Learning a Fourier Transform for Linear Relative Positional Encodings in Transformers

We propose a new class of linear Transformers called FourierLearner-Transformers (FLTs), which incorporate a wide range of relative positional encoding mechanisms (RPEs). These include regular RPE techniques applied for nongeometric data, as well as novel RPEs operating on the sequences of tokens embedded in higher-dimensional Euclidean spaces (e.g. point clouds). FLTs construct the optimal RPE mechanism implicitly by learning its spectral representation. As opposed to other architectures combining efficient low-rank linear attention with RPEs, FLTs remain practical in terms of their memory usage and do not require additional assumptions about the structure of the RPE-mask. FLTs allow also for applying certain structural inductive bias techniques to specify masking strategies, e.g. they provide a way to learn the so-called local RPEs introduced in this paper and providing accuracy gains as compared with several other linear Transformers for language modeling. We also thoroughly tested FLTs on other data modalities and tasks, such as: image classification and 3D molecular modeling. For 3D-data FLTs are, to the best of our knowledge, the first Transformers architectures providing RPE-enhanced linear attention.

Mnemosyne: Learning to Train Transformers with Transformers

Training complex machine learning (ML) architectures requires a compute and time consuming process of selecting the right optimizer and tuning its hyper-parameters. A new paradigm of learning optimizers from data has emerged as a better alternative to hand-designed ML optimizers. We propose Mnemosyne optimizer, that uses Performers: implicit low-rank attention Transformers. It can learn to train entire neural network architectures including other Transformers without any task-specific optimizer tuning. We show that Mnemosyne: (a) generalizes better than popular LSTM optimizer, (b) in particular can successfully train Vision Transformers (ViTs) while meta--trained on standard MLPs and (c) can initialize optimizers for faster convergence in Robotics applications. We believe that these results open the possibility of using Transformers to build foundational optimization models that can address the challenges of regular Transformer training. We complement our results with an extensive theoretical analysis of the compact associative memory used by Mnemosyne.