Shuhuan Wang

Shuhuan Wang, Yuzhen Xie, Jiayi Li et al.

Selective State Space Models (SSMs) achieve linear-time inference, yet their gradient-based sensitivity analysis remains bottlenecked by O(L) memory scaling during backpropagation. This memory constraint precludes genomic-scale modeling (L > 10^5) on consumer-grade hardware. We introduce Phase Gradient Flow (PGF), a framework that computes exact analytical derivatives by operating directly in the state-space manifold, bypassing the need to materialize the intermediate computational graph. By reframing SSM dynamics as Tiled Operator-Space Evolution (TOSE), our method delivers O(1) memory complexity relative to sequence length, yielding a 94% reduction in peak VRAM and a 23x increase in throughput compared to standard Autograd. Unlike parallel prefix scans that exhibit numerical divergence in stiff ODE regimes, PGF ensures stability through invariant error scaling, maintaining near-machine precision across extreme sequences. We demonstrate the utility of PGF on an impulse-response benchmark with 128,000-step sequences - a scale where conventional Autograd encounters prohibitive memory overhead, often leading to out-of-memory (OOM) failures in multi-layered models. Our work enables chromosome-scale sensitivity analysis on a single GPU, bridging the gap between theoretical infinite-context models and practical hardware limitations.

Shuhuan Wang, Yuzhen Xie, Jiayi Li

Astronomical imaging confronts an efficiency-resolution tradeoff that limits large-scale morphological classification and redshift prediction. We introduce WaveletMamba, a theory-driven framework integrating wavelet decomposition with state-space modeling, mathematical regularization, and multi-level bias correction. WaveletMamba achieves 81.72% +/- 0.53% classification accuracy at 64x64 resolution with only 3.54M parameters, delivering high-resolution performance (80.93% +/- 0.27% at 244x244) at low-resolution inputs with 9.7x computational efficiency gains. The framework exhibits Resolution Multistability, where models trained on low-resolution data achieve consistent accuracy across different input scales despite divergent internal representations. The framework's multi-level bias correction synergizes HK distance (distribution-level optimal transport) with Color-Aware Weighting (sample-level fine-tuning), achieving 22.96% Log-MSE improvement and 26.10% outlier reduction without explicit selection function modeling. Here, we show that mathematical rigor enables unprecedented efficiency and comprehensive bias correction in scientific AI, bridging computer vision and astrophysics to revolutionize interdisciplinary scientific discovery.