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.
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...
Multi-norm adversarial defense aims to protect neural networks against perturbations defined by different norm constraints, but existing methods typically optimize competing robustness objectives within a single parameter configuration, leading to substantial training cost and unfavorable robustness trade-offs. We propose Robust CurveMoE, an efficient mixture-of-experts framework that connects models specialized for different perturbation norms through a low-loss path and exploits the complementary robustness profiles of models along this path. Robust CurveMoE derives clean and norm-specialized experts from robustness-constrained curve locations and selectively expertizes only influential layers, while sharing the remaining parameters across routing paths. To further reduce curve-construction cost, we introduce contribution-guided partial updating, which selects influential curve parameters using initialization-based gradient scores. We also theoretically bound the objective gap between partial and full curve optimization. Experiments on CIFAR-100 and ImageNet-100 with WideResNet and Vision Transformer architectures show that Robust CurveMoE consistently improves clean, norm-specific, and Union accuracy over MSD and ERMC. In particular, it improves Union accuracy by 2.37 and 2.13 percentage points over the strongest baseline on CIFAR-100 and ImageNet-100, respectively. Extensive ablations further validate the effectiveness of partial updating, selective expertization, and robustness-constrained expert selection.
Vincent Bürgin, Daniel Herbst, Ya-Wei Eileen Lin +1cs.LG
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.