Di Fang

Di Fang, Yinan Zhu, Runze Fang et al.

Continual learning enables AI models to learn new data sequentially without retraining in real-world scenarios. Most existing methods assume the training data are balanced, aiming to reduce the catastrophic forgetting problem that models tend to forget previously generated data. However, data imbalance and the mixture of new and old data in real-world scenarios lead the model to ignore categories with fewer training samples. To solve this problem, we propose an analytic imbalance rectifier algorithm (AIR), a novel online exemplar-free continual learning method with an analytic (i.e., closed-form) solution for data-imbalanced class-incremental learning (CIL) and generalized CIL scenarios in real-world continual learning. AIR introduces an analytic re-weighting module (ARM) that calculates a re-weighting factor for each class for the loss function to balance the contribution of each category to the overall loss and solve the problem of imbalanced training data. AIR uses the least squares technique to give a non-discriminatory optimal classifier and its iterative update method in continual learning. Experimental results on multiple datasets show that AIR significantly outperforms existing methods in long-tailed and generalized CIL scenarios. The source code is available at https://github.com/fang-d/AIR.

Suoxin Zhang, Run He, Di Fang et al.

Low-rank adaptation (LoRA) is a widely used parameter-efficient fine-tuning method that places trainable low-rank adapters into frozen pre-trained models. Recent studies show that using fewer LoRA adapters may still maintain or even improve performance, but existing methods still distribute adapters broadly, leaving where to place a limited number of adapters to maximize performance largely open. To investigate this, we introduce PAGE (Projected Adapter Gradient Energy), a gradient-based sensitivity probe that estimates the initial trainable gradient energy available to each candidate LoRA adapter. Surprisingly, we find that PAGE is highly concentrated on a single shallow FFN down-projection across two model families and four downstream tasks. We term this module the dominant adaptation module and show that its layer index is architecture-dependent but task-stable. Motivated by this finding, we propose DomLoRA, a placement method that places a single adapter at the dominant adaptation module. With only ~0.7% of vanilla LoRA's trainable parameters, DomLoRA outperforms it on average across various downstream tasks, including instruction following, mathematical reasoning, code generation, and multi-turn conversation. This method also improves other LoRA variants, supporting the dominant adaptation module perspective as a practical placement guideline.

Di Fang, Lei Li

The Generalized Langevin Equation, in history, arises as a natural fix for the rather traditional Langevin equation when the random force is no longer memoryless. It has been proved that with fractional Gaussian noise (fGn) mostly considered by biologists, the overdamped Generalized Langevin equation satisfying fluctuation-dissipation theorem can be written as a fractional stochastic differential equation (FSDE). While the ergodicity is clear for linear forces, it remains less transparent for nonlinear forces. In this work, we present both a direct and a fast algorithm respectively to this FSDE model. The strong orders of convergence are proved for both schemes, where the role of the memory effects can be clearly observed. We verify the convergence theorems using linear forces, and then present the ergodicity study of the double well potentials in both 1D and 2D setups.