Various linear complexity models, such as Linear Transformer (LinFormer), State Space Model (SSM), and Linear RNN (LinRNN), have been proposed to replace the conventional softmax attention in Transformer structures. However, the optimal design of these linear models is still an open question. In this work, we attempt to answer this question by finding the best linear approximation to softmax attention from a theoretical perspective. We start by unifying existing linear complexity models as the linear attention form and then identify three conditions for the optimal linear attention design: i) Dynamic memory ability; ii) Static approximation ability; iii) Least parameter approximation. We find that none of the current linear models meet all three conditions, resulting in suboptimal performance. Instead, we propose Meta Linear Attention (MetaLA) as a solution that satisfies these conditions. Our experiments on Multi-Query Associative Recall (MQAR) task, language modeling, image classification, and Long-Range Arena (LRA) benchmark demonstrate that MetaLA is more effective than the existing linear models.

Spiking neural networks (SNNs) are brain-inspired energy-efficient models that encode information in spatiotemporal dynamics. Recently, deep SNNs trained directly have shown great success in achieving high performance on classification tasks with very few time steps. However, how to design a directly-trained SNN for the regression task of object detection still remains a challenging problem. To address this problem, we propose EMS-YOLO, a novel directly-trained SNN framework for object detection, which is the first trial to train a deep SNN with surrogate gradients for object detection rather than ANN-SNN conversion strategies. Specifically, we design a full-spike residual block, EMS-ResNet, which can effectively extend the depth of the directly-trained SNN with low power consumption. Furthermore, we theoretically analyze and prove the EMS-ResNet could avoid gradient vanishing or exploding. The results demonstrate that our approach outperforms the state-of-the-art ANN-SNN conversion methods (at least 500 time steps) in extremely fewer time steps (only 4 time steps). It is shown that our model could achieve comparable performance to the ANN with the same architecture while consuming 5.83 times less energy on the frame-based COCO Dataset and the event-based Gen1 Dataset.

The Lottery Ticket Hypothesis (LTH) states that a randomly-initialized large neural network contains a small sub-network (i.e., winning tickets) which, when trained in isolation, can achieve comparable performance to the large network. LTH opens up a new path for network pruning. Existing proofs of LTH in Artificial Neural Networks (ANNs) are based on continuous activation functions, such as ReLU, which satisfying the Lipschitz condition. However, these theoretical methods are not applicable in Spiking Neural Networks (SNNs) due to the discontinuous of spiking function. We argue that it is possible to extend the scope of LTH by eliminating Lipschitz condition. Specifically, we propose a novel probabilistic modeling approach for spiking neurons with complicated spatio-temporal dynamics. Then we theoretically and experimentally prove that LTH holds in SNNs. According to our theorem, we conclude that pruning directly in accordance with the weight size in existing SNNs is clearly not optimal. We further design a new criterion for pruning based on our theory, which achieves better pruning results than baseline.