The Potential of Second-Order Optimization for LLMs: A Study with Full Gauss-Newton

Recent efforts to accelerate LLM pretraining have focused on computationally-efficient approximations that exploit second-order structure. This raises a key question for large-scale training: how much performance is forfeited by these approximations? To probe this question, we establish a practical upper bound on iteration complexity by applying full Gauss-Newton (GN) preconditioning to transformer models of up to 150M parameters. Our experiments show that full GN updates yield substantial gains over existing optimizers, achieving a 5.4x reduction in training iterations compared to strong baselines like SOAP and Muon. Furthermore, we find that a precise layerwise GN preconditioner, which ignores cross-layer information, nearly matches the performance of the full GN method. Collectively, our results suggest: (1) the GN approximation is highly effective for preconditioning, implying higher-order loss terms may not be critical for convergence speed; (2) the layerwise Hessian structure contains sufficient information to achieve most of these potential gains; and (3) a significant performance gap exists between current approximate methods and an idealized layerwise oracle.

A Taxonomy of Transcendence

Although language models are trained to mimic humans, the resulting systems display capabilities beyond the scope of any one person. To understand this phenomenon, we use a controlled setting to identify properties of the training data that lead a model to transcend the performance of its data sources. We build on previous work to outline three modes of transcendence, which we call skill denoising, skill selection, and skill generalization. We then introduce a knowledge graph-based setting in which simulated experts generate data based on their individual expertise. We highlight several aspects of data diversity that help to enable the model's transcendent capabilities. Additionally, our data generation setting offers a controlled testbed that we hope is valuable for future research in the area.

Addressing Discrepancies in Semantic and Visual Alignment in Neural Networks

For the task of image classification, neural networks primarily rely on visual patterns. In robust networks, we would expect for visually similar classes to be represented similarly. We consider the problem of when semantically similar classes are visually dissimilar, and when visual similarity is present among non-similar classes. We propose a data augmentation technique with the goal of better aligning semantically similar classes with arbitrary (non-visual) semantic relationships. We leverage recent work in diffusion-based semantic mixing to generate semantic hybrids of two classes, and these hybrids are added to the training set as augmented data. We evaluate whether the method increases semantic alignment by evaluating model performance on adversarially perturbed data, with the idea that it should be easier for an adversary to switch one class to a similarly represented class. Results demonstrate that there is an increase in alignment of semantically similar classes when using our proposed data augmentation method.

Addressing Mistake Severity in Neural Networks with Semantic Knowledge

Robustness in deep neural networks and machine learning algorithms in general is an open research challenge. In particular, it is difficult to ensure algorithmic performance is maintained on out-of-distribution inputs or anomalous instances that cannot be anticipated at training time. Embodied agents will be deployed in these conditions, and are likely to make incorrect predictions. An agent will be viewed as untrustworthy unless it can maintain its performance in dynamic environments. Most robust training techniques aim to improve model accuracy on perturbed inputs; as an alternate form of robustness, we aim to reduce the severity of mistakes made by neural networks in challenging conditions. We leverage current adversarial training methods to generate targeted adversarial attacks during the training process in order to increase the semantic similarity between a model's predictions and true labels of misclassified instances. Results demonstrate that our approach performs better with respect to mistake severity compared to standard and adversarially trained models. We also find an intriguing role that non-robust features play with regards to semantic similarity.