ICLR 2022 Papers

Automatic Music Transcription (AMT), inferring musical notes from raw audio, is a challenging task at the core of music understanding. Unlike Automatic Speech Recognition (ASR), which typically focuses on the words of a single speaker, AMT often requires transcribing multiple instruments simultaneously, all while preserving fine-scale pitch and timing information. Further, many AMT datasets are ``low-resource'', as even expert musicians find music transcription difficult and time-consuming. Thus, prior work has focused on task-specific architectures, tailored to the individual instruments of each task. In this work, motivated by the promising results of sequence-to-sequence transfer learning for low-resource Natural Language Processing (NLP), we demonstrate that a general-purpose Transformer model can perform multi-task AMT, jointly transcribing arbitrary combinations of musical instruments across several transcription datasets. We show this unified training framework achieves high-quality transcription results across a range of datasets, dramatically improving performance for low-resource instruments (such as guitar), while preserving strong performance for abundant instruments (such as piano). Finally, by expanding the scope of AMT, we expose the need for more consistent evaluation metrics and better dataset alignment, and provide a strong baseline for this new direction of multi-task AMT.

Biological spiking neural networks (SNNs) can temporally encode information in their outputs, e.g. in the rank order in which neurons fire, whereas artificial neural networks (ANNs) conventionally do not. As a result, models of SNNs for neuromorphic computing are regarded as potentially more rapid and efficient than ANNs when dealing with temporal input. On the other hand, ANNs are simpler to train, and usually achieve superior performance. Here we show that temporal coding such as rank coding (RC) inspired by SNNs can also be applied to conventional ANNs such as LSTMs, and leads to computational savings and speedups. In our RC for ANNs, we apply backpropagation through time using the standard real-valued activations, but only from a strategically early time step of each sequential input example, decided by a threshold-crossing event. Learning then incorporates naturally also when to produce an output, without other changes to the model or the algorithm. Both the forward and the backward training pass can be significantly shortened by skipping the remaining input sequence after that first event. RC-training also significantly reduces time-to-insight during inference, with a minimal decrease in accuracy. The desired speed-accuracy trade-off is tunable by varying the threshold or a regularization parameter that rewards output entropy. We demonstrate these in two toy problems of sequence classification, and in a temporally-encoded MNIST dataset where our RC model achieves 99.19% accuracy after the first input time-step, outperforming the state of the art in temporal coding with SNNs, as well as in spoken-word classification of Google Speech Commands, outperforming non-RC-trained early inference with LSTMs.

Understanding the source of the superior generalization ability of NNs remains one of the most important problems in ML research. There have been a series of theoretical works trying to derive non-vacuous bounds for NNs. Recently, the compression of information stored in weights (IIW) is proved to play a key role in NNs generalization based on the PAC-Bayes theorem. However, no solution of IIW has ever been provided, which builds a barrier for further investigation of the IIW's property and its potential in practical deep learning. In this paper, we propose an algorithm for the efficient approximation of IIW. Then, we build an IIW-based information bottleneck on the trade-off between accuracy and information complexity of NNs, namely PIB. From PIB, we can empirically identify the fitting to compressing phase transition during NNs' training and the concrete connection between the IIW compression and the generalization. Besides, we verify that IIW is able to explain NNs in broad cases, e.g., varying batch sizes, over-parameterization, and noisy labels. Moreover, we propose an MCMC-based algorithm to sample from the optimal weight posterior characterized by PIB, which fulfills the potential of IIW in enhancing NNs in practice.

Catastrophic forgetting is one of the major challenges in continual learning. To address this issue, some existing methods put restrictive constraints on the optimization space of the new task for minimizing the interference to old tasks. However, this may lead to unsatisfactory performance for the new task, especially when the new task is strongly correlated with old tasks. To tackle this challenge, we propose Trust Region Gradient Projection (TRGP) for continual learning to facilitate the forward knowledge transfer based on an efficient characterization of task correlation. Particularly, we introduce a notion of 'trust region' to select the most related old tasks for the new task in a layer-wise and single-shot manner, using the norm of gradient projection onto the subspace spanned by task inputs. Then, a scaled weight projection is proposed to cleverly reuse the frozen weights of the selected old tasks in the trust region through a layer-wise scaling matrix. By jointly optimizing the scaling matrices and the model, where the model is updated along the directions orthogonal to the subspaces of old tasks, TRGP can effectively prompt knowledge transfer without forgetting. Extensive experiments show that our approach achieves significant improvement over related state-of-the-art methods.

