The study of neural representations, both in biological and artificial systems, is increasingly revealing the importance of geometric and topological structures. Inspired by this, we introduce Event2Vec, a novel framework for learning representations of discrete event sequences. Our model leverages a simple, additive recurrent structure to learn composable, interpretable embeddings. We provide a theoretical analysis demonstrating that, under specific training objectives, our model's learned representations in a Euclidean space converge to an ideal additive structure. This ensures that the representation of a sequence is the vector sum of its constituent events, a property we term the linear additive hypothesis. To address the limitations of Euclidean geometry for hierarchical data, we also introduce a variant of our model in hyperbolic space, which is naturally suited to embedding tree-like structures with low distortion. We present experiments to validate our hypothesis. Quantitative evaluation on the Brown Corpus yields a Silhouette score of 0.0564, outperforming a Word2Vec baseline (0.0215), demonstrating the model's ability to capture structural dependencies without supervision.

Understanding semantic relations between two texts is crucial for many information and document management tasks, in which one must determine whether the content fully overlaps, is completely superseded by another document, or overlaps only partially, with unique information in each. Beyond establishing this relation, it is equally important to provide explainable outputs that specify which pieces of information are present, missing, or newly added between the text pair. In this study, we formally define semantic relations between two texts through the set-theoretic relation between their respective Answerable Question Sets (AQS), the sets of questions each text can answer. Under this formulation, Semantic Text Relation (STR), such as equivalence, inclusion, and mutual overlap, becomes a well-defined set relation between the corresponding texts' AQSs. The set differences between the AQSs also serve as an explanation or diagnostic tool for identifying how the information in the texts diverges. Using this definition, we construct a synthetic benchmark that captures fine-grained informational relations through controlled paraphrasing and deliberate information removal supported by AQS manipulations. We then use this dataset to evaluate several discriminative and generative models for classifying text pairs into STR categories, assessing how well different model architectures capture semantic relations beyond surface-level similarity. We publicly release both the dataset and the data generation code to support further research.

We prove that the detection rate of n-crossing alternating links by many standard link invariants decays exponentially in n, implying that they detect alternating links with probability zero. This phenomenon applies broadly, in particular to the Jones and HOMFLYPT polynomials and integral Khovanov homology. We also use a big-data approach to analyze knots and provide evidence that, for knots as well, these invariants exhibit the same asymptotic failure of detection.

Recent technological advances have made it easier to collect large and complex networks of time-stamped relational events connecting two or more entities. Relational hyper-event models (RHEMs) aim to explain the dynamics of these events by modeling the event rate as a function of statistics based on past history and external information. However, despite the complexity of the data, most current RHEM approaches still rely on a linearity assumption to model this relationship. In this work, we address this limitation by introducing a more flexible model that allows the effects of statistics to vary non-linearly and over time. While time-varying and non-linear effects have been used in relational event modeling, we take this further by modeling joint time-varying and non-linear effects using tensor product smooths. We validate our methodology on both synthetic and empirical data. In particular, we use RHEMs to study how patterns of scientific collaboration and impact evolve over time. Our approach provides deeper insights into the dynamic factors driving relational hyper-events, allowing us to evaluate potential non-monotonic patterns that cannot be identified using linear models.

Mainstream Transformer-based large language models face major efficiency bottlenecks: training computation scales quadratically with sequence length, and inference memory grows linearly, limiting long-context processing. Building large models on non-NVIDIA platforms also poses challenges for stable and efficient training. To address this, we introduce SpikingBrain, a family of brain-inspired models designed for efficient long-context training and inference. SpikingBrain leverages the MetaX GPU cluster and focuses on three aspects: (1) Model Architecture: linear and hybrid-linear attention architectures with adaptive spiking neurons; (2) Algorithmic Optimizations: an efficient, conversion-based training pipeline and a dedicated spike coding framework; (3) System Engineering: customized training frameworks, operator libraries, and parallelism strategies tailored to MetaX hardware. Using these techniques, we develop two models: SpikingBrain-7B, a linear LLM, and SpikingBrain-76B, a hybrid-linear MoE LLM. These models demonstrate the feasibility of large-scale LLM development on non-NVIDIA platforms, and training remains stable for weeks on hundreds of MetaX GPUs with Model FLOPs Utilization at expected levels. SpikingBrain achieves performance comparable to open-source Transformer baselines while using only about 150B tokens for continual pre-training. Our models also significantly improve long-context efficiency and deliver inference with (partially) constant memory and event-driven spiking behavior. For example, SpikingBrain-7B attains over 100x speedup in Time to First Token for 4M-token sequences. Furthermore, the proposed spiking scheme achieves 69.15 percent sparsity, enabling low-power operation. Overall, this work demonstrates the potential of brain-inspired mechanisms to drive the next generation of efficient and scalable large model design.

