Previous work has demonstrated that attention mechanisms are Turing complete. More recently, it has been shown that a looped 9-layer Transformer can function as a universal programmable computer. In contrast, the multi-layer perceptrons with $\mathsf{ReLU}$ activation ($\mathsf{ReLU}$-$\mathsf{MLP}$), one of the most fundamental components of neural networks, is known to be expressive; specifically, a two-layer neural network is a universal approximator given an exponentially large number of hidden neurons. However, it remains unclear whether a $\mathsf{ReLU}$-$\mathsf{MLP}$ can be made into a universal programmable computer using a practical number of weights. In this work, we provide an affirmative answer that a looped 23-layer $\mathsf{ReLU}$-$\mathsf{MLP}$ is capable of performing the basic necessary operations, more efficiently and effectively functioning as a programmable computer than a looped Transformer. This indicates simple modules have stronger expressive power than previously expected and have not been fully explored. Our work provides insights into the mechanisms of neural networks and demonstrates that complex tasks, such as functioning as a programmable computer, do not necessarily require advanced architectures like Transformers.

This paper introduces Force Matching (ForM), a novel framework for generative modeling that represents an initial exploration into leveraging special relativistic mechanics to enhance the stability of the sampling process. By incorporating the Lorentz factor, ForM imposes a velocity constraint, ensuring that sample velocities remain bounded within a constant limit. This constraint serves as a fundamental mechanism for stabilizing the generative dynamics, leading to a more robust and controlled sampling process. We provide a rigorous theoretical analysis demonstrating that the velocity constraint is preserved throughout the sampling procedure within the ForM framework. To validate the effectiveness of our approach, we conduct extensive empirical evaluations. On the half-moons dataset, ForM significantly outperforms baseline methods, achieving the lowest Euclidean distance loss of 0.714, in contrast to vanilla first-order flow matching (5.853) and first- and second-order flow matching (5.793). Additionally, we perform an ablation study to further investigate the impact of our velocity constraint, reaffirming the superiority of ForM in stabilizing the generative process. The theoretical guarantees and empirical results underscore the potential of integrating special relativity principles into generative modeling. Our findings suggest that ForM provides a promising pathway toward achieving stable, efficient, and flexible generative processes. This work lays the foundation for future advancements in high-dimensional generative modeling, opening new avenues for the application of physical principles in machine learning.

As AI research surges in both impact and volume, conferences have imposed submission limits to maintain paper quality and alleviate organizational pressure. In this work, we examine the fairness of desk-rejection systems under submission limits and reveal that existing practices can result in substantial inequities. Specifically, we formally define the paper submission limit problem and identify a critical dilemma: when the number of authors exceeds three, it becomes impossible to reject papers solely based on excessive submissions without negatively impacting innocent authors. Thus, this issue may unfairly affect early-career researchers, as their submissions may be penalized due to co-authors with significantly higher submission counts, while senior researchers with numerous papers face minimal consequences. To address this, we propose an optimization-based fairness-aware desk-rejection mechanism and formally define two fairness metrics: worst-case fairness and average fairness. We prove that optimizing worst-case fairness is NP-hard, whereas average fairness can be efficiently optimized via linear programming. Through case studies, we demonstrate that our proposed system ensures greater equity than existing methods, including those used in CVPR 2025, offering a more socially just approach to managing excessive submissions in AI conferences.

Flow-based generative models have shown promise in various machine learning applications, but they often face challenges in handling noise and ensuring robustness in trajectory estimation. In this work, we propose NRFlow, a novel extension to flow-based generative modeling that incorporates second-order dynamics through acceleration fields. We develop a comprehensive theoretical framework to analyze the regularization effects of high-order terms and derive noise robustness guarantees. Our method leverages a two-part loss function to simultaneously train first-order velocity fields and high-order acceleration fields, enhancing both smoothness and stability in learned transport trajectories. These results highlight the potential of high-order flow matching for robust generative modeling in complex and noisy environments.

Training data privacy is a fundamental problem in modern Artificial Intelligence (AI) applications, such as face recognition, recommendation systems, language generation, and many others, as it may contain sensitive user information related to legal issues. To fundamentally under-stand how privacy mechanisms work in AI applications, we study differential privacy (DP) in the Neural Tangent Kernel (NTK) regression setting, where DP is one of the most powerful tools for measuring privacy under statistical learning, and NTK is one of the most popular analysis frameworks for studying the learning mechanisms of deep neural networks. In our work, we can show provable guarantees for both differential privacy and test accuracy of our NTK regression. Furthermore, we conduct experiments on the basic image classification dataset CIFAR10 to demonstrate that NTK regression can preserve good accuracy under a modest privacy budget, supporting the validity of our analysis. To our knowledge, this is the first work to provide a DP guarantee for NTK regression.

We present TokenCompose, a Latent Diffusion Model for text-to-image generation that achieves enhanced consistency between user-specified text prompts and model-generated images. Despite its tremendous success, the standard denoising process in the Latent Diffusion Model takes text prompts as conditions only, absent explicit constraint for the consistency between the text prompts and the image contents, leading to unsatisfactory results for composing multiple object categories. Our proposed TokenCompose aims to improve multi-category instance composition by introducing the token-wise consistency terms between the image content and object segmentation maps in the finetuning stage. TokenCompose can be applied directly to the existing training pipeline of text-conditioned diffusion models without extra human labeling information. By finetuning Stable Diffusion with our approach, the model exhibits significant improvements in multi-category instance composition and enhanced photorealism for its generated images.11Project done while Zirui WangZhizhou Sha and Yilin Wang interned at UC San Diego.