Machine learning training methods depend plentifully and intricately on hyperparameters, motivating automated strategies for their optimisation. Many existing algorithms restart training for each new hyperparameter choice, at considerable computational cost. Some hypergradient-based one-pass methods exist, but these either cannot be applied to arbitrary optimiser hyperparameters (such as learning rates and momenta) or take several times longer to train than their base models. We extend these existing methods to develop an approximate hypergradient-based hyperparameter optimiser which is applicable to any continuous hyperparameter appearing in a differentiable model weight update, yet requires only one training episode, with no restarts. We also provide a motivating argument for convergence to the true hypergradient, and perform tractable gradient-based optimisation of independent learning rates for each model parameter. Our method performs competitively from varied random hyperparameter initialisations on several UCI datasets and Fashion-MNIST (using a one-layer MLP), Penn Treebank (using an LSTM) and CIFAR-10 (using a ResNet-18), in time only 2-3x greater than vanilla training.

We present an empirical study of scaling properties of encoder-decoder Transformer models used in neural machine translation (NMT). We show that cross-entropy loss as a function of model size follows a certain scaling law. Specifically (i) We propose a formula which describes the scaling behavior of cross-entropy loss as a bivariate function of encoder and decoder size, and show that it gives accurate predictions under a variety of scaling approaches and languages; we show that the total number of parameters alone is not sufficient for such purposes. (ii) We observe different power law exponents when scaling the decoder vs scaling the encoder, and provide recommendations for optimal allocation of encoder/decoder capacity based on this observation. (iii) We also report that the scaling behavior of the model is acutely influenced by composition bias of the train/test sets, which we define as any deviation from naturally generated text (either via machine generated or human translated text). We observe that natural text on the target side enjoys scaling, which manifests as successful reduction of the cross-entropy loss. (iv) Finally, we investigate the relationship between the cross-entropy loss and the quality of the generated translations. We find two different behaviors, depending on the nature of the test data. For test sets which were originally translated from target language to source language, both loss and BLEU score improve as model size increases. In contrast, for test sets originally translated from source language to target language, the loss improves, but the BLEU score stops improving after a certain threshold. We release generated text from all models used in this study.

Recently, deep AUC maximization (DAM) has achieved great success in different domains (e.g., medical image classification). However, the end-to-end training for deep AUC maximization still remains a challenging problem. Previous studies employ an ad-hoc two-stage approach that first trains the network by optimizing a traditional loss (e.g., cross-entropy loss) and then finetunes the network by optimizing an AUC loss. This is because that training a deep neural network from scratch by maximizing an AUC loss usually does not yield a satisfactory performance. This phenomenon can be attributed to the degraded feature representations learned by maximizing the AUC loss from scratch. To address this issue, we propose a novel compositional training framework for end-to-end DAM, namely compositional DAM. The key idea of compositional training is to minimize a compositional objective function, where the outer function corresponds to an AUC loss and the inner function represents a gradient descent step for minimizing a traditional loss, e.g., the cross-entropy (CE) loss. To optimize the non-standard compositional objective, we propose an efficient and provable stochastic optimization algorithm. The proposed algorithm enhances the capabilities of both robust feature learning and robust classifier learning by alternatively taking a gradient descent step for the CE loss and for the AUC loss in a systematic way. We conduct extensive empirical studies on imbalanced benchmark and medical image datasets, which unanimously verify the effectiveness of the proposed method. Our results show that the compositional training approach dramatically improves both the feature representations and the testing AUC score compared with traditional deep learning approaches, and yields better performance than the two-stage approaches for DAM as well. The proposed method is implemented in our open-sourced library LibAUC (https://www.libauc.org) and code is available at https://github.com/Optimization-AI/LibAUC.

Deployment of machine learning models in real high-risk settings (e.g. healthcare) often depends not only on the model's accuracy but also on its fairness, robustness, and interpretability. Generalized Additive Models (GAMs) are a class of interpretable models with a long history of use in these high-risk domains, but they lack desirable features of deep learning such as differentiability and scalability. In this work, we propose a neural GAM (NODE-GAM) and neural GA$^2$M (NODE-GA$^2$M) that scale well and perform better than other GAMs on large datasets, while remaining interpretable compared to other ensemble and deep learning models. We demonstrate that our models find interesting patterns in the data. Lastly, we show that we are able to improve model accuracy via self-supervised pre-training, an improvement that is not possible for non-differentiable GAMs.

A key goal of unsupervised representation learning is ``inverting'' a data generating process to recover its latent properties. Existing work that provably achieves this goal relies on strong assumptions on relationships between the latent variables (e.g., independence conditional on auxiliary information). In this paper, we take a very different perspective on the problem and ask, ``Can we instead identify latent properties by leveraging knowledge of the mechanisms that govern their evolution?'' We provide a complete characterization of the sources of non-identifiability as we vary knowledge about a set of possible mechanisms. In particular, we prove that if we know the exact mechanisms under which the latent properties evolve, then identification can be achieved up to any equivariances that are shared by the underlying mechanisms. We generalize this characterization to settings where we only know some hypothesis class over possible mechanisms, as well as settings where the mechanisms are stochastic. We demonstrate the power of this mechanism-based perspective by showing that we can leverage our results to generalize existing identifiable representation learning results. These results suggest that by exploiting inductive biases on mechanisms, it is possible to design a range of new identifiable representation learning approaches.

