ICON.

Federated learning enables the privacy-preserving training of neural network models using real-world data across distributed clients. FedAvg has become the preferred optimizer for federated learning because of its simplicity and effectiveness. FedAvg uses naive aggregation to update the server model, interpolating client models based on the number of instances used in their training. However, naive aggregation suffers from client-drift when the data is heterogenous (non-IID), leading to unstable and slow convergence. In this work, we propose a novel aggregation approach, elastic aggregation, to overcome these issues. Elastic aggregation interpolates client models adaptively according to parameter sensitivity, which is measured by computing how much the overall prediction function output changes when each parameter is changed. This measurement is performed in an unsupervised and online manner. Elastic aggregation reduces the magnitudes of updates to the more sensitive parameters so as to prevent the server model from drifting to any one client distribution, and conversely boosts updates to the less sensitive parameters to better explore different client distributions. Empirical results on real and synthetic data as well as analytical results show that elastic aggregation leads to efficient training in both convex and non-convex settings, while being fully agnostic to client heterogeneity and robust to large numbers of clients, partial participation, and imbalanced data. Finally, elastic aggregation works well with other federated optimizers and achieves significant improvements across the board.

LiDAR mapping is important yet challenging in self-driving and mobile robotics. To tackle such a global point cloud registration problem, DeepMapping converts the complex map estimation into a self-supervised training of simple deep networks. Despite its broad convergence range on small datasets, DeepMapping still cannot produce satisfactory results on large-scale datasets with thousands of frames. This is due to the lack of loop closures and exact cross-frame point correspondences, and the slow convergence of its global localization network. We propose DeepMapping2 by adding two novel techniques to address these issues: (1) organization of training batch based on map topology from loop closing, and (2) self-supervised local-to-global point consistency loss leveraging pairwise registration. Our experiments and ablation studies on public datasets such as KITTI, NCLT, and Nebula, demonstrate the effectiveness of our method.

Intersection-over-Union (IoU) is the most popular metric to evaluate regression performance in 3D object detection. Recently, there are also some methods applying IoU to the optimization of 3D bounding box regression. However, we demonstrate through experiments and mathematical proof that the 3D IoU loss suffers from abnormal gradient w.r.t. angular error and object scale, which further leads to slow convergence and suboptimal regression process, respectively. In this paper, we propose a Gradient-Corrected IoU (GCIoU) loss to achieve fast and accurate 3D bounding box regression. Specifically, a gradient correction strategy is designed to endow 3D IoU loss with a reasonable gradient. It ensures that the model converges quickly in the early stage of training, and helps to achieve fine-grained refinement of bounding boxes in the later stage. To solve suboptimal regression of 3D IoU loss for objects at different scales, we introduce a gradient rescaling strategy to adaptively optimize the step size. Finally, we integrate GCIoU Loss into multiple models to achieve stable performance gains and faster model convergence. Experiments on KITTI dataset demonstrate superiority of the proposed method. The code is available at https://github.com/ming71/GCIoU-loss.

Novel View Synthesis (NVS) aims at synthesizing an image from an arbitrary viewpoint using multi-view images and camera poses. Among the methods for NVS, Neural Radiance Fields (NeRF) is capable of NVS for an arbitrary resolution as it learns a continuous volumetric representation. However, radiance fields rely heavily on the spectral characteristics of coordinate-based networks. Thus, there is a limit to improving the performance of high-resolution novel view synthesis (HRNVS). To solve this problem, we propose a novel framework using cross-guided optimization of the single-image super-resolution (SISR) and radiance fields. We perform multi-view image super-resolution (MVSR) on train-view images during the radiance fields optimization process. It derives the updated SR result by fusing the feature map obtained from SISR and voxel-based uncertainty fields generated by integrated errors of train-view images. By repeating the updates during radiance fields optimization, train-view images for radiance fields optimization have multi-view consistency and high-frequency details simultaneously, ultimately improving the performance of HRNVS. Experiments of HRNVS and MVSR on various benchmark datasets show that the proposed method significantly surpasses existing methods.

This work addresses the problem of anonymizing the identity of faces in a dataset of images, such that the privacy of those depicted is not violated, while at the same time the dataset is useful for downstream task such as for training machine learning models. To the best of our knowledge, we are the first to explicitly address this issue and deal with two major drawbacks of the existing state-of-the-art approaches, namely that they (i) require the costly training of additional, purpose-trained neural networks, and/or (ii) fail to retain the facial attributes of the original images in the anonymized counterparts, the preservation of which is of paramount importance for their use in downstream tasks. We accordingly present a task-agnostic anonymization procedure that directly optimises the images' latent representation in the latent space of a pre-trained GAN. By optimizing the latent codes directly, we ensure both that the identity is of a desired distance away from the original (with an identity obfuscation loss), whilst preserving the facial attributes (using a novel feature-matching loss in FaRL's deep feature space). We demonstrate through a series of both qualitative and quantitative experiments that our method is capable of anonymizing the identity of the images whilst--crucially--better-preserving the facial attributes. We make the code and the pre-trained models publicly available at: https://github.com/chi0tzp/FALCO.