Previous work [2, 1] has observed that standard training and greedy decoding usually cause models to generate consecutive repetitive texts. These consecutive repetitive texts are redundant and do not convey new information, which is avoided in human language. There are three types of consecutive repetitions: word-level, phrase-level and sentence-level. The phrase-level means that a phrase consisting of several words is repeated consecutively. The sentence in our paper refers to a sequence split by '.!?' is repeated consecutively 2. We calculate the ratio of consecutive repetition in a sequence x as follows.

So far the community has considered`2 as the underlying distance.

Chain-of-thought (CoT) reasoning not only enhances large language model performance but also provides critical insights into decision-making processes, marking it as a useful tool for monitoring model intent and planning. However, recent works have shown that banning the mention of a specific example of reward hacking causes obfuscation of the undesired reasoning traces but the persistence of the undesired behavior, threatening the reliability of CoT monitoring. We provide an extension to these results with regard to the ability of models to learn a specific type of obfuscated reasoning: steganography. First, we show that penalizing the use of specific strings within load-bearing reasoning traces causes models to substitute alternative strings. Crucially, this does not alter the underlying method by which the model performs the task, demonstrating that the model can learn to steganographically encode its reasoning.We further demonstrate that models can generalize an encoding scheme. When the penalized strings belong to an overarching class, the model learns not only to substitute strings seen in training, but also develops a general encoding scheme for all members of the class which it can apply to held-out testing strings.

We consider the optimization of an uncertain objective over continuous and multidimensional decision spaces in problems in which we are only provided with observational data.

Physics-informed statistical learning (PISL) integrates empirical data with physical knowledge to enhance the statistical performance of estimators. While PISL methods are widely used in practice, a comprehensive theoretical understanding of how informed regularization affects statistical properties is still missing. Specifically, two fundamental questions have yet to be fully addressed: (1) what is the trade-off between considering soft penalties versus hard constraints, and (2) what is the statistical gain of incorporating physical knowledge compared to purely data-driven empirical error minimisation. In this paper, we address these questions for PISL in convex classes of functions under physical knowledge expressed as linear equations by developing appropriate complexity dependent error rates based on the small-ball method. We show that, under suitable assumptions, (1) the error rates of physics-informed estimators are comparable to those of hard constrained empirical error minimisers, differing only by constant terms, and that (2) informed penalization can effectively reduce model complexity, akin to dimensionality reduction, thereby improving learning performance. This work establishes a theoretical framework for evaluating the statistical properties of physics-informed estimators in convex classes of functions, contributing to closing the gap between statistical theory and practical PISL, with potential applications to cases not yet explored in the literature.

Adaptive experiments produce dependent data that break i.i.d. assumptions that underlie classical concentration bounds and invalidate standard learning guarantees. In this paper, we develop a self-normalized maximal inequality for martingale empirical processes. Building on this, we first propose an adaptive sample-variance penalization procedure which balances empirical loss and sample variance, valid for general dependent data. Next, this allows us to derive a new variance-regularized pessimistic off-policy learning objective, for which we establish excess-risk guarantees. Subsequently, we show that, when combined with sequential updates and under standard complexity and margin conditions, the resulting estimator achieves fast convergence rates in both parametric and nonparametric regimes, improving over the usual $1/\sqrt{n}$ baseline. We complement our theoretical findings with numerical simulations that illustrate the practical gains of our approach.

Physics-Informed Neural Networks (PINNs) are a class of deep learning models aiming to approximate solutions of PDEs by training neural networks to minimize the residual of the equation. Focusing on non-equilibrium fluctuating systems, we propose a physically informed choice of penalization that is consistent with the underlying fluctuation structure, as characterized by a large deviations principle. This approach yields a novel formulation of PINNs in which the penalty term is chosen to penalize improbable deviations, rather than being selected heuristically. The resulting thermodynamically consistent extension of PINNs, termed THINNs, is subsequently analyzed by establishing analytical a posteriori estimates, and providing empirical comparisons to established penalization strategies.

Data fusion and transfer learning are rapidly growing fields that enhance model performance for a target population by leveraging other related data sources or tasks. The challenges lie in the various potential heterogeneities between the target and external data, as well as various practical concerns that prevent a naïve data integration. We consider a realistic scenario where the target data is limited in size while the external data is large but contaminated with outliers; such data contamination, along with other computational and operational constraints, necessitates proper selection or subsampling of the external data for transfer learning. To our knowledge,transfer learning and subsampling under data contamination have not been thoroughly investigated. We address this gap by studying various transfer learning methods with subsamples of the external data, accounting for outliers deviating from the underlying true model due to arbitrary mean shifts. Two subsampling strategies are investigated: one aimed at reducing biases and the other at minimizing variances. Approaches to combine these strategies are also introduced to enhance the performance of the estimators. We provide non-asymptotic error bounds for the transfer learning estimators, clarifying the roles of sample sizes, signal strength, sampling rates, magnitude of outliers, and tail behaviors of model error distributions, among other factors. Extensive simulations show the superior performance of the proposed methods. Additionally, we apply our methods to analyze the risk of hard landings in A380 airplanes by utilizing data from other airplane types,demonstrating that robust transfer learning can improve estimation efficiency for relatively rare airplane types with the help of data from other types of airplanes.

Contrastive Decoding (CD) has emerged as an effective inference-time strategy for enhancing open-ended text generation by exploiting the divergence in output probabilities between a large expert language model and a smaller amateur model. Although CD improves coherence and fluency, its dependence on a single amateur restricts its capacity to capture the diverse and multifaceted failure modes of language generation, such as repetition, hallucination, and stylistic drift. This paper proposes Multi-Amateur Contrastive Decoding (MACD), a generalization of the CD framework that employs an ensemble of amateur models to more comprehensively characterize undesirable generation patterns. MACD integrates contrastive signals through both averaging and consensus penalization mechanisms and extends the plausibility constraint to operate effectively in the multi-amateur setting. Furthermore, the framework enables controllable generation by incorporating amateurs with targeted stylistic or content biases. Experimental results across multiple domains, such as news, encyclopedic, and narrative, demonstrate that MACD consistently surpasses conventional decoding methods and the original CD approach in terms of fluency, coherence, diversity, and adaptability, all without requiring additional training or fine-tuning.