![[ Archived Post] Hebbian Learning — (57 min) | by Jae Duk Seo | Medium](https://miro.medium.com/max/900/1*6YIBnfaMI-PjrEX1V2QJHg.png)
![[Hebbian Natural Abstractions] Mathematical Foundations — LessWrong](https://39669.cdn.cke-cs.com/rQvD3VnunXZu34m86e5f/images/0b84e2f162888533860134af881e632ef2e7bddd7c828e92.png)
%20and%20introduce%20substantial%20computational%20overhead%2C%20which%20raises%20doubts%20regarding%20their%20biological%20plausibility%20as%20well%20as%20their%20potential%20utility%20for%20neuromorphic%20computing.%20Furthermore%2C%20they%20commonly%20rely%20on%20applying%20infinitesimal%20perturbations%20(nudges)%20to%20output%20units%2C%20which%20is%20impractical%20in%20noisy%20environments.%20Recently%20it%20has%20been%20shown%20that%20by%20modelling%20artificial%20neurons%20as%20dyads%20with%20two%20oppositely%20nudged%20compartments%2C%20it%20is%20possible%20for%20a%20fully%20local%20learning%20algorithm%20named%20%60%60dual%20propagation''%20to%20bridge%20the%20performance%20gap%20to%20backpropagation%2C%20without%20requiring%20separate%20learning%20phases%20or%20infinitesimal%20nudging.%20However%2C%20the%20algorithm%20has%20the%20drawback%20that%20its%20numerical%20stability%20relies%20on%20symmetric%20nudging%2C%20which%20may%20be%20restrictive%20in%20biological%20and%20analog%20implementations.%20In%20this%20work%20we%20first%20provide%20a%20solid%20foundation%20for%20the%20objective%20underlying%20the%20dual%20propagation%20method%2C%20which%20also%20reveals%20a%20surprising%20connection%20with%20adversarial%20robustness.%20Second%2C%20we%20demonstrate%20how%20dual%20propagation%20is%20related%20to%20a%20particular%20adjoint%20state%20method%2C%20which%20is%20stable%20regardless%20of%20asymmetric%20nudging.)
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