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Given the fundamental importance of combinatorial optimization across many diverse domains, there has been widespread interest in the development of unconventional physical computing architectures that can deliver better solutions with lower resource costs. However, a theoretical understanding of their performance remains elusive. We develop such understanding for the case of the coherent Ising machine (CIM), a network of optical parametric oscillators that can be applied to any quadratic unconstrained binary optimization problem. We focus on how the CIM finds low-energy solutions of the Sherrington-Kirkpatrick spin glass. As the laser gain of this system is annealed, the CIM interpolates between gradient descent on coupled soft spins to descent on coupled binary spins. By combining the Kac-Rice formula, the replica method, and supersymmetry breaking, we develop a detailed understanding of the evolving geometry of the high-dimensional energy landscape of the CIM as the laser gain increases, finding several phase transitions in the landscape, from flat to rough to rigid. Additionally, we develop a novel cavity method that provides a geometric interpretation of supersymmetry breaking in terms of the reactivity of a rough landscape to specific external perturbations. Our energy landscape theory successfully matches numerical experiments, provides geometric insights into the principles of CIM operation, and yields optimal annealing schedules.

One of the ambitions of computational neuroscience is that we will continue to make improvements in the field of artificial intelligence that will be informed by advances in our understanding of how the brains of various species evolved to process information. To that end, here the authors propose an expanded version of the Turing test that involves embodied sensorimotor interactions with the world as a new framework for accelerating progress in artificial intelligence.

We describe simulations of the quantum dynamics of a confocal cavity QED system that realizes an intrinsically driven-dissipative spin glass. A close connection between open quantum dynamics and replica symmetry breaking is established, in which individual quantum trajectories are the replicas. We observe that entanglement plays an important role in the emergence of replica symmetry breaking in a fully connected, frustrated spin network of up to 15 spin-1/2 particles. Quantum trajectories of entangled spins reach steady-state spin configurations of lower energy than that of semiclassical trajectories. Cavity emission allows monitoring of the continuous stochastic evolution of spin configurations, while backaction from this projects entangled states into states of broken Ising and replica symmetry. The emergence of spin glass order manifests itself through the simultaneous absence of magnetization and the presence of nontrivial spin overlap density distributions among replicas. Moreover, these overlaps reveal incipient ultrametric order, in line with the Parisi replica symmetry breaking solution for the Sherrington-Kirkpatrick model. A nonthermal Parisi order parameter distribution, however, highlights the driven-dissipative nature of this quantum optical spin glass. This practicable system could serve as a test bed for exploring how quantum effects enrich the physics of spin glasses.

CA1 neurons encode an animal's position within the environment. Here the authors identified in hippocampal neuronal activity a detrimental type of noise that limits accuracy of spatial position, relative to body size.

The authors propose a new framework, deep evolutionary reinforcement learning, evolves agents with diverse morphologies to learn hard locomotion and manipulation tasks in complex environments, and reveals insights into relations between environmental physics, embodied intelligence, and the evolution of rapid learning.

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 of N weakly-coupled neurons to achieve errors that scale as [Formula: see text]. But more interestingly, recent work has introduced networks of leaky integrate-and-fire (LIF) neurons that achieve coding errors that scale superclassically as 1/N by 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 actually improve coding 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 deriving analytical expressions 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.

We introduce a novel, biologically plausible local learning rule that provably increases the robustness of neural dynamics to noise in nonlinear recurrent neural networks with homogeneous nonlinearities. Our learning rule achieves higher noise robustness without sacrificing performance on the task and without requiring any knowledge of the particular task. The plasticity dynamics-an integrable dynamical system operating on the weights of the network-maintains a multiplicity of conserved quantities, most notably the network's entire temporal map of input to output trajectories. The outcome of our learning rule is a synaptic balancing between the incoming and outgoing synapses of every neuron. This synaptic balancing rule is consistent with many known aspects of experimentally observed heterosynaptic plasticity, and moreover makes new experimentally testable predictions relating plasticity at the incoming and outgoing synapses of individual neurons. Overall, this work provides a novel, practical local learning rule that exactly preserves overall network function and, in doing so, provides new conceptual bridges between the disparate worlds of the neurobiology of heterosynaptic plasticity, the engineering of regularized noise-robust networks, and the mathematics of integrable Lax dynamical systems.

We introduce a near-term experimental platform for realizing an associative memory. It can simultaneously store many memories by using spinful bosons coupled to a degenerate multimode optical cavity. The associative memory is realized by a confocal cavity QED neural network, with the modes serving as the synapses, connecting a network of superradiant atomic spin ensembles,which serve as the neurons. Memories are encoded in the connectivity matrix between the spins and can be accessed through the input and output of patterns of light. Each aspect of the scheme is based on recently demonstrated technology using a confocal cavity and Bose-condensed atoms. Our scheme has two conceptually novel elements. First, it introduces a new form of random spin system that interpolates between a ferromagnetic and a spin glass regime as a physical parameter is tuned—the positions of ensembles within the cavity. Second, and more importantly, the spins relax via deterministic steepest-descent dynamics rather than Glauber dynamics. We show that this nonequilibrium quantum-optical scheme has significant advantages for associative memory over Glauber dynamics: These dynamics can enhance the network’s ability to store and recall memories beyond that of the standard Hopfield model. Surprisingly, the cavity QED dynamics can retrieve memories even when the system is in the spin glass phase. Thus, the experimental platform provides a novel physical instantiation of associative memories and spin glasses as well as provides an unusual form of relaxational dynamics that is conducive to memory recall even in regimes where it was thought to be impossible.

