As illustrated by the success of integer linear programming, linear integer arithmetic is a powerful tool for modelling combinatorial problems. Furthermore, the probabilistic extension of linear programming has been used to formulate problems in neurosymbolic AI. However, two key problems persist that prevent the adoption of neurosymbolic techniques beyond toy problems. First, probabilistic inference is inherently hard, #P-hard to be precise. Second, the discrete nature of integers renders the construction of meaningful gradients challenging, which is problematic for learning. In order to mitigate these issues, we formulate linear arithmetic over integer-valued random variables as tensor manipulations that can be implemented in a straightforward fashion using modern deep learning libraries. At the core of our formulation lies the observation that the addition of two integer-valued random variables can be performed by adapting the fast Fourier transform to probabilities in the log-domain. By relying on tensor operations we obtain a differentiable data structure, which unlocks, virtually for free, gradient-based learning. In our experimental validation we show that tensorising probabilistic linear integer arithmetic and leveraging the fast Fourier transform allows us to push the state of the art by several orders of magnitude in terms of inference and learning times.

In the hospital, patients may be in the ICU with ECG/PPG sensors to monitor their already-poor healthcondition. ML methods must rely onlearning toimpute missing signals based onthesignal that is present, rather than learning tocreate ageneral-purpose imputation template thatmimics standard healthybehavior. Likewise, participant movement inboth contexts can result in artifacts(e.g. Inabroadercontext, we want to match the high quality level of other datasets such as PTB-XL, in which 77.01% of thesignal data areofhighest assessed quality [18]. See below for examples of ECG signals with their associated periodogram.

Fourier neural operators (FNOs) can learn highly nonlinear mappings between function spaces, and have recently become a popular tool for learning responses of complex physical systems. However, to achieve good accuracy and efficiency, FNOs rely on the Fast Fourier transform (FFT), which is restricted to modeling problems on rectangular domains. To lift such a restriction and permit FFT on irregular geometries as well as topology changes, we introduce domain agnostic Fourier neural operator (DAFNO), a novel neural operator architecture for learning surrogates with irregular geometries and evolving domains. The key idea is to incorporate a smoothed characteristic function in the integral layer architecture of FNOs, and leverage FFT to achieve rapid computations, in such a way that the geometric information is explicitly encoded in the architecture. In our empirical evaluation, DAFNO has achieved state-of-the-art accuracy as compared to baseline neural operator models on two benchmark datasets of material modeling and airfoil simulation. To further demonstrate the capability and generalizability of DAFNO in handling complex domains with topology changes, we consider a brittle material fracture evolution problem. With only one training crack simulation sample, DAFNO has achieved generalizability to unseen loading scenarios and substantially different crack patterns from the trained scenario.

In this paper, we propose a new Temporal MDS-Vision Transformer (T-MDS-ViT) for multiclass target classification using millimeter-wave FMCW radar micro-Doppler spectrograms. Specifically, we design a transformer-based architecture that processes stacked range-velocity-angle (RVA) spatiotemporal tensors via patch embeddings and cross-axis attention mechanisms to explicitly model the sequential nature of MDS data across multiple frames. The T-MDS-ViT exploits mobility-aware constraints in its attention layer correspondences to maintain separability under target overlaps and partial occlusions. Next, we apply an explainable mechanism to examine how the attention layers focus on characteristic high-energy regions of the MDS representations and their effect on class-specific kinematic features. We also demonstrate that our proposed framework is superior to existing CNN-based methods in terms of classification accuracy while achieving better data efficiency and real-time deployability.

The emergence of accurate open large language models (LLMs) has sparked a push for advanced quantization techniques to enable efficient deployment on end-user devices. In this paper, we revisit the challenge of extreme LLM compression -- targeting ultra-low-bit quantization for both activations and weights -- from a Fourier frequency domain perspective. We propose SpecQuant, a two-stage framework that tackles activation outliers and cross-channel variance. In the first stage, activation outliers are smoothed and transferred into the weight matrix to simplify downstream quantization. In the second stage, we apply channel-wise low-frequency Fourier truncation to suppress high-frequency components while preserving essential signal energy, improving quantization robustness. Our method builds on the principle that most of the weight energy is concentrated in low-frequency components, which can be retained with minimal impact on model accuracy. To enable runtime adaptability, we introduce a lightweight truncation module during inference that adjusts truncation thresholds based on channel characteristics. On LLaMA-3 8B, SpecQuant achieves 4-bit quantization for both weights and activations, narrowing the zero-shot accuracy gap to only 1.5% compared to full precision, while delivering 2 times faster inference and 3times lower memory usage.

Recent research on fine-tuning vision-language models has demonstrated impressive performance in various downstream tasks.