Scaling Recurrent Neural Networks to a Billion Parameters with Zero-Order Optimization

During inference, Recurrent Neural Networks (RNNs) scale constant in both FLOPs and GPU memory with increasing context length, as they compress all prior tokens into a fixed-size memory. In contrast, transformers scale linearly in FLOPs and, at best, linearly in memory during generation, since they must attend to all previous tokens explicitly. Despite this inference-time advantage, training large RNNs on long contexts remains impractical because standard optimization methods depend on Backpropagation Through Time (BPTT). BPTT requires retention of all intermediate activations during the forward pass, causing memory usage to scale linearly with both context length and model size. In this paper, we show that Zero-Order Optimization (ZOO) methods such as Random-vector Gradient Estimation (RGE) can successfully replace BPTT to train RNNs with convergence rates that match, or exceed BPTT by up to 19 fold, while using orders of magnitude less memory and cost, as the model remains in inference mode throughout training. We further demonstrate that Central-Difference RGE (CD-RGE) corresponds to optimizing a smoothed surrogate loss, inherently regularizing training and improving generalization. Our method matches or outperforms BPTT across three settings: (1) overfitting, (2) transduction, and (3) language modeling. Across all tasks, with sufficient perturbations, our models generalize as well as or better than those trained with BPTT, often in fewer steps. Despite the need for more forward passes per step, we can surpass BPTT wall-clock time per step using recent advancements such as FlashRNN and distributed inference.

Beyond Gradient Averaging in Parallel Optimization: Improved Robustness through Gradient Agreement Filtering

We introduce Gradient Agreement Filtering (GAF) to improve on gradient averaging in distributed deep learning optimization. Traditional distributed data-parallel stochastic gradient descent involves averaging gradients of microbatches to calculate a macrobatch gradient that is then used to update model parameters. We find that gradients across microbatches are often orthogonal or negatively correlated, especially in late stages of training, which leads to memorization of the training set, reducing generalization. In this paper, we introduce a simple, computationally effective way to reduce gradient variance by computing the cosine distance between micro-gradients during training and filtering out conflicting updates prior to averaging. We improve validation accuracy with significantly smaller microbatch sizes. We also show this reduces memorizing noisy labels. We demonstrate the effectiveness of this technique on standard image classification benchmarks including CIFAR-100 and CIFAR-100N-Fine. We show this technique consistently outperforms validation accuracy, in some cases by up to 18.2\% compared to traditional training approaches while reducing the computation required nearly an order of magnitude because we can now rely on smaller microbatch sizes without destabilizing training.