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Jiayi Guo

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math.OC Computer Vision math.PR

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preprint2026arXiv

InsightTok: Improving Text and Face Fidelity in Discrete Tokenization for Autoregressive Image Generation

Text and faces are among the most perceptually salient and practically important patterns in visual generation, yet they remain challenging for autoregressive generators built on discrete tokenization. A central bottleneck is the tokenizer: aggressive downsampling and quantization often discard the fine-grained structures needed to preserve readable glyphs and distinctive facial features. We attribute this gap to standard discrete-tokenizer objectives being weakly aligned with text legibility and facial fidelity, as these objectives typically optimize generic reconstruction while compressing diverse content uniformly. To address this, we propose InsightTok, a simple yet effective discrete visual tokenization framework that enhances text and face fidelity through localized, content-aware perceptual losses. With a compact 16k codebook and a 16x downsampling rate, InsightTok significantly outperforms prior tokenizers in text and face reconstruction without compromising general reconstruction quality. These gains consistently transfer to autoregressive image generation in InsightAR, producing images with clearer text and more faithful facial details. Overall, our results highlight the potential of specialized supervision in tokenizer training for advancing discrete image generation.

preprint2026arXiv

Refinement via Regeneration: Enlarging Modification Space Boosts Image Refinement in Unified Multimodal Models

Unified multimodal models (UMMs) integrate visual understanding and generation within a single framework. For text-to-image (T2I) tasks, this unified capability allows UMMs to refine outputs after their initial generation, potentially extending the performance upper bound. Current UMM-based refinement methods primarily follow a refinement-via-editing (RvE) paradigm, where UMMs produce editing instructions to modify misaligned regions while preserving aligned content. However, editing instructions often describe prompt-image misalignment only coarsely, leading to incomplete refinement. Moreover, pixel-level preservation, though necessary for editing, unnecessarily restricts the effective modification space for refinement. To address these limitations, we propose Refinement via Regeneration (RvR), a novel framework that reformulates refinement as conditional image regeneration rather than editing. Instead of relying on editing instructions and enforcing strict content preservation, RvR regenerates images conditioned on the target prompt and the semantic tokens of the initial image, enabling more complete semantic alignment with a larger modification space. Extensive experiments demonstrate the effectiveness of RvR, improving Geneval from 0.78 to 0.91, DPGBench from 84.02 to 87.21, and UniGenBench++ from 61.53 to 77.41.

preprint2023arXiv

Distributionally Robust Optimization under Mean-Covariance Ambiguity Set and Half-Space Support for Bivariate Problems

In this paper, we study a bivariate distributionally robust optimization problem with mean-covariance ambiguity set and half-space support. Under a conventional type of objective function widely adopted in inventory management, option pricing, and portfolio selection, we obtain closed-form tight bounds of the inner problem in six different cases. Through a primal-dual approach, we identify the optimal distributions in each case. As an application in inventory control, we first derive the optimal order quantity and the corresponding worst-case distribution, extending the existing results in the literature. Moreover, we show that under the distributionally robust setting, a centralized inventory system does not necessarily reduce the optimal total inventory, which contradicts conventional wisdom. Furthermore, we identify two effects, a conventional pooling effect, and a novel shifting effect, the combination of which determines the benefit of incorporating the covariance information in the ambiguity set. Finally, we demonstrate through numerical experiments the importance of keeping the covariance information in the ambiguity set instead of compressing the information into one dimension.

preprint2022arXiv

A Unified Framework for Generalized Moment Problems: a Novel Primal-Dual Approach

Generalized moment problems optimize functional expectation over a class of distributions with generalized moment constraints, i.e., the function in the moment can be any measurable function. These problems have recently attracted growing interest due to their great flexibility in representing nonstandard moment constraints, such as geometry-mean constraints, entropy constraints, and exponential-type moment constraints. Despite the increasing research interest, analytical solutions are mostly missing for these problems, and researchers have to settle for nontight bounds or numerical approaches that are either suboptimal or only applicable to some special cases. In addition, the techniques used to develop closed-form solutions to the standard moment problems are tailored for specific problem structures. In this paper, we propose a framework that provides a unified treatment for any moment problem. The key ingredient of the framework is a novel primal-dual optimality condition. This optimality condition enables us to reduce the original infinite dimensional problem to a nonlinear equation system with a finite number of variables. In solving three specific moment problems, the framework demonstrates a clear path for identifying the analytical solution if one is available, otherwise, it produces semi-analytical solutions that lead to efficient numerical algorithms. Finally, through numerical experiments, we provide further evidence regarding the performance of the resulting algorithms by solving a moment problem and a distributionally robust newsvendor problem.

preprint2020arXiv

Bounding probability of small deviation on sum of independent random variables: Combination of moment approach and Berry-Esseen theorem

In the context of bounding probability of small deviation, there are limited general tools. However, such bounds have been widely applied in graph theory and inventory management. We introduce a common approach to substantially sharpen such inequality bounds by combining the semidefinite optimization approach of moments problem and the Berry-Esseen theorem. As an application, we improve the lower bound of Feige's conjecture from 0.14 to 0.1798.

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