The resulting neural network has only logarithmic depth (alleviating the degradation of data as it propagates through the network) and can process sequences in linear time (or in logarithmic time with a linear number of processors). The crucial property of FENs is that they learn by training a quasi-linear number of constant-depth feed-forward neural networks in parallel. The fact that these networks have constant depth means that backpropagation works well. We note that currently the performance of FENs is only conjectured as we are yet to implement them.

Ensuring high-quality video content for wireless users has become increasingly vital. Nevertheless, maintaining a consistent level of video quality faces challenges due to the fluctuating encoded bitrate, primarily caused by dynamic video content, especially in live streaming scenarios. Video compression is typically employed to eliminate unnecessary redundancies within and between video frames, thereby reducing the required bandwidth for video transmission. The encoded bitrate and the quality of the compressed video depend on encoder parameters, specifically, the quantization parameter (QP). Poor choices of encoder parameters can result in reduced bandwidth efficiency and high likelihood of non-conformance. Non-conformance refers to the violation of the peak signal-to-noise ratio (PSNR) constraint for an encoded video segment. To address these issues, a real-time deep learning-based H.264 controller is proposed. This controller dynamically estimates the optimal encoder parameters based on the content of a video chunk with minimal delay. The objective is to maintain video quality in terms of PSNR above a specified threshold while minimizing the average bitrate of the compressed video. Experimental results, conducted on both QCIF dataset and a diverse range of random videos from public datasets, validate the effectiveness of this approach. Notably, it achieves improvements of up to 2.5 times in average bandwidth usage compared to the state-of-the-art adaptive bitrate video streaming, with a negligible non-conformance probability below $10^{-2}$.

These notes aim to shed light on the recently proposed structured projected intermediate gradient optimization technique (SPIGOT, Peng et al., 2018). SPIGOT is a variant of the straight-through estimator (Bengio et al., 2013) which bypasses gradients of the argmax function by back-propagating a surrogate "gradient." We provide a new interpretation to the proposed gradient and put this technique into perspective, linking it to other methods for training neural networks with discrete latent variables. As a by-product, we suggest alternate variants of SPIGOT which will be further explored in future work.