Pre-trained Vision Transformers now serve as powerful tools for computer vision. Yet, efficiently adapting them for multiple tasks remains a challenge that arises from the need to modify the rich hidden representations encoded by the learned weight matrices, without inducing interference between tasks. Current parameter-efficient methods like LoRA, which apply low-rank updates, force tasks to compete within constrained subspaces, ultimately degrading performance. We introduce DiTASK a novel Diffeomorphic Multi-Task Fine-Tuning approach that maintains pre-trained representations by preserving weight matrix singular vectors, while enabling task-specific adaptations through neural diffeomorphic transformations of the singular values. By following this approach, DiTASK enables both shared and task-specific feature modulations with minimal added parameters. Our theoretical analysis shows that DiTASK achieves full-rank updates during optimization, preserving the geometric structure of pretrained features, and establishing a new paradigm for efficient multi-task learning (MTL). Our experiments on PASCAL MTL and NYUD show that DiTASK achieves state-of-the-art performance across four dense prediction tasks, using 75% fewer parameters than existing methods. Our code is available here.

In this paper, we propose a novel activation function tailored specifically for graph data in Graph Neural Networks (GNNs). Motivated by the need for graph-adaptive and flexible activation functions, we introduce DiGRAF, leveraging Continuous Piecewise-Affine Based (CPAB) transformations, which we augment with an additional GNN to learn a graph-adaptive diffeomorphic activation function in an end-to-end manner. In addition to its graph-adaptivity and flexibility, DiGRAF also possesses properties that are widely recognized as desirable for activation functions, such as differentiability, boundness within the domain, and computational efficiency. We conduct an extensive set of experiments across diverse datasets and tasks, demonstrating a consistent and superior performance of DiGRAF compared to traditional and graph-specific activation functions, highlighting its effectiveness as an activation function for GNNs. Our code is available at https://github.com/ipsitmantri/DiGRAF.

Influence maximization (IM) refers to the problem of finding a subset of nodes in a network through which we could maximize our reach to other nodes in the network. This set is often called the "seed set", and its constituent nodes maximize the social diffusion process. IM has previously been studied in various settings, including under a time deadline, subject to constraints such as that of budget or coverage, and even subject to measures other than the centrality of nodes. The solution approach has generally been to prove that the objective function is submodular, or has a submodular proxy, and thus has a close greedy approximation. In this paper, we explore a variant of the IM problem where we wish to reach out to and maximize the probability of infection of a small subset of bounded capacity K. We show that this problem does not exhibit the same submodular guarantees as the original IM problem, for which we resort to the theory of gamma-weakly submodular functions. Subsequently, we develop a greedy algorithm that maximizes our objective despite the lack of submodularity. We also develop a suitable learning model that out-competes baselines on the task of predicting the top-K infected nodes, given a seed set as input.