Flow matching trains a neural network to regress the conditional velocity along a linear interpolant between noise and data, and the number of network evaluations (NFE) sets the cost of sampling. The straight-line interpolant carries an implicit choice: the sample moves at constant speed throughout the trajectory. We relax this choice and introduce Velocity Scheduled Flow Matching (VSFM), which replaces the conditional target x_1 - x_0 with v(t)(x_1 - x_0) for any nonnegative profile v:[0,1]→ℝ_≥ 0 satisfying ∫_0^1 v dt = 1. We study six polynomial profiles drawn from motion planning. The first use of VSFM is at inference time: a pretrained linear flow-matching model can be sampled under any admissible profile by integrating its ODE on a non-uniform τ-schedule, with no retraining and no additional computation; on CIFAR-10 this lowers FID by up to 19.8%. Training from scratch under a braking profile gives a further reduction of 17.4% at 4 NFE. Both gains follow from the local truncation error of the Euler integrator on the induced grid.
Emotion recognition in texts is an important problem in modern natural language processing, currently dominated by transformer architectures. However, their internal mechanisms remain a black box, and classification quality — especially in complex cases — still has room for improvement. This paper proposes a novel hybrid approach that combines the capabilities of modern language models with a deep analysis of their vector representations by adapting the classical statistical pattern recognition method based on decomposition in a space with a generating element (Kunchenko space). The method produces a new set of statistical-geometric features derived from the reconstruction error of vector representations of text messages belonging to the corresponding classes. Experiments conducted on Ukrainian (EMOBENCH-UA) and English (EmoEvent) datasets demonstrate that the proposed hybrid approach yields a statistically significant improvement in classification accuracy. The study also identifies key conditions for the method’s effectiveness: it acts as a powerful refinement mechanism for models fine-tuned on the target task. However, the method is ineffective when applied to raw, non-specialized vector representations. Furthermore, the results indicate that the choice of basis functions for reconstruction is a crucial hyperparameter. This fact allows for adapting the method to the specific geometry of the data space.
Synthetic electrocardiogram generation serves medical AI applications requiring privacy-preserving data sharing and training dataset augmentation. Current diffusion-based methods achieve high generation quality but require hundreds of neural network evaluations during sampling, creating computational bottlenecks for clinical deployment. We propose FlowECG, a flow matching approach that adapts the SSSD-ECG architecture by replacing the iterative diffusion process with continuous flow dynamics. Flow matching learns direct transport paths from noise to data distributions through ordinary differential equation solving. We evaluate our method on the PTB-XL dataset using Dynamic Time Warping, Wasserstein distance, Maximum Mean Discrepancy, and spectral similarity metrics. FlowECG matches SSSD-ECG performance at 200 neural function evaluations, outperforming the baseline on three metrics. The key finding shows that FlowECG maintains generation quality with substantially fewer sampling steps, achieving comparable results with 10-25 evaluations compared to 200 for diffusion methods. This efficiency improvement reduces computational requirements by an order of magnitude while preserving physiologically realistic 12-lead ECG characteristics. The approach enables practical deployment in resource-limited clinical settings where real-time generation or large-scale synthetic data creation is needed.
This paper introduces a unified theoretical perspective that views deep generative models as probability transformation functions. Despite the apparent differences in architecture and training methodologies among various types of generative models - autoencoders, autoregressive models, generative adversarial networks, normalizing flows, diffusion models, and flow matching - we demonstrate that they all fundamentally operate by transforming simple predefined distributions into complex target data distributions. This unifying perspective facilitates the transfer of methodological improvements between model architectures and provides a foundation for developing universal theoretical approaches, potentially leading to more efficient and effective generative modeling techniques.
