Abstract We show that computing the log-partition function (free-energy) of conditioned inhomogeneous Curie--Weiss spin Hamiltonians reduces to an unbalanced 2 → 1 2 \to 1 2 → 1 norm computation, and design a polynomial-time SDP algorithm for this problem with a lower bound proof for the amount of unbalance achieved. Applied to the protein Ubiquitin, the framework starts from a known crystal structure, explores alternative backbone conformations across the free-energy landscape, and identifies flexible regions of the protein while preserving its native secondary structure.
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Kaustav Mehta
Independent researcher, India
AlphaFold2's 93 million parameters, shaped by the evolutionary record of protein structure encoded in the Protein Data Bank and in sequence alignments, are conventionally treated only as machinery for converting sequence to structure. We propose they are also a scientific object that can be analyzed directly: a learned encoding of protein conformational organization that can be probed and characterized. By smoothing the Evoformer's weight tensors with a Gaussian convolution and scaling the result, we show that the trained model produces physically structured conformational landscapes. Under perturbation, ubiquitin's native contacts break in the order established by decades of folding experiments. For KaiB, five independently trained models agree that the alternative fold is not recovered under perturbation. For alpha-synuclein, five models produce five different but coherent landscapes, mapping where the training signal has determined the representation and where it has not. Matched-power noise controls confirm that random corruption of equal magnitude produces debris, not conformations. The model learned to predict static structures; the conformational organization visible under perturbation was not an explicit training target, suggesting it emerged as a byproduct of that objective. AlphaFold2's weights appear to encode structural constraints, shaped by evolutionary and structural training data, that extend beyond what unperturbed inference reveals. We call the approach of reading them neural spectroscopy, and Scaled Gaussian Convolution one such protocol.