L-systems can be made to model and create simulations of many biological processes, such as plant development. Finding an L-system for a given process is typically solved by hand, by experts, in a massively time-consuming process. It would be significant if this could be done automatically from data, such as from sequences of images. In this paper, we are interested in inferring a particular type of L-system, deterministic context-free L-system (D0L-system) from a sequence of strings. We introduce the characteristic graph of a sequence of strings, which we then utilize to translate our problem (inferring D0L-system) in polynomial time into the maximum independent set problem (MIS) and the SAT problem. After that, we offer a classical exact algorithm and an approximate quantum algorithm for the problem.

Graph clustering is an unsupervised machine learning method that partitions the nodes in a graph into different groups. Despite achieving significant progress in exploiting both attributed and structured data information, graph clustering methods often face practical challenges related to data isolation. Moreover, the absence of collaborative methods for graph clustering limits their effectiveness. In this paper, we propose a collaborative graph clustering framework for attributed graphs, supporting attributed graph clustering over vertically partitioned data with different participants holding distinct features of the same data. Our method leverages a novel technique that reduces the sample space, improving the efficiency of the attributed graph clustering method. Furthermore, we compare our method to its centralized counterpart under a proximity condition, demonstrating that the successful local results of each participant contribute to the overall success of the collaboration. We fully implement our approach and evaluate its utility and efficiency by conducting experiments on four public datasets. The results demonstrate that our method achieves comparable accuracy levels to centralized attributed graph clustering methods. Our collaborative graph clustering framework provides an efficient and effective solution for graph clustering challenges related to data isolation.

Federated learning (FL) enables multiple devices to collaboratively train a global model while maintaining data on local servers. Each device trains the model on its local server and shares only the model updates (i.e., gradient weights) during the aggregation step. A significant challenge in FL is managing the feature distribution of novel and unbalanced data across devices. In this paper, we propose an FL approach using few-shot learning and aggregation of the model weights on a global server. We introduce a dynamic early stopping method to balance out-of-distribution classes based on representation learning, specifically utilizing the maximum mean discrepancy of feature embeddings between local and global models. An exemplary application of FL is to orchestrate machine learning models along highways for interference classification based on snapshots from global navigation satellite system (GNSS) receivers. Extensive experiments on four GNSS datasets from two real-world highways and controlled environments demonstrate that our FL method surpasses state-of-the-art techniques in adapting to both novel interference classes and multipath scenarios.

Deep neural networks (DNNs) are often constructed under the closed-world assumption, which may fail to generalize to the out-of-distribution (OOD) data. This leads to DNNs producing overconfident wrong predictions and can result in disastrous consequences in safety-critical applications. Existing OOD detection methods mainly rely on curating a set of OOD data for model training or hyper-parameter tuning to distinguish OOD data from training data (also known as in-distribution data or InD data). However, OOD samples are not always available during the training phase in real-world applications, hindering the OOD detection accuracy. To overcome this limitation, we propose a Gaussian-process-based OOD detection method to establish a decision boundary based on InD data only. The basic idea is to perform uncertainty quantification of the unconstrained softmax scores of a DNN via a multi-class Gaussian process (GP), and then define a score function to separate InD and potential OOD data based on their fundamental differences in the posterior predictive distribution from the GP. Two case studies on conventional image classification datasets and real-world image datasets are conducted to demonstrate that the proposed method outperforms the state-of-the-art OOD detection methods when OOD samples are not observed in the training phase.

The ideas of aleatoric and epistemic uncertainty are widely used to reason about the probabilistic predictions of machine-learning models. We identify incoherence in existing discussions of these ideas and suggest this stems from the aleatoric-epistemic view being insufficiently expressive to capture all of the distinct quantities that researchers are interested in. To explain and address this we derive a simple delineation of different model-based uncertainties and the data-generating processes associated with training and evaluation. Using this in place of the aleatoric-epistemic view could produce clearer discourse as the field moves forward.

Long-term time series prediction involves forecasting future trends over extended periods based on historical changes. This approach is crucial in various fields such as weather [1], traffic [2], and power [3]. The exceptionally long forecast horizon and the complex correlations between channels pose significant challenges to modeling. Traditional methods often fall short in capturing the sequence and inter-channel relationships. In contrast, deep learning architectures, with their superior fitting capabilities, have emerged as effective tools for addressing long-term time series prediction. Consequently, the primary methodologies in this field have shifted towards deep learning models. The core issue in long time series analysis is extracting dependencies within sequences and correlations across channels, which significantly benefits model performance in multi-channel prediction and robustness. Various methods have been developed to capture this information from time series data. Commonly used techniques include Transformers [4, 5, 6, 7, 8, 9, 10], which apply attention mechanisms to effectively capture correlations both within sequences and across channels; Convolutional Neural Networks (CNN) [11, 12] that use 1D or multidimensional convolutions to capture these dependencies; and structures based on Multilayer Perceptrons[13, 14, 15, 16, 17], such as DLinear, which decompose sequences and apply multiple linear layers to capture sequence correlations.

