Encoder-decoder networks with attention have proven to be a powerful way to solve many sequence-to-sequence tasks. In these networks, attention aligns encoder and decoder states and is often used for visualizing network behavior. However, the mechanisms used by networks to generate appropriate attention matrices are still mysterious. Moreover, how these mechanisms vary depending on the particular architecture used for the encoder and decoder (recurrent, feed-forward, etc.) are also not well understood. In this work, we investigate how encoder-decoder networks solve different sequence-to-sequence tasks. We introduce a way of decomposing hidden states over a sequence into temporal (independent of input) and input-driven (independent of sequence position) components. This reveals how attention matrices are formed: depending on the task requirements, networks rely more heavily on either the temporal or input-driven components. These findings hold across both recurrent and feed-forward architectures despite their differences in forming the temporal components. Overall, our results provide new insight into the inner workings of attention-based encoder-decoder networks.

Learned optimizers are algorithms that can themselves be trained to solve optimization problems. In contrast to baseline optimizers (such as momentum or Adam) that use simple update rules derived from theoretical principles, learned optimizers use flexible, high-dimensional, nonlinear parameterizations. Although this can lead to better performance in certain settings, their inner workings remain a mystery. How is a learned optimizer able to outperform a well tuned baseline? Has it learned a sophisticated combination of existing optimization techniques, or is it implementing completely new behavior? In this work, we address these questions by careful analysis and visualization of learned optimizers. We study learned optimizers trained from scratch on three disparate tasks, and discover that they have learned interpretable mechanisms, including: momentum, gradient clipping, learning rate schedules, and a new form of learning rate adaptation. Moreover, we show how the dynamics of learned optimizers enables these behaviors. Our results help elucidate the previously murky understanding of how learned optimizers work, and establish tools for interpreting future learned optimizers.

Despite the widespread application of recurrent neural networks (RNNs) across a variety of tasks, a unified understanding of how RNNs solve these tasks remains elusive. In particular, it is unclear what dynamical patterns arise in trained RNNs, and how those patterns depend on the training dataset or task. This work addresses these questions in the context of a specific natural language processing task: text classification. Using tools from dynamical systems analysis, we study recurrent networks trained on a battery of both natural and synthetic text classification tasks. We find the dynamics of these trained RNNs to be both interpretable and low-dimensional. Specifically, across architectures and datasets, RNNs accumulate evidence for each class as they process the text, using a low-dimensional attractor manifold as the underlying mechanism. Moreover, the dimensionality and geometry of the attractor manifold are determined by the structure of the training dataset; in particular, we describe how simple word-count statistics computed on the training dataset can be used to predict these properties. Our observations span multiple architectures and datasets, reflecting a common mechanism RNNs employ to perform text classification. To the degree that integration of evidence towards a decision is a common computational primitive, this work lays the foundation for using dynamical systems techniques to study the inner workings of RNNs.

Much as replacing hand-designed features with learned functions has revolutionized how we solve perceptual tasks, we believe learned algorithms will transform how we train models. In this work we focus on general-purpose learned optimizers capable of training a wide variety of problems with no user-specified hyperparameters. We introduce a new, neural network parameterized, hierarchical optimizer with access to additional features such as validation loss to enable automatic regularization. Most learned optimizers have been trained on only a single task, or a small number of tasks. We train our optimizers on thousands of tasks, making use of orders of magnitude more compute, resulting in optimizers that generalize better to unseen tasks. The learned optimizers not only perform well, but learn behaviors that are distinct from existing first order optimizers. For instance, they generate update steps that have implicit regularization and adapt as the problem hyperparameters (e.g. batch size) or architecture (e.g. neural network width) change. Finally, these learned optimizers show evidence of being useful for out of distribution tasks such as training themselves from scratch.

Recurrent neural networks (RNNs) are a widely used tool for modeling sequential data, yet they are often treated as inscrutable black boxes. Given a trained recurrent network, we would like to reverse engineer it--to obtain a quantitative, interpretable description of how it solves a particular task. Even for simple tasks, a detailed understanding of how recurrent networks work, or a prescription for how to develop such an understanding, remains elusive. In this work, we use tools from dynamical systems analysis to reverse engineer recurrent networks trained to perform sentiment classification, a foundational natural language processing task. Given a trained network, we find fixed points of the recurrent dynamics and linearize the nonlinear system around these fixed points.

