Jump to Content
Jaehoon Lee

Jaehoon Lee

Jaehoon Lee is a Research Scientist at Google Brain team. His main research interests is fundamental understanding of deep neural networks; actively working on the infinite-width limit of neural networks and their correspondence to the kernel methods. In 2017, he joined Google and started a research career in machine learning as part of the Google Brain Residency program. Before that he was a postdoctoral fellow at University of British Columbia from 2015-2017 working on theoretical high energy physics. Jaehoon obtained his PhD in physics at the Center for Theoretical Physics, Massachusetts Institute of Technology (MIT) in 2015. He served as co-organizer of ICML 2019 workshop on Theoretical Physics for Deep Learning and Aspen Center for Physics 2019 winter conference on Theoretical Physics for Machine Learning.
Authored Publications
Google Publications
Other Publications
Sort By
  • Title
  • Title, descending
  • Year
  • Year, descending
    Fast Neural Kernel Embeddings for General Activations
    Insu Han
    Amir Zandieh
    Amin Karbasi
    NeurIPS 2022 (2022) (to appear)
    Preview abstract Infinite width limit has shed light on generalization and optimization aspects of deep learning by establishing connections between neural networks and kernel methods. Despite their importance, the utility of these kernel methods was limited in large-scale learning settings due to their (super-)quadratic runtime and memory complexities. Moreover, most prior works on neural kernels have focused on the ReLU activation, mainly due to its popularity but also due to the difficulty of computing such kernels for general activations. In this work, we overcome such difficulties by providing methods to work with general activations. First, we compile and expand the list of activation functions admitting exact dual activation expressions to compute neural kernels. When the exact computation is unknown, we present methods to effectively approximate them. We propose a fast sketching method that approximates any multi-layered Neural Network Gaussian Process (NNGP) kernel and Neural Tangent Kernel (NTK) matrices for a wide range of activation functions, going beyond the commonly analyzed ReLU activation. This is done by showing how to approximate the neural kernels using the truncated Hermite expansion of any desired activation functions. While most prior works require data points on the unit sphere, our methods do not suffer from such limitations and are applicable to any dataset of points in ℝ^d. Furthermore, we provide a subspace embedding for NNGP and NTK matrices with near input-sparsity runtime and near-optimal target dimension which applies to any homogeneous dual activation functions with rapidly convergent Taylor expansion. Empirically, with respect to exact convolutional NTK (CNTK) computation, our method achieves 106× speedup for approximate CNTK of a 5-layer Myrtle network on CIFAR-10 dataset. View details
    Preview abstract Language models demonstrate both quantitative improvement and new qualitative capabilities with increasing scale. Despite their potentially transformative impact, these new capabilities are as yet poorly characterized. In order to direct future research, prepare for disruptive new model capabilities, and ameliorate socially harmful effects, it is vital that we understand the present and near-future capabilities and limitations of language models. To address this challenge, we introduce the Beyond the Imitation Game benchmark (BIG-bench). BIG-bench consists of 207 tasks, contributed by over 400 authors across 132 institutions. Task topics are diverse, drawing problems from linguistics, childhood development, math, common sense reasoning, biology, physics, social bias, software development, and beyond. BIG-bench focuses on capabilities that are believed to be beyond current language models. We evaluate the behavior of OpenAI's GPT models, Google-internal dense transformer architectures, and Switch-style sparse transformers on BIG-bench, across model sizes spanning millions to hundreds of billions of parameters. A team of human experts further performed all tasks, to provide a strong baseline. Findings include: model performance and calibration both improve with scale, but are poor in absolute terms (and when compared with human performance); model performance is remarkably similar across model classes; tasks that improve gradually and predictably commonly involve a large knowledge or memorization component, whereas tasks that exhibit ``breakthrough'' behavior at a critical scale often involve a significant reasoning or algorithmic component; social bias typically increases with scale in settings with ambiguous context, but this can be improved with prompting. View details
