CASC: Causal Adversarial Subspace Clustering for Multivariate Spatiotemporal Data

Deep subspace clustering plays a critical role in applications involving multivariate spatiotemporal data, such as sea ice monitoring, disease spread analysis, and tracking neuro-degeneration over time. Despite recent advances, existing methods primarily rely on geometric self-expressiveness, assume static subspace structures, and often fail to capture causal dependencies, local spatial interactions, and long-range temporal dynamics inherent in complex spatiotemporal systems. To address these limitations, we propose a novel Causal Adversarial Subspace Clustering (CASC) framework for discovering evolving latent regimes in high-dimensional spatiotemporal data. CASC integrates a U-Net-inspired deep adversarial clustering architecture with stacked FAConvLSTM layers to preserve spatial and temporal structure while learning robust latent representations. A graph attention transformer-based self-expressive network is introduced to jointly model local spatial relationships, global dependencies, and long-range temporal interactions. Furthermore, we propose two new learning objectives: (1) a Causal Subspace Preservation Loss that aligns self-expression coefficients with latent causal relationships, encouraging clusters to reflect underlying causal processes rather than simple feature similarity, and (2) a Dynamic Temporal Subspace Evolution Loss that captures evolving subspace structures and temporal regime transitions in nonstationary environments. Together, these components transform deep subspace clustering from a correlation-driven paradigm into a causal-temporal regime discovery framework.

Causal Learning with Neural Assemblies

Can Neural Assemblies -- groups of neurons that fire together and strengthen through co-activation -- learn the direction of causal influence between variables? While established as a computationally general substrate for classification, parsing, and planning, neural assemblies have not yet been shown to internalize causal directionality. We demonstrate that the inherent operations of neural assemblies -- projection, local plasticity control, and sparse winner selection -- are sufficient for directional learning. We introduce DIRECT (DIRectional Edge Coupling/Training), a mechanism that co-activates source and target assemblies under an adaptive gain schedule to internalize directed relations. Unlike backpropagation-based methods, DIRECT relies solely on local plasticity, making the resulting causal claims auditable at the mechanism level. Our findings are verified through a dual-readout validation strategy: (i) synaptic-strength asymmetry, measuring the emergent weight gap between forward and reverse links, and (ii) functional propagation overlap, quantifying the reliability of directional signal flow. Across multiple domains, the framework achieves perfect structural recovery under a supervised, known-structure setting. These results establish neural assemblies as an auditable bridge between biologically plausible dynamics and formal causal models, offering an "explainable by design" framework where causal claims are traceable to specific neural winners and synaptic asymmetries.