arXiv subjects

Christopher De Sa

Publications and source records attributed to Christopher De Sa.

At least 55 records · Page 3Linked to original sources

arXiv2022

Low-Precision Stochastic Gradient Langevin Dynamics

While low-precision optimization has been widely used to accelerate deep learning, low-precision sampling remains largely unexplored. As a consequence, sampling is simply infeasible in many large-scale scenarios, despite providing remarkable benefits to generalization and uncertainty estimation for neural networks. In this paper, we provide the first study of low-precision Stochastic Gradient Langevin Dynamics (SGLD), showing that its costs can be significantly reduced without sacrificing performance, due to its intrinsic ability to handle system noise. We prove that the convergence of low-precision SGLD with full-precision gradient accumulators is less affected by the quantization error than its SGD counterpart in the strongly convex setting. To further enable low-precision gradient accumulators, we develop a new quantization function for SGLD that preserves the variance in each update step. We demonstrate that low-precision SGLD achieves comparable performance to full-precision SGLD with only 8 bits on a variety of deep learning tasks.

cs.LG↗

arXiv2022

Structured Pruning is All You Need for Pruning CNNs at Initialization

Pruning is a popular technique for reducing the model size and computational cost of convolutional neural networks (CNNs). However, a slow retraining or fine-tuning procedure is often required to recover the accuracy loss caused by pruning. Recently, a new research direction on weight pruning, pruning-at-initialization (PAI), is proposed to directly prune CNNs before training so that fine-tuning or retraining can be avoided. While PAI has shown promising results in reducing the model size, existing approaches rely on fine-grained weight pruning which requires unstructured sparse matrix computation, making it difficult to achieve real speedup in practice unless the sparsity is very high. This work is the first to show that fine-grained weight pruning is in fact not necessary for PAI. Instead, the layerwise compression ratio is the main critical factor to determine the accuracy of a CNN model pruned at initialization. Based on this key observation, we propose PreCropping, a structured hardware-efficient model compression scheme. PreCropping directly compresses the model at the channel level following the layerwise compression ratio. Compared to weight pruning, the proposed scheme is regular and dense in both storage and computation without sacrificing accuracy. In addition, since PreCropping compresses CNNs at initialization, the computational and memory costs of CNNs are reduced for both training and inference on commodity hardware. We empirically demonstrate our approaches on several modern CNN architectures, including ResNet, ShuffleNet, and MobileNet for both CIFAR-10 and ImageNet.

cs.CV↗

arXiv2022

Maximizing Communication Efficiency for Large-scale Training via 0/1 Adam

1-bit gradient compression and local steps are two representative techniques that enable drastic communication reduction in distributed SGD. Their benefits, however, remain an open question on Adam-based large model pre-training (e.g. BERT and GPT). In this paper, we demonstrate the non-linearity in Adam causes slow convergence even when 1-bit compression or local steps are individually applied. To alleviate this limitation, we propose 0/1 Adam that linearizes each Adam step via approximating its optimizer states using their stale estimates and linear correlation. 0/1 Adam performs an Adam-like step to preserve the adaptivity, while its linearity allows utilizing 1-bit compression and local steps simultaneously for wall-clock time speed up. We provide convergence guarantee for 0/1 Adam on smooth non-convex objectives. On various large-scale benchmarks such as BERT-Base, BERT-Large, GPT-2 pre-training and ImageNet, we demonstrate on up to 128 GPUs that 0/1 Adam is able to reduce up to 87% of data volume, 54% of communication rounds, and achieve up to 2$\times$ higher training throughput and end-to-end training time reduction compared to the state-of-the-art baseline 1-bit Adam; while enjoying the same statistical convergence speed and end task model accuracy on GLUE dataset and ImageNet validation set.

cs.LG↗

arXiv2022

How Low Can We Go: Trading Memory for Error in Low-Precision Training

Low-precision arithmetic trains deep learning models using less energy, less memory and less time. However, we pay a price for the savings: lower precision may yield larger round-off error and hence larger prediction error. As applications proliferate, users must choose which precision to use to train a new model, and chip manufacturers must decide which precisions to manufacture. We view these precision choices as a hyperparameter tuning problem, and borrow ideas from meta-learning to learn the tradeoff between memory and error. In this paper, we introduce Pareto Estimation to Pick the Perfect Precision (PEPPP). We use matrix factorization to find non-dominated configurations (the Pareto frontier) with a limited number of network evaluations. For any given memory budget, the precision that minimizes error is a point on this frontier. Practitioners can use the frontier to trade memory for error and choose the best precision for their goals.

