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We analyze the asymptotic number and typical structure of claw-free graphs at constant edge densities. The first of our main results is a formula for the asymptotics of the logarithm of the number of claw-free graphs of edge density $\gamma \in (0,1)$. We show that the problem exhibits a second-order phase transition at edge density $\gamma^\ast=\frac{5-\sqrt{5}}{4}$. The asymptotic formula arises by solving a variational problem over graphons. For $\gamma\geq\gamma^\ast$ there is a unique optimal graphon, while for $\gamma<\gamma^\ast$ there is an infinite set of optimal graphons. By analyzing more detailed structure, we prove that for $\gamma<\gamma^\ast$, there is in fact a unique graphon $W$ such that almost all claw-free graphs at edge density $\gamma$ are close in cut metric to $W$. We also analyze the probability of claw-freeness in the Erd\H{o}s-R\'enyi random graph $G(n,p)$ for constant $p$, obtaining a formula for the large-deviation rate function for claw-freeness. In this case, the problem exhibits a first-order phase transition at $p^\ast=\frac{3-\sqrt{5}}{2}$, separating distinct structural regimes. At the critical point $p^\ast$, the corresponding graphon variational problem has infinitely many solutions, and we again pinpoint a unique optimal graphon that describes the typical structure of $G(n,p^\ast)$ conditioned on being claw-free.

Concept inventories are standardized assessments that evaluate student understanding of key concepts within academic disciplines. While prevalent across STEM fields, their development lags for advanced computer science topics like dynamic programming (DP) -- an algorithmic technique that poses significant conceptual challenges for undergraduates. To fill this gap, we developed and validated a Dynamic Programming Concept Inventory (DPCI). We detail the iterative process used to formulate multiple-choice questions targeting known student misconceptions about DP concepts identified through prior research studies. We discuss key decisions, tradeoffs, and challenges faced in crafting probing questions to subtly reveal these conceptual misunderstandings. We conducted a preliminary psychometric validation by administering the DPCI to 172 undergraduate CS students finding our questions to be of appropriate difficulty and effectively discriminating between differing levels of student understanding. Taken together, our validated DPCI will enable instructors to accurately assess student mastery of DP. Moreover, our approach for devising a concept inventory for an advanced theoretical computer science concept can guide future efforts to create assessments for other under-evaluated areas currently lacking coverage., Comment: Accepted to SIGCSE 2025

This paper explores the problems of Question Answering (QA) and Named Entity Recognition (NER) in five diverse languages. We tested five Large Language Models with various prompting methods, including zero-shot, chain-of-thought reasoning, and translation techniques. Our results show that while some models consistently outperform others, their effectiveness varies significantly across tasks and languages. We saw that advanced prompting techniques generally improved QA performance but had mixed results for NER; and we observed that language difficulty patterns differed between tasks. Our findings highlight the need for task-specific approaches in multilingual NLP and suggest that current models may develop different linguistic competencies for different tasks., Comment: MRL 2024 Shared Task on Multi-lingual Multi-task Information Retrieval; 4th Multilingual Representation Learning (MRL) Workshop; EMNLP 2024

The discovery of causal relationships between random variables is an important yet challenging problem that has applications across many scientific domains. Differentiable causal discovery (DCD) methods are effective in uncovering causal relationships from observational data; however, these approaches often suffer from limited interpretability and face challenges in incorporating domain-specific prior knowledge. In contrast, Large Language Models (LLMs)-based causal discovery approaches have recently been shown capable of providing useful priors for causal discovery but struggle with formal causal reasoning. In this paper, we propose LLM-DCD, which uses an LLM to initialize the optimization of the maximum likelihood objective function of DCD approaches, thereby incorporating strong priors into the discovery method. To achieve this initialization, we design our objective function to depend on an explicitly defined adjacency matrix of the causal graph as its only variational parameter. Directly optimizing the explicitly defined adjacency matrix provides a more interpretable approach to causal discovery. Additionally, we demonstrate higher accuracy on key benchmarking datasets of our approach compared to state-of-the-art alternatives, and provide empirical evidence that the quality of the initialization directly impacts the quality of the final output of our DCD approach. LLM-DCD opens up new opportunities for traditional causal discovery methods like DCD to benefit from future improvements in the causal reasoning capabilities of LLMs.

