A Variational Principle for the Emergence of Neural Geometry Underlying Bayesian-Like Behavior

A variational principle in recurrent neural networks trained on time-interval reproduction predicts three regimes of learned neural geometry, including boundary distortions and affine readout behavior.

• Why it matters: Neural population geometry shapes how task variables are encoded and read out, but how stimulus statistics determine that geometry—and produce Bayesian-like readouts—remains unclear.
• What they did: The authors balance task accuracy with representational smoothness using stimulus-dependent weighting, then test the bounded-uniform case in recurrent neural networks trained to reproduce time intervals.
• The result: Learned geometries show three boundary-distortion regimes, and an empirical neural-coordinate shape parameter predicts the nonlinear component of mean behavior via affine readout; after affine normalization, the variational coordinate and Bayesian least-squares mean response match closely.

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