In this paper, we address the challenges associated with merging low-rank adaptations of large neural networks. With the rise of parameter-efficient adaptation techniques, such as Low-Rank Adaptation (LoRA), model fine-tuning has become more accessible. While fine-tuning models with LoRA is highly efficient, existing merging methods often sacrifice this efficiency by merging fully-sized weight matrices. We propose the Core Space merging framework, which enables the merging of LoRA-adapted models within a common alignment basis, thereby preserving the efficiency of low-rank adaptation while substantially improving accuracy across tasks. We further provide a formal proof that projection into Core Space ensures no loss of information and provide a complexity analysis showing the efficiency gains. Extensive empirical results demonstrate that Core Space significantly improves existing merging techniques and achieves state-of-the-art results on both vision and language tasks while utilizing a fraction of the computational resources.

The agent learns to organize decision behavior to achieve a behavioral goal, such as reward maximization, and reinforcement learning is often used for this optimization. Learning an optimal behavioral strategy is difficult under the uncertainty that events necessary for learning are only partially observable, called as Partially Observable Markov Decision Process (POMDP). However, the real-world environment also gives many events irrelevant to reward delivery and an optimal behavioral strategy. The conventional methods in POMDP, which attempt to infer transition rules among the entire observations, including irrelevant states, are ineffective in such an environment. Supposing Redundantly Observable Markov Decision Process (ROMDP), here we propose a method for goal-oriented reinforcement learning to efficiently learn state transition rules among reward-related "core states'' from redundant observations. Starting with a small number of initial core states, our model gradually adds new core states to the transition diagram until it achieves an optimal behavioral strategy consistent with the Bellman equation. We demonstrate that the resultant inference model outperforms the conventional method for POMDP. We emphasize that our model only containing the core states has high explainability. Furthermore, the proposed method suits online learning as it suppresses memory consumption and improves learning speed.

Humans are skilled at learning adaptively and efficiently throughout their lives, but learning tasks incrementally causes artificial neural networks to overwrite relevant information learned about older tasks, resulting in 'Catastrophic Forgetting'. Efforts to overcome this phenomenon suffer from poor utilization of resources in many ways, such as through the need to save older data or parametric importance scores, or to grow the network architecture. We propose an algorithm that enables a network to learn continually and efficiently by partitioning the representational space into a Core space, that contains the condensed information from previously learned tasks, and a Residual space, which is akin to a scratch space for learning the current task. The information in the Residual space is then compressed using Principal Component Analysis and added to the Core space, freeing up parameters for the next task. We evaluate our algorithm on P-MNIST, CIFAR-10 and CIFAR-100 datasets. We achieve comparable accuracy to state-of-the-art methods while overcoming the problem of catastrophic forgetting completely. Additionally, we get up to 4.5x improvement in energy efficiency during inference due to the structured nature of the resulting architecture.