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This paper introduces a Cosserat rod based mathematical model for modeling a self-controllable variable curvature soft continuum robot. This soft continuum robot has a hollow inner channel and was developed with the ability to perform variable curvature utilizing a growing spine. The growing spine is able to grow and retract while modifies its stiffness through milli-size particle (glass bubble) granular jamming. This soft continuum robot can then perform continuous curvature variation, unlike previous approaches whose curvature variation is discrete and depends on the number of locking mechanisms or manual configurations. The robot poses an emergent modeling problem due to the variable stiffness growing spine which is addressed in this paper. We investigate the property of growing spine stiffness and incorporate it into the Cosserat rod model by implementing a combined stiffness approach. We conduct experiments with the soft continuum robot in various configurations and compared the results with our developed mathematical model. The results show that the mathematical model based on the adapted Cosserat rod matches the experimental results with only a 3.3\% error with respect to the length of the soft continuum robot.

We propose quantum soft covering problems for fully quantum channels and classical-quantum (CQ) channels using relative entropy as a criterion of operator closeness. We prove covering lemmas by deriving one-shot bounds on the rates in terms of smooth min-entropies and smooth max-divergences, respectively. In the asymptotic regime, we show that for quantum channels, the rate infimum defined as the logarithm of the minimum rank of the input state is the coherent information between the reference and output state; for CQ channels, the rate infimum defined as the logarithm of the minimum number of input codewords is the Helovo information between the input and output state. Furthermore, we present a one-shot quantum decoupling theorem with relative entropy criterion. Our results based on the relative-entropy criterion are tighter than the corresponding results based on the trace norm considered in the literature due to the Pinsker inequality.

Accurately simulating human opinion dynamics is crucial for understanding a variety of societal phenomena, including polarization and the spread of misinformation. However, the agent-based models (ABMs) commonly used for such simulations often over-simplify human behavior. We propose a new approach to simulating opinion dynamics based on populations of Large Language Models (LLMs). Our findings reveal a strong inherent bias in LLM agents towards producing accurate information, leading simulated agents to consensus in line with scientific reality. This bias limits their utility for understanding resistance to consensus views on issues like climate change. After inducing confirmation bias through prompt engineering, however, we observed opinion fragmentation in line with existing agent-based modeling and opinion dynamics research. These insights highlight the promise and limitations of LLM agents in this domain and suggest a path forward: refining LLMs with real-world discourse to better simulate the evolution of human beliefs.

This paper presents a general framework to integrate prior knowledge in the form of logic constraints among a set of task functions into kernel machines. The logic propositions provide a partial representation of the environment, in which the learner operates, that is exploited by the learning algorithm together with the information available in the supervised examples. In particular, we consider a multi-task learning scheme, where multiple unary predicates on the feature space are to be learned by kernel machines and a higher level abstract representation consists of logic clauses on these predicates, known to hold for any input. A general approach is presented to convert the logic clauses into a continuous implementation, that processes the outputs computed by the kernel-based predicates. The learning task is formulated as a primal optimization problem of a loss function that combines a term measuring the fitting of the supervised examples, a regularization term, and a penalty term that enforces the constraints on both supervised and unsupervised examples. The proposed semi-supervised learning framework is particularly suited for learning in high dimensionality feature spaces, where the supervised training examples tend to be sparse and generalization difficult. Unlike for standard kernel machines, the cost function to optimize is not generally guaranteed to be convex. However, the experimental results show that it is still possible to find good solutions using a two stage learning schema, in which first the supervised examples are learned until convergence and then the logic constraints are forced. Some promising experimental results on artificial multi-task learning tasks are reported, showing how the classification accuracy can be effectively improved by exploiting the a priori rules and the unsupervised examples.

