Diagonal Batching Unlocks Parallelism in Recurrent Memory Transformers for Long Contexts

Transformer models struggle with long-context inference due to their quadratic time and linear memory complexity. Recurrent Memory Transformers (RMTs) offer a solution by reducing the asymptotic cost to linear time and constant memory usage. However, their memory update mechanism leads to sequential execution, causing a performance bottleneck. We introduce Diagonal Batching, a scheduling scheme that unlocks parallelism across segments in RMTs while preserving exact recurrence. This approach eliminates the sequential constraint, enabling efficient GPU inference even for single long-context inputs without complex batching and pipelining techniques. Because the technique is purely a run-time computation reordering, existing RMT models adopt it with no retraining. Applied to a LLaMA-1B ARMT model, Diagonal Batching yields a 3.3x speedup over standard full-attention LLaMA-1B and a 1.8x speedup over the sequential RMT implementation on 131,072-token sequences. By removing sequential bottleneck, Diagonal Batching reduces inference cost and latency, thereby strengthening RMTs as a practical solution for real-world, long-context applications.

Birch SGD: A Tree Graph Framework for Local and Asynchronous SGD Methods

We propose a new unifying framework, Birch SGD, for analyzing and designing distributed SGD methods. The central idea is to represent each method as a weighted directed tree, referred to as a computation tree. Leveraging this representation, we introduce a general theoretical result that reduces convergence analysis to studying the geometry of these trees. This perspective yields a purely graph-based interpretation of optimization dynamics, offering a new and intuitive foundation for method development. Using Birch SGD, we design eight new methods and analyze them alongside previously known ones, with at least six of the new methods shown to have optimal computational time complexity. Our research leads to two key insights: (i) all methods share the same "iteration rate" of $O\left(\frac{(R + 1) L \Delta}{\varepsilon} + \frac{\sigma^2 L \Delta}{\varepsilon^2}\right)$, where $R$ the maximum "tree distance" along the main branch of a tree; and (ii) different methods exhibit different trade-offs-for example, some update iterates more frequently, improving practical performance, while others are more communication-efficient or focus on other aspects. Birch SGD serves as a unifying framework for navigating these trade-offs. We believe these results provide a unified foundation for understanding, analyzing, and designing efficient asynchronous and parallel optimization methods.