    Preview abstract The effectiveness of machine learning algorithms arises from being able to extract useful features from large amounts of data. As model and dataset sizes increase, dataset distillation methods that compress large datasets into significantly smaller yet highly performant ones will become valuable in terms of training efficiency and useful feature extraction. To that end, we apply a novel distributed kernel based meta-learning framework to achieve state-of-the-art results for dataset distillation using infinitely wide convolutional neural networks. For instance, using only 10 datapoints (0.02% of original dataset), we obtain over 64% test accuracy on CIFAR-10 image classfication task, a dramatic improvement over the previous best test accuracy of 40%. Our state-of-the-art results extend across many other settings for MNIST, Fashion-MNIST, CIFAR-10, CIFAR-100, and SVHN. Furthermore, we perform some preliminary analyses of our distilled datasets to shed light on how they differ from naturally occurring data. View details
    Dataset Meta-Learning from Kernel Ridge-Regression
    Timothy Chieu Nguyen
    Zhourong Chen
    ICLR 2021
    Preview abstract One of the most fundamental aspects of any machine learning algorithm is the training data used by the algorithm. We introduce the novel concept of -approximation of datasets, obtaining datasets which are much smaller than or are significant corruptions of the original training data while maintaining similar performance. We introduce a meta-learning algorithm Kernel Inducing Points (KIP) for obtaining such remarkable datasets, drawing inspiration from recent developments in the correspondence between infinitely-wide neural networks and kernel ridge-regression (KRR). For KRR tasks, we demonstrate that KIP can compress datasets by one or two orders of magnitude, significantly improving previous dataset distillation and subset selection methods while obtaining state of the art results for MNIST and CIFAR10 classification. Furthermore, our KIP-learned datasets are transferable to the training of finite-width neural networks even beyond the lazy-training regime. Consequently, we obtain state of the art results for neural network dataset distillation with potential applications to privacy-preservation. View details
    Exploring the Uncertainty Properties of Neural Networks’ Implicit Priors in the Infinite-Width Limit
    Jeffrey Pennington
    International Conference on Learning Representations, 2021, International Conference on Learning Representations, 2021, 27 pages
    Preview abstract Modern deep learning models have achieved great success in predictive accuracy for many data modalities. However, their application to many real-world tasks is restricted by poor uncertainty estimates, such as overconfidence on out-of-distribution (OOD) data and ungraceful failing under distributional shift. Previous benchmarks have found that ensembles of neural networks (NNs) are typically the best calibrated models on OOD data. Inspired by this, we leverage recent theoretical advances that characterize the function-space prior of an infinitely-wide NN as a Gaussian process, termed the neural network Gaussian process (NNGP). We use the NNGP with a softmax link function to build a probabilistic model for multi-class classification and marginalize over the latent Gaussian outputs to sample from the posterior. This gives us a better understanding of the implicit prior NNs place on function space and allows a direct comparison of the calibration of the NNGP and its finite-width analogue. We also examine the calibration of previous approaches to classification with the NNGP, which treat classification problems as regression to the one-hot labels. In this case the Bayesian posterior is exact, and we compare several heuristics to generate a categorical distribution over classes. We find these methods are well calibrated under distributional shift. Finally, we consider an infinite-width final layer in conjunction with a pre-trained embedding. This replicates the important practical use case of transfer learning and allows scaling to significantly larger datasets. As well as achieving competitive predictive accuracy, this approach is better calibrated than its finite width analogue. View details
    Preview abstract The test loss of well-trained neural networks often follows precise power-law scaling relations with either the size of the training dataset or the number of parameters in the network. We propose a theory that explains and connects these scaling laws. We identify variance-limited and resolution-limited scaling behavior for both model and dataset size, for a total of four scaling regimes. The variance-limited scaling follows simply from the existence of a well-behaved infinite data or infinite width limit, while the resolution-limited regime can be explained by positing that models are effectively resolving a smooth data manifold. In the large width limit, this can be equivalently obtained from the spectrum of certain kernels, and we present evidence that large width and large dataset resolution-limited scaling exponents are related by a duality. We exhibit all four scaling regimes in the controlled setting of large random feature and pre-trained models and test the predictions empirically on a range of standard architectures and datasets. We also observe several empirical relationships between datasets and scaling exponents: super-classing image classifiers does not change exponents, while changing input distribution (via changing datasets or adding noise) has a strong effect. We further explore the effect of architecture aspect ratio on scaling exponents. View details
