Meta-DSP: A Meta-Learning Approach for Data-Driven Nonlinear Compensation in High-Speed Optical Fiber Systems

Non-linear effects in long-haul, high-speed optical fiber systems significantly hinder channel capacity. While the Digital Backward Propagation algorithm (DBP) with adaptive filter (ADF) can mitigate these effects, it suffers from an overwhelming computational complexity. Recent solutions have incorporated deep neural networks in a data-driven strategy to alleviate this complexity in the DBP model. However, these models are often limited to a specific symbol rate and channel number, necessitating retraining for different settings, their performance declines significantly under high-speed and high-power conditions. We introduce Meta-DSP, a novel data-driven nonlinear compensation model based on meta-learning that processes multi-modal data across diverse transmission rates, power levels, and channel numbers. This not only enhances signal quality but also substantially reduces the complexity of the nonlinear processing algorithm. Our model delivers a 0.7 dB increase in the Q-factor over Electronic Dispersion Compensation (EDC), and compared to DBP, it curtails computational complexity by a factor of ten while retaining comparable performance. From the perspective of the entire signal processing system, the core idea of Meta-DSP can be employed in any segment of the overall communication system to enhance the model's scalability and generalization performance. Our research substantiates Meta-DSP's proficiency in addressing the critical parameters defining optical communication networks.

Prompt Engineering Through the Lens of Optimal Control

Prompt Engineering (PE) has emerged as a critical technique for guiding Large Language Models (LLMs) in solving intricate tasks. Its importance is highlighted by its potential to significantly enhance the efficiency and effectiveness of human-machine interaction. As tasks grow increasingly complex, recent advanced PE methods have extended beyond the limitations of single-round interactions to embrace multi-round interactions, which allows for a deeper and more nuanced engagement with LLMs. In this paper, we propose an optimal control framework tailored for multi-round interactions with LLMs. This framework provides a unified mathematical structure that not only systematizes the existing PE methods but also sets the stage for rigorous analytical improvements. Furthermore, we extend this framework to include PE via ensemble methods and multi-agent collaboration, thereby enlarging the scope of applicability. By adopting an optimal control perspective, we offer fresh insights into existing PE methods and highlight theoretical challenges that warrant future research. Besides, our work lays a foundation for the development of more effective and interpretable PE methods.

A synchronization-capturing multi-scale solver to the noisy integrate-and-fire neuron networks

The noisy leaky integrate-and-fire (NLIF) model describes the voltage configurations of neuron networks with an interacting many-particles system at a microscopic level. When simulating neuron networks of large sizes, computing a coarse-grained mean-field Fokker-Planck equation solving the voltage densities of the networks at a macroscopic level practically serves as a feasible alternative in its high efficiency and credible accuracy. However, the macroscopic model fails to yield valid results of the networks when simulating considerably synchronous networks with active firing events. In this paper, we propose a multi-scale solver for the NLIF networks, which inherits the low cost of the macroscopic solver and the high reliability of the microscopic solver. For each temporal step, the multi-scale solver uses the macroscopic solver when the firing rate of the simulated network is low, while it switches to the microscopic solver when the firing rate tends to blow up. Moreover, the macroscopic and microscopic solvers are integrated with a high-precision switching algorithm to ensure the accuracy of the multi-scale solver. The validity of the multi-scale solver is analyzed from two perspectives: firstly, we provide practically sufficient conditions that guarantee the mean-field approximation of the macroscopic model and present rigorous numerical analysis on simulation errors when coupling the two solvers; secondly, the numerical performance of the multi-scale solver is validated through simulating several large neuron networks, including networks with either instantaneous or periodic input currents which prompt active firing events over a period of time.