After training on large datasets, certain deep neural networks are surprisingly good models of the neural mechanisms of adult primate visual object recognition. Nevertheless, these models are considered poor models of the development of the visual system because they posit millions of sequential, precisely coordinated synaptic updates, each based on a labeled image. While ongoing research is pursuing the use of unsupervised proxies for labels, we here explore a complementary strategy of reducing the required number of supervised synaptic updates to produce an adult-like ventral visual stream (as judged by the match to V1, V2, V4, IT, and behavior). Such models might require less precise machinery and energy expenditure to coordinate these updates and would thus move us closer to viable neuroscientific hypotheses about how the visual system wires itself up. Relative to standard model training on labeled images in ImageNet, we here demonstrate that the total number of supervised weight updates can be substantially reduced using three complementary strategies: First, we find that only 2% of supervised updates (epochs and images) are needed to achieve 80% of the match to adult ventral stream. Specifically, training benefits predictions of higher visual cortex the most whereas early visual cortex predictions only improve marginally over the course of training. Second, by improving the random distribution of synaptic connectivity, we find that 54% of the brain match can already be achieved “at birth" (i.e. no training at all). Third, we find that, by training only 5% of model synapses, we can still achieve nearly 80% of the match to the ventral stream. This approach further improves on ImageNet performance over previous attempts in computer vision of minimizing trained components without substantially increasing the relative number of trained parameters. These results reflect first steps in modeling not just primate adult visual processing during inference, but also how the ventral visual stream might be "wired up" by evolution (a model's "birth" state) and by developmental learning (a model's updates based on visual experience).

A central goal of machine learning is the development of systems that can solve many problems in as many data domains as possible. Current architectures, however, cannot be applied beyond a small set of stereotyped settings, as they bake in domain & task assumptions or scale poorly to large inputs or outputs. In this work, we propose Perceiver IO, a general-purpose architecture that handles data from arbitrary settings while scaling linearly with the size of inputs and outputs. Our model augments the Perceiver with a flexible querying mechanism that enables outputs of various sizes and semantics, doing away with the need for task-specific architecture engineering. The same architecture achieves strong results on tasks spanning natural language and visual understanding, multi-task and multi-modal reasoning, and StarCraft II. As highlights, Perceiver IO outperforms a Transformer-based BERT baseline on the GLUE language benchmark despite removing input tokenization and achieves state-of-the-art performance on Sintel optical flow estimation with no explicit mechanisms for multiscale correspondence.

Research on generalization bounds for deep networks seeks to give ways to predict test error using just the training dataset and the network parameters. While generalization bounds can give many insights about architecture design, training algorithms etc., what they do not currently do is yield good predictions for actual test error. A recently introduced Predicting Generalization in Deep Learning competition aims to encourage discovery of methods to better predict test error. The current paper investigates a simple idea: can test error be predicted using {\em synthetic data,} produced using a Generative Adversarial Network (GAN) that was trained on the same training dataset? Upon investigating several GAN models and architectures, we find that this turns out to be the case. In fact, using GANs pre-trained on standard datasets, the test error can be predicted without requiring any additional hyper-parameter tuning. This result is surprising because GANs have well-known limitations (e.g. mode collapse) and are known to not learn the data distribution accurately. Yet the generated samples are good enough to substitute for test data. Several additional experiments are presented to explore reasons why GANs do well at this task. In addition to a new approach for predicting generalization, the counter-intuitive phenomena presented in our work may also call for a better understanding of GANs' strengths and limitations.

We introduce a new family of particle evolution samplers suitable for constrained domains and non-Euclidean geometries. Stein Variational Mirror Descent and Mirrored Stein Variational Gradient Descent minimize the Kullback-Leibler (KL) divergence to constrained target distributions by evolving particles in a dual space defined by a mirror map. Stein Variational Natural Gradient exploits non-Euclidean geometry to more efficiently minimize the KL divergence to unconstrained targets. We derive these samplers from a new class of mirrored Stein operators and adaptive kernels developed in this work. We demonstrate that these new samplers yield accurate approximations to distributions on the simplex, deliver valid confidence intervals in post-selection inference, and converge more rapidly than prior methods in large-scale unconstrained posterior inference. Finally, we establish the convergence of our new procedures under verifiable conditions on the target distribution.

