Molecular Dynamics (MD) is a powerful computational microscope for probing protein functions. However, the need for fine-grained integration and the long timescales of biomolecular events make MD computationally expensive. To address this, several generative models have been proposed to generate surrogate trajectories at lower cost. Yet, these models typically learn a fixed-lag transition density, causing the training signal to be dominated by frequent but uninformative transitions. We introduce a new class of generative models, MSM Emulators, which instead learn to sample transitions across discrete states defined by an underlying Markov State Model (MSM). We instantiate this class with Markov Space Flow Matching (MarS-FM), whose sampling offers more than two orders of magnitude speedup compared to implicit- or explicit-solvent MD simulations. We benchmark Mars-FM ability to reproduce MD statistics through structural observables such as RMSD, radius of gyration, and secondary structure content. Our evaluation spans protein domains (up to 500 residues) with significant chemical and structural diversity, including unfolding events, and enforces strict sequence dissimilarity between training and test sets to assess generalization. Across all metrics, MarS-FM outperforms existing methods, often by a substantial margin.

In recent years, self-supervised learning has amassed significant interest for training deep neural representations without labeled data. One such self-supervised learning approach is masked spectrogram modeling, where the objective is to learn semantically rich contextual representations by predicting removed or hidden portions of the input audio spectrogram. With the Transformer neural architecture at its core, masked spectrogram modeling has emerged as the prominent approach for learning general purpose audio representations, a.k.a. audio foundation models. Meanwhile, addressing the issues of the Transformer architecture, in particular the underlying Scaled Dot-product Attention operation, which scales quadratically with input sequence length, has led to renewed interest in recurrent sequence modeling approaches. Among them, Selective structured state space models (such as Mamba) and extended Long Short-Term Memory (xLSTM) are the two most promising approaches which have experienced widespread adoption. While the body of work on these two topics continues to grow, there is currently a lack of an adequate overview encompassing the intersection of these topics. In this paper, we present a comprehensive overview of the aforementioned research domains, covering masked spectrogram modeling and the previously mentioned neural sequence modeling architectures, Mamba and xLSTM. Further, we compare Transformers, Mamba and xLSTM based masked spectrogram models in a unified, reproducible framework on ten diverse downstream audio classification tasks, which will help interested readers to make informed decisions regarding suitability of the evaluated approaches to adjacent applications.

Diffusion models are widely used in applications ranging from image generation to inverse problems. However, training diffusion models typically requires clean ground-truth images, which are unavailable in many applications. We introduce the Measurement Score-based diffusion Model (MSM), a novel framework that learns partial measurement scores using only noisy and subsampled measurements. MSM models the distribution of full measurements as an expectation over partial scores induced by randomized subsampling. To make the MSM representation computationally efficient, we also develop a stochastic sampling algorithm that generates full images by using a randomly selected subset of partial scores at each step. We additionally propose a new posterior sampling method for solving inverse problems that reconstructs images using these partial scores. We provide a theoretical analysis that bounds the Kullback-Leibler divergence between the distributions induced by full and stochastic sampling, establishing the accuracy of the proposed algorithm. We demonstrate the effectiveness of MSM on natural images and multi-coil MRI, showing that it can generate high-quality images and solve inverse problems -- all without access to clean training data. Code is available at https://github.com/wustl-cig/MSM.

Recent advancements in machine learning-based signal analysis, coupled with open data initiatives, have fuelled efforts in automatic sleep stage classification. Despite the proliferation of classification models, few have prioritised reducing model complexity, which is a crucial factor for practical applications. In this work, we introduce Multi-Scale and Attention Convolutional Neural Network (MSA-CNN), a lightweight architecture featuring as few as ~10,000 parameters. MSA-CNN leverages a novel multi-scale module employing complementary pooling to eliminate redundant filter parameters and dense convolutions. Model complexity is further reduced by separating temporal and spatial feature extraction and using cost-effective global spatial convolutions. This separation of tasks not only reduces model complexity but also mirrors the approach used by human experts in sleep stage scoring. We evaluated both small and large configurations of MSA-CNN against nine state-of-the-art baseline models across three public datasets, treating univariate and multivariate models separately. Our evaluation, based on repeated cross-validation and re-evaluation of all baseline models, demonstrated that the large MSA-CNN outperformed all baseline models on all three datasets in terms of accuracy and Cohen's kappa, despite its significantly reduced parameter count. Lastly, we explored various model variants and conducted an in-depth analysis of the key modules and techniques, providing deeper insights into the underlying mechanisms. The code for our models, baselines, and evaluation procedures is available at https://github.com/sgoerttler/MSA-CNN.

