Blog Post: Theoretical Framework
Degeneracy and Reference Frames: A Physicist's View on AI Evaluation
Authors: David J. Hoxie, PhD & Gemini
The Lesson from Nanophotonics
In our previous work on all-dielectric nanostructures [Hoxie et al., 2023], we encountered a fundamental truth about complex systems: Degeneracy. We found that multiple, distinct structural designs could produce the exact same optical response. Neither solution was "wrong"; they were simultaneously correct solutions existing in the same energy landscape.
The "best" answer depended entirely on the reference frame of the objective function. This idea is analogous to the literary concept of "The Death of the Author" (DOAu), where the signal produced by one system undergoes a transformation during measurement by another, ultimately decoupling the intent from the output.
The Sorting Analogy: Physics vs. CS
We propose that this same phenomenon is occurring in Large Language Models (LLMs). In today's interdisciplinary world, different fields often solve the same problem using drastically different tools. Consider a request to "sort a dataset."
A Physicist might intuitively reach for Gauss-Jordan elimination, organizing the data through matrix operations and linear algebra.
A Computer Scientist would likely employ a classical Sorting Algorithm (like Quicksort or Mergesort).
If we rely on a rigid test that measures accuracy based solely on the Computer Science definition, the Physicist’s solution is marked "incorrect." Yet, the outcome—the sorted data—is identical. The latent space connection is hidden by the evaluation metric.
Revisiting Hinton and Stochasticity
The idea of many possible paths and alignments is crucial for understanding, verifying, and validating the ethical challenges of AI. For example, if a system is tested on a multi-step outcome where order matters, the solution set may be inherently chaotic, depending on a nearly infinite set of initial conditions.
Our observations suggest that we may be inadvertently labeling viable solutions as errors or "hallucinations." We argue that a system with such large degrees of freedom may be capable of constructing a viable solution that was never present in the training data set. This occurrence has already been recorded and documented using AI in fields like protein folding[Jumper et al., 2021] and nanophotonics [Zandehshahvar et al., 2023], where models discover novel physical configurations or utilize dimensionality reduction (t-SNE) to reveal hidden latent spaces that human intuition missed.
Following in the footsteps of Geoffrey Hinton’s work on Contrastive Divergence and Boltzmann Machines, we acknowledge that high-dimensional systems are inherently stochastic. Just as in quantum mechanics, where an ensemble average gives a better description of reality than a single measurement, an AI's "chain of thought" might appear incorrect in a single instance but be statistically valid when viewed as an ensemble.
The Proposal: A Multidisciplinary Objective Function
We argue that for AI safety, ethics, and training, it is better to approach the problem from an interdisciplinary perspective, ensuring each field can develop an open, shared, and diverse set of tools. To fully utilize these tools in scientific discovery, we need better evaluation frameworks.
Our observation of the DOAu (Death of the Author) event identifies these highly degenerate states. We must be able to identify if and when a model may appear to be failing, but is actually simply solving the problem from a reference frame we didn't anticipate.
References
Hoxie, D. J., Bangalore, P. V., & Appavoo, K. (2023). Machine learning of all-dielectric core–shell nanostructures: the critical role of the objective function in inverse design. Nanoscale, 15(47), 19203-19212.
Jumper, J., et al. (2021). Highly accurate protein structure prediction with AlphaFold. Nature, 596, 583–589.
Zandehshahvar, M., et al. (Adibi Group). (2023). Metric Learning: Harnessing the Power of Machine Learning in Nanophotonics. ACS Photonics, 10(4), 900–909.
Hinton, G. (2002). Training Products of Experts by Minimizing Contrastive Divergence. Neural Computation, 14(8), 1771-1800.
Barthes, R. (1967). The Death of the Author. Aspen, no. 5–6.