The rapid expansion of social media has amplified the spread of harmful content, particularly hate speech, which poses significant societal challenges. This paper introduces the Tensor Synergy Network, a deep learning model designed for multimodal hate speech detection. Leveraging state-of-the-art pretrained models – MPNet for textual representation and EfficientNetV2 for visual representation – the proposed architecture employs a fusion strategy combining vector concatenation and the outer product to capture fine-grained interactions across modalities. The outer product generates a higher-dimensional tensor representation, enabling the model to represent nuanced inter-modal dependencies. Evaluated on benchmark datasets MMHS150K and Facebook Hateful Memes, the Tensor Synergy Network demonstrates competitive performance, achieving robust accuracy and F1 scores. Our results underline the potential of tensor-level fusion to enhance multimodal hate speech detection and highlight directions for integrating external knowledge to address linguistic and cultural nuances.