Parameter-efficient fine-tuning (PEFT) methods have shown promise in adapting large language models, yet existing approaches exhibit counter-intuitive phenomena: integrating either matrix decomposition or mixture-of-experts (MoE) individually decreases performance across tasks, though decomposition improves results on specific domains despite reducing parameters, while MoE increases parameter count without corresponding decrease in training efficiency. Motivated by these observations and the modular nature of PT, we propose PT-MoE, a novel framework that integrates matrix decomposition with MoE routing for efficient PT. Evaluation results across 17 datasets demonstrate that PT-MoE achieves state-of-the-art performance in both question answering (QA) and mathematical problem solving tasks, improving F1 score by 1.49 points over PT and 2.13 points over LoRA in QA tasks, while improving mathematical accuracy by 10.75 points over PT and 0.44 points over LoRA, all while using 25% fewer parameters than LoRA. Our analysis reveals that while PT methods generally excel in QA tasks and LoRA-based methods in math datasets, the integration of matrix decomposition and MoE in PT-MoE yields complementary benefits: decomposition enables efficient parameter sharing across experts while MoE provides dynamic adaptation, collectively enabling PT-MoE to demonstrate cross-task consistency and generalization abilities. These findings, along with ablation studies on routing mechanisms and architectural components, provide insights for future PEFT methods. 1

Parameter-efficient fine-tuning (PEFT) methods have shown promise in adapting large language models, yet existing approaches exhibit counter-intuitive phenomena: integrating either matrix decomposition or mixture-of-experts (MoE) individually decreases performance across tasks, though decomposition improves results on specific domains despite reducing parameters, while MoE increases parameter count without corresponding decrease in training efficiency. Motivated by these observations and the modular nature of PT, we propose PT-MoE, a novel framework that integrates matrix decomposition with MoE routing for efficient PT. Evaluation results across 17 datasets demonstrate that PT-MoE achieves state-of-the-art performance in both question answering (QA) and mathematical problem solving tasks, improving F1 score by 1.49 points over PT and 2.13 points over LoRA in QA tasks, while improving mathematical accuracy by 10.75 points over PT and 0.44 points over LoRA, all while using 25% fewer parameters than LoRA. Our analysis reveals that while PT methods generally excel in QA tasks and LoRA-based methods in math datasets, the integration of matrix decomposition and MoE in PT-MoE yields complementary benefits: decomposition enables efficient parameter sharing across experts while MoE provides dynamic adaptation, collectively enabling PT-MoE to demonstrate cross-task consistency and generalization abilities. These findings, along with ablation studies on routing mechanisms and architectural components, provide insights for future PEFT methods.

Neural Information Processing Systems http://nips.cc/

Motivated by the problem of robust factorization of a low-rank tensor, we study the question of sparse and low-rank tensor decomposition. We present an efficient computational algorithm that modifies Leurgans' algoirthm for tensor factorization. Our method relies on a reduction of the problem to sparse and low-rank matrix decomposition via the notion of tensor contraction. We use well-understood convex techniques for solving the reduced matrix sub-problem which then allows us to perform the full decomposition of the tensor. We delineate situations where the problem is recoverable and provide theoretical guarantees for our algorithm.

Vision transformers (ViTs) have pushed the state-of-the-art for various visual recognition tasks by patch-wise image tokenization followed by self-attention.

First-order methods in convex optimization offer low per-iteration cost but often suffer from slow convergence, while second-order methods achieve fast local convergence at the expense of costly Hessian inversions. In this paper, we highlight a middle ground: minimizing a quadratic majorant with fixed curvature at each iteration. This strategy strikes a balance between per-iteration cost and convergence speed, and crucially allows the reuse of matrix decompositions, such as Cholesky or spectral decompositions, across iterations and varying regularization parameters. We introduce the Quadratic Majorization Minimization with Extrapolation (QMME) framework and establish its sequential convergence properties under standard assumptions. The new perspective of our analysis is to center the arguments around the induced norm of the curvature matrix $H$. To demonstrate practical advantages, we apply QMME to large-scale kernel regularized learning problems. In particular, we propose a novel Sylvester equation modelling technique for kernel multinomial regression. In Julia-based experiments, QMME compares favorably against various established first- and second-order methods. Furthermore, we demonstrate that our algorithms complement existing kernel approximation techniques through more efficiently handling sketching matrices with large projection dimensions. Our numerical experiments and real data analysis are available and fully reproducible at https://github.com/qhengncsu/QMME.jl.

Parameter-efficient fine-tuning (PEFT) methods have shown promise in adapting large language models, yet existing approaches exhibit counter-intuitive phenomena: integrating router into prompt tuning (PT) increases training efficiency yet does not improve performance universally; parameter reduction through matrix decomposition can improve performance in specific domains. Motivated by these observations and the modular nature of PT, we propose PT-MoE, a novel framework that integrates matrix decomposition with mixture-of-experts (MoE) routing for efficient PT. Results across 17 datasets demonstrate that PT-MoE achieves state-of-the-art performance in both question answering (QA) and mathematical problem solving tasks, improving F1 score by 1.49 points over PT and 2.13 points over LoRA in QA tasks, while enhancing mathematical accuracy by 10.75 points over PT and 0.44 points over LoRA, all while using 25% fewer parameters than LoRA. Our analysis reveals that while PT methods generally excel in QA tasks and LoRA-based methods in math datasets, the integration of matrix decomposition and MoE in PT-MoE yields complementary benefits: decomposition enables efficient parameter sharing across experts while MoE provides dynamic adaptation, collectively enabling PT-MoE to demonstrate cross-task consistency and generalization abilities. These findings, along with ablation studies on routing mechanisms and architectural components, provide insights for future PEFT methods.