A major limitation for the broader scope of problems solvable by transformers is the quadratic scaling of computational complexity with input size. In this study, we investigate the recurrent memory augmentation of pre-trained transformer models to extend input context length while linearly scaling compute. Our approach demonstrates the capability to store information in memory for sequences of up to an unprecedented two million tokens while maintaining high retrieval accuracy. Experiments with language modeling tasks show perplexity improvement as the number of processed input segments increases. These results underscore the effectiveness of our method, which has significant potential to enhance long-term dependency handling in natural language understanding and generation tasks, as well as enable large-scale context processing for memory-intensive applications.

This work is dedicated to simultaneous continuous-time trajectory estimation and mapping based on Gaussian Processes (GP). State-of-the-art GP-based models for Simultaneous Localization and Mapping (SLAM) are computationally efficient but can only be used with a restricted class of kernel functions. This paper provides the algorithm based on GP with Random Fourier Features (RFF) approximation for SLAM without any constraints. The advantages of RFF for continuous-time SLAM are that we can consider a broader class of kernels and, at the same time, maintain computational complexity at reasonably low level by operating in the Fourier space of features. The accuracy-speed trade-off can be controlled by the number of features. Our experimental results on synthetic and real-world benchmarks demonstrate the cases in which our approach provides better results compared to the current state-of-the-art.

We consider the problem of improving kernel approximation via randomized feature maps. These maps arise as Monte Carlo approximation to integral representations of kernel functions and scale up kernel methods for larger datasets. Based on an efficient numerical integration technique, we propose a unifying approach that reinterprets the previous random features methods and extends to better estimates of the kernel approximation. We derive the convergence behavior and conduct an extensive empirical study that supports our hypothesis.