  Efficient and biologically plausible alternatives to backpropagation in
neural network training remain a challenge due to issues such as high
computational complexity and additional assumptions about neural networks,
which limit scalability to deeper networks. The likelihood ratio method offers
a promising gradient estimation strategy but is constrained by significant
memory consumption, especially when deploying multiple copies of data to reduce
estimation variance. In this paper, we introduce an approximation technique for
the likelihood ratio (LR) method to alleviate computational and memory demands
in gradient estimation. By exploiting the natural parallelism during the
backward pass using LR, we further provide a high-performance training
strategy, which pipelines both the forward and backward pass, to make it more
suitable for the computation on specialized hardware. Extensive experiments
demonstrate the effectiveness of the approximation technique in neural network
training. This work underscores the potential of the likelihood ratio method in
achieving high-performance neural network training, suggesting avenues for
further exploration.
