非凸优化

As language models continue to scale, Large Language Models (LLMs) have exhibited emerging capabilities in In-Context Learning (ICL), enabling them to solve language tasks by prefixing a few in-context demonstrations (ICDs) as context. Inspired by these advancements, researchers have extended these techniques to develop Large Multimodal Models (LMMs) with ICL capabilities. However, existing LMMs face a critical issue: they often fail to effectively leverage the visual context in multimodal demonstrations and instead simply follow textual patterns. This indicates that LMMs do not achieve effective alignment between multimodal demonstrations and model outputs. To address this problem, we propose Symbol Demonstration Direct Preference Optimization (SymDPO). Specifically, SymDPO aims to break the traditional paradigm of constructing multimodal demonstrations by using random symbols to replace text answers within instances. This forces the model to carefully understand the demonstration images and establish a relationship between the images and the symbols to answer questions correctly. We validate the effectiveness of this method on multiple benchmarks, demonstrating that with SymDPO, LMMs can more effectively understand the multimodal context within examples and utilize this knowledge to answer questions better. Code is available at https://github.com/APiaoG/SymDPO.

We propose a novel unsupervised cross-modal homography estimation learning framework, named Split Supervised Homography estimation Network (SSHNet). SSHNet reformulates the unsupervised cross-modal homography estimation into two supervised sub-problems, each addressed by its specialized network: a homography estimation network and a modality transfer network. To realize stable training, we introduce an effective split optimization strategy to train each network separately within its respective sub-problem. We also formulate an extra homography feature space supervision to enhance feature consistency, further boosting the estimation accuracy. Moreover, we employ a simple yet effective distillation training technique to reduce model parameters and improve cross-domain generalization ability while maintaining comparable performance. The training stability of SSHNet enables its cooperation with various homography estimation architectures. Experiments reveal that the SSHNet using IHN as homography estimation network, namely SSHNet-IHN, outperforms previous unsupervised approaches by a significant margin. Even compared to supervised approaches MHN and LocalTrans, SSHNet-IHN achieves 47.4% and 85.8% mean average corner errors (MACEs) reduction on the challenging OPT-SAR dataset. Source code is available at https://github.com/Junchen-Yu/SSHNet.

Latent diffusion models with Transformer architectures excel at generating high-fidelity images. However, recent studies reveal an optimization dilemma in this two-stage design: while increasing the per-token feature dimension in visual tokenizers improves reconstruction quality, it requires substantially larger diffusion models and more training iterations to achieve comparable generation performance. Consequently, existing systems often settle for sub-optimal solutions, either producing visual artifacts due to information loss within tokenizers or failing to converge fully due to expensive computation costs. We argue that this dilemma stems from the inherent difficulty in learning unconstrained high-dimensional latent spaces. To address this, we propose aligning the latent space with pre-trained vision foundation models when training the visual tokenizers. Our proposed VA-VAE (Vision foundation model Aligned Variational AutoEncoder) significantly expands the reconstruction-generation frontier of latent diffusion models, enabling faster convergence of Diffusion Transformers (DiT) in high-dimensional latent spaces. To exploit the full potential of VA-VAE, we build an enhanced DiT baseline with improved training strategies and architecture designs, termed LightningDiT. The integrated system achieves state-of-the-art (SOTA) performance on ImageNet 256 generation with an FID score of 1.35 while demonstrating remarkable training efficiency by reaching an FID score of 2.11 in just 64 epochs -- representing an over 21 times convergence speedup compared to the original DiT. Models and codes are available at https://github.com/hustvl/LightningDiT.

