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Squealer: When the Data Model Lets Out a Shriek ✛ ✦

Original: "The Squealer: Sensification of model exploration and model misfit"
· Andrew Gelman, Andrew H. Jaffe, Eliot Carlson, Philip Greengard
arXiv:2606.29842 · 2026-06-29 · CC BY 4.0 · 1 min
physics.data-an Cosmology stat.ME
The program turns the tension between data and model into an audible signal, allowing you to literally hear the errors.

A flexible ruler pressed against a table at several points forms a smooth curve. Move one section and you'll hear a creak: the ruler resists deformation. Squealer works the same way: the user drags a curve on the graph, and the program turns the model's resistance into sound — the louder, the more rigidly the model refuses to accept new data. In cosmology, this revealed an unexpected rigidity of models. Satellite images of the cosmic microwave background (the echo of the Big Bang) must match the curve describing the expansion of the universe under the influence of dark matter and dark energy.

An attempt to adjust the curve in one region provoked a sharp shriek — the model categorically disagreed.

Other areas responded with quiet noise, allowing flexibility. The method, combining machine learning and numerical simulation, reveals tensions invisible to the eye. A surprising discovery: the loudest cacophony occurs where the model conflicts with the laws of Edwin Hubble and Georges Lemaître, as well as with Alan Guth's theory of inflation, as if the data were 'shouting' about new phenomena beyond known physics.

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In the test version, a perfect curve resonated like a tuning fork, but the slightest shift produced a grinding sound — thus the creators realized they were hearing the model's 'pain.' The farther a point is from the prediction, the higher the pitch of the noise, so experienced users can gauge the magnitude of error by the pitch without looking at the screen.

p(\theta|y) \propto p(\theta|y) \, \mathcal{N}(y^* | g(x^*|\theta), \sigma_*^2)
The augmented posterior density is obtained by multiplying the original by a normal distribution centered at the desired curve value y* with small variance sigma_*^2, which acts as a soft constraint.
k(t, t') = \alpha \exp\left(-\frac{(t-t')^2}{2\ell^2}\right)
The kernel defines the covariance between two time points t and t' with amplitude parameter alpha and characteristic correlation length ell.
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Andrey Markov
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overfitting least squares fitting goodness of fit regularisation information criterion ai speech analysis parameter fitting data assimilation profile likelihood gaussian process computer simulation classifier model comparison simulated data speech recognition model selection cross correlation statistical analysis scalable parameter