Network properties determine neural network performance.

Machine learning influences numerous aspects of modern society, empowers new technologies, from Alphago to ChatGPT, and increasingly materializes in consumer products such as smartphones and self-driving cars. Despite the vital role and broad applications of artificial neural networks, we lack systematic approaches, such as network science, to understand their underlying mechanism. The difficulty is rooted in many possible model configurations, each with different hyper-parameters and weighted architectures determined by noisy data. We bridge the gap by developing a mathematical framework that maps the neural network's performance to the network characters of the line graph governed by the edge dynamics of stochastic gradient descent differential equations. This framework enables us to derive a neural capacitance metric to universally capture a model's generalization capability on a downstream task and predict model performance using only early training results. The numerical results on 17 pre-trained ImageNet models across five benchmark datasets and one NAS benchmark indicate that our neural capacitance metric is a powerful indicator for model selection based only on early training results and is more efficient than state-of-the-art methods.

Correction: MSPM: A modularized and scalable multi-agent reinforcement learning-based system for financial portfolio management.

[This corrects the article DOI: 10.1371/journal.pone.0263689.].

MSPM: A modularized and scalable multi-agent reinforcement learning-based system for financial portfolio management.

Financial portfolio management (PM) is one of the most applicable problems in reinforcement learning (RL) owing to its sequential decision-making nature. However, existing RL-based approaches rarely focus on scalability or reusability to adapt to the ever-changing markets. These approaches are rigid and unscalable to accommodate the varying number of assets of portfolios and increasing need for heterogeneous data input. Also, RL agents in the existing systems are ad-hoc trained and hardly reusable for different portfolios. To confront the above problems, a modular design is desired for the systems to be compatible with reusable asset-dedicated agents. In this paper, we propose a multi-agent RL-based system for PM (MSPM). MSPM involves two types of asynchronously-updated modules: Evolving Agent Module (EAM) and Strategic Agent Module (SAM). An EAM is an information-generating module with a Deep Q-network (DQN) agent, and it receives heterogeneous data and generates signal-comprised information for a particular asset. An SAM is a decision-making module with a Proximal Policy Optimization (PPO) agent for portfolio optimization, and it connects to multiple EAMs to reallocate the corresponding assets in a financial portfolio. Once been trained, EAMs can be connected to any SAM at will, like assembling LEGO blocks. With its modularized architecture, the multi-step condensation of volatile market information, and the reusable design of EAM, MSPM simultaneously addresses the two challenges in RL-based PM: scalability and reusability. Experiments on 8-year U.S. stock market data prove the effectiveness of MSPM in profit accumulation by its outperformance over five different baselines in terms of accumulated rate of return (ARR), daily rate of return (DRR), and Sortino ratio (SR). MSPM improves ARR by at least 186.5% compared to constant rebalanced portfolio (CRP), a widely-used PM strategy. To validate the indispensability of EAM, we back-test and compare MSPMs on four different portfolios. EAM-enabled MSPMs improve ARR by at least 1341.8% compared to EAM-disabled MSPMs.