Mode Connectivity Beyond Classifiers: Evidence from Generative and Contrastive Models

The loss landscape of Deep Neural Networks (DNNs) exhibits highly complex and non-convex properties. Recent studies have revealed the phenomenon of mode connectivity, demonstrating that independently trained network modes can be connected via a continuous low-loss path. However, existing mode connectivity research is predominantly confined to classifier-based models, leaving it an open question whether similar geometric properties exist in modern complex models. In this paper, we extend the boundaries of mode connectivity to generative and contrastive domains (specifically DDPM and NanoCLIP). Addressing the unique architecture of DDPM and CLIP, we propose an architecture-aware connection building algorithm. Extensive empirical results demonstrate for the first time that we successfully discover mode connectivity between independently trained DDPM and NanoCLIP modes. Our work provides a novel perspective for understanding the geometric properties of the loss landscapes in modern generative and contrastive models.

From the Loss Landscape to Diverse Feature Learning in Neural Networks

Over the course of the last decade, neural networks have grown from an academic curiosity to moving the markets of nations. Despite this explosion in both research and deployment, relatively little is understood about how they achieve the solutions they do. This is both scientifically relevant, and pressing for society. When neural networks make decisions across self-driving, construction, law, hiring and health, there have been and will continue to be unintended consequences. However, attempting to generalize the failures of the largest and most important production systems makes for a very difficult task. Yet signs of these failures exist at all scales of neural networks, so we should be able to study a much more tractable setting. All neural networks must undergo an optimization process, called training, to be useful. To a great degree, understanding neural networks is understanding their optimization: through what process and exposure to which data did they arrive at their results. Yet our knowledge on this topic as a field is quite imprecise. In particular, a curious phenomenon called mode connectivity, the ability to connect neural networks in the loss surface, defies explanation entirely. This dissertation elucidates, explains and exploits this special structure in the loss landscape...

Beyond Structural Symmetries: Linear Mode Connectivity via Neuron Identifiability

Many striking phenomena in deep learning, such as linear mode connectivity and the structured behavior of training dynamics, are closely tied to parameter symmetries: transformations that leave the realized function unchanged. Despite growing attention to parameter symmetries, the exact interplay between parameters, data, and representations remains underexplored. To investigate this, we develop a theoretical framework of effective function classes, i.e., the set of functions a neuron can realize on its input support, and the norm cost of realizing them. We then formalize effective symmetry breaking via neuron identifiability across independent training runs. Our analysis shows that neural networks can admit large families of approximately equivalent solutions even in structurally asymmetric models. We further show that neuron identifiability enables representation merging without prior alignment, and characterize when such merging admits a linear low-loss path. These findings highlight the role of effective function classes in affecting the loss landscape.