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1,217篇论文匹配“Discrete Optimization”
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Applications · Computer Vision

Xindi Yang, Zeke Xie, Xiong Zhou, Boyu Liu, Buhua Liu, Yi Liu, Haoran Wang, YUNFENG CAI, Mingming Sun

Neural field methods have seen great progress in various long-standing tasks in computer vision and computer graphics, including novel view synthesis and geometry reconstruction. As existing neural field methods try to predict some coordinate-based continuous target values, such as RGB for Neural Radiance Field (NeRF), all of these methods are regression models and are optimized by some regression loss. However, are regression models really better than classification models for neural field methods? In this work, we try to visit this very fundamental but overlooked question for neural fields from a machine learning perspective. We successfully propose a novel Neural Field Classifier (NFC) framework which formulates existing neural field methods as classification tasks rather than regression tasks. The proposed NFC can easily transform arbitrary Neural Field Regressor (NFR) into its classification variant via employing a novel Target Encoding module and optimizing a classification loss. By encoding a continuous regression target into a high-dimensional discrete encoding, we naturally formulate a multi-label classification task. Extensive experiments demonstrate the impressive effectiveness of NFC at the nearly free extra computational costs. Moreover, NFC also shows robustness to sparse inputs, corrupted images, and dynamic scenes.

Optimization · Discrete and Combinatorial Optimization

Hanni Cheng, Ya Cong, Weihao Jiang, Shiliang Pu

Neural methods have shown significant merit in solving combinatorial optimization (CO) problems, including the Bin Packing Problem (BPP). However, most existing ML-based approaches focus on geometric BPP like 3DBPP, neglecting complex vector BPP. In this study, we introduce a vector BPP variant called Class-Constrained Bin Packing Problem (CCBPP), dealing with items of both classes and sizes, and the objective is to pack the items in the least amount of bins respecting the bin capacity and the number of different classes that it can hold. To enhance the efficiency and practicality of solving CCBPP, we propose a learning-based Encoder-Decoder Model. The Encoder employs a Graph Convolution Network (GCN) to generate a heat-map, representing probabilities of different items packing together. The Decoder decodes and fine-tunes the solution through Cluster Decode and Active Search methods, thereby producing high-quality solutions for CCBPP instances. Extensive experiments demonstrate that our proposed method consistently yields high-quality solutions for various kinds of CCBPP with a very small gap from the optimal. Moreover, our Encoder-Decoder Model also shows promising performance on one practical application of CCBPP, the *Manufacturing Order Consolidation Problem* (OCP).

Optimization

Xun Tang, Michael Shavlovsky, Holakou Rahmanian, Elisa Tardini, Kiran Thekumparampil, Tesi Xiao, Lexing Ying

Computing the optimal transport distance between statistical distributions is a fundamental task in machine learning. One remarkable recent advancement is entropic regularization and the Sinkhorn algorithm, which utilizes only matrix scaling and guarantees an approximated solution with near-linear runtime. Despite the success of the Sinkhorn algorithm, its runtime may still be slow due to the potentially large number of iterations needed for convergence. To achieve possibly super-exponential convergence, we introduce Sinkhorn-Newton-Sparse (SNS), an extension to the Sinkhorn algorithm, by introducing early stopping for the matrix scaling steps and a second stage featuring a Newton-type subroutine. Adopting the variational viewpoint that the Sinkhorn algorithm maximizes a concave Lyapunov potential, we offer the insight that the Hessian matrix of the potential function is approximately sparse. Sparsification of the Hessian results in a fast $O(n^2)$ per-iteration complexity, the same as the Sinkhorn algorithm. In terms of total iteration count, we observe that the SNS algorithm converges orders of magnitude faster across a wide range of practical cases, including optimal transportation between empirical distributions and calculating the Wasserstein $W_1, W_2$ distance of discretized continuous densities. The empirical performance is corroborated by a rigorous bound on the approximate sparsity of the Hessian matrix.

Deep Learning · Large Language Models

Junyuan Hong, Jiachen (Tianhao) Wang, Chenhui Zhang, Zhangheng LI, Bo Li, Zhangyang Wang

Large Language Models (LLMs) have emerged as dominant tools for various tasks, particularly when tailored for a specific target by prompt tuning. Nevertheless, concerns surrounding data privacy present obstacles due to the tuned prompts' dependency on sensitive private information. A practical solution is to host a local LLM and optimize a soft prompt privately using data. Yet, hosting a local model becomes problematic when model ownership is protected. Alternative methods, like sending data to the model's provider for training, intensify these privacy issues facing an untrusted provider. In this paper, we present a novel solution called Differentially-Private Offsite Prompt Tuning (DP-OPT) to address this challenge. Our approach involves tuning a discrete prompt on the client side and then applying it to the desired cloud models. We demonstrate that prompts suggested by LLMs themselves can be transferred without compromising performance significantly. To ensure that the prompts do not leak private information, we introduce the first private prompt generation mechanism, by a differentially-private (DP) ensemble of in-context learning with private demonstrations. With DP-OPT, generating privacy-preserving prompts by Vicuna-7b can yield competitive performance compared to non-private in-context learning on GPT3.5 or local private prompt tuning.Codes are available at https://github.com/VITA-Group/DP-OPT.

