#01Nov 5, 2026
cs.AI
Circe: Training-Free LLM Self-Evaluation via Component Interaction Consistency
Shuyi Miao, Zheng Li, Xu Xie and 4 more
As large language models (LLMs) are increasingly deployed in real-world applications, evaluating the correctness of their responses is crucial for reliable use. However, such evaluation is challenging because reference answers are rarely available in practice. Existing reference-free methods mainly rely on output signals, which may assign high scores to incorrect responses and thus do not necessarily reflect correctness. This motivates exploring the model's internal computation for complementary correctness signals. Recent studies exploit internal states, but they mainly analyze hidden-state trajectories across layers, which record only the combined updates of attention and feed-forward networks (FFNs) and overlook how these components interact. We therefore propose Circe, a training-free self-evaluation method that assesses a response using both internal and external signals, without reference answers or repeated sampling. For internal signals, we first introduce component interaction consistency (CIC), which measures the directional alignment between attention updates in earlier layers and attention-induced FFN output changes in later layers. We further incorporate representation geometry (RG) to characterize normalized displacement and angular changes along layerwise hidden-state trajectories. For the external signal, we convert the mean negative log-likelihood of generated tokens into a bounded likelihood confidence (LC) score. Finally, we fuse CIC, RG, and LC into a unified correctness score. Experiments on five LLMs and six benchmarks across four domains show that our method distinguishes correct from incorrect responses more effectively than existing baselines, and generalizes to multilingual, multimodal, and open-world settings.
#02Nov 5, 2026
cs.LG
Tight Asymptotic Bounds on the Maximum Number of Linear Regions of Piecewise-Linear Kolmogorov--Arnold networks
Ye Su, Yong Liu
Schoots et al.~\citep{schoots2025relating} (AISTATS 2025) established a generally loose upper bound on the number of linear regions of continuous piecewise-linear (CPWL) Kolmogorov--Arnold networks (KANs), without providing a lower bound. We consider a $T$-layer network with width vector $\mathbf n=(n_0,\ldots,n_T)$, input dimension $n_0=d$, output width $n_T=1$, and at most $k\geq2$ affine segments per edge. Our matching upper and lower bounds determine the tight growth order $Θ_{\mathbf n}(k^{\sum_{\ell=1}^{T}ρ_{\ell-1}})$ in $k$, where $ρ_{\ell-1}:=\min_{0\leq s\leq\ell-1}n_s$. When every hidden width is at least $d$, the tight order simplifies to $Θ_{\mathbf n}(k^{dT})$. The upper bound of \citep{schoots2025relating} is $k^{\sum_{\ell=1}^{T}n_{\ell-1}n_\ell}$. Our upper bound improves it by a factor of $Θ_{\mathbf n}\!\left(k^{\sum_{\ell=1}^{T}n_{\ell-1}n_\ell-\sum_{\ell=1}^{T}ρ_{\ell-1}} \right)$, with strict asymptotic improvement whenever a hidden layer has width greater than one. We further compare CPWL KANs with rectified linear unit (ReLU) networks using dense parameterizations with at most $Λ$ parameters per model and the same fixed nonlinear depth $T$. Counting trainable knot locations and optimizing the widths and $k$, we prove that the maximum region count of CPWL KANs divided by that of ReLU networks is $Θ_{d,T}(Λ^{d\lfloor T/2\rfloor})$ as $Λ\to\infty$, yielding a polynomial advantage for KANs when $T\geq2$. These tight bounds characterize the attainable geometric complexity of CPWL KANs, providing a foundation for understanding their expressive power and guiding architectural design.
#03Nov 5, 2026
cs.DC
ZeroRAG: Adaptive Semantic Peer Routing for Decentralized Retrieval-Augmented Generation
Petru Neague, Quinten Stokkink, Martijn de Vos and 4 more
Retrieval-augmented generation (RAG) is a standard approach to enhance the reliability of large language model (LLM) outputs by retrieving documents relevant to a query and supplying them in the LLM prompt. Today's RAG systems collect, index, and serve these documents from centralized stores. In practice, however, documents are owned by organizations, devices, and individuals who cannot or will not surrender custody of them to a central party, e.g., because of privacy, copyright or regulatory compliance. Existing modern decentralized retrieval techniques either reintroduce a coordinating authority, or rely on a global data structure that requires continuous network-wide coordination (e.g., DHTs). We present ZeroRAG, a decentralized routing layer for document retrieval in RAG that performs semantic query routing across an overlay of peers with- out global data structures or centralized orchestration. Documents remain with the peers that own them, and each peer keeps only lightweight local state: a bounded set of neighbor advertisements and a cache of recently routed queries. Using these, ZeroRAG steers each query through a best-first walk that progressively rewires the overlay toward semantically relevant neighbors, so recall improves over time as the network self-organizes. We evaluate ZeroRAG using three real-world workloads and two decentralized baselines. We find that ZeroRAG outperforms baselines in terms of recall and required network messages, approaches the recall and LLM answer accuracy of a centralized document store, self-heals after catastrophic peer failures, and scales to 100 000 peers.
#04Nov 5, 2026
cs.AI
GuidedWAM: Training-Free Energy Guidance for World Action Models in Autonomous Driving
Xiyan Su, Finn Rasmus Schäfer, Hojun Lim and 3 more
World action models (WAMs) for autonomous driving couple the driving policy and the visual world model in a single generative network whose objectives are fixed post-training. Conditioning on a new driving objective requires retraining. We study energy guidance as a general mechanism and present GuidedWAM, a model-agnostic framework for injecting driving objectives into frozen WAMs at sampling time. Our framework constructs each objective as differentiable energies on the sampler's intermediate clean-action estimate, which needs only forward access to the frozen model, and is stabilized by sampling-time guidance scheduling, per-energy normalization, and velocity-bounded correction. On the NAVSIM v2 hard-split, guidance improves all three frozen, publicly released WAMs by 1.8 to 3.6 EPDMS, averaged over three sampler seeds, and adds less than 10% to the sampling time per step. These results position energy guidance as a practical post-training control channel for WAMs.
#05Nov 5, 2026
cs.AI
TCSExam: Evaluating Frontier LLMs on the Full Range of TCS Research
Yifan Luo, Zhengying Liu, Yang Yuan and 2 more
Can large language models (LLMs) advance theoretical computer science and resolve its long-standing open conjectures? To study progress toward this goal, we introduce TCSExam, a unified framework and benchmark covering the full range of TCS research. It evaluates theorem proving, solver engineering, and constructions alongside direct attempts to resolve open conjectures, capturing both concrete research accomplishments and progress toward long-standing research goals. TCSExam-Full contains 100 expert-reviewed tasks, with submissions checked by the Lean kernel or an executable task checker. TCSExam-Lite selects 20 tasks, five per track, reducing the number of task attempts by 80% at the same per-attempt budget. We evaluate eight agents on Full and nine on Lite. The TCSExam Index combines all four tracks: GPT-6 Astra leads Full (71.9), and Opus 5.5 leads Lite (72.3). Full and Lite rankings are strongly aligned across eight shared agents (Spearman's $ρ=0.93$), supporting Lite as a compact, discriminative benchmark. The evaluations yield improved solver outputs and mathematical constructions, together with independently verified special cases and bounds from open-conjecture attempts. TCSExam provides an extensible framework with task sources, Docker build recipes, and evaluation tools for reproducible use.