Daily Papers

Singly-TASE operators for the numerical solution of stiff differential equations were proposed by Calvo et al. in J.Sci. Comput. 2023 to reduce the computational cost of Runge-Kutta-TASE (RKTASE) methods when the involved linear systems are solved by some LU factorization. In this paper we propose a modification of these methods to improve the efficiency by considering different TASE operators for each stage of the Runge-Kutta. We prove that the resulting RKTASE methods are equivalent to W-methods (Steihaug and Wolfbrandt, Mathematics of Computation,1979) and this allows us to obtain the order conditions of the proposed Modified Singly-RKTASE methods (MSRKTASE) through the theory developed for the W-methods. We construct new MSRKTASE methods of order two and three and demonstrate their effectiveness through numerical experiments on both linear and nonlinear stiff systems. The results show that the MSRKTASE schemes significantly enhance efficiency and accuracy compared to previous Singly-RKTASE schemes.

Prostate cancer is one of the most common and lethal cancers among men, making its early detection critically important. Although ultrasound imaging offers greater accessibility and cost-effectiveness compared to MRI, traditional transrectal ultrasound methods suffer from low sensitivity, especially in detecting anteriorly located tumors. Ultrasound computed tomography provides quantitative tissue characterization, but its clinical implementation faces significant challenges, particularly under anatomically constrained limited-angle acquisition conditions specific to prostate imaging. To address these unmet needs, we introduce OpenPros, the first large-scale benchmark dataset explicitly developed for limited-view prostate USCT. Our dataset includes over 280,000 paired samples of realistic 2D speed-of-sound (SOS) phantoms and corresponding ultrasound full-waveform data, generated from anatomically accurate 3D digital prostate models derived from real clinical MRI/CT scans and ex vivo ultrasound measurements, annotated by medical experts. Simulations are conducted under clinically realistic configurations using advanced finite-difference time-domain and Runge-Kutta acoustic wave solvers, both provided as open-source components. Through comprehensive baseline experiments, we demonstrate that state-of-the-art deep learning methods surpass traditional physics-based approaches in both inference efficiency and reconstruction accuracy. Nevertheless, current deep learning models still fall short of delivering clinically acceptable high-resolution images with sufficient accuracy. By publicly releasing OpenPros, we aim to encourage the development of advanced machine learning algorithms capable of bridging this performance gap and producing clinically usable, high-resolution, and highly accurate prostate ultrasound images. The dataset is publicly accessible at https://open-pros.github.io/.

The dominant line of work in domain adaptation has focused on learning invariant representations using domain-adversarial training. In this paper, we interpret this approach from a game theoretical perspective. Defining optimal solutions in domain-adversarial training as a local Nash equilibrium, we show that gradient descent in domain-adversarial training can violate the asymptotic convergence guarantees of the optimizer, oftentimes hindering the transfer performance. Our analysis leads us to replace gradient descent with high-order ODE solvers (i.e., Runge-Kutta), for which we derive asymptotic convergence guarantees. This family of optimizers is significantly more stable and allows more aggressive learning rates, leading to high performance gains when used as a drop-in replacement over standard optimizers. Our experiments show that in conjunction with state-of-the-art domain-adversarial methods, we achieve up to 3.5% improvement with less than of half training iterations. Our optimizers are easy to implement, free of additional parameters, and can be plugged into any domain-adversarial framework.

Linear-time attention and State Space Models (SSMs) promise to solve the quadratic cost bottleneck in long-context language models employing softmax attention. We introduce Error-Free Linear Attention (EFLA), a numerically stable, fully parallelism and generalized formulation of the delta rule. Specifically, we formulate the online learning update as a continuous-time dynamical system and prove that its exact solution is not only attainable but also computable in linear time with full parallelism. By leveraging the rank-1 structure of the dynamics matrix, we directly derive the exact closed-form solution effectively corresponding to the infinite-order Runge-Kutta method. This attention mechanism is theoretically free from error accumulation, perfectly capturing the continuous dynamics while preserving the linear-time complexity. Through an extensive suite of experiments, we show that EFLA enables robust performance in noisy environments, achieving lower language modeling perplexity and superior downstream benchmark performance than DeltaNet without introducing additional parameters. Our work provides a new theoretical foundation for building high-fidelity, scalable linear-time attention models.