In open-ended generation, LLMs frequently fall into the "likelihood trap", marked by repetitive degeneration and vocabulary dullness, creating a discrepancy between machine-generated and human-written text. While post-hoc tail truncation (e.g., Top-$p$, Min-$p$) avoids sampling from the unreliable tail, it can over-sample from the uncalibrated head and misalign generation with human lexical preferences; fixed scalar repetition penalties likewise ignore variation in logit scale across inference steps, potentially disrupting semantic coherence. To address both limitations, we propose Variance-Calibrated Modulation (VCM), a training-free pre-decoding intervention that reshapes the probability distribution before truncation through two dynamic mechanisms: (1) Contextual Searchlight via PMI, which suppresses global stopwords while elevating context-evoked tokens, and (2) Adaptive Self-Debiasing, which uses real-time logit standard deviation for scale-invariant penalization. Across open-ended generation, factual QA, and mathematical reasoning, VCM consistently mitigates the likelihood trap. With negligible computational overhead, VCM integrates with existing decoding strategies, improving diversity, coherence, and, particularly at higher decoding temperatures, reasoning accuracy.

Robust verbal confidence generated by large language models (LLMs) is crucial for the deployment of LLMs to help ensure transparency, trust, and safety in many applications, including those involving human-AI interactions. In this paper, we present the first comprehensive study on the robustness of verbal confidence under adversarial attacks. We introduce attack frameworks targeting verbal confidence scores through both perturbation and jailbreak-based methods, and demonstrate that these attacks can significantly impair verbal confidence estimates and lead to frequent answer changes. We examine a variety of prompting strategies, model sizes, and application domains, revealing that current verbal confidence is vulnerable and that commonly used defence techniques are largely ineffective or counterproductive. Our findings underscore the need to design robust mechanisms for confidence expression in LLMs, as even subtle semantic-preserving modifications can lead to misleading confidence in responses.

Control algorithms in production environments typically require domain experts to tune their parameters and logic for specific scenarios. However, existing research predominantly focuses on algorithmic performance under ideal or default configurations, overlooking the critical aspect of Tuning Potential. To bridge this gap, we introduce Crucible, an agent that employs an LLM-driven, multi-level expert simulation to turn algorithms and defines a formalized metric to quantitatively evaluate their Tuning Potential. We demonstrate Crucible's effectiveness across a wide spectrum of case studies, from classic control tasks to complex computer systems, and validate its findings in a real-world deployment. Our experimental results reveal that Crucible systematically quantifies the tunable space across different algorithms. Furthermore, Crucibleprovides a new dimension for algorithm analysis and design, which ultimately leads to performance improvements.

We show that reinforcement learning with verifiable reward using one training example (1-shot RLVR) is effective in incentivizing the mathematical reasoning capabilities of large language models (LLMs).

Time Series Forecasting (TSF) is a crucial task in various domains, yet existing TSF models rely heavily on high-quality data and insufficiently exploit all available data. This paper explores a novel self-supervised approach to re-label time series datasets by inherently constructing candidate datasets. During the optimization of a simple reconstruction network, intermediates are used as pseudo labels in a self-supervised paradigm, improving generalization for any predictor. We introduce the SelfCorrection with Adaptive Mask (SCAM), which discards overfitted components and selectively replaces them with pseudo labels generated from reconstructions. Additionally, we incorporate Spectral Norm Regularization (SNR) to further suppress overfitting from a loss landscape perspective. Our experiments on eleven real-world datasets demonstrate that SCAM consistently improves the performance of various backbone models. This work offers a new perspective on constructing datasets and enhancing the generalization of TSF models through self-supervised learning. The code is available at https://github.com/SuDIS-ZJU/SCAM.

We develop Hamiltonian dynamics-based algorithms for smooth convex optimization that achieve accelerated rates of convergence. By exploiting contraction of averaged Hamiltonian flow trajectories rather than requiring contraction at trajectory endpoints, we show that Hamiltonian dynamics-based optimization methods admit deterministic and accelerated convergence guarantees, extending prior work that is limited to quadratic objectives or holds only in expectation. We analyze an idealized continuous-time algorithm and derive practical discrete-time implementations with optimal first-order complexity, thereby establishing Hamiltonian dynamics as a useful algorithmic primitive for deterministic accelerated convex optimization.

Recent years have witnessed substantial progress on monocular depth estimation, particularly as measured by the success of large models on standard benchmarks. However, performance on standard benchmarks does not offer a complete assessment, because most evaluate accuracy but not robustness. In this work, we introduce PDE (Procedural Depth Evaluation), a new benchmark which enables systematic evaluation of robustness to changes in 3D scene content. PDE uses procedural generation to create 3D scenes that test robustness to various controlled perturbations, including object, camera, material and lighting changes. Our analysis yields interesting findings on what perturbations are challenging for state-of-the-art depth models, which we hope will inform further research.

In this paper, we establish Berry-Esseen-type bounds for federated linear stochastic approximation (LSA). Our results provide the first federated Gaussian approximations for LSA that explicitly capture communication-computation trade-offs and heterogeneity-aware error terms, quantifying the effects of local step size, number of local updates, and heterogeneity on convergence rates. We present results for both (i) constant step size regime and (ii) decreasing step size with an increasing number of local iterations, recovering the recent rates of Bonnerjee et al. [2025] as a special case. As a primary application of our results, we develop an online multiplier bootstrap procedure for inference on the last iterate, which avoids explicit estimation of the asymptotic covariance matrix, and obtain non-asymptotic validity guarantees for this procedure.