Empirically, we verify the computational efficiency of our methods.

A.1 Hyper-Parameters For all datasets, the surrogate gradient function isσ(x) = 1π arctan(π2αx) + 12, thus σ0(x) = The results on the three networks are consistent, indicating that RTD is a general sequential data augmentationmethod. We compare different surrogate functions, including Rectangular (σ0(x) = sign(|x| < 12)),ArcTan(σ0(x) = 11+(πx)2)and Constant 1(σ0(x) 1),intheSNNs on CIFAR-10. The results are shown in Tab.9. Tab.9 indicates that the choice of surrogate function has a considerable influence on the SNN's performance. Although Rectangular and Constant 1 can avoid the gradient exploding/vanishing problems in Eq.(8), they still cause lower accuracy or even make the optimization not converges.

Recurrent spiking neural networks (RSNNs) hold great potential for advancing artificial general intelligence, as they draw inspiration from the biological nervous system and show promise in modeling complex dynamics.

Humans learn efficiently from their environment by engaging multiple interacting neural systems that support distinct yet complementary forms of control, including model-based (goal-directed) planning, model-free (habitual) responding, and episodic memory-based learning. Model-based mechanisms compute prospective action values using an internal model of the environment, supporting flexible but computationally costly planning; model-free mechanisms cache value estimates and build heuristics that enable fast, efficient habitual responding; and memory-based mechanisms allow rapid adaptation from individual experience. In this work, we aim to elucidate the computational principles underlying this biological efficiency and translate them into a sampling algorithm for scalable Bayesian inference through effective exploration of the posterior distribution. More specifically, our proposed algorithm comprises three components: a model-based module that uses the target distribution for guided but computationally slow sampling; a model-free module that uses previous samples to learn patterns in the parameter space, enabling fast, reflexive sampling without directly evaluating the expensive target distribution; and an episodic-control module that supports rapid sampling by recalling specific past events (i.e., samples). We show that this approach advances Bayesian methods and facilitates their application to large-scale statistical machine learning problems. In particular, we apply our proposed framework to Bayesian deep learning, with an emphasis on proper and principled uncertainty quantification.

Safe reinforcement learning (RL) studies problems where an intelligent agent has to not only maximize reward but also avoid exploring unsafe areas. In this study, we propose CUP, a novel policy optimization method based on Constrained Update Projection framework that enjoys rigorous safety guarantee. Central to our CUP development is the newly proposed surrogate functions along with the performance bound. Compared to previous safe reinforcement learning methods, CUP enjoys the benefits of 1) CUP generalizes the surrogate functions to generalized advantage estimator (GAE), leading to strong empirical performance.

A new strategy for fair supervised machine learning is proposed. The main advantages of the proposed strategy as compared to others in the literature are as follows. (a) We introduce a new smooth nonconvex surrogate to approximate the Heaviside functions involved in discontinuous unfairness measures. The surrogate is based on smoothing methods from the optimization literature, and is new for the fair supervised learning literature. The surrogate is a tight approximation which ensures the trained prediction models are fair, as opposed to other (e.g., convex) surrogates that can fail to lead to a fair prediction model in practice. (b) Rather than rely on regularizers (that lead to optimization problems that are difficult to solve) and corresponding regularization parameters (that can be expensive to tune), we propose a strategy that employs hard constraints so that specific tolerances for unfairness can be enforced without the complications associated with the use of regularization. (c) Our proposed strategy readily allows for constraints on multiple (potentially conflicting) unfairness measures at the same time. Multiple measures can be considered with a regularization approach, but at the cost of having even more difficult optimization problems to solve and further expense for tuning. By contrast, through hard constraints, our strategy leads to optimization models that can be solved tractably with minimal tuning.