#01Aug 21, 2026
math.OC
Primal Acceleration of Newton's Method
Nikita Doikov
We develop a new direct accelerated Newton method for minimizing convex functions with Lipschitz continuous Hessian. The algorithm uses only primal variables and performs just one linear solve per iteration. With a simple predetermined choice of parameters, it achieves the global convergence rate of $O(1/k^3)$ in terms of the functional residual. To the best of our knowledge, this is the first second-order method for this problem class attaining this rate while relying solely on one linear system solve per iteration (without solving auxiliary nonlinear regularized subproblems, such as cubic regularization, performing nonlinear parameter searches, or using dual extragradient corrections). Our method can be implemented in a Hessian-free way, using an inexact linear system solver, while preserving the fast global rate. We further extend our construction to arbitrary geometry through Bregman divergence, and to composite optimization problems.
#02Aug 21, 2026
cs.LG
Time-Aware Tranformer-Based Prediction Model for AECOPD
Weihao Qu, Ling Zheng, Dongyang Wang and 2 more
The rapid symptom change of Acute exacerbation of chronic obstructive pulmonary disease (AECOPD) makes it critical to have time-sensitive prediction models. However, most current machine learning models studying AECOPD use clinical and laboratory data, which will inevitably cause latency. To ensure timely detection of AECOPD and minimize latency, this paper focuses on home monitoring scenarios where only respiratory data from daily-use ventilators is available. We introduce a Time-Aware transformer-based AECOPD prediction model, which generates meaningful patient representations using the Time-Aware transformer to capture the symptoms and their temporal progression in ventilator data. Our experimental results demonstrate that our Time-Aware transformer-based approach outperforms traditional methods in multiple classification tasks, highlighting its potential to enhance AECOPD prediction accuracy.
#03Aug 21, 2026
cs.CV
Difficulty-Calibrated Interpolation Paths for Conditional Flow Matching
Airin Akter Tania, Md Raihan Khan
Conditional Flow Matching trains generative models by regressing a network onto the velocity of a prescribed noise-to-data interpolation path. The interpolation schedule that shapes this path is known to affect convergence and sample quality, yet it is invariably fixed in advance, independent of both the data and the model. We show that the regression difficulty of Conditional Flow Matching varies systematically along the path, and we propose Difficulty-Calibrated Flow Matching, which derives the schedule from the model itself: a short pilot run with the linear path records the per-time loss, and the schedule is set to the quantile function of this difficulty profile, so the trajectory lingers where the velocity is hardest to learn. The method has a single hyperparameter, leaves the training objective and its gradient equivalence intact, composes with classifier-free guidance, and adds about two percent training overhead. In controlled experiments on CIFAR-10, MNIST, and Fashion-MNIST with an identical compact U-Net, the calibrated path attains the best FID on CIFAR-10 at full sampling budget and clearly outperforms all fixed schedules in the large-batch, few-update regime, precisely the setting where compute is scarcest.
#04Aug 21, 2026
cs.LG
Asymmetric Capacity Allocation in Self-Refinement Pipelines
Zhuoyi Yang, Ian G. Harris, Salar Hashemitaheri and 7 more
Self-refinement, typically structured as generation, critique, and revision, is a widely adopted paradigm for improving LLM generation and serves as a core mechanism in many LLM agents. While the three stages involve different cognitive demands, most existing approaches conveniently treat the model size as an implementation detail rather than a subject of study, which may lead to a waste of resources. Little work has systematically examined how model size affects each stage or whether effective self-refinement requires equally capable models for generation, critique, and revision. We present the first stage-wise model size study of the self-refinement pipeline on 5 benchmarks from different domains using 6 model sizes of Qwen3 and 4 model sizes of Gemma 3. We conclude that larger generators and refiners generally improve the pipeline, whereas an undersized refiner can even harm performance. Second, performance is highly insensitive to the size of the critic, although including even a small critic consistently outperforms omitting critique altogether. Our findings demonstrate that model capacity should not be allocated uniformly across self-refinement pipelines. Instead, different stages exhibit distinct size scaling characteristics, providing practical guidance for designing more computationally efficient multi-stage language model systems.
#05Aug 21, 2026
cs.AI
Anatomy-Informed Neural Networks: Encoding Anatomic Priors in Loss and Architecture, with an SE(3) Formulation of Guidewire-Induced Aortoiliac Deformation
David P. Stonko
Deep-learning models of anatomy can be numerically plausible yet anatomically impossible, and they generalize poorly when data are scarce. We introduce Anatomy-Informed Neural Networks (AINN), in which soft anatomic priors enter as penalty terms in the loss (e.g., a branching penalty that treats a renal transplant artery off the iliac instead of the aorta as unexpected rather than impossible), in direct analogy to a physics-informed neural network, and hard anatomic priors (e.g., continuity of the vessel) are built into the architecture and state representation, making such invalid predictions impossible by construction wherever the prior admits architectural enforcement. We develop it on a clinical test case with limited data: how the aortoiliac tree deforms when a stiff wire is introduced endoluminally. This is important to contemporary aortic surgery and will matter to autonomous endovascular navigation. We lift the vessel centerline and the wire path from R^3 to curves of frames in the Lie group SE(3), and couple a Cosserat-rod wire to a tortuosity-modulated, anatomically anchored vessel through a unilateral lumen-contact inequality. The prediction is a constrained minimizer of the coupled elastic energy, with contact forces as its Lagrange multipliers. Supervision is a Wasserstein-2 optimal-transport loss between the predicted projection through the C-arm geometry and the observed angiogram, so a 2D angiogram can train a 3D prediction. The kinematics, loss and projection are verified against known ground truth; the mechanics solver only against its own optimality conditions, and predicted displacement is not yet mesh-converged. Here, no network is trained. Future work will transfer this in silico model to real CT scans and test whether it improves predictive accuracy and reduces the training data required.