In this work, we propose a first-order sampling method called the Metropolis-adjusted Preconditioned Langevin Algorithm for approximate sampling from a target distribution whose support is a proper convex subset of $\mathbb{R}^{d}$. Our proposed method is the result of applying a Metropolis-Hastings filter to the Markov chain formed by a single step of the preconditioned Langevin algorithm with a metric $\mathscr{G}$, and is motivated by the natural gradient descent algorithm for optimisation. We derive non-asymptotic upper bounds for the mixing time of this method for sampling from target distributions whose potentials are bounded relative to $\mathscr{G}$, and for exponential distributions restricted to the support. Our analysis suggests that if $\mathscr{G}$ satisfies stronger notions of self-concordance introduced in Kook and Vempala (2024), then these mixing time upper bounds have a strictly better dependence on the dimension than when is merely self-concordant. We also provide numerical experiments that demonstrates the practicality of our proposed method. Our method is a high-accuracy sampler due to the polylogarithmic dependence on the error tolerance in our mixing time upper bounds.

Feature selection is essential in the analysis of molecular systems and many other fields, but several uncertainties remain: What is the optimal number of features for a simplified, interpretable model that retains essential information? How should features with different units be aligned, and how should their relative importance be weighted? Here, we introduce the Differentiable Information Imbalance (DII), an automated method to rank information content between sets of features. Using distances in a ground truth feature space, DII identifies a low-dimensional subset of features that best preserves these relationships. Each feature is scaled by a weight, which is optimized by minimizing the DII through gradient descent. This allows simultaneously performing unit alignment and relative importance scaling, while preserving interpretability. DII can also produce sparse solutions and determine the optimal size of the reduced feature space. We demonstrate the usefulness of this approach on two benchmark molecular problems: (1) identifying collective variables that describe conformations of a biomolecule, and (2) selecting features for training a machine-learning force field. These results show the potential of DII in addressing feature selection challenges and optimizing dimensionality in various applications. The method is available in the Python library DADApy.

Robust training of machine learning models in the presence of outliers has garnered attention across various domains. The use of robust losses is a popular approach and is known to mitigate the impact of outliers. We bring to light two literatures that have diverged in their ways of designing robust losses: one using M-estimation, which is popular in robotics and computer vision, and another using a risk-minimization framework, which is popular in deep learning. We first show that a simple modification of the Black-Rangarajan duality provides a unifying view. The modified duality brings out a definition of a robust loss kernel $\sigma$ that is satisfied by robust losses in both the literatures. Secondly, using the modified duality, we propose an Adaptive Alternation Algorithm (AAA) for training machine learning models with outliers. The algorithm iteratively trains the model by using a weighted version of the non-robust loss, while updating the weights at each iteration. The algorithm is augmented with a novel parameter update rule by interpreting the weights as inlier probabilities, and obviates the need for complex parameter tuning. Thirdly, we investigate convergence of the adaptive alternation algorithm to outlier-free optima. Considering arbitrary outliers (i.e., with no distributional assumption on the outliers), we show that the use of robust loss kernels {\sigma} increases the region of convergence. We experimentally show the efficacy of our algorithm on regression, classification, and neural scene reconstruction problems. We release our implementation code: https://github.com/MIT-SPARK/ORT.

This study evaluates fine-tuning strategies for text classification using the DistilBERT model, specifically the distilbert-base-uncased-finetuned-sst-2-english variant. Through structured experiments, we examine the influence of hyperparameters such as learning rate, batch size, and epochs on accuracy, F1-score, and loss. Polynomial regression analyses capture foundational and incremental impacts of these hyperparameters, focusing on fine-tuning adjustments relative to a baseline model. Results reveal variability in metrics due to hyperparameter configurations, showing trade-offs among performance metrics. For example, a higher learning rate reduces loss in relative analysis (p=0.027) but challenges accuracy improvements. Meanwhile, batch size significantly impacts accuracy and F1-score in absolute regression (p=0.028 and p=0.005) but has limited influence on loss optimization (p=0.170). The interaction between epochs and batch size maximizes F1-score (p=0.001), underscoring the importance of hyperparameter interplay. These findings highlight the need for fine-tuning strategies addressing non-linear hyperparameter interactions to balance performance across metrics. Such variability and metric trade-offs are relevant for tasks beyond text classification, including NLP and computer vision. This analysis informs fine-tuning strategies for large language models and promotes adaptive designs for broader model applicability.