#01Oct 30, 2026
cs.NI
RAMA: Retrieval-Augmented Multi-Agent Routing with Episodic Memory for LEO Satellite Networks
Xin Ming Li, Peng Hu
Low-Earth orbit (LEO) satellite networks present a challenging routing environment due to rapidly changing topology, traffic, and link conditions. Existing deep reinforcement learning (DRL) routing methods typically rely on current observations and information encoded in network weights, limiting their ability to exploit successful past experiences. We propose RAMA, a retrieval-augmented multi-agent DRL framework with Approximate Information State (AIS), in which each satellite combines its local observation, recent routing history, neighboring state information, and retrieved entries from a per-satellite episodic memory. Retrieved experiences are integrated through a Transformer-based decision network trained with AIS-based auxiliary objectives. With weights frozen in a 140-satellite Kepler constellation, RAMA reduces mean end-to-end latency by 13.4% and 99th-percentile latency by 66.7% relative to the state-of-theart double deep Q-network (DDQN) routing method, mainly by avoiding long detours. Updated online, RAMA remains stable while DDQN degrades. On the 1,584-satellite Starlink shell 1, the reduction in mean latency grows to 93.2%, and updating RAMA online lowers its mean latency by a further 25.5%. These results demonstrate the effectiveness of retrieval-augmented memory for scalable decentralized routing in LEO satellite networks.
#02Oct 30, 2026
math.OC
Near-Optimal Second-Order Convex Finite-Sum Optimization under Individual Smoothness
Xinliang Zhang, Lesi Chen, Zonghan Li and 1 more
We study the stochastic second-order oracle complexity of solving smooth convex finite-sum optimization with $n$ components. Very recently, Tsedenov \& Kovalev (2026) showed that the minimax optimal complexity under averaged smoothness and convexity is $\tildeΘ(n + n^{6/7} ε^{-2/7})$ by establishing nearly matching upper and lower bounds. In this paper, we show that individual smoothness and convexity provably enable further acceleration, where the lower complexity bound is $Ω(n+ n^{5/7} ε^{-2/7})$ under this stronger assumption. Then, by establishing a novel second-order self-bounding inequality, we design a new Taylor-corrected lazy Newton method, which can lead to a better complexity of $\tilde{\mathcal{O}}(n + n^{5/7} ε^{-2/7})$ by applying the optimal Monteiro-Svaiter acceleration, matching our lower bound up to only logarithmic factors.
#03Oct 30, 2026
cs.LG
Gradient Descent on Two ReLU Neurons: Global Landscape and Bifurcation Dynamics
Binghua Li, Mengzhe Li, Denny Wu and 1 more
Understanding how gradient descent learns features remains a central challenge in neural network theory. We study this question in a minimal multi-index setting that already exhibits rich multi-phase gradient dynamics: a well-specified two-neuron ReLU teacher-student model under isotropic Gaussian inputs, trained by population gradient flow from small initialization. We show that the dynamics are organized by two directions: the "easy" bisector direction, which carries the leading signal, and the "hard" splitting direction, which governs specialization. To characterize the loss structure and learning behavior, we analyze the population squared-loss landscape and show that every critical point with both student weights nonzero is either a global minimum or a saddle. We then track the gradient-flow trajectory, showing that student neurons first collapse toward a bisector saddle before escaping and specializing to teacher neurons. Our results provide both a landscape and dynamics account of the multi-phase symmetry-breaking behavior that arises in a simple multi-index model and under standard algorithmic and architectural choices.
#04Oct 30, 2026
cs.CV
A Better Critic Matters for Distribution Matching Distillation
Zongze Wu, Xianbang Wang, Zhengyang Geng and 5 more
Distribution Matching Distillation (DMD) trains a few-step student using the difference between a teacher's score and an online critic's estimate of the student distribution's score. We investigate what the critic needs, in capacity and in information, to provide a reliable training signal. On the capacity side, controlled experiments across seven SiT model sizes on ImageNet show that increasing teacher size while keeping a small critic fixed can degrade student quality and cause training collapse. Scaling the critic alongside the teacher, a strategy we call joint scaling, prevents collapse in our experiments and allows the student to benefit from larger teachers. On the information side, rather than forcing the critic to model a step-agnostic mixture of student outputs, we introduce a step-aware critic (STAC) that conditions on the student's generation step to estimate step-specific scores. Together, joint scaling and STAC consistently improve few-step distillation across class-conditional ImageNet generation, text-to-image generation with SDXL and FLUX.2, and text-to-video generation with Wan2.1.
#05Oct 30, 2026
stat.ML
Regret-Optimal Wasserstein-Robust Linear Regression
Sloan Nietert, Daniel Kuhn
Distributionally robust optimization (DRO) minimizes worst-case risk under distributional uncertainty, but its decisions can be suboptimal in terms of their excess risk, or regret. We study this gap for multivariate least-squares regression, assuming that the observed source law and unknown target law differ by an adversarial 2-Wasserstein perturbation of size $\varepsilon$. We first identify the asymptotic complexity of robust decision-making in the $\varepsilon \to 0$ limit, characterized by a problem-specific condition number $κ$. Here, a wide spectrum of simple algorithms, including DRO, achieve the instance-optimal rate of $O(κ\varepsilon^2)$. For fixed $\varepsilon > 0$, we prove that DRO still achieves the minimax rate if the problem has bounded residual effective rank. On the other hand, we identify significant failure modes where DRO is provably suboptimal by dimension-dependent factors. Fortunately, we prove that two alternative procedures, minimax regret optimization (MRO) and spectral-norm regularization (SNR), attain the minimax rate. We derive an exact convex reformulation of MRO and an accelerated proximal algorithm for SNR, along with high-probability finite-sample guarantees. We support these theoretical results with numerical experiments separating the performance of MRO and SNR from DRO.