#01Nov 6, 2026
cs.LG
On the (non-)closedness of the set of ReLU networks
Eloi Martinet, Leon Bungert
We prove that the set $\mathcal{N}_N$ of ReLU networks with one hidden layer and at most $N\in\mathbb N$ neurons is weakly closed in $W^{1,p}(Ω)$, for a bounded connected open set $Ω\subset\mathbb R^d$. Consequently, every coercive, weakly lower semicontinuous energy on this space attains its minimum over $\mathcal{N}_N$. This covers the Deep Ritz method with convex integrands, Sobolev training and Lipschitz learning. Moreover, as the weight decay parameter tends to zero, minimizers of the regularized problem converge, up to subsequences, to minimizers with minimal parameter norm. We also prove that the set of ReLU networks with two hidden layers of bounded widths is not closed in $W^{1,p}(Ω)$ or in $C(\overlineΩ)$. This disproves a conjecture of Petersen, Raslan and Voigtlaender.
#02Nov 6, 2026
cs.AI
Assessing the Impact of Retrieval-Augmented Generation on Algorithmic Problem-Solving
Gabriel Souza Baggio, Gabriel Machado Lunardi, Guilherme Medeiros Machado and 3 more
Competitive programming problems pose distinctive challenges for Large Language Models, as they demand not only proficient code generation but also advanced algorithmic reasoning. This study presents a Retrieval-Augmented Generation approach specifically designed to enhance the capacity of Large Language Models to address such problems. Our approach integrates an embedding-based retrieval mechanism and a similarity search algorithm to identify analogous problems within a knowledge database, employing a dynamically adjusted threshold to mitigate retrieval noise. We conducted an evaluation using the CodeContests dataset, focusing on the test split problems that exhibit similarity to instances from the training split. The experimental framework considered three conditions: (i) problems provided solely with their original descriptions, (ii) problems supplemented with randomly selected examples from the training split, and (iii) problems augmented with similar examples retrieved through the proposed method. In addition, we incorporated a Min-K membership inference analysis to examine whether the generated code solutions were influenced by potential memorization of training data within the evaluated Large Language Models. This complementary perspective enables a deeper understanding of model behavior by distinguishing genuine generalization through retrieval from implicit recall of pretraining samples. Performance was assessed using both pass rates and the CodeForces Elo rating of the problems. The results provide empirical evidence that similarity-based retrieval substantially enhances Large Language Models performance in competitive programming scenarios, offering an scalable framework for improving code generation in algorithmic problem-solving contexts.
#03Nov 6, 2026
cs.SE
When Instruction Files Go Stale: Documentation Debt and Hidden Cost in Coding Agents
Tural Mehtiyev, Biruk Tadesse, Lawrence Arkoh and 1 more
LLM-based coding agents such as Claude Code are guided by repository instruction files (also called context files or agent configuration files) like AGENTS.md and CLAUDE.md, which are read in every agent session. As any documentation artifact, these files can fall behind the code and become stale (e.g., a test folder moves, but the file still points to the old one). In technical debt terms, such a stale instruction is documentation debt, and its interest is the cost it adds to every later agent session. Evaluations that check only task success can miss this cost, and the stale file can persist. In this study, we ask what leads agents to act on a stale instruction, how it affects their behavior and at what cost, and how they recover. We study three real-world stale instructions from active open-source repositories in depth, each a different kind of guidance: a test command, a code location, and a procedure for adding a component. Agents fix 22 maintenance tasks under three versions of each instruction (left stale, corrected to the current path, and removed), with the code and the task held fixed, and we analyze 732 trajectories of two models at the level of individual tool calls. We find that agents follow stale guidance when it is relevant to their tasks, sometimes even when correct information is available elsewhere. On the stale test command, Claude Sonnet 5.5 needed about two extra tool calls per run, a third more than with the corrected command; in the other cases, we could not detect a difference. Although agents generally recovered from the immediate failures, none repaired the underlying instruction file. Correcting the instructions eliminated operations on obsolete paths, while removing them prevented most. Our findings show that task success alone can hide the costs of documentation debt, highlighting the need to evaluate agent behavior beyond final outcomes.
#04Nov 6, 2026
cs.LG
Quasipolynomial-Time Planning for Decodable POMDPs
Oliver Dobson, Varun Jog, Chun Hei Michael Shiu
We study planning for finite-horizon partially observable Markov decision processes (POMDPs) with finite state, action, and observation spaces. Both exact and approximate planning are known to be computationally hard in this setting, so prior work has explored natural assumptions that make planning easier. Recent work [Golowich et al., 2022] gave quasipolynomial-time approximate planning algorithms for observable POMDPs. These are POMDPs whose observation channels satisfy an $\ell_1$-observability condition, but notably, no assumptions are required on the transition dynamics. In a similar vein, for every fixed $ρ>0$, we give quasipolynomial-time approximate planning algorithms for $ρ$-decodable POMDPs. We show that decodability is implied by both $\ell_1$- and $\ell_2$-observability and is strictly weaker than observability. Moreover, we show that the optimal decodability constant can be computed in polynomial time, whereas computing the optimal $\ell_1$-observability constant is NP-hard in the worst case. We also show that the fast filter-forgetting guarantee underlying the approach of [Golowich et al., 2022] does not extend directly from $\ell_1$-observability to constant $\ell_2$-observability. Thus, decodability is an easy-to-check, unifying assumption under which quasipolynomial-time approximate planning for POMDPs is possible.
#05Nov 6, 2026
cs.AI
On the Reliability of Majority-Vote Pseudo-Labels in Test-Time Reinforcement Learning
Haoyu Wang, Ru Wang, Yuanyuan Wang and 2 more
Test-time reinforcement learning (TTRL) adapts pretrained language models to unlabeled target-domain data using self-generated pseudo-labels, whose reliability remains poorly understood. We analyze majority-vote supervision for TTRL with online Direct Preference Optimization (DPO) and decompose its error into population-majority bias and prompt-dependent finite-rollout variation. Because population-majority bias is generally unidentifiable without external supervision, we focus on mitigating the downstream effects of finite-rollout variation. We propose \emph{Prompt-Conditional Distributionally Robust DPO (PC-Dr.DPO)}, which conditions within-prompt robust reweighting on observed vote reliability to make updates from sampling-sensitive prompts more conservative. We further introduce a cache-based mechanism to reduce self-supervised forgetting during online adaptation. Across six mathematical and knowledge-intensive reasoning benchmarks and five model backbones, PC-Dr.DPO matches or outperforms the strongest TTRL baseline in 24 of 30 settings.