For simplicity, we omit the schedule coefficients in (5).

Kernel dimensionality reduction (KDR) algorithms find a low dimensional representation of the original data by optimizing kernel dependency measures that are capable ofcapturing nonlinear relationships.

Kernel dimensionality reduction (KDR) algorithms find a low dimensional representation of the original data by optimizing kernel dependency measures that are capable of capturing nonlinear relationships. The standard strategy is to first map the data into a high dimensional feature space using kernels prior to a projection onto a low dimensional space. While KDR methods can be easily solved by keeping the most dominant eigenvectors of the kernel matrix, its features are no longer easy to interpret. Alternatively, Interpretable KDR (IKDR) is different in that it projects onto a subspace \textit{before} the kernel feature mapping, therefore, the projection matrix can indicate how the original features linearly combine to form the new features. Unfortunately, the IKDR objective requires a non-convex manifold optimization that is difficult to solve and can no longer be solved by eigendecomposition.

While 2D diffusion models generate realistic, high-detail images, 3D shape generation methods like Score Distillation Sampling (SDS) built on these 2D diffusion models produce cartoon-like, over-smoothed shapes. To help explain this discrepancy, we show that the image guidance used in Score Distillation can be understood as the velocity field of a 2D denoising generative process, up to the choice of a noise term. In particular, after a change of variables, SDS resembles a high-variance version of Denoising Diffusion Implicit Models (DDIM) with a differently-sampled noise term: SDS introduces noise i.i.d.

For simplicity, we omit the schedule coefficients in (5).

A Picture is Worth a Thousand Prompts? Efficacy of Iterative Human-Driven Prompt Refinement in Image Regeneration T asks Khoi Trinh 1, Scott Seidenberger 1, Raveen Wijewickrama 2, Murtuza Jadliwala 2, Anindya Maiti 1 1 University of Oklahoma 2 University of Texas at San Antonio khoitrinh@ou.edu, Abstract With AI-generated content becoming ubiquitous across the web, social media, and other digital platforms, it is vital to examine how such content are inspired and generated. The creation of AIgenerated images often involves refining the input prompt iteratively to achieve desired visual outcomes. This study focuses on the relatively un-derexplored concept of image regeneration using AI, in which a human operator attempts to closely recreate a specific target image by iteratively refining their prompt. Image regeneration is distinct from normal image generation, which lacks any predefined visual reference. A separate challenge lies in determining whether existing image similarity metrics (ISMs) can provide reliable, objective feedback in iterative workflows, given that we do not fully understand if subjective human judgments of similarity align with these metrics. Consequently, we must first validate their alignment with human perception before assessing their potential as a feedback mechanism in the iterative prompt refinement process. To address these research gaps, we present a structured user study evaluating how iterative prompt refinement affects the similarity of regenerated images relative to their targets, while also examining whether ISMs capture the same improvements perceived by human observers. Our findings suggest that incremental prompt adjustments substantially improve alignment, verified through both subjective evaluations and quantitative measures--underscoring the broader potential of iterative workflows to enhance generative AI content creation across various application domains. 1 Introduction The rise of AI-generated content on online platforms has made it crucial to investigate how this type of content is created, specifically through the iterative processes of image generation and regeneration. While prior work has explored AI-led iterative refinement, this paper highlights the human's leading role in refining prompts and improving outcomes through their own judgment and control. The field of generative artificial intelligence (GenAI) has recently seen significant advancements, particularly in the development of text-to-image ( txt2img) models. These models provide an easy and fast process for creating high-quality artwork.

Summary: [19] has proposed recently an efficient iterative spectral (eigendecomposition) method (ISM) for the non-convex interpretable kernel dimensionality reduction (IKDR) objective in the context of alternative clustering. It established theoretical guarantees of ISM for the Gaussian kernel. The paper extends the theoretical guarantees of ISM to a family of kernels [Definition 1]. Each kernel in the ISM family has an associated surrogate matrix \Phi and the optimal projection is formed by the most dominant eigenvectors of \Phi [Theorem 1 and 2]. They showed that any conic combination of the ISM kernels is still an ISM kernel [Proposition 1] and therefore ISM can be extend to conic combination of kernels.

Kernel dimensionality reduction (KDR) algorithms find a low dimensional representation of the original data by optimizing kernel dependency measures that are capable of capturing nonlinear relationships. The standard strategy is to first map the data into a high dimensional feature space using kernels prior to a projection onto a low dimensional space. While KDR methods can be easily solved by keeping the most dominant eigenvectors of the kernel matrix, its features are no longer easy to interpret. Alternatively, Interpretable KDR (IKDR) is different in that it projects onto a subspace \textit{before} the kernel feature mapping, therefore, the projection matrix can indicate how the original features linearly combine to form the new features. Unfortunately, the IKDR objective requires a non-convex manifold optimization that is difficult to solve and can no longer be solved by eigendecomposition.