Jeffrey Gu, Kuan-Chieh Wang, Serena Yeung

Neural fields, which represent signals as a function parameterized by a neural network, are a promising alternative to traditional discrete vector or grid-based representations. Compared to discrete representations, neural representations both scale well with increasing resolution, are continuous, and can be many-times differentiable. However, given a dataset of signals that we would like to represent, having to optimize a separate neural field for each signal is inefficient, and cannot capitalize on shared information or structures among signals. Existing generalization methods view this as a meta-learning problem and employ gradient-based meta-learning to learn an initialization which is then fine-tuned with test-time optimization, or learn hypernetworks to produce the weights of a neural field. We instead propose a new paradigm that views the large-scale training of neural representations as a part of a partially-observed neural process framework, and leverage neural process algorithms to solve this task. We demonstrate that this approach outperforms both state-of-the-art gradient-based meta-learning approaches and hypernetwork approaches.

Beier Zhu, Yulei Niu, Yucheng Han, Yue Wu, Hanwang Zhang

Thanks to the large pre-trained vision-language models (VLMs) like CLIP, we can craft a zero-shot classifier by discrete prompt design, e.g., the confidence score of an image being "[CLASS]" can be obtained by using the VLM provided similarity between the image and the prompt sentence "a photo of a [CLASS]". Furthermore, prompting shows great potential for fast adaptation of VLMs to downstream tasks if we fine-tune the soft prompts with few samples. However, we find a common failure that improper fine-tuning or learning with extremely few-shot samples may even under-perform the zero-shot prediction. Existing methods still address this problem by using traditional anti-overfitting techniques such as early stopping and data augmentation, which lack a principled solution specific to prompting. In this paper, we present Prompt-aligned Gradient, dubbed ProGrad to prevent prompt tuning from forgetting the general knowledge learned from VLMs. In particular, ProGrad only updates the prompt whose gradient is aligned (or non-conflicting) to the general knowledge, which is represented as the optimization direction offered by the predefined prompt predictions. Extensive experiments under the few-shot learning, domain generalization, base-to-new generalization and cross-dataset transfer settings demonstrate the stronger few-shot generalization ability of ProGrad over state-of-the-art prompt tuning methods. Codes and theoretical proof are in Appendix.

Zezeng Li, Shenghao Li, Zhanpeng Wang, Na Lei, Zhongxuan Luo, David Xianfeng Gu

Sampling from diffusion probabilistic models (DPMs) can be viewed as a piecewise distribution transformation, which generally requires hundreds or thousands of steps of the inverse diffusion trajectory to get a high-quality image. Recent progress in designing fast samplers for DPMs achieves a trade-off between sampling speed and sample quality by knowledge distillation or adjusting the variance schedule or the denoising equation. However, it can't be optimal in both aspects and often suffer from mode mixture in short steps. To tackle this problem, we innovatively regard inverse diffusion as an optimal transport (OT) problem between latents at different stages and propose DPM-OT, a unified learning framework for fast DPMs with the direct expressway represented by OT map, which can generate high-quality samples within around 10 function evaluations. By calculating the semi-discrete optimal transport between the data latents and the white noise, we obtain the expressway from the prior distribution to the data distribution, while significantly alleviating the problem of mode mixture. In addition, we give the error bound of the proposed method, which theoretically guarantees the stability of the algorithm. Extensive experiments validate the effectiveness and advantages of DPM-OT in terms of speed and quality (FID and mode mixture), thus representing an efficient solution for generative modeling. Source codes are available at https://github.com/cognaclee/DPM-OT

Chen Geng, Hong-Xing Yu, Sharon Zhang, Maneesh Agrawala, Jiajun Wu

We study inferring a tree-structured representation from a single image for object shading. Prior work typically uses the parametric or measured representation to model shading, which is neither interpretable nor easily editable. We propose using the shade tree representation, which combines basic shading nodes and compositing methods to factorize object surface shading. The shade tree representation enables novice users who are unfamiliar with the physical shading process to edit object shading in an efficient and intuitive manner. A main challenge in inferring the shade tree is that the inference problem involves both the discrete tree structure and the continuous parameters of the tree nodes. We propose a hybrid approach to address this issue. We introduce an auto-regressive inference model to generate a rough estimation of the tree structure and node parameters, and then we fine-tune the inferred shade tree through an optimization algorithm. We show experiments on synthetic images, captured reflectance, real images, and non-realistic vector drawings, allowing downstream applications such as material editing, vectorized shading, and relighting. Project website: https://chen-geng.com/inv-shade-trees.

