Niccolò Ajroldi

Albert Catalan-Tatjer, Niccolò Ajroldi, Jonas Geiping

While post-training quantization is widely adopted for efficient deployment of large language models, the mechanisms underlying quantization robustness remain unclear. We conduct a comprehensive analysis of quantization degradation across open-source language model training trajectories up to 32B parameters and 15T training tokens to accurately assess the relationship between training dynamics and quantization performance. Our key finding is that quantization errors in large-scale training runs are driven by a complex interplay between learning rate and other training hyperparameters. Specifically, once learning rates decay, validation loss and quantization error diverge, largely independent of training data scale. To investigate interventions on the training dynamics and identify specific configurations that can modulate quantization robustness favorably, we train our own models in controlled experiments up to 100B tokens. Our results challenge the assumption that increasing dataset scale inherently compromises quantization effectiveness, demonstrating instead that strategic training hyperparameter interventions can improve quantization quality at scale.

Rustem Islamov, Niccolò Ajroldi, Antonio Orvieto et al.

Optimization methods play a crucial role in modern machine learning, powering the remarkable empirical achievements of deep learning models. These successes are even more remarkable given the complex non-convex nature of the loss landscape of these models. Yet, ensuring the convergence of optimization methods requires specific structural conditions on the objective function that are rarely satisfied in practice. One prominent example is the widely recognized Polyak-Lojasiewicz (PL) inequality, which has gained considerable attention in recent years. However, validating such assumptions for deep neural networks entails substantial and often impractical levels of over-parametrization. In order to address this limitation, we propose a novel class of functions that can characterize the loss landscape of modern deep models without requiring extensive over-parametrization and can also include saddle points. Crucially, we prove that gradient-based optimizers possess theoretical guarantees of convergence under this assumption. Finally, we validate the soundness of our new function class through both theoretical analysis and empirical experimentation across a diverse range of deep learning models.

Fay Elhassan, Niccolò Ajroldi, Antonio Orvieto et al.

The indistinguishability of AI-generated content from human text raises challenges in transparency and accountability. While several methods exist to watermark models behind APIs, embedding watermark strategies directly into model weights that are later reflected in the outputs of the model is challenging. In this study we propose a strategy to finetune a pair of low-rank adapters of a model, one serving as the text-generating model, and the other as the detector, so that a subtle watermark is embedded into the text generated by the first model and simultaneously optimized for detectability by the second. In this way, the watermarking strategy is fully learned end-to-end. This process imposes an optimization challenge, as balancing watermark robustness, naturalness, and task performance requires trade-offs. We discuss strategies on how to optimize this min-max objective and present results showing the effect of this modification to instruction finetuning.

Niccolò Ajroldi, Antonio Orvieto, Jonas Geiping

Averaging checkpoints along the training trajectory is a simple yet powerful approach to improve the generalization performance of Machine Learning models and reduce training time. Motivated by these potential gains, and in an effort to fairly and thoroughly benchmark this technique, we present an extensive evaluation of averaging techniques in modern Deep Learning, which we perform using AlgoPerf \citep{dahl_benchmarking_2023}, a large-scale benchmark for optimization algorithms. We investigate whether weight averaging can reduce training time, improve generalization, and replace learning rate decay, as suggested by recent literature. Our evaluation across seven architectures and datasets reveals that averaging significantly accelerates training and yields considerable efficiency gains, at the price of a minimal implementation and memory cost, while mildly improving generalization across all considered workloads. Finally, we explore the relationship between averaging and learning rate annealing and show how to optimally combine the two to achieve the best performances.

Rustem Islamov, Niccolo Ajroldi, Antonio Orvieto et al.

Modern optimization algorithms that incorporate momentum and adaptive step-size offer improved performance in numerous challenging deep learning tasks. However, their effectiveness is often highly sensitive to the choice of hyperparameters, especially the step-size. Tuning these parameters is often difficult, resource-intensive, and time-consuming. Therefore, recent efforts have been directed toward enhancing the stability of optimizers across a wide range of hyperparameter choices [Schaipp et al., 2024]. In this paper, we introduce an algorithm that matches the performance of state-of-the-art optimizers while improving stability to the choice of the step-size hyperparameter through a novel adaptation of the NGN step-size method [Orvieto and Xiao, 2024]. Specifically, we propose a momentum-based version (NGN-M) that attains the standard convergence rate of $\mathcal{O}(1/\sqrt{K})$ under less restrictive assumptions, without the need for interpolation condition or assumptions of bounded stochastic gradients or iterates, in contrast to previous approaches. Additionally, we empirically demonstrate that the combination of the NGN step-size with momentum results in enhanced robustness to the choice of the step-size hyperparameter while delivering performance that is comparable to or surpasses other state-of-the-art optimizers.