Conformal prediction has been explored as a general and efficient way to provide uncertainty quantification for time series. However, current methods struggle to handle time series data with change points - sudden shifts in the underlying data-generating process. In this paper, we propose a novel Conformal Prediction for Time-series with Change points (CPTC) algorithm, addressing this gap by integrating a model to predict the underlying state with online conformal prediction to model uncertainties in non-stationary time series. We prove CPTC's validity and improved adaptivity in the time series setting under minimum assumptions, and demonstrate CPTC's practical effectiveness on 6 synthetic and real-world datasets, showing improved validity and adaptivity compared to state-of-the-art baselines.

To address the lack of public power system data for machine learning research in energy networks, we investigate the use of variational graph autoencoders (VGAEs) for synthetic distribution grid generation. Using two open-source datasets, ENGAGE and DINGO, we evaluate four decoder variants and compare generated networks against the original grids using structural and spectral metrics. Results indicate that simple decoders fail to capture realistic topologies, while GCN-based approaches achieve strong fidelity on ENGAGE but struggle on the more complex DINGO dataset, producing artifacts such as disconnected components and repeated motifs. These findings highlight both the promise and limitations of VGAEs for grid synthesis, underscoring the need for more expressive generative models and robust evaluation. We release our models and analysis as open source to support benchmarking and accelerate progress in ML-driven power system research.

Although current large audio language models (LALMs) extend text large language models (LLMs) with generic acoustic understanding abilities, they usually suffer from prompt sensitivity, where different instructions of the same intention can yield drastically different outcomes. In this work, we propose AHAMask, where we simply mask some of the attention heads in the decoder-only LLM backbone of LALMs, to trigger specific acoustic task functionalities without instructions. These masks are efficiently obtained by training on an LALM, with the number of trainable parameters equal to the attention head count in its LLM backbone. We show by experiments that applying such selective attention head masks achieves comparable or even better performance than using instructions, either on single or composite tasks. Besides achieving reliable acoustic task specification for LALMs, this also reveals that LALMs exhibit certain "functional pathways" in their attention heads.

AI researchers and practitioners increasingly apply large language models (LLMs) to what we call reasoning-intensive regression (RiR), i.e., deducing subtle numerical scores from text. Unlike standard language regression tasks, e.g., for sentiment or similarity, RiR often appears instead in ad-hoc problems such as rubric-based scoring, modeling dense rewards in complex environments, or domain-specific retrieval, where much deeper analysis of context is required while only limited task-specific training data and computation are available. We cast four realistic problems as RiR tasks to establish an initial benchmark, and use that to test our hypothesis that prompting frozen LLMs and finetuning Transformer encoders via gradient descent will both often struggle in RiR. We then propose MENTAT, a simple and lightweight method that combines batch-reflective prompt optimization with neural ensemble learning. MENTAT achieves up to 65% improvement over both baselines, though substantial room remains for future advances in RiR.

Time-dependent density functional theory (TDDFT) is a widely used method to investigate electron dynamics under external time-dependent perturbations such as laser fields. In this work, we present a machine learning approach to accelerate electron dynamics simulations based on real time TDDFT using autoregressive neural operators as time-propagators for the electron density. By leveraging physics-informed constraints and featurization, and high-resolution training data, our model achieves superior accuracy and computational speed compared to traditional numerical solvers. We demonstrate the effectiveness of our model on a class of one-dimensional diatomic molecules under the influence of a range of laser parameters. This method has potential in enabling on-the-fly modeling of laser-irradiated molecules and materials by utilizing fast machine learning predictions in a large space of varying experimental parameters of the laser.