Recurrent neural networks (RNNs) are a widely used tool for modeling sequential data, yet they are often treated as inscrutable black boxes. Given a trained recurrent network, we would like to reverse engineer it--to obtain a quantitative, interpretable description of how it solves a particular task. Even for simple tasks, a detailed understanding of how recurrent networks work, or a prescription for how to develop such an understanding, remains elusive. In this work, we use tools from dynamical systems analysis to reverse engineer recurrent networks trained to perform sentiment classification, a foundational natural language processing task. Given a trained network, we find fixed points of the recurrent dynamics and linearize the nonlinear system around these fixed points. Despite their theoretical capacity to implement complex, high-dimensional computations, we find that trained networks converge to highly interpretable, low-dimensional representations. In particular, the topological structure of the fixed points and corresponding linearized dynamics reveal an approximate line attractor within the RNN, which we can use to quantitatively understand how the RNN solves the sentiment analysis task. Finally, we find this mechanism present across RNN architectures (including LSTMs, GRUs, and vanilla RNNs) trained on multiple datasets, suggesting that our findings are not unique to a particular architecture or dataset. Overall, these results demonstrate that surprisingly universal and human interpretable computations can arise across a range of recurrent networks.

State-of-the art vision models can achieve superhuman performance on image classification tasks when testing and training data come from the same distribution. However, when models are tested on corrupted images (e.g. due to scale changes, translations, or shifts in brightness or contrast), performance degrades significantly. Here, we explore the possibility of meta-training a learned optimizer that can train image classification models such that they are robust to common image corruptions. Specifically, we are interested training models that are more robust to noise distributions not present in the training data. We find that a learned optimizer meta-trained to produce models which are robust to Gaussian noise trains models that are more robust to Gaussian noise at other scales compared to traditional optimizers like Adam. The effect of meta-training is more complicated when targeting a more general set of noise distributions, but led to improved performance on half of held-out corruption tasks. Our results suggest that meta-learning provides a novel approach for studying and improving the robustness of deep learning models.

Deep learning has shown that learned functions can dramatically outperform hand-designed functions on perceptual tasks. Analogously, this suggests that learned optimizers may similarly outperform current hand-designed optimizers, especially for specific problems. However, learned optimizers are notoriously difficult to train and have yet to demonstrate wall-clock speedups over hand-designed optimizers, and thus are rarely used in practice. Typically, learned optimizers are trained by truncated backpropagation through an unrolled optimization process. The resulting gradients are either strongly biased (for short truncations) or have exploding norm (for long truncations). In this work we propose a training scheme which overcomes both of these difficulties, by dynamically weighting two unbiased gradient estimators for a variational loss on optimizer performance. This allows us to train neural networks to perform optimization of a specific task faster than tuned first-order methods. Moreover, by training the optimizer against validation loss (as opposed to training loss), we are able to learn optimizers that train networks to generalize better than first order methods. We demonstrate these results on problems where our learned optimizer trains convolutional networks faster in wall-clock time compared to tuned first-order methods and with an improvement in test loss.

Many applications in machine learning require optimizing a function whose true gradient is unknown, but where surrogate gradient information (directions that may be correlated with, but not necessarily identical to, the true gradient) is available instead. This arises when an approximate gradient is easier to compute than the full gradient (e.g. in meta-learning or unrolled optimization), or when a true gradient is intractable and is replaced with a surrogate (e.g. in certain reinforcement learning applications, or when using synthetic gradients). We propose Guided Evolutionary Strategies, a method for optimally using surrogate gradient directions along with random search. We define a search distribution for evolutionary strategies that is elongated along a guiding subspace spanned by the surrogate gradients. This allows us to estimate a descent direction which can then be passed to a first-order optimizer. We analytically and numerically characterize the tradeoffs that result from tuning how strongly the search distribution is stretched along the guiding subspace, and we use this to derive a setting of the hyperparameters that works well across problems. Finally, we apply our method to example problems including truncated unrolled optimization and a synthetic gradient problem, demonstrating improvement over both standard evolutionary strategies and first-order methods that directly follow the surrogate gradient. We provide a demo of Guided ES at https://github.com/brain-research/guided-evolutionary-strategies

A major goal of unsupervised learning is to discover data representations that are useful for subsequent tasks, without access to supervised labels during training. Typically, this goal is approached by minimizing a surrogate objective, such as the negative log likelihood of a generative model, with the hope that representations useful for subsequent tasks will arise as a side effect. In this work, we propose instead to directly target a later desired task by meta-learning an unsupervised learning rule, which leads to representations useful for that task. Here, our desired task (meta-objective) is the performance of the representation on semi-supervised classification, and we meta-learn an algorithm -- an unsupervised weight update rule -- that produces representations that perform well under this meta-objective. Additionally, we constrain our unsupervised update rule to a be a biologically-motivated, neuron-local function, which enables it to generalize to novel neural network architectures. We show that the meta-learned update rule produces useful features and sometimes outperforms existing unsupervised learning techniques. We show that the meta-learned unsupervised update rule generalizes to train networks with different widths, depths, and nonlinearities. It also generalizes to train on data with randomly permuted input dimensions and even generalizes from image datasets to a text task.