Teng Long, Nanne van Noord

Hierarchical clustering is a natural approach to discover ontologies from data. Yet, existing approaches are hampered by their inability to scale to large datasets and the discrete encoding of the hierarchy. We introduce scalable Hyperbolic Hierarchical Clustering (sHHC) which overcomes these limitations by learning continuous hierarchies in hyperbolic space. Our hierarchical clustering is of high quality and can be obtained in a fraction of the runtime. Additionally, we demonstrate the strength of sHHC on a downstream cross-modal self-supervision task. By using the discovered hierarchies from sound and vision to construct continuous hierarchical pseudo-labels we can efficiently optimize a network for activity recognition and obtain competitive performance compared to recent self-supervised learning models. Our findings demonstrate the strength of Hyperbolic Hierarchical Clustering and its potential for Self-Supervised Learning.

Chao Chen, Yu-Shen Liu, Zhizhong Han

Learning implicit representations has been a widely used solution for surface reconstruction from 3D point clouds. The latest methods infer a distance or occupancy field by overfitting a neural network on a single point cloud. However, these methods suffer from a slow inference due to the slow convergence of neural networks and the extensive calculation of distances to surface points, which limits them to small scale points. To resolve the scalability issue in surface reconstruction, we propose GridPull to improve the efficiency of learning implicit representations from large scale point clouds. Our novelty lies in the fast inference of a discrete distance field defined on grids without using any neural components. To remedy the lack of continuousness brought by neural networks, we introduce a loss function to encourage continuous distances and consistent gradients in the field during pulling queries onto the surface in grids near to the surface. We use uniform grids for a fast grid search to localize sampled queries, and organize surface points in a tree structure to speed up the calculation of distances to the surface. We do not rely on learning priors or normal supervision during optimization, and achieve superiority over the latest methods in terms of complexity and accuracy. We evaluate our method on shape and scene benchmarks, and report numerical and visual comparisons with the latest methods to justify our effectiveness and superiority. The code is available at https://github.com/chenchao15/GridPull.

Ishit Mehta, Manmohan Chandraker, Ravi Ramamoorthi

We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse rendering of geometry rely on silhouette gradients for topology changes, such signals are sparse. In contrast, our theory derives topological derivatives that relate the introduction of vanishing holes and phases to changes in image intensity. As a result, we enable differentiable shape perturbations in the form of hole or phase nucleation. We validate the proposed theory with optimization of closed curves in 2D and surfaces in 3D to lend insights into limitations of current methods and enable improved applications such as image vectorization, vector-graphics generation from text prompts, single-image reconstruction of shape ambigrams and multiview 3D reconstruction.

Sijia Jiang, Jing Hua, Zhizhong Han

In recent years, huge progress has been made on learn- ing neural implicit representations from multi-view images for 3D reconstruction. As an additional input complement- ing coordinates, using sinusoidal functions as positional encodings plays a key role in revealing high frequency de- tails with coordinate-based neural networks. However, high frequency positional encodings make the optimization un- stable, which results in noisy reconstructions and artifacts in empty space. To resolve this issue in a general sense, we introduce to learn neural implicit representations with quantized coordinates, which reduces the uncertainty and ambiguity in the field during optimization. Instead of con- tinuous coordinates, we discretize continuous coordinates into discrete coordinates using nearest interpolation among quantized coordinates which are obtained by discretizing the field in an extremely high resolution. We use discrete coordinates and their positional encodings to learn implicit functions through volume rendering. This significantly re- duces the variations in the sample space, and triggers more multi-view consistency constraints on intersections of rays from different views, which enables to infer implicit function in a more effective way. Our quantized coordinates do not bring any computational burden, and can seamlessly work upon the latest methods. Our evaluations under the widely used benchmarks show our superiority over the state-of-the- art. Our code is available at https://github.com/ MachinePerceptionLab/CQ-NIR.

