HEDP: A Hybrid Energy-Distance Prompt-based Framework for Domain Incremental Learning

Domain Incremental Learning is a critical scenario that requires models to continuously adapt to new data domains without retraining. However, domain shifts often cause severe performance degradation. To address this, we propose Hybrid Energy-Distance Prompt, a domain-incremental framework inspired by Helmholtz free energy. HEDP introduces an energy regularization loss to enhance the separability of domain representations and a hybrid energy-distance weighted mechanism that fuses energy-based and distance-based cues to improve domain selection and generalization. Experiments on multiple benchmarks, including CORe50, show that HEDP achieves superior performance on unseen domains with a 2.57\% accuracy gain, effectively mitigating catastrophic forgetting and enhancing open-world adaptability. Our code is \href{https://github.com/dannis97500/HEDP/}{available here}.

Conditional Inverse Learning of Time-Varying Reproduction Numbers Inference

Estimating time-varying reproduction numbers from epidemic incidence data is a central task in infectious disease surveillance, yet it poses an inherently ill-posed inverse problem. Existing approaches often rely on strong structural assumptions derived from epidemiological models, which can limit their ability to adapt to non-stationary transmission dynamics induced by interventions or behavioral changes, leading to delayed detection of regime shifts and degraded estimation accuracy. In this work, we propose a Conditional Inverse Reproduction Learning framework (CIRL) that addresses the inverse problem by learning a {conditional mapping} from historical incidence patterns and explicit time information to latent reproduction numbers. Rather than imposing strongly enforced parametric constraints, CIRL softly integrates epidemiological structure with flexible likelihood-based statistical modeling, using the renewal equation as a forward operator to enforce dynamical consistency. The resulting framework combines epidemiologically grounded constraints with data-driven temporal representations, producing reproduction number estimates that are robust to observation noise while remaining responsive to abrupt transmission changes and zero-inflated incidence observations. Experiments on synthetic epidemics with controlled regime changes and real-world SARS and COVID-19 data demonstrate the effectiveness of the proposed approach.