Shankar Krishnan

Jeremy M. Cohen, Behrooz Ghorbani, Shankar Krishnan et al. · deepmind

Very little is known about the training dynamics of adaptive gradient methods like Adam in deep learning. In this paper, we shed light on the behavior of these algorithms in the full-batch and sufficiently large batch settings. Specifically, we empirically demonstrate that during full-batch training, the maximum eigenvalue of the preconditioned Hessian typically equilibrates at a certain numerical value -- the stability threshold of a gradient descent algorithm. For Adam with step size $η$ and $β_1 = 0.9$, this stability threshold is $38/η$. Similar effects occur during minibatch training, especially as the batch size grows. Yet, even though adaptive methods train at the ``Adaptive Edge of Stability'' (AEoS), their behavior in this regime differs in a significant way from that of non-adaptive methods at the EoS. Whereas non-adaptive algorithms at the EoS are blocked from entering high-curvature regions of the loss landscape, adaptive gradient methods at the AEoS can keep advancing into high-curvature regions, while adapting the preconditioner to compensate. Our findings can serve as a foundation for the community's future understanding of adaptive gradient methods in deep learning.

George E. Dahl, Frank Schneider, Zachary Nado et al. · deepmind, utoronto

Training algorithms, broadly construed, are an essential part of every deep learning pipeline. Training algorithm improvements that speed up training across a wide variety of workloads (e.g., better update rules, tuning protocols, learning rate schedules, or data selection schemes) could save time, save computational resources, and lead to better, more accurate, models. Unfortunately, as a community, we are currently unable to reliably identify training algorithm improvements, or even determine the state-of-the-art training algorithm. In this work, using concrete experiments, we argue that real progress in speeding up training requires new benchmarks that resolve three basic challenges faced by empirical comparisons of training algorithms: (1) how to decide when training is complete and precisely measure training time, (2) how to handle the sensitivity of measurements to exact workload details, and (3) how to fairly compare algorithms that require hyperparameter tuning. In order to address these challenges, we introduce a new, competitive, time-to-result benchmark using multiple workloads running on fixed hardware, the AlgoPerf: Training Algorithms benchmark. Our benchmark includes a set of workload variants that make it possible to detect benchmark submissions that are more robust to workload changes than current widely-used methods. Finally, we evaluate baseline submissions constructed using various optimizers that represent current practice, as well as other optimizers that have recently received attention in the literature. These baseline results collectively demonstrate the feasibility of our benchmark, show that non-trivial gaps between methods exist, and set a provisional state-of-the-art for future benchmark submissions to try and surpass.

Nikunj Saunshi, Stefani Karp, Shankar Krishnan et al.

Given the increasing scale of model sizes, novel training strategies like gradual stacking [Gong et al., 2019, Reddi et al., 2023] have garnered interest. Stacking enables efficient training by gradually growing the depth of a model in stages and using layers from a smaller model in an earlier stage to initialize the next stage. Although efficient for training, the model biases induced by such growing approaches are largely unexplored. In this work, we examine this fundamental aspect of gradual stacking, going beyond its efficiency benefits. We propose a variant of gradual stacking called MIDAS that can speed up language model training by up to 40%. Furthermore we discover an intriguing phenomenon: MIDAS is not only training-efficient but surprisingly also has an inductive bias towards improving downstream tasks, especially tasks that require reasoning abilities like reading comprehension and math problems, despite having similar or slightly worse perplexity compared to baseline training. To further analyze this inductive bias, we construct reasoning primitives -- simple synthetic tasks that are building blocks for reasoning -- and find that a model pretrained with stacking is significantly better than standard pretraining on these primitives, with and without fine-tuning. This provides stronger and more robust evidence for this inductive bias towards reasoning. These findings of training efficiency and inductive bias towards reasoning are verified at 1B, 2B and 8B parameter language models. Finally, we conjecture the underlying reason for this inductive bias by exploring the connection of stacking to looped models and provide strong supporting empirical analysis.

Sourabh Medapati, Priya Kasimbeg, Shankar Krishnan et al.

If we want to train a neural network using any of the most popular optimization algorithms, we are immediately faced with a dilemma: how to set the various optimization and regularization hyperparameters? When computational resources are abundant, there are a variety of methods for finding good hyperparameter settings, but when resources are limited the only realistic choices are using standard default values of uncertain quality and provenance, or tuning only a couple of the most important hyperparameters via extremely limited handdesigned sweeps. Extending the idea of default settings to a modest tuning budget, Metz et al. (2020) proposed using ordered lists of well-performing hyperparameter settings, derived from a broad hyperparameter search on a large library of training workloads. However, to date, no practical and performant hyperparameter lists that generalize to representative deep learning workloads have been demonstrated. In this paper, we present hyperparameter lists for NAdamW derived from extensive experiments on the realistic workloads in the AlgoPerf: Training Algorithms benchmark. Our hyperparameter lists also include values for basic regularization techniques (i.e. weight decay, label smoothing, and dropout). In particular, our best NAdamW hyperparameter list performs well on AlgoPerf held-out workloads not used to construct it, and represents a compelling turn-key approach to tuning when restricted to five or fewer trials. It also outperforms basic learning rate/weight decay sweeps and an off-the-shelf Bayesian optimization tool when restricted to the same budget.

Saurabh Singh, Shankar Krishnan

Batch Normalization (BN) uses mini-batch statistics to normalize the activations during training, introducing dependence between mini-batch elements. This dependency can hurt the performance if the mini-batch size is too small, or if the elements are correlated. Several alternatives, such as Batch Renormalization and Group Normalization (GN), have been proposed to address this issue. However, they either do not match the performance of BN for large batches, or still exhibit degradation in performance for smaller batches, or introduce artificial constraints on the model architecture. In this paper we propose the Filter Response Normalization (FRN) layer, a novel combination of a normalization and an activation function, that can be used as a replacement for other normalizations and activations. Our method operates on each activation channel of each batch element independently, eliminating the dependency on other batch elements. Our method outperforms BN and other alternatives in a variety of settings for all batch sizes. FRN layer performs $\approx 0.7-1.0\%$ better than BN on top-1 validation accuracy with large mini-batch sizes for Imagenet classification using InceptionV3 and ResnetV2-50 architectures. Further, it performs $>1\%$ better than GN on the same problem in the small mini-batch size regime. For object detection problem on COCO dataset, FRN layer outperforms all other methods by at least $0.3-0.5\%$ in all batch size regimes.