Yuzhen Ding, Hongying Feng, Jianfeng Zhao, Jason Holmes, Martin Bues, Lisa A. McGee, Jean-Claude M. Rwigema, Nathan Y. Yu 等 17 位作者
Background and purpose: Intensity-modulated proton therapy (IMPT) enables conformal dose delivery for head and neck (H&N) cancers. However, its sensitivity to inter-fractional anatomical changes motivates online adaptations, where rapid and accurate Monte Carlo (MC) dose calculation remains a major bottleneck. Low-statistics MC simulations reduce computation time but introduce noise. This study aimed to develop a diffusion-transformer framework to recover high-statistics dose distributions from noisy MC simulations. Materials and methods: A diffusion-transformer-based dose denoising framework was developed. Eighty H&N patients were used for training and additional 10 H&N patients and 30 patients with lung, breast, and prostate cancers (10 per site) were used for evaluation. Noisy and high-statistics dose maps were generated using MCsquare. The model was trained using noisy dose maps and CT images as inputs and high-statistics dose maps as ground truth, with mean squared error, residual, regional mean absolute error (MAE), and dose-volume histogram (DVH) losses. Performance was evaluated using MAE, 3D gamma passing rates, and DVH indices. Results: Mean whole-body MAE ranged from 0.08 +/- 0.06 to 0.20 +/- 0.11 Gy (Relative Biological Effectiveness, RBE) (RBE = 1.1) across test cohorts. Mean whole-body 3 %/2 mm gamma passing rates ranged from 95.8 +/- 0.8 % to 97.6 +/- 0.9 %. DVH indices from high-statistics and predicted dose distributions showed close agreement for clinical target volumes and organs of interest. Conclusions: The diffusion-transformer-based framework denoised low-statistics MC dose distributions. Despite being trained on H&N data, the model generalized to lung, breast, and prostate cohorts without retraining.
Justin Y. Chen, Ying Feng, Piotr Indyk, Michael Kapralov, Ekaterina Kochetkova, Boris Prokhorov
A growing body of work on KV-cache compression aims to reduce the memory requirements of autoregressive generation. These methods compress the stored context while approximately preserving attention computation, enabling generation with reduced memory consumption. Almost tight theoretical results on the worst case space complexity of attention have recently been obtained, but they are achieved by instances where queries can be perfectly aligned with keys. This directly contradicts the observed anisotropy of the key/query geometry in real transformers. In particular, it has been shown empirically that key/query cosine similarities are small even for most correlated pairs, i.e., near-perfect alignment of queries with keys does not happen in practice. In this paper, we study the space complexity of attention approximation under the assumption that key/query cosine similarities belong to a small interval around zero, i.e., a query cannot align too much with any key. We give a nearly space optimal algorithm and a corresponding space lower bound. Surprisingly, the distribution of key/query cosine similarities in our lower bound exhibits the anisotropy property empirically established and studied in the literature. Additionally, we show that the simple uniform sampling algorithm is nearly optimal for a typical range of parameters, supporting its surprising effectiveness on real datasets.
David P. Woodruff, Vincent Cohen-Addad, Lalit Jain, Jieming Mao, Song Zuo, MohammadHossein Bateni, Simina Branzei, Michael P. Brenner 等 36 位作者
Recent advances in large language models (LLMs) have opened new avenues for accelerating scientific research. While models are increasingly capable of assisting with routine tasks, their ability to contribute to novel, expert-level mathematical discovery is less understood. We present a collection of case studies demonstrating how researchers have successfully collaborated with advanced AI models, specifically Google's Gemini-based models (in particular Gemini Deep Think and its advanced variants), to solve open problems, refute conjectures, and generate new proofs across diverse areas in theoretical computer science, as well as other areas such as economics, optimization, and physics. Based on these experiences, we extract common techniques for effective human-AI collaboration in theoretical research, such as iterative refinement, problem decomposition, and cross-disciplinary knowledge transfer. While the majority of our results stem from this interactive, conversational methodology, we also highlight specific instances that push beyond standard chat interfaces. These include deploying the model as a rigorous adversarial reviewer to detect subtle flaws in existing proofs, and embedding it within a "neuro-symbolic" loop that autonomously writes and executes code to verify complex derivations. Together, these examples highlight the potential of AI not just as a tool for automation, but as a versatile, genuine partner in the creative process of scientific discovery.