The increasing size of deep learning models has created the need for more efficient alternatives to the standard error backpropagation algorithm, that make better use of asynchronous, parallel and distributed computing. One major shortcoming of backpropagation is the interlocking between the forward phase of the algorithm, which computes a global loss, and the backward phase where the loss is backpropagated through all layers to compute the gradients, which are used to update the network parameters. To address this problem, we propose a method that parallelises SGD updates across the layers of a model by asynchronously updating them from multiple threads. Furthermore, since we observe that the forward pass is often much faster than the backward pass, we use separate threads for the forward and backward pass calculations, which allows us to use a higher ratio of forward to backward threads than the usual 1:1 ratio, reducing the overall staleness of the parameters. Thus, our approach performs asynchronous stochastic gradient descent using separate threads for the loss (forward) and gradient (backward) computations and performs layer-wise partial updates to parameters in a distributed way. We show that this approach yields close to state-of-the-art results while running up to 2.97 faster than Hogwild! We theoretically prove the convergence of the algorithm using a novel theoretical framework based on stochastic differential equations and the drift diffusion process, by modeling the asynchronous parameter updates as a stochastic process. Scaling up modern deep learning models requires massive resources and training time.

The Random Forest (RF) algorithm can be applied to a broad spectrum of problems, including time series prediction. However, neither the classical IID (Independent and Identically distributed) bootstrap nor block bootstrapping strategies (as implemented in rangerts) completely account for the nature of the Data Generating Process (DGP) while resampling the observations. We propose the combination of RF with a residual bootstrapping technique where we replace the IID bootstrap with the AR-Sieve Bootstrap (ARSB), which assumes the DGP to be an autoregressive process. To assess the new model's predictive performance, we conduct a simulation study using synthetic data generated from different types of DGPs. It turns out that ARSB provides more variation amongst the trees in the forest. Moreover, RF with ARSB shows greater accuracy compared to RF with other bootstrap strategies. However, these improvements are achieved at some efficiency costs.

The ubiquitous backpropagation algorithm requires sequential updates through the network introducing a locking problem. In addition, back-propagation relies on the transpose of forward weight matrices to compute updates, introducing a weight transport problem across the network. Locking and weight transport are problems because they prevent efficient parallelization and horizontal scaling of the training process. We propose a new method to address both these problems and scale up the training of large models. Our method works by dividing a deep neural network into blocks and introduces a feedback network that propagates the information from the targets backwards to provide auxiliary local losses. Forward and backward propagation can operate in parallel and with different sets of weights, addressing the problems of locking and weight transport. Our approach derives from a statistical interpretation of training that treats output activations of network blocks as parameters of probability distributions. The resulting learning framework uses these parameters to evaluate the agreement between forward and backward information. Error backpropagation is then performed locally within each block, leading to "block-local" learning. Several previously proposed alternatives to error backpropagation emerge as special cases of our model. We present results on a variety of tasks and architectures, demonstrating state-of-the-art performance using block-local learning. These results provide a new principled framework for training networks in a distributed setting.