Free energy properties in cultured neural networks.

<p>Transitions during learning (left) and overall before-and-after changes (right) in connection strengths (top) and in three descriptors of evoked responses modeled on information-theoretic functions (bottom). <b>(A)</b> Connection strengths of the neural population estimated from the number of evoked response per trial. Black circles and squares are <i>W</i>₁₁ and <i>W</i>₂₂. White circles and squares are <i>W</i>₁₂ and <i>W</i>₂₁. Bars are S.E.M. <b>(B)</b> The change in connection strengths (trial 1 vs. trial 100). <i>W</i>₁₁ and <i>W</i>₂₂ significantly increased after training (****, <i>p</i> < 10⁻⁶; <i>n</i> = 46 from 23 cultures), while <i>W</i>₁₂ and <i>W</i>₂₁ tended to decrease (<i>p</i> = 0.069; <i>n</i> = 46 from 23 cultures). <b>(C)</b> Transition of the expectation of internal energy (〈<i>U</i>〉; white circles), Shannon entropy (<i>H</i>; black circles), and free energy (<i>F</i>; red circles) in cultured neural networks estimated from evoked responses per trial. Bars are S.E.M. <b>(D)</b> The change in 〈<i>U</i>〉, <i>H</i>, and <i>F</i> (trial 1 vs. trial 100). After training, the expectation of internal energy decreased (*, <i>p</i> = 0.023; <i>n</i> = 23 cultures), Shannon entropy significantly increased (****, <i>p</i> < 10⁻⁴; <i>n</i> = 23 cultures), and free energy significantly decreased (****, <i>p</i> < 10⁻⁴; <i>n</i> = 23 cultures). These results suggest that learning in cultured neural networks was governed by the free-energy principle.