Superposition and Anomaly Detection: Does Feature Overlap Predict Scaling Law Failures in Irregular or Adversarial Data?

TL;DR: Could superposition serve as an early warning for scaling law breakdowns, especially when data distribution shifts or contains adversarial features? Test this by introducing controlled anomalies or out-of-distribution samples, measuring superposition and scaling law adherence.

Research Question: Is the degree of feature superposition a robust predictor for when neural scaling laws will fail, especially under data distribution shifts or adversarial conditions?

Hypothesis: High or pathological levels of superposition correlate with increased vulnerability to scaling law breakdowns in the presence of anomalies or adversarial data.

Experiment Plan: Train models on clean data, then introduce anomalies (e.g., rare features, adversarial perturbations, or non-power-law distributions). Track superposition metrics (representation overlap, feature packing) and loss scaling. Analyze whether changes in superposition precede or coincide with deviations from expected scaling laws. Apply models like SentinelGNN or anomaly detection benchmarks for comparative analysis.

References:

• Liu, Y., Liu, Z., & Gore, J. (2025). Superposition Yields Robust Neural Scaling. arXiv.org.
• Kombou, V., Gao, J., Xia, Q., Xia, H., Richard, B. S., & Brinda, K. S. (2025). SentinelGNN: A Neural Network Architecture for Detecting Anomalies in Attributed Multi-graphs. IEEE International Joint Conference on Neural Network.