University of Pennsylvania engineers have conducted research challenging a long-standing view of foam behavior, finding that the internal motion of foams mathematically resembles deep learning processes. Traditionally, foams were believed to behave similarly to glass, with components in fixed positions.
Key Findings
- Foams maintain their overall shape but exhibit constant internal motion.
- The mathematics describing this internal motion closely align with the techniques used in modern artificial intelligence systems, specifically deep learning.
- This suggests that "learning" in a mathematical sense might be a shared organizing principle across various systems, including physical, biological, and computational ones.
Research Details
The study, published in Proceedings of the National Academy of Sciences, utilized computer simulations to track bubble movements within wet foam. Instead of becoming stationary, bubbles continuously shifted through various arrangements. This behavior mirrors how deep learning systems adjust their parameters during training, rather than settling into a single, fixed state.
Professor John C. Crocker, co-senior author, stated that "Foams constantly reorganize themselves," noting the striking similarity in mathematical principles between foams and modern AI.
Challenging Traditional Theories
Foams typically appear solid at a macroscopic level and have been used as model systems for other dense, dynamic materials. Traditional theories suggested that foam bubbles would move into lower energy positions and then remain static, similar to an object resting at the bottom of a valley. However, real-world data did not support these predictions, indicating a mismatch between theory and observed behavior.
Parallels with Artificial Intelligence
The resolution of this discrepancy involved an approach that accounts for systems that continuously change without settling into a single, fixed arrangement. Modern AI systems, particularly those employing deep learning, learn by iteratively adjusting numerical parameters. Researchers realized that pushing AI models into the "deepest" optimal solutions could lead to fragility. Instead, allowing systems to operate within "flatter" regions of the solution landscape, where multiple configurations perform similarly well, enables better generalization.
Professor Robert Riggleman, co-senior author, explained that "keeping it in flatter parts of the landscape, where lots of solutions perform similarly well, turns out to be what allows these models to generalize." The Penn team's re-examination of foam data confirmed that foam bubbles similarly do not settle into deeply stable positions but rather move within broad regions where many configurations are equally viable. This ongoing motion parallels AI learning processes.
Broader Implications
These findings prompt a reevaluation of complex systems previously thought to be well understood. The research could inform the creation of adaptive materials and offer new insights into living structures, such as the cytoskeleton within cells, which must continuously reorganize while maintaining overall structure. Crocker suggests that the applicability of deep learning mathematics beyond its original context could open new avenues of scientific inquiry.
The research was conducted at the University of Pennsylvania School of Engineering and Applied Science and supported by the National Science Foundation.