While Large Language Models (LLMs) excel at generalized reasoning, standard retrieval-augmented approaches fail to address the disconnected nature of long-term agentic memory. To bridge this gap, we introduce Synapse (Synergistic Associative Processing Semantic Encoding), a unified memory architecture that transcends static vector similarity. Drawing from cognitive science, Synapse models memory as a dynamic graph where relevance emerges from spreading activation rather than pre-computed links. By integrating lateral inhibition and temporal decay, the system dynamically highlights relevant sub-graphs while filtering interference. We implement a Triple Hybrid Retrieval strategy that fuses geometric embeddings with activation-based graph traversal. Extensive evaluations on the LoCoMo benchmark show that Synapse significantly outperforms state-of-the-art methods in complex temporal and multi-hop reasoning tasks, offering a robust solution to the "Contextual Tunneling" problem.

Fine-tuning large language models (LLMs) faces significant memory challenges due to the high cost of back-propagation. MeZO addresses this using zeroth-order (ZO) optimization, matching memory usage to inference but suffering from slow convergence due to varying curvatures across model parameters. To overcome this limitation, We propose HELENE, a scalable and memory-efficient optimizer that integrates annealed A-GNB gradients with diagonal Hessian estimation and layer-wise clipping as a second-order pre-conditioner. HELENE provably accelerates and stabilizes convergence by reducing dependence on total parameter space and scaling with the largest layer dimension. Experiments on RoBERTa-large and OPT-1.3B show up to a 20× speedup over MeZO with an average accuracy improvement of 1.5%. HELENE supports full and parameter-efficient fine-tuning, outperforming several state-of-the-art optimizers.