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Neural circuits consist of many noisy, slow components, with individual neurons subject to ion channel noise, axonal propagation delays, and unreliable and slow synaptic transmission. This raises a fundamental question: how can reliable computation emerge from such unreliable components? A classic strategy is to simply average over a population ofNweakly-coupled neurons to achieve errors that scale as $1/\sqrt{N}$. But more interestingly, recent work has introduced networks of leaky integrate-and-fire (LIF) neurons that achieve coding errors that scalesuperclassicallyas 1/Nby combining the principles of predictive coding and fast and tight inhibitory-excitatory balance. However, spike transmission delays preclude such fast inhibition, and computational studies have observed that such delays can cause pathological synchronization that in turn destroys superclassical coding performance. Intriguingly, it has also been observed in simulations that noise can actuallyimprovecoding performance, and that there exists some optimal level of noise that minimizes coding error. However, we lack a quantitative theory that describes this fascinating interplay between delays, noise and neural coding performance in spiking networks. In this work, we elucidate the mechanisms underpinning this beneficial role of noise by derivinganalyticalexpressions for coding error as a function of spike propagation delay and noise levels in predictive coding tight-balance networks of LIF neurons. Furthermore, we compute the minimal coding error and the associated optimal noise level, finding that they grow as power-laws with the delay. Our analysis reveals quantitatively how optimal levels of noise can rescue neural coding performance in spiking neural networks with delays by preventing the build up of pathological synchrony without overwhelming the overall spiking dynamics. This analysis can serve as a foundation for the further study of precise computation in the presence of noise and delays in efficient spiking neural circuits. 

The recent striking success of deep neural networks in machine learning raises profound questions about the theoretical principles underlying their success. For example, what can such deep networks compute? How can we train them? How does information propagate through them? Why can they generalize? And how can we teach them to imagine? We review recent work in which methods of physical analysis rooted in statistical mechanics have begun to provide conceptual insights into these questions. These insights yield connections between deep learning and diverse physical and mathematical topics, including random landscapes, spin glasses, jamming, dynamical phase transitions, chaos, Riemannian geometry, random matrix theory, free probability, and nonequilibrium statistical mechanics. Indeed, the fields of statistical mechanics and machine learning have long enjoyed a rich history of strongly coupled interactions, and recent advances at the intersection of statistical mechanics and deep learning suggest these interactions will only deepen going forward. 

Perceptual experiences may arise from neuronal activity patterns in mammalian neocortex. We probed mouse neocortex during visual discrimination using a red-shifted channelrhodopsin (ChRmine, discovered through structure-guided genome mining) alongside multiplexed multiphoton-holography (MultiSLM), achieving control of individually specified neurons spanning large cortical volumes with millisecond precision. Stimulating a critical number of stimulus-orientation-selective neurons drove widespread recruitment of functionally related neurons, a process enhanced by (but not requiring) orientation-discrimination task learning. Optogenetic targeting of orientation-selective ensembles elicited correct behavioral discrimination. Cortical layer–specific dynamics were apparent, as emergent neuronal activity asymmetrically propagated from layer 2/3 to layer 5, and smaller layer 5 ensembles were as effective as larger layer 2/3 ensembles in eliciting orientation discrimination behavior. Population dynamics emerging after optogenetic stimulation both correctly predicted behavior and resembled natural internal representations of visual stimuli at cellular resolution over volumes of cortex.