Accurate localization is essential for autonomous driving, but GNSS-based methods struggle in challenging environments such as urban canyons. Cross-view pose optimization offers an effective solution for localization by directly estimating vehicle pose using satellite-view images. However, existing methods primarily rely on cross-view features at a given pose, neglecting fine-grained contexts for precision and global contexts for robustness against large initial pose errors. To overcome these limitations, we propose PIDLoc, a novel cross-view pose optimization approach inspired by the proportional-integral-derivative (PID) controller. Using RGB images and LiDAR data, the PIDLoc models cross-view feature relationships through the PID branches and estimates pose via the spatially aware pose estimator (SPE). To enhance localization accuracy, the PID branches leverage feature differences for local context (P), aggregated feature differences for global context (I), and gradients of feature differences for fine-grained context (D). Integrated with the PID branches, the SPE captures spatial relationships within the PID-branch features for consistent localization. Experimental results demonstrate that the PIDLoc achieves state-of-the-art performance in cross-view pose estimation for the KITTI dataset, reducing position error by 37.8% compared with the previous state-of-the-art. Our code is available at https://github.com/url-kaist/PIDLoc.

Problems in differentiable rendering often involve optimizing scene parameters that cause motion in image space. The gradients for such parameters tend to be sparse, leading to poor convergence. While existing methods address this sparsity through proxy gradients such as topological derivatives or lagrangian derivatives, they make simplifying assumptions about rendering. Multi-resolution image pyramids offer an alternative approach but prove unreliable in practice. We introduce a method that uses locally orderless images --- where each pixel maps to a histogram of intensities that preserves local variations in appearance. Using an inverse rendering objective that minimizes histogram distance, our method extends support for sparsely defined image gradients and recovers optimal parameters. We validate our method on various inverse problems using both synthetic and real data.

Neural Radiance Fields (NeRF) has demonstrated its superior capability to represent 3D geometry but require accurately precomputed camera poses during training. To mitigate this requirement, existing methods jointly optimize camera poses and NeRF often relying on good pose initialisation or depth priors. However, these approaches struggle in challenging scenarios, such as large rotations, as they map each camera to a world coordinate system. We propose a novel method that eliminates prior dependencies by modeling continuous camera motions as time-dependent angular velocity and velocity. Relative motions between cameras are learned first via velocity integration, while camera poses can be obtained by aggregating such relative motions up to a world coordinate system defined at a single time step within the video. Specifically, accurate continuous camera movements are learned through a time-dependent NeRF, which captures local scene geometry and motion by training from neighboring frames for each time step. The learned motions enable fine-tuning the NeRF to represent the full scene geometry. Experiments on Co3D and Scannet show our approach achieves superior camera pose and depth estimation and comparable novel-view synthesis performance compared to state-of-the-art methods.

Weight decay is a widely used technique in training machine learning models, known to empirically enhance the generalization of Stochastic Gradient Descent (SGD). While intuitively weight decay allows SGD to train a regularized model rather than the original one, there is limited theoretical understanding of why SGD with weight decay (SGDW) yields results consistent with the unregularized model, or how weight decay improves generalization. This paper establishes a convergence theory for SGDW in the context of the unregularized model, under weaker assumptions than previous analyses of weight decay. Our theory demonstrates that weight decay does not accelerate the convergence of SGD. For generalization, we provide the first theoretical proof of weight decay's benefit in nonconvex optimization. Additionally, we extend our results to sign-based stochastic gradient algorithms, such as SignSGD. Numerical experiments on classical benchmarks validate our theoretical findings.

Active learning (AL) is a label-efficient machine learning paradigm that focuses on selectively annotating high-value instances to maximize learning efficiency. Its effectiveness can be further enhanced by incorporating weak supervision, which uses rough yet cost-effective annotations instead of exact (i.e., full) but expensive annotations. We introduce a novel AL framework, Instance-wise Supervision-Level Optimization (ISO), which not only selects the instances to annotate but also determines their optimal annotation level within a fixed annotation budget. Its optimization criterion leverages the value-to-cost ratio (VCR) of each instance while ensuring diversity among the selected instances. In classification experiments, ISO consistently outperforms traditional AL methods and surpasses a state-of-the-art AL approach that combines full and weak supervision, achieving higher accuracy at a lower overall cost.

