#01Nov 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.
#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.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.
#04Nov 6, 2026
cs.AI
Ensemble Methodology for Reference-Free Confidence Estimation in LLM-based Code Summarization
Marco Colombo, Balaji A Jayaram, Sowmyakumari Selvaraj and 5 more
This paper describes an approach and use case to estimate the correctness of LLM-generated COBOL summaries without access to human-authored references. The core intuition is that inter-model agreement on semantics is informative about truth, and that an LLM-as-judge can provide higher-fidelity pairwise assessments than traditional string- or embedding-based metrics. We operationalise this intuition with (i) controlled summary generation from diverse models; (ii) a LLM evaluator that compares pairs of summaries and emits structured judgments; and (iii) a calibrated aggregation rule that combines supportive evidence while penalising only corroborated contradictions.
#05Nov 6, 2026
cs.AI
BitDecoding-FP4: Native FP4 KV Cache Decoding via Algorithm-System Co-Design
Dayou Du, Woon Yee Ng, Guangming Sheng and 3 more
The key-value (KV) cache dominates memory capacity and bandwidth in long-context LLM serving. While 4-bit microscaling formats (NVFP4, MXFP4) shrink the cache and run attention on FP4 Tensor Cores, a fundamental gap remains between algorithmic quantization and system-aware acceleration: existing FP4 KV systems use vanilla quantization that causes severe accuracy drops, whereas accuracy-oriented 4-bit algorithms rely on vector codebooks whose lookup overhead degrades decoding throughput. We present BitDecoding-FP4, an algorithm--system co-design for accurate and efficient native FP4 KV decoding. We mitigate three error sources: Dual-Residual Query Quantization splits queries into two FP4 tensors, cutting query logit error from 60% to 1%; Underflow-Aware Probability Scaling prevents E4M3 scales from rounding long-context probabilities to zero; and Outlier-Aware Key Quantization combines static smoothing, Hadamard rotation, and scale search to suppress key outliers under token-wise scaling. At the system level, we remove the softmax bottleneck via transposed softmax with fused probability quantization and stacked query MMA on paged KV caches. Across dense and MoE models with GQA and MLA, BitDecoding-FP4 stays within 0.5 points of BF16 KV accuracy with NVFP4 (1 point with MXFP4), and tracks BF16 KV in RL training rollouts. In end-to-end serving on NVIDIA B300 with Qwen3-4B and Qwen3-30B-A3B, it delivers 2.4-3.0$\times$ higher peak serving throughput than BF16 KV. The implementation is available at https://github.com/OpenBitSys/BitDecoding-FP4.