cs.LG↗

arXiv2022

Optimal Complexity in Decentralized Training

Decentralization is a promising method of scaling up parallel machine learning systems. In this paper, we provide a tight lower bound on the iteration complexity for such methods in a stochastic non-convex setting. Our lower bound reveals a theoretical gap in known convergence rates of many existing decentralized training algorithms, such as D-PSGD. We prove by construction this lower bound is tight and achievable. Motivated by our insights, we further propose DeTAG, a practical gossip-style decentralized algorithm that achieves the lower bound with only a logarithm gap. Empirically, we compare DeTAG with other decentralized algorithms on image classification tasks, and we show DeTAG enjoys faster convergence compared to baselines, especially on unshuffled data and in sparse networks.

cs.LG↗

arXiv2022

Equivariant Manifold Flows

Tractably modelling distributions over manifolds has long been an important goal in the natural sciences. Recent work has focused on developing general machine learning models to learn such distributions. However, for many applications these distributions must respect manifold symmetries -- a trait which most previous models disregard. In this paper, we lay the theoretical foundations for learning symmetry-invariant distributions on arbitrary manifolds via equivariant manifold flows. We demonstrate the utility of our approach by using it to learn gauge invariant densities over $SU(n)$ in the context of quantum field theory.

stat.ML↗

arXiv2021

Hyperparameter Optimization Is Deceiving Us, and How to Stop It

Recent empirical work shows that inconsistent results based on choice of hyperparameter optimization (HPO) configuration are a widespread problem in ML research. When comparing two algorithms J and K searching one subspace can yield the conclusion that J outperforms K, whereas searching another can entail the opposite. In short, the way we choose hyperparameters can deceive us. We provide a theoretical complement to this prior work, arguing that, to avoid such deception, the process of drawing conclusions from HPO should be made more rigorous. We call this process epistemic hyperparameter optimization (EHPO), and put forth a logical framework to capture its semantics and how it can lead to inconsistent conclusions about performance. Our framework enables us to prove EHPO methods that are guaranteed to be defended against deception, given bounded compute time budget t. We demonstrate our framework's utility by proving and empirically validating a defended variant of random search.

cs.LG↗

arXiv2021

Accuracy-Efficiency Trade-Offs and Accountability in Distributed ML Systems

Trade-offs between accuracy and efficiency pervade law, public health, and other non-computing domains, which have developed policies to guide how to balance the two in conditions of uncertainty. While computer science also commonly studies accuracy-efficiency trade-offs, their policy implications remain poorly examined. Drawing on risk assessment practices in the US, we argue that, since examining these trade-offs has been useful for guiding governance in other domains, we need to similarly reckon with these trade-offs in governing computer systems. We focus our analysis on distributed machine learning systems. Understanding the policy implications in this area is particularly urgent because such systems, which include autonomous vehicles, tend to be high-stakes and safety-critical. We 1) describe how the trade-off takes shape for these systems, 2) highlight gaps between existing US risk assessment standards and what these systems require to be properly assessed, and 3) make specific calls to action to facilitate accountability when hypothetical risks concerning the accuracy-efficiency trade-off become realized as accidents in the real world. We close by discussing how such accountability mechanisms encourage more just, transparent governance aligned with public values.

cs.CY↗

arXiv2021

Tecnologica cosa: Modeling Storyteller Personalities in Boccaccio's Decameron

We explore Boccaccio's Decameron to see how digital humanities tools can be used for tasks that have limited data in a language no longer in contemporary use: medieval Italian. We focus our analysis on the question: Do the different storytellers in the text exhibit distinct personalities? To answer this question, we curate and release a dataset based on the authoritative edition of the text. We use supervised classification methods to predict storytellers based on the stories they tell, confirming the difficulty of the task, and demonstrate that topic modeling can extract thematic storyteller "profiles."