    Preview abstract We perform a careful, thorough, and large scale empirical study of the correspondence between wide neural networks and kernel methods. By doing so, we resolve a variety of open questions related to the study of infinitely wide neural networks. Our experimental results include: kernel methods outperform fully connected finite width networks, but underperform convolutional finite width networks; neural network Gaussian process (NNGP) kernels frequently outperform neural tangent (NT) kernels; ensembles of finite networks have reduced posterior variance and behave similarly to infinite networks; weight decay and the use of a large learning rate break the correspondence of finite and infinite networks; the NTK parameterization outperforms the standard parameterization for finite width networks; finite network performance depends non-monotonically on width in ways not captured by double descent phenomena. Our experiments additionally motivate an improved layer-wise scaling for weight decay which improves generalization in finite-width networks. Finally, we develop improved best practices for using NNGP and NT kernels for prediction. Using these best practices we achieve state-of-the-art results for non-trainable kernels on CIFAR-10 classification tasks. View details
    Preview abstract Neural Tangents is a library designed to enable research into infinite-width neural networks. It provides a high-level API for specifying complex and hierarchical neural network architectures. These networks can then be trained and evaluated either at finite-width as usual or in their infinite-width limit. Infinite-width networks can be trained analytically using exact Bayesian inference or using gradient descent via the Neural Tangent Kernel. Additionally, Neural Tangents provides tools to study gradient descent training dynamics of wide but finite networks in either function space or weight space. The entire library runs out-of-the-box on CPU, GPU, or TPU. All computations can be automatically distributed over multiple accelerators with near-linear scaling in the number of devices. Neural Tangents is available at https://github.com/google/neural-tangents We also provide an accompanying interactive Colab notebook at https://colab.sandbox.google.com/github/neural-tangents/neural-tangents/blob/master/notebooks/neural_tangents_cookbook.ipynb View details
    Towards NNGP-guided Neural Architecture Search
    Daiyi Peng
    Daniel S. Park
    Jascha Sohl-dickstein
    ArXiv (2020)
    Preview abstract Bayesian inference in the parameter space of deep neural networks can be approximated by Gaussian processes (GPs). While the exact kernels of these GPs are known for a class of models, computation for competitive architectures are often expensive or intractable. One can obtain approximation of these kernels through Monte-Carlo estimation using finite networks at initialization. Monte-Carlo neural network Gaussian process (NNGP) training and inference are orders-of-magnitude cheaper in FLOPs compared to the gradient-based counter-parts when the dataset size is small. Since NNGP inference provides a cheap measure of performance of the network, we investigate its potential as a signal for neural architecture search (NAS). We compute the NNGP performance of approximately 423k networks in the NAS-bench 101 dataset on CIFAR-10 and compare its utility against conventional performance measures obtained by shortened gradient-based training. We carry out a similar analysis on 10k randomly sampled networks in the mobile neural architecture search (MNAS) space for ImageNet. We discover comparative advantages of NNGP-based metrics, and discuss potential applications. In particular, we propose that NNGP performance is an inexpensive signal independent of metrics obtained from training that can either be used for reducing big search spaces, or improving training-based performance measures. View details
