EMP: Enhanced Multi-modal Prediction for fashion sales using Fourier Mapping and ERP-based contrastive learning

Predicting sales for newly introduced fashion products presents a significant challenge due to the absence of historical data and the inherently multi-modal nature of the inputs. To address this issue, we propose the Enhanced Multi-modal Prediction (EMP) model, a novel framework for zero-shot time series forecasting. EMP follows a two-stage architecture: (1) ERP-Aware Contrastive Learning, which retrieves reference items using Edit Distance with Real Penalty (ERP), a metric-based elastic distance designed to measure similarity between real-valued time series, to construct a meaningful embedding space, and (2) a Transformer-based encoder-decoder, which predicts 12-week sales trajectories using Fourier-mapped embeddings. Unlike prior models that rely on external signals, EMP leverages internal reference item sales, thereby eliminating dependency on third-party APIs and enhancing forecasting accuracy. It introduces Fourier Mapping, which generates scale-aware embeddings that preserve the absolute magnitude of sales values while enabling interpretability through inverse mapping. This representation mitigates spectral bias and allows the model to effectively capture both low- and high-frequency sales patterns. To maximize this benefit, Fourier Mapping is applied selectively to internal reference item sales, where high frequency variation is more prominent than in external signals. We further present a theoretical analysis of the Lipschitz continuity of Fourier Mapping, demonstrating that it maintains a higher Lipschitz constant than conventional scaling methods. This property ensures the preservation of fine-grained input variations, thereby improving the model's sensitivity to subtle fluctuations in sales trajectories. Experiments on both private and benchmark datasets demonstrate that EMP achieves superior forecasting accuracy compared to existing methods, validating its effectiveness in fashion sales prediction. The implementation of our method is available at the following URL: https://github.com/sanguk-ys/EMP.