Accelerated Training through Iterative Gradient Propagation Along the Residual Path

TL;DR

The paper addresses the bottleneck of backpropagation in training deep models by introducing Highway-BP, an architecture-aware iterative gradient propagation method that leverages residual paths to parallelize the backward pass. It formalizes a gradient decomposition over residual paths and presents an iterative, parallelizable scheme that can approximate the true gradient with a controllable number of iterations, k. Empirical results across ResNets, Transformers, and RNNs show that Highway-BP achieves substantial speedups (around 2x–3x) with minimal performance degradation, and even the k=0 setting provides reasonable learning behavior. The approach enables faster training of very deep or long-sequence models and can be adapted to distributed, layer-distributed settings, with future work focusing on architecture-specific optimizations and CUDA-level improvements.

Abstract

Despite being the cornerstone of deep learning, backpropagation is criticized for its inherent sequentiality, which can limit the scalability of very deep models. Such models faced convergence issues due to vanishing gradient, later resolved using residual connections. Variants of these are now widely used in modern architecture. However, the computational cost of backpropagation remains a major burden, accounting for most of the training time. Taking advantage of residual-like architectural designs, we introduce Highway backpropagation, a parallelizable iterative algorithm that approximates backpropagation, by alternatively i) accumulating the gradient estimates along the residual path, and ii) backpropagating them through every layer in parallel. This algorithm is naturally derived from a decomposition of the gradient as the sum of gradients flowing through all paths and is adaptable to a diverse set of common architectures, ranging from ResNets and Transformers to recurrent neural networks. Through an extensive empirical study on a large selection of tasks and models, we evaluate Highway-BP and show that major speedups can be achieved with minimal performance degradation.

Figures (7)

• Figure 1: (a) Illustration of a layer $f_i$ decomposed as the composition of a block $g_i$ and a residual function $r_i$. (b) Backpropagation through the residual layer. Gray terms correspond to intermediate losses that are only present in RNNs. (c) Illustration of the gradient decomposition (Theorem \ref{['th:gradient_decomposition']}) as the sum of the gradients flowing through only the residual connections ($k=0$ in blue), through only one block ($k=1$, in yellow, orange and red), and so on for $k=2$, $3$, ... until $k=L$.
• Figure 2: Final performance of deep sequential models versus the number $k$ of Highway-BP iterations used for training (red), compared to backpropagation (black).
• Figure 3: Validation loss during training for the GPT-2 model, with different algorithms.
• Figure 3: Speedup of training with Highway-BP vs. backpropagation for the RNN experiments (more details in Table \ref{['tab:speeds']}).
• Figure 4: Final performance of RNNs versus the number $k$ of Highway-BP iterations used for training (red), compared to backpropagation (black) and fixed-point iteration (blue).

Theorems & Definitions (2)

• Theorem 1: Decomposition of the gradient over all paths
• Theorem 2: Iterative computation of the gradient