L2T-Hyena: Enhancing State-Space Models with an Adaptive Learn-to-Teach Framework

State-Space Models (SSMs) have emerged as efficient alternatives to computationally intensive architectures like Transformers, particularly for sequence modeling. However, a fundamental challenge in their training is the reliance on static loss functions, which may not be optimal across all learning stages. To address this issue, in this paper a hybrid model integrating the Hyena architecture with a Dynamic Loss Network (DLN) is proposed which is guided by a Learn-to-Teach (L2T) approach (L2T-DLN). In this framework, the Hyena model is a student, and its loss function is optimized adaptively. A teacher model, leveraging a memory of the student's past performance, guides the DLN in dynamically balancing the primary cross-entropy loss and a regularization term. Experiments on the Penn Treebank (PTB) dataset show that our approach significantly improves language modeling performance. Our proposed model achieved a validation Perplexity of 102.6, a notable improvement over the 110.4 achieved by a baseline Hyena model using a static loss function. This research indicates that combining SSMs with adaptive loss function markedly enhances the quality and efficiency of deep learning models for sequential data, showing potential for applications in Natural Language Processing (NLP), time-series analysis, and biological signal processing.