Self-Referential Gradient Propagation in Large Language Models: A Study of Recursive Training Feedback Mechanisms

Recursive optimization strategies for Large Language Models (LLMs) introduce additional complexity into gradient-based learning processes, particularly when weight updates depend on prior optimization states. The introduction of self-referential gradient propagation presents an alternative mechanism where LLM parameters are adjusted based on internal evaluations of past gradient trajectories, modifying conventional optimization pathways through an adaptive recursive feedback loop. A structured evaluation of the method compared training dynamics, computational efficiency, and stability characteristics against conventional backpropagation-based training methodologies. Experimental results indicated that self-referential updates contributed to more stable weight adjustments, reducing abrupt fluctuations in gradient magnitudes while maintaining competitive performance across a range of tasks. The impact of recursive gradient storage on memory consumption was analyzed, highlighting the trade-off between additional computational overhead and potential improvements in optimization smoothness. The sensitivity of self-referential updates to hyperparameter variations was assessed, revealing that LLMs trained with recursive optimization exhibited reduced volatility in loss trajectories compared to conventional approaches. An evaluation of robustness under noisy input conditions demonstrated that LLMs trained with recursive adjustments retained greater accuracy when exposed to corrupted inputs. The findings suggested that self-referential optimization introduced an alternative framework for gradient-based learning, modifying parameter updates through internally computed adjustments rather than externally applied heuristic scheduling.