Muyu Xu, Fangneng Zhan, Jiahui Zhang, Yingchen Yu, Xiaoqin Zhang, Christian Theobalt, Ling Shao, Shijian Lu

Neural Radiance Field (NeRF) has shown impressive performance in novel view synthesis via implicit scene representation. However, it usually suffers from poor scalability as requiring densely sampled images for each new scene. Several studies have attempted to mitigate this problem by integrating Multi-View Stereo (MVS) technique into NeRF while they still entail a cumbersome fine-tuning process for new scenes. Notably, the rendering quality will drop severely without this fine-tuning process and the errors mainly appear around the high-frequency features. In the light of this observation, we design WaveNeRF, which integrates wavelet frequency decomposition into MVS and NeRF to achieve generalizable yet high-quality synthesis without any per-scene optimization. To preserve high-frequency information when generating 3D feature volumes, WaveNeRF builds Multi-View Stereo in the Wavelet domain by integrating the discrete wavelet transform into the classical cascade MVS, which disentangles high-frequency information explicitly. With that, disentangled frequency features can be injected into classic NeRF via a novel hybrid neural renderer to yield faithful high-frequency details, and an intuitive frequency-guided sampling strategy can be designed to suppress artifacts around high-frequency regions. Extensive experiments over three widely studied benchmarks show that WaveNeRF achieves superior generalizable radiance field modeling when only given three images as input.

Nissim Maruani, Roman Klokov, Maks Ovsjanikov, Pierre Alliez, Mathieu Desbrun

In stark contrast to the case of images, finding a concise, learnable discrete representation of 3D surfaces remains a challenge. In particular, while polygon meshes are arguably the most common surface representation used in geometry processing, their irregular and combinatorial structure often make them unsuitable for learning-based applications. In this work, we present VoroMesh, a novel and differentiable of watertight 3D shape surfaces. From a set of 3D points (called generators) and their associated occupancy, we define our boundary representation through the Voronoi diagram of the generators as the subset of Voronoi faces whose two associated (equidistant) generators are of opposite occupancy: the resulting polygon mesh forms a watertight approximation of the target shape's boundary. To learn the position of the generators, we propose a novel loss function, dubbed VoroLoss, that minimizes the distance from ground truth surface samples to the closest faces of the Voronoi diagram which does not require an explicit construction of the entire Voronoi diagram. A direct optimization of the Voroloss to obtain generators on the Thingi32 dataset demonstrates the geometric efficiency of our representation compared to axiomatic meshing algorithms and recent learning-based mesh representations. We further use VoroMesh in a learning-based mesh prediction task from input SDF grids on the ABC dataset, and show comparable performance to state-of-the-art methods while guaranteeing closed output surfaces free of self-intersections.

Yuhong Li, Jiajie Li, Cong Hao, Pan Li, Jinjun Xiong, Deming Chen

Efficient or near-zero-cost proxies were proposed recently to address the demanding computational issues of Neural Architecture Search (NAS) in designing deep neural networks (DNNs), where each candidate architecture network only requires one iteration of backpropagation. The values obtained from proxies are used as predictions of architecture performance for downstream tasks. However, two significant drawbacks hinder the wide adoption of these efficient proxies: 1. they are not adaptive to various NAS search spaces and 2. they are not extensible to multi-modality downstream tasks. To address these two issues, we first propose an Extensible proxy (Eproxy) that utilizes self-supervised, few-shot training to achieve near-zero costs. A key component to our Eproxy's efficiency is the introduction of a barrier layer with randomly initialized frozen convolution parameters, which adds non-linearities to the optimization spaces so that Eproxy can discriminate the performance of architectures at an early stage. We further propose a Discrete Proxy Search (DPS) method to find the optimized training settings for Eproxy with only a handful of benchmarked architectures on the target tasks. Our extensive experiments confirm the effectiveness of both Eproxy and DPS. On the NDS-ImageNet search spaces, Eproxy+DPS achieves a higher average ranking correlation (Spearman r = 0.73) than the previous efficient proxy (Spearman r = 0.56). On the NAS-Bench-Trans-Micro search spaces with seven tasks, Eproxy+DPS delivers comparable performance with the early stopping method (146x faster). For the end-to-end task such as DARTS-ImageNet-1k, our method delivers better results than NAS performed on CIFAR-10 while only requiring one GPU hour with a single batch of CIFAR-10 images.