In-context learning has emerged as a groundbreaking ability of Large Language Models (LLMs) and revolutionized various fields by providing a few task-relevant demonstrations in the prompt. However, trustworthy issues with LLM's response, such as hallucination, have also been actively discussed. Existing works have been devoted to quantifying the uncertainty in LLM's response, but they often overlook the complex nature of LLMs and the uniqueness of in-context learning. In this work, we delve into the predictive uncertainty of LLMs associated with in-context learning, highlighting that such uncertainties may stem from both the provided demonstrations (aleatoric uncertainty) and ambiguities tied to the model's configurations (epistemic uncertainty). We propose a novel formulation and corresponding estimation method to quantify both types of uncertainties. The proposed method offers an unsupervised way to understand the prediction of in-context learning in a plug-and-play fashion. Extensive experiments are conducted to demonstrate the effectiveness of the decomposition. The code and data are available at: \url{//github.com/lingchen0331/UQ_ICL}.

Mutation validation (MV) is a recently proposed approach for model selection, garnering significant interest due to its unique characteristics and potential benefits compared to the widely used cross-validation (CV) method. In this study, we empirically compared MV and $k$-fold CV using benchmark and real-world datasets. By employing Bayesian tests, we compared generalization estimates yielding three posterior probabilities: practical equivalence, CV superiority, and MV superiority. We also evaluated the differences in the capacity of the selected models and computational efficiency. We found that both MV and CV select models with practically equivalent generalization performance across various machine learning algorithms and the majority of benchmark datasets. MV exhibited advantages in terms of selecting simpler models and lower computational costs. However, in some cases MV selected overly simplistic models leading to underfitting and showed instability in hyperparameter selection. These limitations of MV became more evident in the evaluation of a real-world neuroscientific task of predicting sex at birth using brain functional connectivity.

We revisit the problems of pitch spelling and tonality guessing with a new algorithm for their joint estimation from a MIDI file including information about the measure boundaries. Our algorithm does not only identify a global key but also local ones all along the analyzed piece. It uses Dynamic Programming techniques to search for an optimal spelling in term, roughly, of the number of accidental symbols that would be displayed in the engraved score. The evaluation of this number is coupled with an estimation of the global key and some local keys, one for each measure. Each of the three informations is used for the estimation of the other, in a multi-steps procedure. An evaluation conducted on a monophonic and a piano dataset, comprising 216 464 notes in total, shows a high degree of accuracy, both for pitch spelling (99.5% on average on the Bach corpus and 98.2% on the whole dataset) and global key signature estimation (93.0% on average, 95.58% on the piano dataset). Designed originally as a backend tool in a music transcription framework, this method should also be useful in other tasks related to music notation processing.

Pre-trained Language Models (PLMs) which are trained on large text corpus via self-supervised learning method, have yielded promising performance on various tasks in Natural Language Processing (NLP). However, though PLMs with huge parameters can effectively possess rich knowledge learned from massive training text and benefit downstream tasks at the fine-tuning stage, they still have some limitations such as poor reasoning ability due to the lack of external knowledge. Research has been dedicated to incorporating knowledge into PLMs to tackle these issues. In this paper, we present a comprehensive review of Knowledge-Enhanced Pre-trained Language Models (KE-PLMs) to provide a clear insight into this thriving field. We introduce appropriate taxonomies respectively for Natural Language Understanding (NLU) and Natural Language Generation (NLG) to highlight these two main tasks of NLP. For NLU, we divide the types of knowledge into four categories: linguistic knowledge, text knowledge, knowledge graph (KG), and rule knowledge. The KE-PLMs for NLG are categorized into KG-based and retrieval-based methods. Finally, we point out some promising future directions of KE-PLMs.

The notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology. In line with the statistical tradition, uncertainty has long been perceived as almost synonymous with standard probability and probabilistic predictions. Yet, due to the steadily increasing relevance of machine learning for practical applications and related issues such as safety requirements, new problems and challenges have recently been identified by machine learning scholars, and these problems may call for new methodological developments. In particular, this includes the importance of distinguishing between (at least) two different types of uncertainty, often refereed to as aleatoric and epistemic. In this paper, we provide an introduction to the topic of uncertainty in machine learning as well as an overview of hitherto attempts at handling uncertainty in general and formalizing this distinction in particular.

We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.