A central challenge in sensory neuroscience involves understanding how neural circuits shape computations across cascaded cell layers. Here we attempt to reconstruct the response properties of experimentally unobserved neurons in the interior of a multilayered neural circuit, using cascaded linear-nonlinear (LN-LN) models. We combine non-smooth regularization with proximal consensus algorithms to overcome difficulties in fitting such models that arise from the high dimensionality of their parameter space. We apply this framework to retinal ganglion cell processing, learning LN-LN models of retinal circuitry consisting of thousands of parameters, using 40 minutes of responses to white noise. Our models demonstrate a 53% improvement in predicting ganglion cell spikes over classical linear-nonlinear (LN) models. Internal nonlinear subunits of the model match properties of retinal bipolar cells in both receptive field structure and number. Subunits have consistently high thresholds, supressing all but a small fraction of inputs, leading to sparse activity patterns in which only one subunit drives ganglion cell spiking at any time. From the model's parameters, we predict that the removal of visual redundancies through stimulus decorrelation across space, a central tenet of efficient coding theory, originates primarily from bipolar cell synapses. Furthermore, the composite nonlinear computation performed by retinal circuitry corresponds to a boolean OR function applied to bipolar cell feature detectors. Our methods are statistically and computationally efficient, enabling us to rapidly learn hierarchical non-linear models as well as efficiently compute widely used descriptive statistics such as the spike triggered average (STA) and covariance (STC) for high dimensional stimuli. This general computational framework may aid in extracting principles of nonlinear hierarchical sensory processing across diverse modalities from limited data.

Across many studies, animals with enhanced synaptic plasticity exhibit either enhanced or impaired learning, raising a conceptual puzzle: how enhanced plasticity can yield opposite learning outcomes? Here, we show that the recent history of experience can determine whether mice with enhanced plasticity exhibit enhanced or impaired learning in response to the same training. Mice with enhanced cerebellar LTD, due to double knockout (DKO) of MHCI H2-Kb/H2-Db (KbDb−/−), exhibited oculomotor learning deficits. However, the same mice exhibited enhanced learning after appropriate pre-training. Theoretical analysis revealed that synapses with history-dependent learning rules could recapitulate the data, and suggested that saturation may be a key factor limiting the ability of enhanced plasticity to enhance learning. Optogenetic stimulation designed to saturate LTD produced the same impairment in WT as observed in DKO mice. Overall, our results suggest that the recent history of activity and the threshold for synaptic plasticity conspire to effect divergent learning outcomes.

A fundamental problem in modern high-dimensional data analysis involves efficiently inferring a set of P unknown model parameters governing the relationship between the inputs and outputs of N noisy measurements. Various methods have been proposed to regress the outputs against the inputs to recover the P parameters. What are fundamental limits on the accuracy of regression, given finite signal-to-noise ratios, limited measurements, prior information, and computational tractability requirements? How can we optimally combine prior information with measurements to achieve these limits? Classical statistics gives incisive answers to these questions as the measurement density α=(N/P)→∞. However, these classical results are not relevant to modern high-dimensional inference problems, which instead occur at finite α. We employ replica theory to answer these questions for a class of inference algorithms, known in the statistics literature as M-estimators. These algorithms attempt to recover the P model parameters by solving an optimization problem involving minimizing the sum of a loss function that penalizes deviations between the data and model predictions, and a regularizer that leverages prior information about model parameters. Widely cherished algorithms like maximum likelihood (ML) and maximum-a posteriori (MAP) inference arise as special cases of M-estimators. Our analysis uncovers fundamental limits on the inference accuracy of a subclass of M-estimators corresponding to computationally tractable convex optimization problems. These limits generalize classical statistical theorems like the Cramer-Rao bound to the high-dimensional setting with prior information. We further discover the optimal M-estimator for log-concave signal and noise distributions; we demonstrate that it can achieve our high-dimensional limits on inference accuracy, while ML and MAP cannot. Intriguingly, in high dimensions, these optimal algorithms become computationally simpler than ML and MAP while still outperforming them. For example, such optimal M-estimation algorithms can lead to as much as a 20% reduction in the amount of data to achieve the same performance relative to MAP. Moreover, we demonstrate a prediction of replica theory that no inference procedure whatsoever can outperform our optimal M-estimation procedure when signal and noise distributions are log-concave, by uncovering an equivalence between optimal M-estimation and optimal Bayesian inference in this setting. Our analysis also reveals insights into the nature of generalization and predictive power in high dimensions, information theoretic limits on compressed sensing, phase transitions in quadratic inference, and connections to central mathematical objects in convex optimization theory and random matrix theory.