Short-Term Residential Load Forecasting (STRLF) is a core task in smart grid dispatching and energy management, and its accuracy directly affects the economy and stability of power systems. Current mainstream methods still have limitations in addressing issues such as complex temporal patterns, strong stochasticity of load data, and insufficient model interpretability. To this end, this paper proposes an explainable and efficient forecasting framework named KAN+Transformer, which integrates Kolmogorov–Arnold Networks (KAN) with Transformers. The framework achieves performance breakthroughs through three innovative designs: constructing a Reversible Mixture of KAN Experts (RMoK) layer, which optimizes expert weight allocation using a load-balancing loss to enhance feature extraction capability while preserving model interpretability; designing an attention-guided cascading mechanism to dynamically fuse the local temporal patterns extracted by KAN with the global dependencies captured by the Transformer; and introducing a multi-objective loss function to explicitly model the periodicity and trend characteristics of load data. Experiments on four power benchmark datasets show that KAN+Transformer significantly outperforms advanced models such as Autoformer and Informer; ablation studies confirm that the KAN module and the specialized loss function bring accuracy improvements of 7.2% and 4.8%, respectively; visualization analysis further verifies the model’s decision-making interpretability through weight-feature correlation, providing a new paradigm for high-precision and explainable load forecasting in smart grids. Collectively, the results demonstrate our model’s superior capability in representing complex residential load dynamics and capturing both transient and stable consumption behaviors. By enabling more accurate, interpretable, and computationally efficient short-term load forecasting, the proposed KAN+Transformer framework provides effective support for demand-side management, renewable energy integration, and intelligent grid operation. As such, it contributes to improving energy utilization efficiency and enhancing the sustainability and resilience of modern power systems.