GeoCert: Certified Geometric AI for Reliable Forecasting

Forecasting systems in science must be accurate, physically consistent, and certifiably reliable. Most existing models address prediction, constraint enforcement, and verification separately, limiting scalability and interpretability. We introduce GeoCert, a geometric AI framework that unifies forecasting, physical reasoning, and formal verification within a single differentiable computation. GeoCert formulates forecasting as evolution along a hyperbolic manifold, where negative curvature induces contraction dynamics, intrinsic robustness, and logarithmic-time certification. A hierarchical constraint architecture separates universal physical laws from domain-specific dynamics, enabling certified generalization across energy, climate, finance, and transportation systems. GeoCert achieves state-of-the-art accuracy while reducing computational cost by 97.5% and maintaining better certification rates. By embedding verification into the geometry of learning, GeoCert transforms forecasting from empirical approximation to formally verified inference, offering a scalable foundation for trustworthy, reproducible, and physically grounded scientific AI.

HMamba: Hyperbolic Mamba for Sequential Recommendation

Sequential recommendation systems have become a cornerstone of personalized services, adept at modeling the temporal evolution of user preferences by capturing dynamic interaction sequences. Existing approaches predominantly rely on traditional models, including RNNs and Transformers. Despite their success in local pattern recognition, Transformer-based methods suffer from quadratic computational complexity and a tendency toward superficial attention patterns, limiting their ability to infer enduring preference hierarchies in sequential recommendation data. Recent advances in Mamba-based sequential models introduce linear-time efficiency but remain constrained by Euclidean geometry, failing to leverage the intrinsic hyperbolic structure of recommendation data. To bridge this gap, we propose Hyperbolic Mamba, a novel architecture that unifies the efficiency of Mamba's selective state space mechanism with hyperbolic geometry's hierarchical representational power. Our framework introduces (1) a hyperbolic selective state space that maintains curvature-aware sequence modeling and (2) stabilized Riemannian operations to enable scalable training. Experiments across four benchmarks demonstrate that Hyperbolic Mamba achieves 3-11% improvement while retaining Mamba's linear-time efficiency, enabling real-world deployment. This work establishes a new paradigm for efficient, hierarchy-aware sequential modeling.

M2Rec: Multi-scale Mamba for Efficient Sequential Recommendation

Sequential recommendation systems aim to predict users' next preferences based on their interaction histories, but existing approaches face critical limitations in efficiency and multi-scale pattern recognition. While Transformer-based methods struggle with quadratic computational complexity, recent Mamba-based models improve efficiency but fail to capture periodic user behaviors, leverage rich semantic information, or effectively fuse multimodal features. To address these challenges, we propose \model, a novel sequential recommendation framework that integrates multi-scale Mamba with Fourier analysis, Large Language Models (LLMs), and adaptive gating. First, we enhance Mamba with Fast Fourier Transform (FFT) to explicitly model periodic patterns in the frequency domain, separating meaningful trends from noise. Second, we incorporate LLM-based text embeddings to enrich sparse interaction data with semantic context from item descriptions. Finally, we introduce a learnable gate mechanism to dynamically balance temporal (Mamba), frequency (FFT), and semantic (LLM) features, ensuring harmonious multimodal fusion. Extensive experiments demonstrate that \model\ achieves state-of-the-art performance, improving Hit Rate@10 by 3.2\% over existing Mamba-based models while maintaining 20\% faster inference than Transformer baselines. Our results highlight the effectiveness of combining frequency analysis, semantic understanding, and adaptive fusion for sequential recommendation. Code and datasets are available at: https://anonymous.4open.science/r/M2Rec.