cs.CL↗

arXiv2021

Differentiating through the Fréchet Mean

Recent advances in deep representation learning on Riemannian manifolds extend classical deep learning operations to better capture the geometry of the manifold. One possible extension is the Fréchet mean, the generalization of the Euclidean mean; however, it has been difficult to apply because it lacks a closed form with an easily computable derivative. In this paper, we show how to differentiate through the Fréchet mean for arbitrary Riemannian manifolds. Then, focusing on hyperbolic space, we derive explicit gradient expressions and a fast, accurate, and hyperparameter-free Fréchet mean solver. This fully integrates the Fréchet mean into the hyperbolic neural network pipeline. To demonstrate this integration, we present two case studies. First, we apply our Fréchet mean to the existing Hyperbolic Graph Convolutional Network, replacing its projected aggregation to obtain state-of-the-art results on datasets with high hyperbolicity. Second, to demonstrate the Fréchet mean's capacity to generalize Euclidean neural network operations, we develop a hyperbolic batch normalization method that gives an improvement parallel to the one observed in the Euclidean setting.

stat.ML↗

arXiv2021

Meta-Learning Divergences of Variational Inference

Variational inference (VI) plays an essential role in approximate Bayesian inference due to its computational efficiency and broad applicability. Crucial to the performance of VI is the selection of the associated divergence measure, as VI approximates the intractable distribution by minimizing this divergence. In this paper we propose a meta-learning algorithm to learn the divergence metric suited for the task of interest, automating the design of VI methods. In addition, we learn the initialization of the variational parameters without additional cost when our method is deployed in the few-shot learning scenarios. We demonstrate our approach outperforms standard VI on Gaussian mixture distribution approximation, Bayesian neural network regression, image generation with variational autoencoders and recommender systems with a partial variational autoencoder.

cs.LG↗

arXiv2021

Variance Reduced Training with Stratified Sampling for Forecasting Models

In large-scale time series forecasting, one often encounters the situation where the temporal patterns of time series, while drifting over time, differ from one another in the same dataset. In this paper, we provably show under such heterogeneity, training a forecasting model with commonly used stochastic optimizers (e.g. SGD) potentially suffers large variance on gradient estimation, and thus incurs long-time training. We show that this issue can be efficiently alleviated via stratification, which allows the optimizer to sample from pre-grouped time series strata. For better trading-off gradient variance and computation complexity, we further propose SCott (Stochastic Stratified Control Variate Gradient Descent), a variance reduced SGD-style optimizer that utilizes stratified sampling via control variate. In theory, we provide the convergence guarantee of SCott on smooth non-convex objectives. Empirically, we evaluate SCott and other baseline optimizers on both synthetic and real-world time series forecasting problems, and demonstrate SCott converges faster with respect to both iterations and wall clock time.

cs.LG↗

arXiv2021

Low-Precision Reinforcement Learning: Running Soft Actor-Critic in Half Precision

Low-precision training has become a popular approach to reduce compute requirements, memory footprint, and energy consumption in supervised learning. In contrast, this promising approach has not yet enjoyed similarly widespread adoption within the reinforcement learning (RL) community, partly because RL agents can be notoriously hard to train even in full precision. In this paper we consider continuous control with the state-of-the-art SAC agent and demonstrate that a naïve adaptation of low-precision methods from supervised learning fails. We propose a set of six modifications, all straightforward to implement, that leaves the underlying agent and its hyperparameters unchanged but improves the numerical stability dramatically. The resulting modified SAC agent has lower memory and compute requirements while matching full-precision rewards, demonstrating that low-precision training can substantially accelerate state-of-the-art RL without parameter tuning.

cs.LG↗

arXiv2021

OverQ: Opportunistic Outlier Quantization for Neural Network Accelerators

Outliers in weights and activations pose a key challenge for fixed-point quantization of neural networks. While they can be addressed by fine-tuning, this is not practical for ML service providers (e.g., Google or Microsoft) who often receive customer models without training data. Specialized hardware for handling activation outliers can enable low-precision neural networks, but at the cost of nontrivial area overhead. We instead propose overwrite quantization (OverQ), a lightweight hardware technique that opportunistically increases bitwidth for activation outliers by overwriting nearby zeros. It has two major modes of operation: range overwrite and precision overwrite. Range overwrite reallocates bits to increase the range of outliers, while precision overwrite reuses zeros to increase the precision of non-outlier values. Combining range overwrite with a simple cascading logic, we handle the vast majority of outliers to significantly improve model accuracy at low bitwidth. Our experiments show that with modest cascading, we can consistently handle over 90% of outliers and achieve +5% ImageNet Top-1 accuracy on a quantized ResNet-50 at 4 bits. Our ASIC prototype shows OverQ can be implemented efficiently on top of existing weight-stationary systolic arrays with small area increases per processing element. We imagine this technique can complement modern DNN accelerator designs to provide small increases in accuracy with insignificant area overhead.