Lying at the interface between Network Science and Machine Learning, node embedding algorithms take a graph as input and encode its structure onto output vectors that represent nodes in an abstract geometric space, enabling various vector-based downstream tasks such as network modelling, data compression, link prediction, and community detection. Two apparently unrelated limitations affect these algorithms. On one hand, it is not clear what the basic operation defining vector spaces, i.e. the vector sum, corresponds to in terms of the original nodes in the network. On the other hand, while the same input network can be represented at multiple levels of resolution by coarse-graining the constituent nodes into arbitrary block-nodes, the relationship between node embeddings obtained at different hierarchical levels is not understood. Here, building on recent results in network renormalization theory, we address these two limitations at once and define a multiscale node embedding method that, upon arbitrary coarse-grainings, ensures statistical consistency of the embedding vector of a block-node with the sum of the embedding vectors of its constituent nodes. We illustrate the power of this approach on two economic networks that can be naturally represented at multiple resolution levels: namely, the international trade between (sets of) countries and the input-output flows among (sets of) industries in the Netherlands. We confirm the statistical consistency between networks retrieved from coarse-grained node vectors and networks retrieved from sums of fine-grained node vectors, a result that cannot be achieved by alternative methods. Several key network properties, including a large number of triangles, are successfully replicated already from embeddings of very low dimensionality, allowing for the generation of faithful replicas of the original networks at arbitrary resolution levels.

Time series data has become increasingly prevalent across numerous domains, driving a growing demand for time series machine learning techniques. Among these, time series clustering (TSCL) stands out as one of the most popular machine learning tasks. TSCL serves as a powerful exploratory analysis tool and is also employed as a preprocessing step or subroutine for various tasks, including anomaly detection, segmentation, and classification. The most popular TSCL algorithms are either fast (in terms of run time) but perform poorly on benchmark problems, or perform well on benchmarks but scale poorly. We present a new TSCL algorithm, the $k$-means (K) accelerated (A) Stochastic subgradient (S) Barycentre (B) Average (A) (KASBA) clustering algorithm. KASBA is a $k$-means clustering algorithm that uses the Move-Split-Merge (MSM) elastic distance at all stages of clustering, applies a randomised stochastic subgradient gradient descent to find barycentre centroids, links each stage of clustering to accelerate convergence and exploits the metric property of MSM distance to avoid a large proportion of distance calculations. It is a versatile and scalable clusterer designed for real-world TSCL applications. It allows practitioners to balance run time and clustering performance. We demonstrate through extensive experimentation that KASBA produces significantly better clustering than the faster state of the art clusterers and is offers orders of magnitude improvement in run time over the most performant $k$-means alternatives.

Some one million eligible voters in the Indian Ocean Mauritius will head out to vote on Sunday amid an explosive scandal that has implicated government figures in a covert wiretapping operation. Since independence from Britain in 1968, the southeast African country has maintained a strong, vibrant parliamentary democracy. This will be its 12th national election. Elections are usually deemed free and fair and turnout is normally high, at close to 80 percent. This time, however, the unusual drama caused by the leaked recordings has sparked national agitation and dominated the campaign season.

Efficient sampling in biomolecular simulations is critical for accurately capturing the complex dynamical behaviors of biological systems. Adaptive sampling techniques aim to improve efficiency by focusing computational resources on the most relevant regions of phase space. In this work, we present a framework for identifying the optimal sampling policy through metric driven ranking. Our approach systematically evaluates the policy ensemble and ranks the policies based on their ability to explore the conformational space effectively. Through a series of biomolecular simulation case studies, we demonstrate that choice of a different adaptive sampling policy at each round significantly outperforms single policy sampling, leading to faster convergence and improved sampling performance. This approach takes an ensemble of adaptive sampling policies and identifies the optimal policy for the next round based on current data. Beyond presenting this ensemble view of adaptive sampling, we also propose two sampling algorithms that approximate this ranking framework on the fly. The modularity of this framework allows incorporation of any adaptive sampling policy making it versatile and suitable as a comprehensive adaptive sampling scheme.

Molecular dynamics (MD) is a powerful technique for studying microscopic phenomena, but its computational cost has driven significant interest in the development of deep learning-based surrogate models. We introduce generative modeling of molecular trajectories as a paradigm for learning flexible multi-task surrogate models of MD from data. By conditioning on appropriately chosen frames of the trajectory, we show such generative models can be adapted to diverse tasks such as forward simulation, transition path sampling, and trajectory upsampling. By alternatively conditioning on part of the molecular system and inpainting the rest, we also demonstrate the first steps towards dynamics-conditioned molecular design. We validate the full set of these capabilities on tetrapeptide simulations and show that our model can produce reasonable ensembles of protein monomers. Altogether, our work illustrates how generative modeling can unlock value from MD data towards diverse downstream tasks that are not straightforward to address with existing methods or even MD itself. Code is available at https://github.com/bjing2016/mdgen.

We present Flow Matching for Reaction Coordinates (FMRC), a novel deep learning algorithm designed to identify optimal reaction coordinates (RC) in biomolecular reversible dynamics. FMRC is based on the mathematical principles of lumpability and decomposability, which we reformulate into a conditional probability framework for efficient data-driven optimization using deep generative models. While FMRC does not explicitly learn the well-established transfer operator or its eigenfunctions, it can effectively encode the dynamics of leading eigenfunctions of the system transfer operator into its low-dimensional RC space. We further quantitatively compare its performance with several state-of-the-art algorithms by evaluating the quality of Markov State Models (MSM) constructed in their respective RC spaces, demonstrating the superiority of FMRC in three increasingly complex biomolecular systems. Finally, we discuss its potential applications in downstream applications such as enhanced sampling methods and MSM construction.