That is, we simultaneously both solve for the DEQ fixed point and optimize over network inputs, all within a single "augmented" DEQ model that jointly encodes both the original network and the optimization

As the cost of training large language models (LLMs) rises, protecting their intellectual property has become increasingly critical. Model merging, which integrates multiple expert models into a single model capable of performing multiple tasks, presents a growing risk of unauthorized and malicious usage. While fingerprinting techniques have been studied for asserting model ownership, existing methods have primarily focused on fine-tuning, leaving model merging underexplored. To address this gap, we propose a novel fingerprinting method MergePrint that embeds robust fingerprints designed to preserve ownership claims even after model merging. By optimizing against a pseudo-merged model, which simulates post-merged model weights, MergePrint generates fingerprints that remain detectable after merging. Additionally, we optimize the fingerprint inputs to minimize performance degradation, enabling verification through specific outputs from targeted inputs. This approach provides a practical fingerprinting strategy for asserting ownership in cases of misappropriation through model merging.

We present a new approach for input optimization of ReLU networks that explicitly takes into account the effect of changes in activation patterns. We analyze local optimization steps in both the input space and the space of activation patterns to propose methods with superior local descent properties. To accomplish this, we convert the discrete space of activation patterns into differentiable representations and propose regularization terms that improve each descent step. Our experiments demonstrate the effectiveness of the proposed input-optimization methods for improving the state-of-the-art in various areas, such as adversarial learning, generative modeling, and reinforcement learning.