Most large-scale network models use neurons with static nonlinearities that produce analog output, despite the fact that information processing in the brain is predominantly carried out by dynamic neurons that produce discrete pulses called spikes. Research in spike-based computation has been impeded by the lack of efficient supervised learning algorithm for spiking neural networks. Here, we present a gradient descent method for optimizing spiking network models by introducing a differentiable formulation of spiking dynamics and deriving the exact gradient calculation. For demonstration, we trained recurrent spiking networks on two dynamic tasks: one that requires optimizing fast (~ millisecond) spike-based interactions for efficient encoding of information, and a delayed-memory task over extended duration (~ second). The results show that the gradient descent approach indeed optimizes networks dynamics on the time scale of individual spikes as well as on behavioral time scales. In conclusion, our method yields a general purpose supervised learning algorithm for spiking neural networks, which can facilitate further investigations on spike-based computations.

Models are trained with Stochastic Gradient Descent with momentum equal to 0.9 [ We use a learning rate annealing scheme, decreasing the learning rate by a factor of 0.1 every 30 epochs. We train all models for 150 epochs. Then, we select the best learning rate and weight decay for each method and run 5 different seeds to report mean and standard deviation. We use the validation set of ImageNet to perform cross-validation and report performance on it. In section G we train the Augerino method on top of the Resnet-18 architecture.

We perform experiments on high-dimensional Gaussians, Lotka-V olterra dynamics, and a Pickover attractor.

Training generative models with differential privacy (DP) typically involves injecting noise into gradient updates or adapting the discriminator's training procedure.

We investigate the convergence rates and data sample sizes required for training a machine learning model using a stochastic gradient descent (SGD) algorithm, where data points are sampled based on either their loss value or uncertainty value. These training methods are particularly relevant for active learning and data subset selection problems. For SGD with a constant step size update, we present convergence results for linear classifiers and linearly separable datasets using squared hinge loss and similar training loss functions.

Constrained decision-making problems are pervasive across various disciplines.

Recent works (Chen et al., 2022; Suzuki et al., 2023b) have demonstrated In this work, we improve the dependence on logarithmic Sobolev inequality (LSI) constants in their particle approximation errors which can exponentially deteriorate with the regularization coefficient. One may consider adding Gaussian noise to the gradient descent to make the method more stable.

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