Mathematical Principles and Experimental Discoveries of the Emergence of Symbolic Patterns in Artificial Neural Networks

arXiv:2608.06839 · cs.LG · Submitted 2026-08-07 · Read on arXiv

Quanshi Zhang, Qihan Ren, Siyu Lou

cs.LG

Submitted: 2026-08-07

Updated: 2026-08-10

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Sparsity — 20× in this paper · explained in 5 episodes
• Transferability — 14× in this paper · explained in 5 episodes
• Generalizability — 8× in this paper · explained in 6 episodes
• Fidelity — 7× in this paper · explained in 2 episodes
• Monotonicity — 6× in this paper · explained in 2 episodes
• Generalization — 5× in this paper · explained in 14 episodes
• Overfitting — 5× in this paper · explained in 2 episodes
• Faithfulness — 3× in this paper · explained in 2 episodes
• Interpretability — 3× in this paper · explained in 15 episodes
• Explainability — 2× in this paper · explained in 4 episodes
• Large Language Model — 2× in this paper
• Objective Function — 2× in this paper · explained in 2 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Large Language Model (LLM) — 1× in this paper · explained in 3 episodes
• Lasso — 1× in this paper · explained in 2 episodes
• Phase Transition — 1× in this paper · explained in 3 episodes
• Phase Transitions — 1× in this paper · explained in 2 episodes
• Point Clouds — 1× in this paper · explained in 2 episodes
• Reinforcement Learning — 1× in this paper · explained in 4 episodes
• Stochastic Gradient Descent (SGD) — 1× in this paper · explained in 5 episodes
• Weight Decay — 1× in this paper · explained in 2 episodes

Sources

• Very Deep Convolutional Networks for Large-Scale Image Recognition
• Qwen2.5 Technical Report
• Phi-4 Technical Report
• Deep Learning Face Attributes in the Wild
• Technical Report: Quantifying and Analyzing the Generalization Power of a DNN

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