Noise-contrastive estimation (NCE) is a statistically consistent method for learning unnormalized probabilistic models. It has been empirically observed that the choice of the noise distribution is crucial for NCE’s performance. However, such observation has never been made formal or quantitative. In fact, it is not even clear whether the difficulties arising from a poorly chosen noise distribution are statistical or algorithmic in nature. In this work, we formally pinpoint reasons for NCE’s poor performance when an inappropriate noise distribution is used. Namely, we prove these challenges arise due to an ill-behaved (more precisely, flat) loss landscape. To address this, we introduce a variant of NCE called \emph{eNCE} which uses an exponential loss and for which \emph{normalized gradient descent} addresses the landscape issues \emph{provably} when the target and noise distributions are in a given exponential family.

Recently, Vision Transformers (ViTs) have shown competitive performance on image recognition while requiring less vision-specific inductive biases. In this paper, we investigate if such performance can be extended to image generation. To this end, we integrate the ViT architecture into generative adversarial networks (GANs). For ViT discriminators, we observe that existing regularization methods for GANs interact poorly with self-attention, causing serious instability during training. To resolve this issue, we introduce several novel regularization techniques for training GANs with ViTs. For ViT generators, we examine architectural choices for latent and pixel mapping layers to faciliate convergence. Empirically, our approach, named ViTGAN, achieves comparable performance to the leading CNN- based GAN models on three datasets: CIFAR-10, CelebA, and LSUN bedroom.

Among a wide range of success of deep learning, convolutional neural networks have been extensively utilized in several tasks such as speech recognition, image processing, and natural language processing, which require inputs with large dimensions. Several studies have investigated function estimation capability of deep learning, but most of them have assumed that the dimensionality of the input is much smaller than the sample size. However, for typical data in applications such as those handled by the convolutional neural networks described above, the dimensionality of inputs is relatively high or even infinite. In this paper, we investigate the approximation and estimation errors of the (dilated) convolutional neural networks when the input is infinite dimensional. Although the approximation and estimation errors of neural networks are affected by the curse of dimensionality in the existing analyses for typical function spaces such as the \Holder and Besov spaces, we show that, by considering anisotropic smoothness, they can alleviate exponential dependency on the dimensionality but they only depend on the smoothness of the target functions. Our theoretical analysis supports the great practical success of convolutional networks. Furthermore, we show that the dilated convolution is advantageous when the smoothness of the target function has a sparse structure.

Recently over-smoothing phenomenon of Transformer-based models is observed in both vision and language fields. However, no existing work has delved deeper to further investigate the main cause of this phenomenon. In this work, we make the attempt to analyze the over-smoothing problem from the perspective of graph, where such problem was first discovered and explored. Intuitively, the self-attention matrix can be seen as a normalized adjacent matrix of a corresponding graph. Based on the above connection, we provide some theoretical analysis and find that layer normalization plays a key role in the over-smoothing issue of Transformer-based models. Specifically, if the standard deviation of layer normalization is sufficiently large, the output of Transformer stacks will converge to a specific low-rank subspace and result in over-smoothing. To alleviate the over-smoothing problem, we consider hierarchical fusion strategies, which combine the representations from different layers adaptively to make the output more diverse. Extensive experiment results on various data sets illustrate the effect of our fusion method.

Message-passing neural networks (MPNNs) are the leading architecture for deep learning on graph-structured data, in large part due to their simplicity and scalability. Unfortunately, it was shown that these architectures are limited in their expressive power. This paper proposes a novel framework called Equivariant Subgraph Aggregation Networks (ESAN) to address this issue. Our main observation is that while two graphs may not be distinguishable by an MPNN, they often contain distinguishable subgraphs. Thus, we propose to represent each graph as a set of subgraphs derived by some predefined policy, and to process it using a suitable equivariant architecture. We develop novel variants of the 1-dimensional Weisfeiler-Leman (1-WL) test for graph isomorphism, and prove lower bounds on the expressiveness of ESAN in terms of these new WL variants. We further prove that our approach increases the expressive power of both MPNNs and more expressive architectures. Moreover, we provide theoretical results that describe how design choices such as the subgraph selection policy and equivariant neural architecture affect our architecture's expressive power. To deal with the increased computational cost, we propose a subgraph sampling scheme, which can be viewed as a stochastic version of our framework. A comprehensive set of experiments on real and synthetic datasets demonstrates that our framework improves the expressive power and overall performance of popular GNN architectures.

Exploration remains a central challenge for reinforcement learning (RL). Virtually all existing methods share the feature of a *monolithic* behaviour policy that changes only gradually (at best). In contrast, the exploratory behaviours of animals and humans exhibit a rich diversity, namely including forms of *switching* between modes. This paper presents an initial study of mode-switching, non-monolithic exploration for RL. We investigate different modes to switch between, at what timescales it makes sense to switch, and what signals make for good switching triggers. We also propose practical algorithmic components that make the switching mechanism adaptive and robust, which enables flexibility without an accompanying hyper-parameter-tuning burden. Finally, we report a promising initial study on Atari, using two-mode exploration and switching at sub-episodic time-scales.