Without using explicit reward, direct preference optimization (DPO) employs paired human preference data to fine-tune generative models, a method that has garnered considerable attention in large language models (LLMs). However, exploration of aligning text-to-image (T2I) diffusion models with human preferences remains limited. In comparison to supervised fine-tuning, existing methods that align diffusion model suffer from low training efficiency and subpar generation quality due to the long Markov chain process and the intractability of the reverse process. To address these limitations, we introduce DDIM-InPO, an efficient method for direct preference alignment of diffusion models. Our approach conceptualizes diffusion model as a single-step generative model, allowing us to fine-tune the outputs of specific latent variables selectively. In order to accomplish this objective, we first assign implicit rewards to any latent variable directly via a reparameterization technique. Then we construct an Inversion technique to estimate appropriate latent variables for preference optimization. This modification process enables the diffusion model to only fine-tune the outputs of latent variables that have a strong correlation with the preference dataset. Experimental results indicate that our DDIM-InPO achieves state-of-the-art performance with just 400 steps of fine-tuning, surpassing all preference aligning baselines for T2I diffusion models in human preference evaluation tasks.

We propose a method, HotSpot, for optimizing neural signed distance functions. Existing losses, such as the eikonal loss, act as necessary but insufficient constraints and cannot guarantee that the recovered implicit function represents a true distance function, even if the output minimizes these losses almost everywhere. Furthermore, the eikonal loss suffers from stability issues in optimization. Finally, in conventional methods, regularization losses that penalize surface area distort the reconstructed signed distance function. We address these challenges by designing a loss function using the solution of a screened Poisson equation. Our loss, when minimized, provides an asymptotically sufficient condition to ensure the output converges to a true distance function. Our loss also leads to stable optimization and naturally penalizes large surface areas. We present theoretical analysis and experiments on both challenging 2D and 3D datasets and show that our method provides better surface reconstruction and a more accurate distance approximation.

Federated Learning (FL) has emerged as a promising framework for distributed machine learning, enabling collaborative model training without sharing local data, thereby preserving privacy and enhancing security. However, data heterogeneity resulting from differences across user behaviors, preferences, and device characteristics poses a significant challenge for federated learning. Most previous works overlook the adjustment of aggregation weights, relying solely on dataset size for weight assignment, which often leads to unstable convergence and reduced model performance. Recently, several studies have sought to refine aggregation strategies by incorporating dataset characteristics and model alignment. However, adaptively adjusting aggregation weights while ensuring data security--without requiring additional proxy data--remains a significant challenge. In this work, we propose Federated learning with Adaptive Weight Aggregation (FedAWA), a novel method that adaptively adjusts aggregation weights based on client vectors during the learning process. The client vector captures the direction of model updates, reflecting local data variations, and is used to optimize the aggregation weight without requiring additional datasets or violating privacy. By assigning higher aggregation weights to local models whose updates align closely with the global optimization direction, FedAWA enhances the stability and generalization of the global model. Extensive experiments under diverse scenarios demonstrate the superiority of our method, providing a promising solution to the challenges of data heterogeneity in federated learning.

Recent advancements in 3D editing have highlighted the potential of text-driven methods in real-time, user-friendly AR/VR applications. However, current methods rely on 2D diffusion models without adequately considering multi-view information, resulting in multi-view inconsistency. While 3D Gaussian Splatting (3DGS) significantly improves rendering quality and speed, its 3D editing process encounters difficulties with inefficient optimization, as pre-trained Gaussians retain excessive source information, hindering optimization. To address these limitations, we propose EditSplat, a novel 3D editing framework that integrates Multi-view Fusion Guidance (MFG) and Attention-Guided Trimming (AGT). Our MFG ensures multi-view consistency by incorporating essential multi-view information into the diffusion process, leveraging classifier-free guidance from the text-to-image diffusion model and the geometric properties of 3DGS. Additionally, our AGT leverages the explicit representation of 3DGS to selectively prune and optimize 3D Gaussians, enhancing optimization efficiency and enabling precise, semantically rich local edits. Through extensive qualitative and quantitative evaluations, EditSplat achieves superior multi-view consistency and editing quality over existing methods, significantly enhancing overall efficiency.

