theory->optimization

Diffusion-based text-to-image (T2I) models have recently excelled in high-quality image generation, particularly in a training-free manner, enabling cost-effective adaptability and generalization across diverse tasks. However, while the existing methods have been continuously focusing on several challenges such as "missing objects" and "mismatched attributes," another critical issue of "mislocated objects" remains where generated spatial positions fail to align with text prompts. Surprisingly, ensuring such seemingly basic functionality remains challenging in popular T2I models due to the inherent difficulty of imposing explicit spatial guidance via text forms. To address this, we propose STORM (Spatial Transport Optimization by Repositioning Attention Map), a novel training-free approach for spatially coherent T2I synthesis. STORM employs Spatial Transport Optimization (STO), rooted in optimal transport theory, to dynamically adjust object attention maps for precise spatial adherence, supported by a Spatial Transport (ST) Cost function that enhances spatial understanding. Our analysis shows that integrating spatial awareness is most effective in the early denoising stages, while later phases refine details. Extensive experiments demonstrate that STORM surpasses existing methods, effectively mitigating mislocated objects while improving missing and mismatched attributes, setting a new benchmark for spatial alignment in T2I synthesis.

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.

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.

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.

Ranking entities such as algorithms, devices, methods, or models based on their performances, while accounting for application-specific preferences, is a challenge. To address this challenge, we establish the foundations of a universal theory for performance-based ranking. First, we introduce a rigorous framework built on top of both the probability and order theories. Our new framework encompasses the elements necessary to (1) manipulate performances as mathematical objects, (2) express which performances are worse than or equivalent to others, (3) model tasks through a variable called satisfaction, (4) consider properties of the evaluation, (5) define scores, and (6) specify application-specific preferences through a variable called importance. On top of this framework, we propose the first axiomatic definition of performance orderings and performance-based rankings. Then, we introduce a universal parametric family of scores, called ranking scores, that can be used to establish rankings satisfying our axioms, while considering application-specific preferences. Finally, we show, in the case of two-class classification, that the family of ranking scores encompasses well-known performance scores, including the accuracy, the true positive rate (recall, sensitivity), the true negative rate (specificity), the positive predictive value (precision), and F1. However, we also show that some other scores commonly used to compare classifiers are unsuitable to derive performance orderings satisfying the axioms.

We present EvOcc, a novel evidential semantic occupancy mapping framework. It consists of two parts: (1) an evidential approach for calculating the ground-truth 3D semantic occupancy maps from noisy LiDAR measurements, and (2) a method for training image-based occupancy estimation models through a new loss formulation. In contrast to state-of-the-art semantic occupancy maps, our approach explicitly models the uncertainty introduced by unobserved spaces or contradicting measurements and we show that using it results in significantly stronger models. Evaluated as ray-based mIoU, our evidential semantic occupancy mapping approach improves over the baselines by at least 15.8\% for the ground truth and 5.5\% for the trained model. Overall, we make a significant contribution towards more detailed and uncertainty-aware 3D environment understanding and safe operation in autonomous driving.

Existing domain adaptation systems can hardly be applied to real-world problems with new classes presenting at deployment time, especially regarding source-free scenarios where multiple source domains do not share the label space despite being given a few labeled target data. To address this, we consider a challenging problem: multi-source semi-supervised open-set domain adaptation and propose a learning theory via joint error, effectively tackling strong domain shift. To generalize the algorithm into source-free cases, we introdcue a computationally efficient and architecture-flexible attention-based feature generation module. Extensive experiments on various data sets demonstrate the significant improvement of our proposed algorithm over baselines.