Loss Landscape Degeneracy Drives Stagewise Development in Transformers (2402.02364v2)

Abstract: Deep learning involves navigating a high-dimensional loss landscape over the neural network parameter space. Over the course of training, complex computational structures form and re-form inside the neural network, leading to shifts in input/output behavior. It is a priority for the science of deep learning to uncover principles governing the development of neural network structure and behavior. Drawing on the framework of singular learning theory, we propose that model development is deeply linked to degeneracy in the local geometry of the loss landscape. We investigate this link by monitoring loss landscape degeneracy throughout training, as quantified by the local learning coefficient, for a transformer LLM and an in-context linear regression transformer. We show that training can be divided into distinct periods of change in loss landscape degeneracy, and that these changes in degeneracy coincide with significant changes in the internal computational structure and the input/output behavior of the transformers. This finding underscores the potential of a degeneracy-based perspective for understanding modern deep learning.

• The paper establishes a framework to detect developmental milestones in transformers through innovative use of local learning coefficients and essential dynamics.
• It identifies significant shifts in model complexity, with varying LLC values marking transitions between distinct training stages.
• The research demonstrates that trajectory PCA effectively distills high-dimensional learning data into key developmental features, enhancing AI interpretability.

In-Context Learning in Transformers

Overview of In-Context Learning and Structural Development

Transformers reveal a nuanced developmental process through training, which can be dissected into distinct developmental stages, akin to the progression observed in biological systems. This paper introduces a robust framework to detect the transitional milestones between these stages. The paper focuses on two primary settings: LLMing with transformers around 3M parameters and linear regression tasks utilizing a 50k parameter transformer. The methodology adopts two pivotal techniques. Firstly, it leverages the local learning coefficient (LLC) from Singular Learning Theory to probe the loss landscape's geometry in parameter space. Secondly, it employs essential dynamics (ED) to examine the geometry of the learning trajectory in function space. These innovative tools provide insights into the complex yet structured pattern of deep learning development.

Methodological Advancements

This research emphasizes the geometrical analysis of the developmental trajectory for transformers, employing two novel yet foundational methods. The local learning coefficient offers a measure of the loss landscape's degeneracy and acts as a nuanced indicator of model complexity. The paper also introduces trajectory PCA, involving essential dynamics, to distill the monumental trajectory data into digestible, low-dimensional presentations while also capturing critical developmental features.

The research makes a compelling case through conclusive validations. By correlating behavioral and structural changes with the identified stages, the paper fortifies the credibility of the detected milestones. Furthermore, the paper explores the concept of forms—remarkable geometric structures in function space manifesting at pivotal milestones. The existence of these forms corroborates the presence of a developmental trajectory shaping transformers' training process.

Numerical and Contradictory Results

The paper presents transformative conclusions, showcasing a significant increase in the LLC during certain stages, which aligns with a complexity elevation in model architecture. Conversely, other stages exhibit LLC reductions, indicating a simplification in the model. Intriguingly, metrics derived from Hessian-based analyses capture only some milestones, underscoring the LLC's robustness for uncovering subtle developmental changes. Additionally, the paper posits the emergence of potential additional substages within certain developmental stages upon modifying the milepost detection criteria.

Final Thoughts on Structure and Learning Process

The paper contributes to the broader discourse on interpretability by proposing links between distinct forms of structural collapses in various network components and the corresponding decrease in the LLC. While the research stops short of establishing a causal relationship, it sets the groundwork for further exploration of these intricate dynamics.

In a field where understanding the "why" and "how" behind AI's learning behavior is as critical as its performance, this paper steers attention towards the developmental journey of transformers. Through its rigorous exploration of in-context learning and developmental stages, it casts light on the underlying structure that orchestrates models' growth from initialization to maturity, positioning these learnings as powerful interpretive tools for AI development.