This paper examines the use of tensor networks, which can efficiently represent high-dimensional quantum states, in language modeling. It is a distillation and continuation of the work done in (van der Poel, 2023). To do so, we will abstract the problem down to modeling Motzkin spin chains, which exhibit long-range correlations reminiscent of those found in language. The Matrix Product State (MPS), also known as the tensor train, has a bond dimension which scales as the length of the sequence it models. To combat this, we use the factored core MPS, whose bond dimension scales sub-linearly. We find that the tensor models reach near perfect classifying ability, and maintain a stable level of performance as the number of valid training examples is decreased., Comment: See source code at https://github.com/ConstantijnvdP/eidolon

Helical molecules have been identified as potential candidates for investigating electronic transport, spin filtering, or even piezoelectricity. However, the description of the transport mechanism is not straightforward in single molecular junctions. In this work, we study the electronic transport in break junctions of a series of three helical molecules: dithia[$n$]helicenes, with $n=7, 9, 11$ molecular units, and detail the synthesis of two kinds of dithia[11]helicenes, varying the location of the sulfur atoms. Our experimental study demonstrates low conductance values that remain similar across different biases and molecules. Additionally, we assess the length dependence of the conductance for each helicene, revealing an exponential decay characteristic of off-resonant transport. This behaviour is primarily attributed to the misalignment between the energy levels of the molecule-electrodes system. The length dependence trend described above is supported by \textit{ab initio} calculations, further confirming the off-resonant transport mechanism.

Synthetic datasets constructed from formal languages allow fine-grained examination of the learning and generalization capabilities of machine learning systems for sequence classification. This article presents a new benchmark for machine learning systems on sequence classification called MLRegTest, which contains training, development, and test sets from 1,800 regular languages. Different kinds of formal languages represent different kinds of long-distance dependencies, and correctly identifying long-distance dependencies in sequences is a known challenge for ML systems to generalize successfully. MLRegTest organizes its languages according to their logical complexity (monadic second order, first order, propositional, or monomial expressions) and the kind of logical literals (string, tier-string, subsequence, or combinations thereof). The logical complexity and choice of literal provides a systematic way to understand different kinds of long-distance dependencies in regular languages, and therefore to understand the capacities of different ML systems to learn such long-distance dependencies. Finally, the performance of different neural networks (simple RNN, LSTM, GRU, transformer) on MLRegTest is examined. The main conclusion is that performance depends significantly on the kind of test set, the class of language, and the neural network architecture., Comment: Accepted for publication in the Journal of Machine Learning Research. Dataset available at https://doi.org/10.5061/dryad.dncjsxm4h , code available at https://github.com/heinz-jeffrey/subregular-learning

Despite significant progress in the quality of language generated from abstractive summarization models, these models still exhibit the tendency to hallucinate, i.e., output content not supported by the source document. A number of works have tried to fix--or at least uncover the source of--the problem with limited success. In this paper, we identify a simple criterion under which models are significantly more likely to assign more probability to hallucinated content during generation: high model uncertainty. This finding offers a potential explanation for hallucinations: models default to favoring text with high marginal probability, i.e., high-frequency occurrences in the training set, when uncertain about a continuation. It also motivates possible routes for real-time intervention during decoding to prevent such hallucinations. We propose a decoding strategy that switches to optimizing for pointwise mutual information of the source and target token--rather than purely the probability of the target token--when the model exhibits uncertainty. Experiments on the XSum dataset show that our method decreases the probability of hallucinated tokens while maintaining the Rouge and BertS scores of top-performing decoding strategies., Comment: EMNLP 2022

While the 10-year survival rate for localized prostate cancer patients is very good (>98%), side effects of treatment may limit quality of life significantly. Erectile dysfunction (ED) is a common burden associated with increasing age as well as prostate cancer treatment. Although many studies have investigated the factors affecting erectile dysfunction (ED) after prostate cancer treatment, only limited studies have investigated whether ED can be predicted before the start of treatment. The advent of machine learning (ML) based prediction tools in oncology offers a promising approach to improve accuracy of prediction and quality of care. Predicting ED may help aid shared decision making by making the advantages and disadvantages of certain treatments clear, so that a tailored treatment for an individual patient can be chosen. This study aimed to predict ED at 1-year and 2-year post-diagnosis based on patient demographics, clinical data and patient-reported outcomes (PROMs) measured at diagnosis.

Here, we develop a data-centric approach enabling to analyse which activities, function, and characteristics of the environment surrounding the slow charging infrastructure impact the distribution of the electricity consumed at slow charging infrastructure. To gain a basic insight, we analysed the probabilistic distribution of energy consumption and its relation to indicators characterizing charging events. We collected geospatial datasets and utilizing statistical methods for data pre-processing, we prepared features modelling the spatial context in which the charging infrastructure operates. To enhance the statistical reliability of results, we applied the bootstrap method together with the Lasso method that combines regression with variable selection ability. We evaluate the statistical distributions of the selected regression coefficients. We identified the most influential features correlated with energy consumption, indicating that the spatial context of the charging infrastructure affects its utilization pattern. Many of these features are related to the economic prosperity of residents. Application of the methodology to a specific class of charging infrastructure enables the differentiation of selected features, e.g. by the used rollout strategy. Overall, the paper demonstrates the application of statistical methodologies to energy data and provides insights on factors potentially shaping the energy consumption that could be utilized when developing models to inform charging infrastructure deployment and planning of power grids.