cs.LG↗

arXiv2021

Revisiting BFloat16 Training

State-of-the-art generic low-precision training algorithms use a mix of 16-bit and 32-bit precision, creating the folklore that 16-bit hardware compute units alone are not enough to maximize model accuracy. As a result, deep learning accelerators are forced to support both 16-bit and 32-bit floating-point units (FPUs), which is more costly than only using 16-bit FPUs for hardware design. We ask: can we train deep learning models only with 16-bit floating-point units, while still matching the model accuracy attained by 32-bit training? Towards this end, we study 16-bit-FPU training on the widely adopted BFloat16 unit. While these units conventionally use nearest rounding to cast output to 16-bit precision, we show that nearest rounding for model weight updates often cancels small updates, which degrades the convergence and model accuracy. Motivated by this, we study two simple techniques well-established in numerical analysis, stochastic rounding and Kahan summation, to remedy the model accuracy degradation in 16-bit-FPU training. We demonstrate that these two techniques can enable up to 7% absolute validation accuracy gain in 16-bit-FPU training. This leads to 0.1% lower to 0.2% higher validation accuracy compared to 32-bit training across seven deep learning applications.

cs.LG↗

arXiv2020

Asymptotically Optimal Exact Minibatch Metropolis-Hastings

Metropolis-Hastings (MH) is a commonly-used MCMC algorithm, but it can be intractable on large datasets due to requiring computations over the whole dataset. In this paper, we study minibatch MH methods, which instead use subsamples to enable scaling. We observe that most existing minibatch MH methods are inexact (i.e. they may change the target distribution), and show that this inexactness can cause arbitrarily large errors in inference. We propose a new exact minibatch MH method, TunaMH, which exposes a tunable trade-off between its batch size and its theoretically guaranteed convergence rate. We prove a lower bound on the batch size that any minibatch MH method must use to retain exactness while guaranteeing fast convergence-the first such bound for minibatch MH-and show TunaMH is asymptotically optimal in terms of the batch size. Empirically, we show TunaMH outperforms other exact minibatch MH methods on robust linear regression, truncated Gaussian mixtures, and logistic regression.

cs.LG↗

arXiv2020

Moniqua: Modulo Quantized Communication in Decentralized SGD

Running Stochastic Gradient Descent (SGD) in a decentralized fashion has shown promising results. In this paper we propose Moniqua, a technique that allows decentralized SGD to use quantized communication. We prove in theory that Moniqua communicates a provably bounded number of bits per iteration, while converging at the same asymptotic rate as the original algorithm does with full-precision communication. Moniqua improves upon prior works in that it (1) requires zero additional memory, (2) works with 1-bit quantization, and (3) is applicable to a variety of decentralized algorithms. We demonstrate empirically that Moniqua converges faster with respect to wall clock time than other quantized decentralized algorithms. We also show that Moniqua is robust to very low bit-budgets, allowing 1-bit-per-parameter communication without compromising validation accuracy when training ResNet20 and ResNet110 on CIFAR10.

cs.LG↗

arXiv2020

Neural Manifold Ordinary Differential Equations

To better conform to data geometry, recent deep generative modelling techniques adapt Euclidean constructions to non-Euclidean spaces. In this paper, we study normalizing flows on manifolds. Previous work has developed flow models for specific cases; however, these advancements hand craft layers on a manifold-by-manifold basis, restricting generality and inducing cumbersome design constraints. We overcome these issues by introducing Neural Manifold Ordinary Differential Equations, a manifold generalization of Neural ODEs, which enables the construction of Manifold Continuous Normalizing Flows (MCNFs). MCNFs require only local geometry (therefore generalizing to arbitrary manifolds) and compute probabilities with continuous change of variables (allowing for a simple and expressive flow construction). We find that leveraging continuous manifold dynamics produces a marked improvement for both density estimation and downstream tasks.

stat.ML↗