Varun Sarathchandran | Searcharxiv

arXiv2026

Joint Simplicial Complex Learning via Binary Linear Programming

Learning the topology of higher-order networks from data is a fundamental challenge in many signal processing and machine learning applications. Simplicial complexes provide a principled framework for modeling multi-way interactions, yet learning their structure is challenging due to the strong coupling across different simplicial levels imposed by the inclusion property. In this work, we propose a joint framework for simplicial complex learning that enforces the inclusion property through a linear constraint, enabling the formulation of the problem as a binary linear program. The objective function consists of a combination of smoothness measures across all considered simplicial levels, allowing for the incorporation of arbitrary smoothness criteria. This formulation enables the simultaneous estimation of edges and higher-order simplices within a single optimization problem. Experiments on simulated and real-world data demonstrate that the proposed joint approach outperforms hierarchical and greedy baselines, while more faithfully enforcing higher-order structural priors.

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arXiv2025

BlockGPT: Spatio-Temporal Modelling of Rainfall via Frame-Level Autoregression

Predicting precipitation maps is a highly complex spatiotemporal modeling task, critical for mitigating the impacts of extreme weather events. Short-term precipitation forecasting, or nowcasting, requires models that are not only accurate but also computationally efficient for real-time applications. Current methods, such as token-based autoregressive models, often suffer from flawed inductive biases and slow inference, while diffusion models can be computationally intensive. To address these limitations, we introduce BlockGPT, a generative autoregressive transformer using batched tokenization (Block) method that predicts full two-dimensional fields (frames) at each time step. Conceived as a model-agnostic paradigm for video prediction, BlockGPT factorizes space-time by using self-attention within each frame and causal attention across frames; in this work, we instantiate it for precipitation nowcasting. We evaluate BlockGPT on two precipitation datasets, viz. KNMI (Netherlands) and SEVIR (U.S.), comparing it to state-of-the-art baselines including token-based (NowcastingGPT) and diffusion-based (DiffCast+Phydnet) models. The results show that BlockGPT achieves superior accuracy, event localization as measured by categorical metrics, and inference speeds up to 31x faster than comparable baselines.

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