Direct Preference Optimization (DPO) has been proposed as an effective and efficient alternative to reinforcement learning from human feedback (RLHF). In this paper, we propose a novel and enhanced version of DPO based on curriculum learning for text-to-image generation. Our method is divided into two training stages. First, a ranking of the examples generated for each prompt is obtained by employing a reward model. Then, increasingly difficult pairs of examples are sampled and provided to a text-to-image generative (diffusion or consistency) model. Generated samples that are far apart in the ranking are considered to form easy pairs, while those that are close in the ranking form hard pairs. In other words, we use the rank difference between samples as a measure of difficulty. The sampled pairs are split into batches according to their difficulty levels, which are gradually used to train the generative model. Our approach, Curriculum DPO, is compared against state-of-the-art fine-tuning approaches on nine benchmarks, outperforming the competing methods in terms of text alignment, aesthetics and human preference. Our code is available at https://github.com/CroitoruAlin/Curriculum-DPO.

Effective Class Incremental Segmentation (CIS) requires simultaneously mitigating catastrophic forgetting and ensuring sufficient plasticity to integrate new classes. The inherent conflict above often leads to a back-and-forth, which turns the objective into finding the balance between the performance of previous (old) and incremental (new) classes. To address this conflict, we introduce a novel approach, Conflict Mitigation via Branched Optimization (CoMBO). Within this approach, we present the Query Conflict Reduction module, designed to explicitly refine queries for new classes through lightweight, class-specific adapters. This module provides an additional branch for the acquisition of new classes while preserving the original queries for distillation. Moreover, we develop two strategies to further mitigate the conflict following the branched structure, i.e., the Half-Learning Half-Distillation (HDHL) over classification probabilities, and the Importance-Based Knowledge Distillation (IKD) over query features. HDHL selectively engages in learning for classification probabilities of queries that match the ground truth of new classes, while aligning unmatched ones to the corresponding old probabilities, thus ensuring retention of old knowledge while absorbing new classes via learning negative samples. Meanwhile, IKD assesses the importance of queries based on their matching degree to old classes, prioritizing the distillation of important features and allowing less critical features to evolve. Extensive experiments in Class Incremental Panoptic and Semantic Segmentation settings have demonstrated the superior performance of CoMBO. Project page: https://guangyu-ryan.github.io/CoMBO.

Aligning text-to-image (T2I) diffusion models with prefer-ence optimization is valuable for human-annotated datasets, but the heavy cost of manual data collection limits scalability. Using reward models offers an alternative, however, current preference optimization methods fall short in exploiting the rich information, as they only consider pairwise preference distribution. Furthermore, they lack generalization to multi-preference scenarios and struggle to handle inconsistencies between rewards. To address this, we present Calibrated Preference Optimization (CaPO), a novel method to align T2I diffusion models by incorporating the general preference from multiple reward models without human annotated data. The core of our approach involves a reward calibration method to approximate the general preference by computing the expected win-rate against the samples generated by the pretrained models. Additionally, we propose a frontier-based pair selection method that effectively manages the multi-preference distribution by selecting pairs from Pareto frontiers. Finally, we use regression loss to fine-tune diffusion models to match the difference between calibrated rewards of a selected pair. Experimental results show that CaPO consistently outperforms prior methods, such as Direct Preference Optimization (DPO), in both single and multi-reward settings validated by evaluation on T2I benchmarks, including GenEval and T2I-Compbench.

Achieving controllable and consistent editing in dynamic 3D scenes remains a significant challenge. Previous work is largely constrained by its editing backbones, resulting in inconsistent edits and limited controllability. We propose to address this challenge using personalized diffusion models. In our work, we introduce a novel framework that first fine-tunes the InstructPix2Pix model, followed by a two-stage optimization of the scene based on deformable 3D Gaussians. The fine-tuning enables the model to "learn" the editing ability from a single edited reference image. This reduces the more complex task of dynamic scene editing to the more simple 2D image editing problem. By directly learning editing regions and styles from the reference, our approach enables consistent and precise local edits without the need for tracking desired editing regions, effectively addressing key challenges in dynamic scene editing. Then, our two-stage optimization progressively edits the trained dynamic scene, using a designed edited image buffer to accelerate convergence and improve temporal consistency. Compared to state-of-the-art methods, our approach offers more flexible and controllable local scene editing, achieving high-quality and consistent results.

