#01Nov 5, 2026
stat.ML
Joint Modeling of Conditional Mean and Variability in Multilevel Functional Data: Application to Postprandial Glucose Trajectories in the AEGIS Study
Yang Xiao, Francisco Gude, Marcos Matabuena
Functional data analysis provides a framework for studying time-varying associations between covariates and high-frequency biological signals. In digital health, participants often contribute repeated functional trajectories, yet existing multilevel regression methods largely focus on the conditional mean, overlooking variability and its role in biological heterogeneity. We propose a heteroskedastic functional mixed-effects regression framework that jointly models the conditional mean and variance of repeated trajectories, with participant-specific random effects in both components. We also develop a participant-level bootstrap to quantify uncertainty in estimated functional parameters. We apply the method to postprandial glucose trajectories from the AEGIS study. Premeal glucose, carbohydrate intake, and meal type show distinct time-dependent associations with glucose variability, whereas HbA1c is more strongly associated with the conditional mean than with variability. Substantial between-participant differences in residual variability remain even after accounting for observed covariates. These findings show that modeling conditional variability alongside the mean provides insights into glucose regulation and individual heterogeneity that mean-focused analyses may miss. More broadly, the proposed framework enables joint characterization of average responses, variability, and participant-specific heterogeneity in repeated biological signals.
#02Nov 5, 2026
cs.AI
How Finite Brains Generalize Without Bound: Spatial Memory as a Universal Computer
Yuhang He, Si Wu
A child who learns to add small numbers adds numbers of any length. LSTMs and Transformers trained on short sequences fail on longer ones. We trace the difference to what a learner reads when it decides. A position, a count or a time keeps taking new values as the input grows: it is a coordinate, and a learner that reads one meets in every long input values its experience never covered. Whether two things are the same has the same two answers at every size: it is a coincidence, and a learner that reads only coincidences finds in a long input nothing that short inputs lacked, so finite experience fixes its rule for every size. The memory carries the size of the input and the rule stays finite, and this determines the memory a generalizing brain can have: a memory that grows while what the learner reads of it stays finite has to look the same from every place, so it is made of cycles, and the past is reached by asking what happened when the cycles last stood where they stand now. The cycles are the grid modules, the cells that detect their return the place cells, the records the hippocampal index; a prefrontal controller moves the cycles and never sees them. Reading only coincidences costs no power: what finite experience fixes in such a learner is what Turing machines compute in step with their input, which is why a circuit that evolved to find the way home can learn arithmetic and grammar. In a network of neurons this machine of cycles is the dynamics seen through its symmetry, and symbols are its invariants. Trained on strings up to 40 symbols, the machine is at least 99% correct, on average over lengths 41 to 500, on nine of fifteen benchmark tasks, five of them tasks that no LSTM or Transformer solves; given new cycles after training it reverses strings of 15,015 symbols without error and fails beyond that on the curve the theory predicts; and its controllers run unchanged on neurons.
#03Nov 5, 2026
cs.AI
A Behavioural Framework for Predicting and Understanding Loss of Control in Frontier Artificial Intelligence Systems
Yao Huang, Yichi Zhang, Yifan Wang and 8 more
Frontier artificial intelligence (AI) systems are increasingly operating over longer horizons with diminishing human oversight, raising the risk of loss of control: systems acting beyond effective human control with potentially irreversible consequences. Because such failures may become observable only after containment is difficult, they must be assessed prospectively. We introduce a behavioural framework that decomposes loss-of-control risk into three factors: misaligned motive, harm-enabling capability, and monitoring evasion. We operationalise these factors through 13 measurable aspects and 29 evaluation tasks, whose scores are combined into a single loss-of-control (LoC) score. Across 13 frontier models, the LoC score shows strong prospective validity, correlating with failure rates in contained long-horizon risk scenarios (Pearson r = 0.84). Risk varies systematically across models and cannot be explained by capability alone. We further show that the framework can guide targeted mitigations: fine-tuning and monitoring directed at diagnosed vulnerabilities reduce failure rates while largely preserving general performance. These results provide a practical basis for predicting, understanding, and mitigating loss-of-control risk before it materialises.
#04Nov 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.
#05Nov 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.