A.3 Proof of Theorem 1 In this subsection, we prove Theorem 1 with Assumption 1. Assumption 1. l = 1,, N, t = 1,, T, diag null As described in Sections 4.1 and 4.2, for gradients of OTTT, we have Remark 2. The above conclusion mainly focuses on the gradients for connection weights Remark 3. Note that the gradients based on spike representation may also include small errors since A.4 Proof of Theorem 2 In this subsection, we prove Theorem 2. Theorem 2. If Assumption 1 holds, As described in Sections 4.1 and 4.2 and similar to the proof of Theorem 1, let Remark 4. The above conclusion considers the single-layer condition. It can be generalized to the multi-layer condition. Therefore, the conclusion can be directly generalized to these conditions as well. L} based on the gradient-based optimizer. For VGG network structures, we directly impose sWS on all weights. For more illustrations and other details, please directly refer to [4].

Histopathology is the study and diagnosis of disease by microscopic inspection of tissue.

Multivariate time-series forecasting plays a crucial role in many real-world applications.

In the simulations in subsection 3.2, all linear networks have The backbone architecture consists of a stack of 12 Conv-LSTM modules, and each module contains 32 units (channels). The backbone architecture is illustrated in Figure 7. To demonstrate ARMA networks' applicability to image segmentation, we evaluate it on a challenging The network architecture is illustrated in Figure 15a. The experimental results are summarized in Table 5. Since image classifications tasks do not require convolu-tional layers to have large receptive fields, the learned autoregressive coefficients concentrate around 0, as shown in Figure 6.