Jian-Nan Chen

Jun-Jie Zhang, Dong-Xiao Zhang, Jian-Nan Chen et al.

In this study, we explore the inherent trade-off between accuracy and robustness in neural networks, drawing an analogy to the uncertainty principle in quantum mechanics. We propose that neural networks are subject to an uncertainty relation, which manifests as a fundamental limitation in their ability to simultaneously achieve high accuracy and robustness against adversarial attacks. Through mathematical proofs and empirical evidence, we demonstrate that this trade-off is a natural consequence of the sharp boundaries formed between different class concepts during training. Our findings reveal that the complementarity principle, a cornerstone of quantum physics, applies to neural networks, imposing fundamental limits on their capabilities in simultaneous learning of conjugate features. Meanwhile, our work suggests that achieving human-level intelligence through a single network architecture or massive datasets alone may be inherently limited. Our work provides new insights into the theoretical foundations of neural network vulnerability and opens up avenues for designing more robust neural network architectures.

Jun-Jie Zhang, Nan Cheng, Fu-Peng Li et al.

Understanding the mechanisms behind neural network optimization is crucial for improving network design and performance. While various optimization techniques have been developed, a comprehensive understanding of the underlying principles that govern these techniques remains elusive. Specifically, the role of symmetry breaking, a fundamental concept in physics, has not been fully explored in neural network optimization. This gap in knowledge limits our ability to design networks that are both efficient and effective. Here, we propose the symmetry breaking hypothesis to elucidate the significance of symmetry breaking in enhancing neural network optimization. We demonstrate that a simple input expansion can significantly improve network performance across various tasks, and we show that this improvement can be attributed to the underlying symmetry breaking mechanism. We further develop a metric to quantify the degree of symmetry breaking in neural networks, providing a practical approach to evaluate and guide network design. Our findings confirm that symmetry breaking is a fundamental principle that underpins various optimization techniques, including dropout, batch normalization, and equivariance. By quantifying the degree of symmetry breaking, our work offers a practical technique for performance enhancement and a metric to guide network design without the need for complete datasets and extensive training processes.

Jun-Jie Zhang, Jiahao Song, Xiu-Cheng Wang et al.

We uncover a phenomenon largely overlooked by the scientific community utilizing AI: neural networks exhibit high susceptibility to minute perturbations, resulting in significant deviations in their outputs. Through an analysis of five diverse application areas -- weather forecasting, chemical energy and force calculations, fluid dynamics, quantum chromodynamics, and wireless communication -- we demonstrate that this vulnerability is a broad and general characteristic of AI systems. This revelation exposes a hidden risk in relying on neural networks for essential scientific computations, calling further studies on their reliability and security.