SoK: On Finding Common Ground in Loss Landscapes Using Deep Model Merging Techniques

Understanding neural networks is crucial to creating reliable and trustworthy deep learning models. Most contemporary research in interpretability analyzes just one model at a time via causal intervention or activation analysis. Yet despite successes, these methods leave significant gaps in our understanding of the training behaviors of neural networks, how their inner representations emerge, and how we can predictably associate model components with task-specific behaviors. Seeking new insights from work in related fields, here we survey literature in the field of model merging, a field that aims to combine the abilities of various neural networks by merging their parameters and identifying task-specific model components in the process. We analyze the model merging literature through the lens of loss landscape geometry, an approach that enables us to connect observations from empirical studies on interpretability, security, model merging, and loss landscape analysis to phenomena that govern neural network training and the emergence of their inner representations. To systematize knowledge in this area, we present a novel taxonomy of model merging techniques organized by their core algorithmic principles. Additionally, we distill repeated empirical observations from the literature in these fields into characterizations of four major aspects of loss landscape geometry: mode convexity, determinism, directedness, and connectivity. We argue that by improving our understanding of the principles underlying model merging and loss landscape geometry, this work contributes to the goal of ensuring secure and trustworthy machine learning in practice.

On Logical Extrapolation for Mazes with Recurrent and Implicit Networks

Recent work has suggested that certain neural network architectures-particularly recurrent neural networks (RNNs) and implicit neural networks (INNs) are capable of logical extrapolation. That is, one may train such a network on easy instances of a specific task and then apply it successfully to more difficult instances of the same task. In this paper, we revisit this idea and show that (i) The capacity for extrapolation is less robust than previously suggested. Specifically, in the context of a maze-solving task, we show that while INNs (and some RNNs) are capable of generalizing to larger maze instances, they fail to generalize along axes of difficulty other than maze size. (ii) Models that are explicitly trained to converge to a fixed point (e.g. the INN we test) are likely to do so when extrapolating, while models that are not (e.g. the RNN we test) may exhibit more exotic limiting behaviour such as limit cycles, even when they correctly solve the problem. Our results suggest that (i) further study into why such networks extrapolate easily along certain axes of difficulty yet struggle with others is necessary, and (ii) analyzing the dynamics of extrapolation may yield insights into designing more efficient and interpretable logical extrapolators.