Transformers learn through gradual rank increase

We identify incremental learning dynamics in transformers, where the difference between trained and initial weights progressively increases in rank. We rigorously prove this occurs under the simplifying assumptions of diagonal weight matrices and small initialization. Our experiments support the theory and also show that phenomenon can occur in practice without the simplifying assumptions.

Position Prediction as an Effective Pretraining Strategy

Transformers have gained increasing popularity in a wide range of applications, including Natural Language Processing (NLP), Computer Vision and Speech Recognition, because of their powerful representational capacity. However, harnessing this representational capacity effectively requires a large amount of data, strong regularization, or both, to mitigate overfitting. Recently, the power of the Transformer has been unlocked by self-supervised pretraining strategies based on masked autoencoders which rely on reconstructing masked inputs, directly, or contrastively from unmasked content. This pretraining strategy which has been used in BERT models in NLP, Wav2Vec models in Speech and, recently, in MAE models in Vision, forces the model to learn about relationships between the content in different parts of the input using autoencoding related objectives. In this paper, we propose a novel, but surprisingly simple alternative to content reconstruction~-- that of predicting locations from content, without providing positional information for it. Doing so requires the Transformer to understand the positional relationships between different parts of the input, from their content alone. This amounts to an efficient implementation where the pretext task is a classification problem among all possible positions for each input token. We experiment on both Vision and Speech benchmarks, where our approach brings improvements over strong supervised training baselines and is comparable to modern unsupervised/self-supervised pretraining methods. Our method also enables Transformers trained without position embeddings to outperform ones trained with full position information.

The Slingshot Mechanism: An Empirical Study of Adaptive Optimizers and the Grokking Phenomenon

The grokking phenomenon as reported by Power et al. ( arXiv:2201.02177 ) refers to a regime where a long period of overfitting is followed by a seemingly sudden transition to perfect generalization. In this paper, we attempt to reveal the underpinnings of Grokking via a series of empirical studies. Specifically, we uncover an optimization anomaly plaguing adaptive optimizers at extremely late stages of training, referred to as the Slingshot Mechanism. A prominent artifact of the Slingshot Mechanism can be measured by the cyclic phase transitions between stable and unstable training regimes, and can be easily monitored by the cyclic behavior of the norm of the last layers weights. We empirically observe that without explicit regularization, Grokking as reported in ( arXiv:2201.02177 ) almost exclusively happens at the onset of Slingshots, and is absent without it. While common and easily reproduced in more general settings, the Slingshot Mechanism does not follow from any known optimization theories that we are aware of, and can be easily overlooked without an in depth examination. Our work points to a surprising and useful inductive bias of adaptive gradient optimizers at late stages of training, calling for a revised theoretical analysis of their origin.

Efficient Embedding of Semantic Similarity in Control Policies via Entangled Bisimulation

Learning generalizeable policies from visual input in the presence of visual distractions is a challenging problem in reinforcement learning. Recently, there has been renewed interest in bisimulation metrics as a tool to address this issue; these metrics can be used to learn representations that are, in principle, invariant to irrelevant distractions by measuring behavioural similarity between states. An accurate, unbiased, and scalable estimation of these metrics has proved elusive in continuous state and action scenarios. We propose entangled bisimulation, a bisimulation metric that allows the specification of the distance function between states, and can be estimated without bias in continuous state and action spaces. We show how entangled bisimulation can meaningfully improve over previous methods on the Distracting Control Suite (DCS), even when added on top of data augmentation techniques.

Uncertainty Weighted Actor-Critic for Offline Reinforcement Learning

Offline Reinforcement Learning promises to learn effective policies from previously-collected, static datasets without the need for exploration. However, existing Q-learning and actor-critic based off-policy RL algorithms fail when bootstrapping from out-of-distribution (OOD) actions or states. We hypothesize that a key missing ingredient from the existing methods is a proper treatment of uncertainty in the offline setting. We propose Uncertainty Weighted Actor-Critic (UWAC), an algorithm that detects OOD state-action pairs and down-weights their contribution in the training objectives accordingly. Implementation-wise, we adopt a practical and effective dropout-based uncertainty estimation method that introduces very little overhead over existing RL algorithms. Empirically, we observe that UWAC substantially improves model stability during training. In addition, UWAC out-performs existing offline RL methods on a variety of competitive tasks, and achieves significant performance gains over the state-of-the-art baseline on datasets with sparse demonstrations collected from human experts.

Collegial Ensembles

Modern neural network performance typically improves as model size increases. A recent line of research on the Neural Tangent Kernel (NTK) of over-parameterized networks indicates that the improvement with size increase is a product of a better conditioned loss landscape. In this work, we investigate a form of over-parameterization achieved through ensembling, where we define collegial ensembles (CE) as the aggregation of multiple independent models with identical architectures, trained as a single model. We show that the optimization dynamics of CE simplify dramatically when the number of models in the ensemble is large, resembling the dynamics of wide models, yet scale much more favorably. We use recent theoretical results on the finite width corrections of the NTK to perform efficient architecture search in a space of finite width CE that aims to either minimize capacity, or maximize trainability under a set of constraints. The resulting ensembles can be efficiently implemented in practical architectures using group convolutions and block diagonal layers. Finally, we show how our framework can be used to analytically derive optimal group convolution modules originally found using expensive grid searches, without having to train a single model.