Neuromorphic hardware implementations of Spiking Neural Networks (SNNs) promise energy-efficient, low-latency AI through sparse, event-driven computation. Yet, training SNNs under fine temporal discretization remains a major challenge, hindering both low-latency responsiveness and the mapping of software-trained SNNs to efficient hardware. In current approaches, spiking neurons are modeled as self-recurrent units, embedded into recurrent networks to maintain state over time, and trained with BPTT or RTRL variants based on surrogate gradients. These methods scale poorly with temporal resolution, while online approximations often exhibit instability for long sequences and tend to fail at capturing temporal patterns precisely. To address these limitations, we develop spiking neurons with internal recursive memory structures that we combine with sigma-delta spike-coding. We show that this SpikingGamma model supports direct error backpropagation without surrogate gradients, can learn fine temporal patterns with minimal spiking in an online manner, and scale feedforward SNNs to complex tasks and benchmarks with competitive accuracy, all while being insensitive to the temporal resolution of the model. Our approach offers both an alternative to current recurrent SNNs trained with surrogate gradients, and a direct route for mapping SNNs to neuromorphic hardware.

翻译：脉冲神经网络（SNNs）的神经形态硬件实现通过稀疏的事件驱动计算，有望实现高能效、低延迟的人工智能。然而，在精细时间离散化下训练SNNs仍然是一个重大挑战，既阻碍了低延迟响应能力，也影响了将软件训练的SNNs映射到高效硬件。在当前方法中，脉冲神经元被建模为自循环单元，嵌入循环网络中以随时间保持状态，并基于替代梯度使用BPTT或RTRL变体进行训练。这些方法的时间分辨率扩展性差，而在线近似方法通常对长序列表现出不稳定性，且难以精确捕捉时间模式。为解决这些局限性，我们开发了具有内部递归记忆结构的脉冲神经元，并将其与sigma-delta脉冲编码相结合。我们证明，这种SpikingGamma模型支持无需替代梯度的直接误差反向传播，能够以在线方式用最少的脉冲学习精细时间模式，并将前馈SNNs扩展到复杂任务和基准测试中，同时保持具有竞争力的准确率，且对模型的时间分辨率不敏感。我们的方法既为当前使用替代梯度训练的循环SNNs提供了一种替代方案，也为将SNNs映射到神经形态硬件提供了一条直接路径。