    Preview abstract There is a previously identified equivalence between wide fully connected neural networks (FCNs) and Gaussian processes (GPs). This equivalence enables, for instance, test set predictions that would have resulted from a fully Bayesian, infinitely wide trained FCN to be computed without ever instantiating the FCN, but by instead evaluating the corresponding GP. In this work, we derive an analogous equivalence for multi-layer convolutional neural networks (CNNs) both with and without pooling layers, and achieve state of the art results on CIFAR10 for GPs without trainable kernels. We also introduce a Monte Carlo method to estimate the GP corresponding to a given neural network architecture, even in cases where the analytic form has too many terms to be computationally feasible. Surprisingly, in the absence of pooling layers, the GPs corresponding to CNNs with and without weight sharing are identical. As a consequence, translation equivariance, beneficial in finite channel CNNs trained with stochastic gradient descent (SGD), is guaranteed to play no role in the Bayesian treatment of the infinite channel limit – a qualitative difference between the two regimes that is not present in the FCN case. We confirm experimentally, that while in some scenarios the performance of SGD-trained finite CNNs approaches that of the corresponding GPs as the channel count increases, with careful tuning SGD-trained CNNs can significantly outperform their corresponding GPs, suggesting advantages from SGD training compared to fully Bayesian parameter estimation. View details
    Preview abstract A longstanding goal in deep learning research has been to precisely characterize training and generalization. However, the often complex loss landscapes of neural networks have made a theory of learning dynamics elusive. In this work, we show that for wide neural networks the learning dynamics simplify considerably and that, in the infinite width limit, they are governed by a linear model obtained from the first-order Taylor expansion of the network around its initial parameters. Furthermore, mirroring the correspondence between wide Bayesian neural networks and Gaussian processes, gradient-based training of wide neural networks with a squared loss produces test set predictions drawn from a Gaussian process with a particular compositional kernel. While these theoretical results are only exact in the infinite width limit, we nevertheless find excellent empirical agreement between the predictions of the original network and those of the linearized version even for finite practically-sized networks. This agreement is robust across different architectures, optimization methods, and loss functions. View details
    Deep Neural Networks as Gaussian Processes
    Sam Schoenholz
    Jeffrey Pennington
    Jascha Sohl-dickstein
    ICLR (2018)
    Preview abstract It has long been known that a single-layer fully-connected neural network with an i.i.d. prior over its parameters is equivalent to a Gaussian process (GP), in the limit of infinite network width. This correspondence enables exact Bayesian inference for infinite width neural networks on regression tasks by means of evaluating the corresponding GP. Recently, kernel functions which mimic multi-layer random neural networks have been developed, but only outside of a Bayesian framework. As such, previous work has not identified that these kernels can be used as covariance functions for GPs and allow fully Bayesian prediction with a deep neural network. In this work, we derive the exact equivalence between infinitely wide deep networks and GPs. We further develop a computationally efficient pipeline to compute the covariance function for these GPs. We then use the resulting GPs to perform Bayesian inference for wide deep neural networks on MNIST and CIFAR10. We observe that trained neural network accuracy approaches that of the corresponding GP with increasing layer width, and that the GP uncertainty is strongly correlated with trained network prediction error. We further find that test performance increases as finite-width trained networks are made wider and more similar to a GP, and thus that GP predictions typically outperform those of finite-width networks. Finally we connect the performance of these GPs to the recent theory of signal propagation in random neural networks. View details
    Preview abstract Recent hardware developments have made unprecedented amounts of data parallelism available for accelerating neural network training. Among the simplest ways to harness next-generation accelerators is to increase the batch size in standard mini-batch neural network training algorithms. In this work, we aim to experimentally characterize the effects of increasing the batch size on training time, as measured by the number of steps necessary to reach a goal out-of-sample error. Eventually, increasing the batch size will no longer reduce the number of training steps required, but the exact relationship between the batch size and how many training steps are necessary is of critical importance to practitioners, researchers, and hardware designers alike. We study how this relationship varies with the training algorithm, model, and data set and find extremely large variation between workloads. Along the way, we reconcile disagreements in the literature on whether batch size affects model quality. Finally, we discuss the implications of our results for efforts to train neural networks much faster in the future. View details
    No Results Found