Spiking Neural Networks (SNNs) are biologically inspired models that process visual inputs over multiple time steps. However, they often struggle with limited feature discrimination along the temporal dimension due to inherent spatiotemporal invariance. This limitation arises from the redundant activation of certain regions and shared supervision for multiple time steps, constraining the network’s ability to adapt and learn diverse features. To address this challenge, we propose a novel Temporal-Self-Erasing (TSE) supervision method that dynamically adapts the learning regions of interest for different time steps. The TSE method operates by identifying highly activated regions from predictions across multiple time steps and adaptively suppressing them during model training, thereby encouraging the network to focus on less activated yet potentially informative regions. This approach not only enhances the feature discrimination capability of SNNs but also facilitates more effective multi-time-step inference by exploiting more semantic information. Experimental results on benchmark datasets demonstrate that our TSE method significantly improves the classification accuracy and robustness of SNNs.

Spiking Neural Networks (SNNs), with their biologically inspired spatio-temporal dynamics and spike-driven processing, are emerging as a promising low-power alternative to traditional Artificial Neural Networks (ANNs). However, the complex neuronal dynamics and non-differentiable spike communication mechanisms in SNNs present substantial challenges for efficient training. By analyzing the membrane potentials in spiking neurons, we found that their distributions can increasingly deviate from the firing threshold as time progresses, which tends to cause diminished backpropagation gradients and unbalanced optimization. To address these challenges, we propose Deep Temporal-Aligned Gradient Enhancement (DeepTAGE), a novel approach that improves optimization gradients in SNNs from both internal surrogate gradient functions and external supervision methods. Our DeepTAGE dynamically adjusts surrogate gradients in accordance with the membrane potential distribution across different time steps, enhancing their respective gradients in a temporal-aligned manner that promotes balanced training. Moreover, to mitigate issues of gradient vanishing or deviating during backpropagation, DeepTAGE incorporates deep supervision at both spatial (network stages) and temporal (time steps) levels to ensure more effective and robust network optimization. Importantly, our method can be seamlessly integrated into existing SNN architectures without imposing additional inference costs or requiring extra control modules. We validate the efficacy of DeepTAGE through extensive experiments on static benchmarks (CIFAR10, CIFAR100, and ImageNet-1k) and a neuromorphic dataset (DVS-CIFAR10), demonstrating significant performance improvements.

As we know, the classical operational law of uncertain variables initiated by Liu, which gives a major push to the development of uncertainty theory, restricts the uncertain variables being dealt with to those with regular uncertainty distributions. This restriction makes the operational law no longer applicable when some uncertain variables whose distributions are not regular are involved. Therefore, a generalized operational law is proposed in this paper, for uncertain variables with continuous distributions, of which regular distributions can be treated as special cases. By utilizing this extended operational law, the uncertainty distributions of strictly monotonic functions of uncertain variables with continuous (not necessarily regular) distributions can be analytically deduced, similarly to that suggested by the classical one. Furthermore, some new conclusions on the expected values of uncertain variables with continuous distributions are presented as well. Finally, as an important application of the generalized operational law, it is proved that some types of uncertain programming involving uncertain parameters with continuous distributions can be translated into deterministic counterparts, and then be handled by classic optimization techniques without any other additional efforts.