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Atli Kosson

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7 papers

2 author rows

TMLR Journal 2025 Journal Article

Training Dynamics of the Cooldown Stage in Warmup-Stable-Decay Learning Rate Scheduler

Aleksandr Dremov
Alexander Hägele
Atli Kosson
Martin Jaggi

Learning rate scheduling is essential in transformer training, where the final annealing plays a crucial role in getting the best performance. However, the mechanisms behind this cooldown phase, with its characteristic drop in loss, remain poorly understood. To address this, we provide a comprehensive analysis focusing solely on the cooldown phase in the Warmup-Stable-Decay (WSD) learning rate scheduler. Our analysis reveals that different cooldown shapes reveal a fundamental bias-variance trade-off in the resulting models, with shapes that balance exploration and exploitation consistently outperforming alternatives. Similarly, we find substantial performance variations — comparable to those from cooldown shape selection — when tuning AdamW hyperparameters. Notably, we observe consistent improvements with higher values of $\beta_2$ during cooldown. From a loss landscape perspective, we provide visualizations of the landscape during cooldown, supporting the river valley loss perspective empirically. These findings offer practical recommendations for configuring the WSD scheduler in transformer training, emphasizing the importance of optimizing the cooldown phase alongside traditional hyperparameter tuning.

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NeurIPS Conference 2024 Conference Paper

Analyzing & Reducing the Need for Learning Rate Warmup in GPT Training

Atli Kosson
Bettina Messmer
Martin Jaggi

Learning Rate Warmup is a popular heuristic for training neural networks, especially at larger batch sizes, despite limited understanding of its benefits. Warmup decreases the update size $\Delta \mathbf{w}_t = \eta_t \mathbf{u}_t$ early in training by using lower values for the learning rate $\eta_t$. In this work we argue that warmup benefits training by keeping the overall size of $\Delta \mathbf{w}_t$ limited, counteracting large initial values of $\mathbf{u}_t$. Focusing on small-scale GPT training with AdamW/Lion, we explore the following question: *Why and by which criteria are early updates $\mathbf{u}_t$ too large? * We analyze different metrics for the update size including the $\ell_2$-norm, resulting directional change, and impact on the representations of the network, providing a new perspective on warmup. In particular, we find that warmup helps counteract large angular updates as well as a limited critical batch size early in training. Finally, we show that the need for warmup can be significantly reduced or eliminated by modifying the optimizer to explicitly normalize $\mathbf{u}_t$ based on the aforementioned metrics.

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AAAI Conference 2024 Conference Paper

Ghost Noise for Regularizing Deep Neural Networks

Atli Kosson
Dongyang Fan
Martin Jaggi

Batch Normalization (BN) is widely used to stabilize the optimization process and improve the test performance of deep neural networks. The regularization effect of BN depends on the batch size and explicitly using smaller batch sizes with Batch Normalization, a method known as Ghost Batch Normalization (GBN), has been found to improve generalization in many settings. We investigate the effectiveness of GBN by disentangling the induced ``Ghost Noise'' from normalization and quantitatively analyzing the distribution of noise as well as its impact on model performance. Inspired by our analysis, we propose a new regularization technique called Ghost Noise Injection (GNI) that imitates the noise in GBN without incurring the detrimental train-test discrepancy effects of small batch training. We experimentally show that GNI can provide a greater generalization benefit than GBN. Ghost Noise Injection can also be beneficial in otherwise non-noisy settings such as layer-normalized networks, providing additional evidence of the usefulness of Ghost Noise in Batch Normalization as a regularizer.

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ICML Conference 2024 Conference Paper

Rotational Equilibrium: How Weight Decay Balances Learning Across Neural Networks

Atli Kosson
Bettina Messmer
Martin Jaggi

This study investigates how weight decay affects the update behavior of individual neurons in deep neural networks through a combination of applied analysis and experimentation. Weight decay can cause the expected magnitude and angular updates of a neuron’s weight vector to converge to a steady state we call rotational equilibrium. These states can be highly homogeneous, effectively balancing the average rotation—a proxy for the effective learning rate—across different layers and neurons. Our work analyzes these dynamics across optimizers like Adam, Lion, and SGD with momentum, offering a new simple perspective on training that elucidates the efficacy of widely used but poorly understood methods in deep learning. We demonstrate how balanced rotation plays a key role in the effectiveness of normalization like Weight Standardization, as well as that of AdamW over Adam with L2-regularization. Finally, we show that explicitly controlling the rotation provides the benefits of weight decay while substantially reducing the need for learning rate warmup.

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NeurIPS Conference 2024 Conference Paper

Scaling Laws and Compute-Optimal Training Beyond Fixed Training Durations

Alexander Hägele
Elie Bakouch
Atli Kosson
Loubna B. allal
Leandro Von Werra
Martin Jaggi

Scale has become a main ingredient in obtaining strong machine learning models. As a result, understanding a model's scaling properties is key to effectively designing both the right training setup as well as future generations of architectures. In this work, we argue that scale and training research has been needlessly complex due to reliance on the cosine schedule, which prevents training across different lengths for the same model size. We investigate the training behavior of a direct alternative --- constant learning rate and cooldowns --- and find that it scales predictably and reliably similar to cosine. Additionally, we show that stochastic weight averaging yields improved performance along the training trajectory, without additional training costs, across different scales. Importantly, with these findings we demonstrate that scaling experiments can be performed with significantly reduced compute and GPU hours by utilizing fewer but reusable training runs. Our code is available at https: //github. com/epfml/schedules-and-scaling/.

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NeurIPS Conference 2023 Conference Paper

Multiplication-Free Transformer Training via Piecewise Affine Operations

Atli Kosson
Martin Jaggi

Multiplications are responsible for most of the computational cost involved in neural network training and inference. Recent research has thus looked for ways to reduce the cost associated with them. Inspired by Mogami 2020, we replace multiplication with a cheap piecewise affine approximation that is achieved by adding the bit representation of the floating point numbers together as integers. We show that transformers can be trained with the resulting modified matrix multiplications on both vision and language tasks with little to no performance impact, and without changes to the training hyperparameters. We further replace all non-linearities in the networks making them fully and jointly piecewise affine in both inputs and weights. Finally, we show that we can eliminate all multiplications in the entire training process, including operations in the forward pass, backward pass and optimizer update, demonstrating the first successful training of modern neural network architectures in a fully multiplication-free fashion.

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NeurIPS Conference 2019 Conference Paper

Online Normalization for Training Neural Networks

Vitaliy Chiley
Ilya Sharapov
Atli Kosson
Urs Koster
Ryan Reece
Sofia Samaniego de la Fuente
Vishal Subbiah
Michael James

Online Normalization is a new technique for normalizing the hidden activations of a neural network. Like Batch Normalization, it normalizes the sample dimension. While Online Normalization does not use batches, it is as accurate as Batch Normalization. We resolve a theoretical limitation of Batch Normalization by introducing an unbiased technique for computing the gradient of normalized activations. Online Normalization works with automatic differentiation by adding statistical normalization as a primitive. This technique can be used in cases not covered by some other normalizers, such as recurrent networks, fully connected networks, and networks with activation memory requirements prohibitive for batching. We show its applications to image classification, image segmentation, and language modeling. We present formal proofs and experimental results on ImageNet, CIFAR, and PTB datasets.

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