Learned image compression (LIC) using deep learning architectures has seen significant advancements, yet standard rate-distortion (R-D) optimization often encounters imbalanced updates due to diverse gradients of the rate and distortion objectives. This imbalance can lead to suboptimal optimization, where one objective dominates, thereby reducing overall compression efficiency. To address this challenge, we reformulate R-D optimization as a multi-objective optimization (MOO) problem and introduce two balanced R-D optimization strategies that adaptively adjust gradient updates to achieve more equitable improvements in both rate and distortion. The first proposed strategy utilizes a coarse-to-fine gradient descent approach along standard R-D optimization trajectories, making it particularly suitable for training LIC models from scratch. The second proposed strategy analytically addresses the reformulated optimization as a quadratic programming problem with an equality constraint, which is ideal for fine-tuning existing models. Experimental results demonstrate that both proposed methods enhance the R-D performance of LIC models, achieving around a 2% BD-Rate reduction with acceptable additional training cost, leading to a more balanced and efficient optimization process. Code will be available at https://gitlab.com/viper-purdue/Balanced-RD.

Generating visually appealing images is fundamental to modern text-to-image generation models. A potential solution to better aesthetics is direct preference optimization (DPO), which has been applied to diffusion models to improve general image quality including prompt alignment and aesthetics. Popular DPO methods propagate preference labels from clean image pairs to all the intermediate steps along the two generation trajectories. However, preference labels provided in existing datasets are blended with layout and aesthetic opinions, which would disagree with aesthetic preference. Even if aesthetic labels were provided (at substantial cost), it would be hard for the two-trajectory methods to capture nuanced visual differences at different steps. To improve aesthetics economically, this paper uses existing generic preference data and introduces step-by-step preference optimization (SPO) that discards the propagation strategy and allows fine-grained image details to be assessed. Specifically, at each denoising step, we 1) sample a pool of candidates by denoising from a shared noise latent, 2) use a step-aware preference model to find a suitable win-lose pair to supervise the diffusion model, and 3) randomly select one from the pool to initialize the next denoising step. This strategy ensures that diffusion models focus on the subtle, fine-grained visual differences instead of layout aspect. We find that aesthetics can be significantly enhanced by accumulating these improved minor differences. When fine-tuning Stable Diffusion v1.5 and SDXL, SPO yields significant improvements in aesthetics compared with existing DPO methods while not sacrificing image-text alignment compared with vanilla models. Moreover, SPO converges much faster than DPO methods due to the use of more correct preference labels provided by the step-aware preference model. Code and models are available at https://github.com/RockeyCoss/SPO.

Recently, model merging methods have demonstrated powerful strengths in combining abilities on various tasks from multiple Large Language Models (LLMs). While previous model merging methods mainly focus on merging homogeneous models with identical architecture, they meet challenges when dealing with Multimodal Large Language Models (MLLMs) with inherent heterogeneous property, including differences in model architecture and the asymmetry in the parameter space. In this work, we propose AdaMMS, a novel model merging method tailored for heterogeneous MLLMs. Our method tackles the challenges in three steps: mapping, merging and searching. Specifically, we first design mapping function between models to apply model merging on MLLMs with different architecture. Then we apply linear interpolation on model weights to actively adapt the asymmetry in the heterogeneous MLLMs. Finally in the hyper-parameter searching step, we propose an unsupervised hyper-parameter selection method for model merging. As the first model merging method capable of merging heterogeneous MLLMs without labeled data, extensive experiments on various model combinations demonstrated that AdaMMS outperforms previous model merging methods on various vision-language benchmarks.