Shivam Kumar

Shivam Kumar, Yixin Wang, Lizhen Lin

Flow matching has emerged as a simulation-free alternative to diffusion-based generative modeling, producing samples by solving an ODE whose time-dependent velocity field is learned along an interpolation between a simple source distribution (e.g., a standard normal) and a target data distribution. Flow-based methods often exhibit greater training stability and have achieved strong empirical performance in high-dimensional settings where data concentrate near a low-dimensional manifold, such as text-to-image synthesis, video generation, and molecular structure generation. Despite this success, existing theoretical analyses of flow matching assume target distributions with smooth, full-dimensional densities, leaving its effectiveness in manifold-supported settings largely unexplained. To this end, we theoretically analyze flow matching with linear interpolation when the target distribution is supported on a smooth manifold. We establish a non-asymptotic convergence guarantee for the learned velocity field, and then propagate this estimation error through the ODE to obtain statistical consistency of the implicit density estimator induced by the flow-matching objective. The resulting convergence rate is near minimax-optimal, depends only on the intrinsic dimension, and reflects the smoothness of both the manifold and the target distribution. Together, these results provide a principled explanation for how flow matching adapts to intrinsic data geometry and circumvents the curse of dimensionality.

Shivam Kumar, Samrat Chatterjee

Spatial transcriptomics (ST) enables the visualization of gene expression within the context of tissue morphology. This emerging discipline has the potential to serve as a foundation for developing tools to design precision medicines. However, due to the higher costs and expertise required for such experiments, its translation into a regular clinical practice might be challenging. Despite the implementation of modern deep learning to enhance information obtained from histological images using AI, efforts have been constrained by limitations in the diversity of information. In this paper, we developed a model, HistoSPACE that explore the diversity of histological images available with ST data to extract molecular insights from tissue image. Our proposed study built an image encoder derived from universal image autoencoder. This image encoder was connected to convolution blocks to built the final model. It was further fine tuned with the help of ST-Data. This model is notably lightweight in compared to traditional histological models. Our developed model demonstrates significant efficiency compared to contemporary algorithms, revealing a correlation of 0.56 in leave-one-out cross-validation. Finally, its robustness was validated through an independent dataset, showing a well matched preditction with predefined disease pathology.

Shivam Kumar, Samrat Chatterjee

Predicting traits from images lacking visual cues is challenging, as algorithms are designed to capture visually correlated ground truth. This problem is critical in biomedical sciences, and their solution can improve the efficacy of non-invasive methods. For example, a recent challenge of predicting MGMT methylation status from MRI images is critical for treatment decisions of glioma patients. Using less robust models poses a significant risk in these critical scenarios and underscores the urgency of addressing this issue. Despite numerous efforts, contemporary models exhibit suboptimal performance, and underlying reasons for this limitation remain elusive. In this study, we demystify the complexity of MGMT status prediction through a comprehensive exploration by performing benchmarks of existing models adjoining transfer learning. Their architectures were further dissected by observing gradient flow across layers. Additionally, a feature selection strategy was applied to improve model interpretability. Our finding highlighted that current models are unlearnable and may require new architectures to explore applications in the real world. We believe our study will draw immediate attention and catalyse advancements in predictive modelling with non-visible cues.