Heng Zhang, Daqing Liu, Zezhong Lv, Bing Su, Dacheng Tao

Paired video and language data is naturally temporal concurrency, which requires the modeling of the temporal dynamics within each modality and the temporal alignment across modalities simultaneously. However, most existing video-language representation learning methods only focus on discrete semantic alignment that encourages aligned semantics to be close in the latent space, or temporal context dependency that captures short-range coherence, failing in building the temporal concurrency. In this paper, we propose to learn video-language representations by modeling video-language pairs as Temporal Concurrent Processes (TCP) via a process-wised distance metric learning framework. Specifically, we employ the soft Dynamic Time Warping (DTW) to measure the distance between two processes across modalities and then optimize the DTW costs. Meanwhile, we further introduce a regularization term that enforces the embeddings of each modality approximating a stochastic process to guarantee the inherent dynamics. Experimental results on three benchmarks demonstrate that TCP stands as a state-of-the-art method for various video-language understanding tasks, including paragraph-to-video retrieval, video moment retrieval, and video question-answering. Code is available at https://github.com/hengRUC/TCP.

Ari Seff, Brian Cera, Dian Chen, Mason Ng, Aurick Zhou, Nigamaa Nayakanti, Khaled S. Refaat, Rami Al-Rfou, Benjamin Sapp

Reliable forecasting of the future behavior of road agents is a critical component to safe planning in autonomous vehicles. Here, we represent continuous trajectories as sequences of discrete motion tokens and cast multi-agent motion prediction as a language modeling task over this domain. Our model, MotionLM, provides several advantages: First, it does not require anchors or explicit latent variable optimization to learn multimodal distributions. Instead, we leverage a single standard language modeling objective, maximizing the average log probability over sequence tokens. Second, our approach bypasses post-hoc interaction heuristics where individual agent trajectory generation is conducted prior to interactive scoring. Instead, MotionLM produces joint distributions over interactive agent futures in a single autoregressive decoding process. In addition, the model's sequential factorization enables temporally causal conditional rollouts. The proposed approach establishes new state-of-the-art performance for multi-agent motion prediction on the Waymo Open Motion Dataset, ranking 1st on the interactive challenge leaderboard.

Zhiqiang Gao, Kaizhu Huang, Rui Zhang, Dawei Liu, Jieming Ma

Recent studies have investigated how to achieve robustness for unsupervised domain adaptation (UDA). While most efforts focus on adversarial robustness, i.e. how the model performs against unseen malicious adversarial perturbations, robustness against benign common corruption (RaCC) surprisingly remains under-explored for UDA. Towards improving RaCC for UDA methods in an unsupervised manner, we propose a novel Distributionally and Discretely Adversarial Regularization (DDAR) framework in this paper. Formulated as a min-max optimization with a distribution distance, DDAR is theoretically well-founded to ensure generalization over unknown common corruptions. Meanwhile, we show that our regularization scheme effectively reduces a surrogate of RaCC, i.e., the perceptual distance between natural data and common corruption. To enable a better adversarial regularization, the design of the optimization pipeline relies on an image discretization scheme that can transform "out-of-distribution" adversarial data into "in-distribution" data augmentation. Through extensive experiments, in terms of RaCC, our method is superior to conventional unsupervised regularization mechanisms, widely improves the robustness of existing UDA methods, and achieves state-of-the-art performance.

Haotian Wang, Yuxuan Xi, Hang Chen 0001, Jun Du 0002, Yan Song 0001, Qing Wang 0008, Hengshun Zhou, Chenxi Wang, Jiefeng Ma, Pengfei Hu 0006 等

In this paper, we propose a novel framework for recognizing both discrete and dimensional emotions. In our framework, deep features extracted from foundation models are used as robust acoustic and visual representations of raw video. Three different structures based on attention-guided feature gathering (AFG) are designed for deep feature fusion. Then, we introduce a joint decoding structure for emotion classification and valence regression in the decoding stage. A multi-task loss based on uncertainty is also designed to optimize the whole process. Finally, by combining three different structures on the posterior probability level, we obtain the final predictions of discrete and dimensional emotions. When tested on the dataset of multimodal emotion recognition challenge (MER 2023), the proposed framework yields consistent improvements in both emotion classification and valence regression. Our final system achieves state-of-the-art performance and ranks third on the leaderboard on MER-MULTI sub-challenge.

Wuyuan Xie, Miaohui Wang

Surface from gradient (SfG) is one of the fundamental methods to densely reconstruct 3D object surface in computer vision. However, the reconstruction of micro-geometric details has not been satisfactorily solved in existing SfG methods due to their non-integrability. In this paper, we present an effective discrete geometric approach to reconstruct fine-grained sharp surface feature with non-integrability. Specifically, We investigate the fine-grained structure of surfaces in the micro geometry domain. based on an adaptive projection on vertexes constrained by neighboring gradient vectors, and develop a gradient angle-guided energy optimization to generate a fine-grained surface. Experimental results on various challenging synthetic and real-world data show that the proposed method is able to effectively reconstruct challenging micro-geometric details for general SfG methods.